robertogreco : math   505

 « earlier
Pi Day is a lie: celebrate tau, the true circle constant instead - The Verge

"But Palais and Hartl’s arguments both boil down to some basic math. Step back in time to when you first learned geometry and recall the simple origins: no matter what circle you’re using, if you divide the circumference of the circle by the diameter, you’ll get the same answer: an endless number, starting with the digits 3.14159265... (aka pi).

And right there is the fundamental flaw. The thing is, we don’t actually use diameter to describe circles. We use the radius, or one-half the diameter. The circle equation uses the radius, the area of a circle uses the radius, and the fundamental definition of a circle — “the set of all points in a plane that are at a given distance from a given point, the center” — is based on the radius. Plugging that into our circle constant equation gives us a new circle constant equivalent to 2π, or 6.28318530717..., colloquially referred to with the Greek letter τ (tau). Switching to τ isn’t making some arbitrary change for the sake of it. It’s bringing one of the most important constants in math in line with how we actually do math."
math  mathematics  pi  2019  vihart  2018  tau  numbers  culture
4 weeks ago by robertogreco
Yong Zhao "What Works May Hurt: Side Effects in Education" - YouTube
"Proponents of standardized testing and privatization in education have sought to prove their effectiveness in improving education with an abundance of evidence. These efforts, however, can have dangerous side effects, causing long-lasting damage to children, teachers, and schools. Yong Zhao, Foundation Distinguished Professor in the School of Education at the University of Kansas, will argue that education interventions are like medical products: They can have serious, sometimes detrimental, side effects while also providing cures. Using standardized testing and privatization as examples, Zhao, author of the internationally bestselling Who’s Afraid of the Big Bad Dragon? Why China Has the Best (and Worst) Education System in the World, will talk about his new book on why and how pursuing a narrow set of short-term outcomes causes irreparable harm in education."
yongzhao  2018  schools  schooling  pisa  education  testing  standardizedtesting  standardization  china  us  history  testscores  children  teaching  howweteach  howwelearn  sideeffects  privatization  tims  math  reading  confidence  assessment  economics  depression  diversity  entrepreneurship  japan  creativity  korea  vietnam  homogenization  intolerance  prosperity  tolerance  filtering  sorting  humans  meritocracy  effort  inheritance  numeracy  literacy  achievementgap  kindergarten  nclb  rttt  policy  data  homogeneity  selectivity  charterschools  centralization  decentralization  local  control  inequity  curriculum  autonomy  learning  memorization  directinstruction  instruction  poverty  outcomes  tfa  teachforamerica  finland  singapore  miltonfriedman  vouchers  resilience  growthmindset  motivation  psychology  research  positivepsychology  caroldweck  intrinsicmotivation  choice  neoliberalism  high-stakestesting
5 weeks ago by robertogreco
Why so many U.S. students aren’t learning math | University of California
"Stigler has also analyzed how other countries — such as Australia, Japan, the Netherlands, Switzerland and the Czech Republic — teach math and science, which, he says, helps us understand U.S. teaching practices more clearly.

“American students think math is about memorizing procedures,” Stigler said. “They’re not learning in a deep way. They think learning is supposed to be easy. That’s really not what learning is about. Students need practice in the things they can’t learn by doing a Google search. They need to think and struggle — like when they are practicing a sport or a musical instrument.”

In other countries, students are asked to work on a variety of problems. In the U.S., students work on many repetitions of, essentially, the same problem, making it unnecessary for U.S. students to think hard about each individual problem. We teach math as disconnected facts and as a series of steps or procedures — do this, and this and this — without connecting procedures with concepts, and without thinking or problem-solving.

“Don’t just memorize it and spit it back on the test,” Stigler said.

American eighth graders, for example, rarely spend time engaged in the serious study of mathematical concepts, Stigler said. Japanese eighth graders, in contrast, engage in serious study of mathematical concepts and are asked to develop their own solutions for math problems that they have not seen before.

Stigler thinks this memorization of facts and procedures applies to the teaching of many subjects in the United States.

Improving teaching has proven to be extremely difficult, and efforts to do so have achieved only limited success. But this disappointing record has not discouraged Stigler.

One of his projects, funded by a grant from the Chan Zuckerberg Initiative, is to create and continually improve a university course. The course, which focuses on introductory statistics, includes an online, interactive “textbook” with more than 100 web pages and about 800 assessment questions.

Stigler began creating the course in 2015 in collaboration with Ji Son, a professor at Cal State Los Angeles, and Karen Givvin, a UCLA researcher and adjunct professor of psychology. He taught the course for the first time last spring and is doing so again this quarter.

As students work their way through the course, Stigler and his team collect all the data and can see what the students are learning and what they are not learning.

“Most professors don’t realize how little information we have about how much students are learning,” Sigler said. “I observed a professor once give a lecture where not a single student said anything. I asked him afterwards how he thought it went, and he thought it was great. But how could he tell if it was clear to the students without eliciting any information from students?”

With his interactive course, Stigler can get real-time information. He offers his statistics course for free to any instructor in exchange for getting access to the data showing what, and how, students are learning.

His goal is incremental improvement in teaching, believing that rapid, dramatic results are not realistic. “I want millions of students to get one percent better every year in what they learn,” Stigler said.

Stigler and Givvin are playing leading roles in a new organization, the Precision Institute — created by National University to test innovative teaching ideas and collect data with the goal of helping to solve some of the most challenging issues in higher education. Stigler is one of the institute’s first fellows. National University, a San Diego-based non-profit, offers more than 100 programs, both online and at more than two dozen locations in California and Nevada, and has more than 150,000 alumni.

Through the Precision Institute and its National Precision Research and Innovation Network, National University gets researchers to address its educational challenges, while researchers get to test their education theories in real time in a university setting.

Stigler hopes to add his statistics course to the National University curriculum. Ideas that work can be implemented at National University right away.

Students in the same course can be randomly assigned to use different materials, and Stigler and his team can analyze data and figure out which approach is more effective. Stigler will soon do this in his UCLA undergraduate statistics course and will bring this approach to the National University project as well.

“We’re improving the course while students are taking the course,” said Stigler, who believes strongly in the importance of collecting data to see what actually helps students learn. “We’re trying to measure what they actually learn and figure out how we can help them to learn more.”

Any academic content area could profit from this approach, and the intent of Stigler’s research team is to broaden its application in the future.

“I don’t know what the answers are and don’t have an ax to grind,” Stigler said. “I don’t want to argue in the abstract about theories of education. Let’s test ideas on the ground and see which ones help students.”

Teaching is hard to change. Stigler and Givvin are struck by how similar teaching methods are within each country they have studied, and the striking differences in methods they observed across countries. While the United States is very diverse, the national variation in eighth grade mathematics teaching is much smaller than Stigler and Givvin expected to find.

“The focus on teachers has some merit, of course,” Stigler said, “but we believe that a focus on improving of teaching — the methods that teachers use in the classroom — will yield greater returns.

“Even the countries at the top are trying to improve teaching and learning,” Stigler said. “It is a central problem faced by all societies.”"
math  mathematics  education  teaching  howweteach  us  learning  children  jamesstigler  jison  problemsolving  memorization  howwelearn
october 2018 by robertogreco
Japanese Designers May Have Created the Most Accurate Map of Our World: See the AuthaGraph | Open Culture
"The currently accepted world map dates from 1569 when Gerardus Mercator originally designed it. Hajime Narukawa has been working on a more accurate version of the planet's continents for years now and was awarded the 2016 Good Design Award for his new world map."]
maps  mapping  2016  authagraph  projections  tessellations  hajimenarukawa  cartography  math  mathematics
october 2018 by robertogreco
CoCalc - Collaborative Calculation in the Cloud
"CoCalc is a sophisticated online environment for

• Mathematical calculation: SageMath, GAP, SymPy, Maxima, …;
• Statistics and Data Science: R Project, Pandas, Statsmodels, Scikit-Learn, TensorFlow, NLTK, …;
• Document authoring: LaTeX, Markdown/HTML, ...
• General purpose computing: Python, Octave, Julia, Scala, …

Zero Setup: getting started does not require any software setup.

1. First, create your personal account.
2. Then, create a project to instantiate your own private workspace.
3. Finally, create a worksheet or upload your own files: CoCalc supports online editing of Jupyter Notebooks, Sage Worksheets, LaTeX files, etc.

Collaborative Environment

• Share your files privately with project collaborators — all files are synchronized in real-time.
• Time-travel is a detailed history of all your edits and everything is backed up in consistent snapshots.
• Finally, you can select any document to publish it online.

A default project under a free plan has a quota of 1.0 GB memory and 3.0 GB of disk space. Subscriptions make hosting more robust and increase quotas."
computing  collaboration  cloud  math  python  latex  chromebooks
august 2018 by robertogreco
EquatIO Math Writing Software. A Digital Math Tool For Teachers & Students Of All Abilities | Texthelp
"easily add equations, formulas, graphs and more to g suite for education apps and microsoft word"

Made to help mathematics and STEM teachers and students at all levels, EquatIO® lets everyone create mathematical equations, formulas, Desmos graphs, and more on their computer or Chromebook.

Input’s easy. Type, handwrite, or dictate any expression, with no tricky coding or math languages to master. There’s a huge library of ready-made expressions to save you time, from simple formulas to complex functions. And when you’re done, just add the math to your document with a click."
math  mathematics  applications  chromebooks  android  mac  windows  osx  webapps  chromeos
june 2018 by robertogreco
Imaginary Numbers Are Real [Part 1: Introduction] - YouTube
[full playlist of all parts: https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF ]

"Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.

Part 1: Introduction
Part 2: A Little History
Part 3: Cardan's Problem
Part 4: Bombelli's Solution
Part 5: Numbers are Two Dimensional
Part 6: The Complex Plane
Part 7: Complex Multiplication
Part 8: Math Wizardry
Part 9: Closure
Part 10: Complex Functions
Part 11: Wandering in Four Dimensions
Part 12: Riemann's Solution
Part 13: Riemann Surfaces

Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources ."
math  mathematics  imaginarynumbers  algebra  2015  via:agentdana  negativenumbers  history
may 2018 by robertogreco
Immersive Math
"The world's first linear algebra book with fully interactive figures."
linearalgebra  textbooks  free  math  mathematics
may 2018 by robertogreco
Looking at Perfect Shuffles - Numberphile - YouTube
"How do cards move in a perfectly shuffled deck.
More links & stuff in full description below ↓↓↓

This continues on Numberphile2 at: http://youtu.be/UawZn7X42OM (including a look at 52 card decks)
Featuring Federico Ardila from San Francisco State University.

More cards and shuffling videos: http://bit.ly/Cards_Shuffling "
federicoardila  math  mathematics  classideas  shuffling  cards  2015
april 2018 by robertogreco
Combinatorics and Higher Dimensions - Numberphile - YouTube
"Featuring Federico Ardila from San Francisco State University - filmed at MSRI.
More links & stuff in full description below ↓↓↓

Federico previously on Numberphile ["Looking at Perfect Shuffles"]: https://www.youtu.be/OfEv5ZdSrhY
Federico's webpage: http://math.sfsu.edu/federico/

Antarctica Timelapse: https://www.youtu.be/o71TFQBTCG0

federicoardila  math  mathematics  combinatorics  geometry  classideas  geometriccombinatorics
april 2018 by robertogreco
QuantumCamp
"We were founded in 2009 on the simple idea that humans love to learn, and intentionally design an educational experience that supports this in our classrooms. The result is an exciting intellectual and social environment where students leave a class or a summer camp fulfilled, energized, and excited to continue exploring these ideas.

QC AT-A-GLANCE
QuantumCamp is a school enterprise with a core mission of delivering amazing, hands-on math and science courses to kids via three main platforms:

1. In-School Labs
2. Home School
3. Summer Camps

Students
Both homeschoolers and summer campers come from all backgrounds and from all academic skill levels. QuantumCamp students come from all nine Bay Area counties.

Faculty

QuantumCamp instructors are given one main task: facilitate an environment which allows student-driven discovery. We pride ourselves on our curriculum - developed by in-house content experts, and value the importance of collaboration. We are looking for innovative educators, who are excited to teach small classes, and contribute to our growing math and science program."
homeschool  marin  education  lcproject  openstudioproject  bayarea  camps  math  science
march 2018 by robertogreco
FACES OF WOMEN IN MATHEMATICS on Vimeo
"In February 2018, women mathematicians from all over the world responded to a call for clips in which they were asked to introduce themselves. The result includes 146 clips of 243 women mathematicians from 36 different countries and speaking 31 different languages. Supported by the Committee for Women in Mathematics of the International Mathematical Union."
math  mathematics  mathematicians  video  gender  women  diversity  2018
march 2018 by robertogreco
Mathematician Federico Ardila Dances to the Joys and Sorrows of Discovery | Quanta Magazine
"When you came to the United States, as an undergraduate at MIT, it was your turn to feel like the “other.”

It’s not that anybody did anything to mistreat me or to doubt me or to explicitly make me feel unwelcome, but I definitely felt very different. I mean, my mathematical education was outstanding and I had fantastic access to professors and really interesting material, but I only realized in retrospect that I was extremely isolated.

There’s a system in place that makes certain people comfortable and others uncomfortable, I think just by the nature of who’s in the space. And I say that without wanting to point fingers, because I think you can be critical about the spaces that “other” you, but you also have to be critical about the ways in which you “other” other people.

I think because mathematics sees itself as very objective, we think we can just say, “Well, logically, this seems to make sense that we’re doing everything correctly.” I think sometimes we’re a little bit oblivious as to what is the culture of a place, or who feels welcome, or what are we doing to make them feel welcome?

So when I try to create mathematical spaces, I try to be very mindful of letting people be their full human selves. And I hope that will give people more access to tools and opportunities.

What are some of the ways you do that in your teaching?

In a classroom I’m the professor, and so in some sense I’m the culture keeper. And one thing that I try to do — and it’s a little bit scary and it’s not easy — is to really try to shift the power dynamic and make sure that students feel like equally powerful contributors to the place. I try to create spaces where we’re kind of together constructing a mathematical reality.

So, for example, I taught a combinatorics class, and in every single class every single student did something active and communicated their mathematical ideas to somebody else. The structure of the class was such that they couldn’t just sit there and be passive.

I believe in the power of music, and so I got each one of them to play a song for the rest for us at the beginning of each class. At the beginning it felt like this wild experiment where I didn’t know what was going to happen, but I was really moved by their responses.

Some of them would dedicate the song to their mom and talk about how whenever they’re studying math, they’re very aware that their mom worked incredibly hard to give them the opportunity to be the first ones in their family to go to college. Another student played this song in Arabic called “Freedom.” And she was talking about how in this day and age it’s very difficult for her to feel at home and welcome and free in this country, and how mathematics for her is a place where nobody can take her freedom away.

That classroom felt like no other classroom that I’ve ever taught in. It was a very human experience, and it was one of the richest math classrooms that I’ve had. I think one worries when you do that, “Are you covering enough mathematics?” But when students are engaged so actively and when you really listen to their ideas, then magic happens that you couldn’t have done by preparing a class and just delivering it.

Mathematics has this stereotype of being an emotionless subject, but you describe it in very emotional terms — for instance, in course curricula you promise your students a “joyful” experience.

I think doing mathematics is tremendously emotional, and I think that anybody who does mathematics knows this. I just don’t think that we have the emotional awareness or vocabulary to talk about this as a community. But you walk around this building and people are making these discoveries, and there are so many emotions going on — a lot of frustration and a lot of joy.

I think one thing that happens is we don’t acknowledge this as a culture — because mathematics is emotional in sometimes very difficult ways. It can really make you feel very bad about yourself sometimes. You can be pushing on something for six months and then have it collapse, and that hurts. I don’t think we talk about that hurt enough. And the joy of discovering something after six months of working on it is really deep."
federicoardila  math  mathematics  music  combinatorics  teaching  2017  education  inclusivity  inclusion  culture  accessibility  howwweteach  community
january 2018 by robertogreco
Multiplying Non-Numbers — Math3ma
"In last last week's episode of PBS Infinite Series, we talked about different flavors of multiplication (like associativity and commutativity) to think about when multiplying things that aren't numbers. My examples of multiplying non-numbers were vectors and matrices, which come from the land of algebra. Today I'd like to highlight another example:

"We can multiply shapes!"

It's true! To illustrate, here's the multiplication table for a point, a line, a circle, and a square."
math  mathematics  classideas
january 2018 by robertogreco
dani on Twitter: "It started with x+4... and I couldn’t unhear it. I was supposed to do my math homework but instead I figured out what the Cantina Theme wou… https://t.co/OkYdzAcuN9"
"It started with x+4... and I couldn’t unhear it.
I was supposed to do my math homework but instead I figured out what the Cantina Theme would sound like if your instrument was a pencil. (Volume all the way up)

With music for those wondering what the heck this is.
(Excuse my reddit tag, I wasn’t about to re-edit the video for Twitter, no sir)

Here’s the Imperial March my friends"
music  math  mathematics  fun  humor  sound  classideas  2018  starwars
january 2018 by robertogreco
Simon Gregg on Twitter: "So this is beautiful. 3 cuboids, the bases: 1x2, 2x3 & 3x4; the heights are the area of the base; the volume is the height squared, and diag… https://t.co/biJntgUMbw"
"So this is beautiful. 3 cuboids, the bases: 1x2, 2x3 & 3x4; the heights are the area of the base; the volume is the height squared, and diagonal is the height plus one."

math  mathematics  classideas
january 2018 by robertogreco
Stacy Speyer
"You are invited to explore these creative projects which blur the boundary between looking at art and learning from it.

Click here to visit the Bookstore where you can get your own copies of Polyhedra: Eye Candy to Feed the Mind and the 3D coloring books - Cubes and Things."

stacyspeyer  math  mathematics  polyhedra  classideas
january 2018 by robertogreco
long-view micro school
"Imagine . . .

a school that speaks up and not down to the intellects of children. A school that communicates to students that understanding derives from activity -- making, doing, creating -- and encourages kids to think like producers, not consumers.

Imagine a school that doesn't close the doors after students enter but instead seeks to be open and networked, connecting students to their community and the world. A school that takes "the long view" by prioritizing construction of meaning, asking good questions, seeking connections, and considering multiple perspectives, over consumption of information, rote practice, and shallow skill coverage.

Education Re-Imagined.

For the Long-View."

"If you are a parent seeking an education focused on strong academics, you know the problem:
Your child is not challenged and there is a great deal of lost learning time. Additionally, the areas you may be most concerned about -- math and science -- are not taught very deeply or thoughtfully in elementary school.

At Long-View, all that changes.

We focus on long-term, transferable skills and they all add up to a love of learning.

Our curriculum is founded on deep learning. Our vision is to ensure we are looking ahead, and making sure we are keeping the long term, transferrable skills foremost in our curriculum. We have high expectations for our students, support them as they stretch and grow, and we don't waste our kids' time.

We seek to inculcate certain habits of mind that begin fundamentally with a love of learning for its own sake."

"We don't adhere to a rigid schedule of 45-minute subject increments at Long-View. And we don't have grade levels.

Our students learn in blocks of time that are typically 90 minutes to 2 hours long, as blocks promote deeper thinking and persistence with an idea or concept. Blocks help us learn "more seriously."

And we consistently push ahead, leaving the grade levels that so often restrict learning behind. Our kids are on an upwards trajectory and multi-age cohorts promote stronger learning.

Long-View doesn't look like your ordinary school. Our classrooms are radically different than most, so it is hard for us to even use the word "classroom."

What's different? Everything moves. There are no chairs. And we write on the walls (among other things). The "classroom" belongs to the kids and it is flexible, creative, and transparent."

"Long-View's schedule is more balanced.
Our 4-day schedule means Fridays are a time for families, for sports or music lessons, for trips to the museum with friends, for projects based on a kid's passions, or some needed free time playing outside on a pretty day.

From 9:00 - 2:30, Mondays-Thursdays, we are working hard at Long-View. Unlike many schools, we don't waste time or spend our academic minutes on busy work. Kids are working hard, thinking hard. Homework is minimal and focused on daily independent reading or finishing up a research quest.

Long-View's focus is on math, reading, writing, science, and computer science. The focused academic footprint means parents have the opportunity to customize the rest of their child's education. There's time for a specialized art class, a violin lesson, a favorite sport, or parkour. You know your child and his or her passions. With academics taken care of by Long-View, you can add in the right art, music, theater, or sports experiences in the afternoons and on Fridays and keep your child's week more balanced."

"The micro school opportunity lies in the fact that we have:
Small Learning Communities
Multi-Age Cohorts
Lower Operation Complexity
Personal Connections
Rapid Idea Iteration
Teacher Empowerment
Unique Curriculum

Perhaps the best way to think of us is to compare us to the restaurant industry. Think of a big, standardized, chain restaurant with a menu as big as an encyclopedia. Now think of your favorite neighborhood, farm-to-table restaurant that serves a few spectacular dishes made from the best ingredients.

We are Farm-to-Table for schools.

One of the opportunities of the micro-school model lies in controlling costs and ensuring tuition doesn't become accessible only to a minority of families.

With a focused academic footprint (i.e. Long-View does not strive to deliver on breadth and instead focuses on quality), simple facilities, and low operation complexity, we can deliver high-quality academics at a price point that is accessible to a larger range of families.

Additionally, because we are a small school community and because our facilities are not major drivers in our tuition model, Long-View families enjoy a more stable annual tuition over years."
schools  microschools  sfsh  lcproject  openstudioproject  education  children  learning  austin  texas  math  mathematics
november 2017 by robertogreco
Mathematics must be creative, else it ain’t mathematics
"Students recoil from algebra as if it descended from Mars; who could blame them? Studied in isolation, algebra is ugly and utterly confusing. But when we lift its veil of abstraction and link algebra to its close relative, co-ordinate geometry, we arrive at a whole new plane of understanding. The idea of representing every point in a plane using just two numbers — what we now know as the x and y co-ordinates — was Descartes’ own nod to creativity."

"If only students were encouraged to transcend their study of individual topics. When a GCSE exam question dared to combine a quadratic equation with basic probability, the students roared with disapproval. Among them was my niece, who defiantly proclaimed that this isn’t how she were taught. Quadratics, fine. Probability, no problem. But a question that requires both? Call the press; it’s time to create another headline about a fiendish maths problem.

The tyranny of school maths lies in the false promise that stuffing oneself with facts and procedures prepares you for creativity. The act of creativity is deferred to an unspecified time — presumably it is for older, more knowledgeable people. It’s as if Tokio was instructed to learn his scales but never put hand to piano. No mathematician I have ever met learned their craft this way. They dived deep into topics for sure, but they habitually sought to join up concepts and apply their knowledge in novel ways to create entirely new understandings of mathematics. Young age is no barrier — my most impressive students are also the shortest; it only takes a well-crafted maths problem to unleash their innate creativity.

It helps to organise mathematical knowledge. There are obvious benefits to going deep in a particular area and I always offer a gracious nod to the fluency and fundamentals of mathematics. But mathematics at its most fundamental is an integrated body of ideas, replete in patterns. The patterns and connections are what makes it mathematics. Let that be your next headline."
math  mathematics  education  teaching  creativity  2017  interdisciplinary
november 2017 by robertogreco
How Systemic Control Stunts Creative Growth – Rafranz Davis – Medium
"Last week our cohort of students began designing their making/coding engineering projects and as exciting as it was, we still had a moment of pause in which we thought that perhaps we needed to insert a little more control and guidance.
…for the sake of time and because it would’ve been much easier.

In the aftermath of “plan day” and amidst the exhaustion of coaching and continuously trying to promote more “yes and” in lieu of “but”, I’ve thought about the diversity of ideas that kids had and the joy in their eyes as they were creating.

One of our groups is making a Scorpion-Dragon and another is making a combination of a Rube Goldberg machine with diet coke exploder. While I have no idea what the latter is, I am so excited to see it and am honestly still mortified at the thought that I even considered an outcome where kids would not have had such choices.

You see, I am one who is fortunate enough to have a front row seat to the power of creativity through my role as a nurturer for my nephew. I watch him experiment with a plethora of artistic choices and am constantly in awe of how much he learns just because he feels like it and most often because his project of choice demands it.

I’m also painfully aware how much a majority of his creative freedoms occur at home because school is most often not a place that is open to such thinking/doing…unless it is “holiday week”, early release day or the weeks after state testing is done.

This is the reality for so many but in all fairness, this is how we’ve been conditioned to “do” school in the face of accountability.

…and as much as teachers get a hard time for their lack of creative ventures, especially considering technology, it’s unfair to blame those who have no choice but to do as the system was created to do.

Too often, the de-creativeness of kids begins as soon as they enter the doors of early childhood. Creative play is replaced with scheduled assessments. Individuality is replaced with school uniforms of one color. Gender roles define everything from activities kids get to do, to who they sit with at lunch and who stands before or after them in line.

…the line where kids learn early to stand in silence with “bubbles in mouths” and hands behind backs

We still misinterpret quiet classrooms as the best classrooms.

If kids do get to create, they are all creating the same thing because the thought of “different” immediately triggers adult fears concerning time and we all know that in every classroom, time is a pretty hot commodity.

There just seems to be not enough of it.

I remember the first day in my high school algebra class when I decided to stop teaching according to the “lesson cycle” formula that our program seemed to have adopted. Kids lots their minds!

They wanted the template. They wanted the steps. They wanted me to do the thinking for them. They did not have the skills to creatively problem solve because in all the years that they had been in school, we did a great job of slowly but surely stripping this important ability away.

…an ability inherent in kids since birth as they utilize their senses to figure out the world around them.

…most often through curiosity driven play.

Right now, I’m sitting beside my nephew as he draws the header image for this piece. I spent yesterday watching him design and make an animatronic Christmas scene and over the last few weeks he’s been creating digital images and uploading his creations to redbubble so that for a small price, others could experience his vivid imagination.

This…in addition to his extensive work in puppetry, minecraft, oil painting, clay molding, music and just about anything that he feels like learning.

I’m not worried about my nephew though. He has us to support and guide him.

Not every kid has that and perhaps school should be the place that cultivates creativity in lieu of controlling it."
rafranzdavis  2017  creativity  math  mathematics  problemsolving  algebra  teaching  learning  howwelearn  control  freedom  children  unschooling  deschooling  sfsh  curiosity  schools  schooling  schooliness  making  art  education  howweteach  openstudioproject  lcproject
november 2017 by robertogreco
I love math, but quit teaching it because I was forced to make it boring - The Globe and Mail
"As a math teacher, there were many days I hated math more than my students did. Way more.

So I quit in 2013, happily leaving behind job security, a pension and the holy grail of teacher benefits: summers off.

Everyone thought I was crazy. I was in the early years of a divorce and had a mother and two kids to support. Almost nobody – and rightfully so, I suppose – supported my ostensibly hasty decision to abandon the education ship. There were no safety boats waiting and I was not a great swimmer. What the hell was I thinking?

In fact I was leaping off the Titanic – where actual math education is relegated to third class and was drowning along with its students.

The hardest thing to teach is mathematics. Not so much because math is hard – so is shooting three-pointers or making risotto – but because education makes it hard. Boring curriculum. Constant testing. Constant arguments over pedagogy. Lack of time. It's a Gong Show.

I found a sizable chunk of the math that I was forced to teach either a) boring; b) benign; c) banal; or d) Byzantine. The guilt of being paid to shovel this anachronistic heap of emaciated and disconnected mathematics around finally caught up with me.

I quit because I felt like a charlatan when I implicitly or explicitly told my students that what we were learning reflected the heart of mathematics or that it was the core of lifelong practicality. "When are we going to use this?" has been the No. 1 whine in math classes for a few generations. We should stop trying to sell mathematics for its usefulness. It's not why you or I should learn it.

Earlier this year, Francis Su, the outgoing president of the Mathematical Association of America, gave a speech for the ages. He referenced a prisoner named Christopher serving a long prison sentence, teaching himself mathematics. "Mathematics helps people flourish," he said. "Mathematics is for human flourishing." In a follow-up interview, Su talked about how math should involve beauty, truth, justice, love and play. Not sure about you, but my math education and Ontario teaching experience were the furthest things from these virtues. In Ontario, kids are imprisoned with criminally bland mathematics – so are the teachers.

I left teaching because my impact on math education lay beyond my classroom and my school. I felt I could contribute my passion/understanding for mathematics on a larger stage – maybe global. I was dreaming, but sometimes chasing your dreams is worth all the outside skepticism and uphill climbs. At one point, I was penniless at 50, stressed, confused and disappointed. But I wasn't unhappy. I was rescued by the light and humanity of mathematics.

Fast forward four years. I've written a book about the hidden happiness of math. I work remotely for a Canadian digital math resource company and I travel all over North America speaking about my almost gnawing passion of mathematics. I felt that I couldn't share that passion for most of my teaching career because the unchecked bureaucracy of the education system was more interested in data from standardized test scores and putting pedagogy ahead of mathematics. As such, the culture of mathematics has almost been shaded into obscurity.

So now, when I see the flood of math articles about Ontario's low math scores, I put my head in my hands and worry my eyes might just roll too far back into my head.

Every year is a contest to see who will win this year's huffing and puffing award about the province's low standardized test scores. For the past few years, arguments about old math versus new math have been running away with the trophy. Although, headlines crying Elementary Teachers Need More Math Training are often the runner-up.

As a student, I went through that "old" system. Sure, I got plenty of As and gold stars, but it took me well into my teaching career to really understand a fraction of the things I thought I knew.

Calculus? Pfff. Get rid of that thing, it belongs in university after a serious boot camp of algebra. Fractions, as with unsafe firecrackers, need to be pulled out of the hands of younger students and introduced to them in their hormonal years. Why are teachers asking students to flip and multiply fractions when you need to divide them? Anyone care to explain that to children – why fractions are doing gymnastics to arrive at the correct answer?

There are so many amazing teachers fighting the good fight. But until the real culprit – the government – gets called out for manufacturing a dog's breakfast of math education, students will continue to suffer in the classroom."
sfsh  mth  mathematics  teaching  education  testing  standardizedtesting  2017  sunilsingh  calculus  curriculum  pedagogy  cv  learning  francissu  math  beauty  truth  justice  love  play  happiness  bureaucracy  oldmath  newmath  fractions
october 2017 by robertogreco
OBJECT AMERICA
"The Observational Practices Lab, Parsons, (co-directed by Pascal Glissmann and Selena Kimball) launches a multi-phase project and investigation, OBJECT AMERICA, to explore the idea of “America” through everyday objects. The aim is to use comparative research and observational methods—which may range from the scientific to the absurd—to expose unseen histories and speculate about the future of the country as a concept. The contemporary global media landscape is fast-moving and undercut by “fake news” and “alternative facts” which demands that students and researchers build a repertoire of strategies to assess and respond to sources of information. For the first phase of OBJECT AMERICA launching in the fall of 2017, we invited Ellen Lupton, Senior Curator of Contemporary Design at Cooper Hewitt, Smithsonian Design Museum, to choose an object for this investigation which she believed would represent “America” into the future (she chose the Model 500 Telephone by Henry Dreyfuss designed in 1953). Researchers will investigate this object through different disciplinary lenses — including art, climate science, cultural geography, data visualization, economics, history of mathematics, medicine, media theory, material science, music, poetry, and politics — in order to posit alternative ways of seeing."

objects  pascalglissmann  selenakimball  ellenlupton  art  climate  science  culturalgeography  datavisualization  economics  mathematics  math  medicine  mediatheory  materialscience  music  poetry  politics  seeing  waysofseeing  geography  culture  history  climatescience  dataviz  infoviz
october 2017 by robertogreco
Why there’s no such thing as a gifted child | Education | The Guardian
"Even Einstein was unexceptional in his youth. Now a new book questions our fixation with IQ and says adults can help almost any child become gifted"

"When Maryam Mirzakhani died at the tragically early age of 40 this month, the news stories talked of her as a genius. The only woman to win the Fields Medal – the mathematical equivalent of a Nobel prize – and a Stanford professor since the age of 31, this Iranian-born academic had been on a roll since she started winning gold medals at maths Olympiads in her teens.

It would be easy to assume that someone as special as Mirzakhani must have been one of those gifted children who excel from babyhood. The ones reading Harry Potter at five or admitted to Mensa not much later. The child that takes maths GCSE while still in single figures, or a rarity such as Ruth Lawrence, who was admitted to Oxford while her contemporaries were still in primary school.

But look closer and a different story emerges. Mirzakhani was born in Tehran, one of three siblings in a middle-class family whose father was an engineer. The only part of her childhood that was out of the ordinary was the Iran-Iraq war, which made life hard for the family in her early years. Thankfully it ended around the time she went to secondary school.

Mirzakhani, did go to a highly selective girls’ school but maths wasn’t her interest – reading was. She loved novels and would read anything she could lay her hands on; together with her best friend she would prowl the book stores on the way home from school for works to buy and consume.

As for maths, she did rather poorly at it for the first couple of years in her middle school, but became interested when her elder brother told her about what he’d learned. He shared a famous maths problem from a magazine that fascinated her – and she was hooked. The rest is mathematical history.

Is her background unusual? Apparently not. Most Nobel laureates were unexceptional in childhood. Einstein was slow to talk and was dubbed the dopey one by the family maid. He failed the general part of the entry test to Zurich Polytechnic – though they let him in because of high physics and maths scores. He struggled at work initially, failing to get academic post and being passed over for promotion at the Swiss Patent Office because he wasn’t good enough at machine technology. But he kept plugging away and eventually rewrote the laws of Newtonian mechanics with his theory of relativity.

Lewis Terman, a pioneering American educational psychologist, set up a study in 1921 following 1,470 Californians, who excelled in the newly available IQ tests, throughout their lives. None ended up as the great thinkers of their age that Terman expected they would. But he did miss two future Nobel prize winners – Luis Alvarez and William Shockley, both physicists – whom he dismissed from the study as their test scores were not high enough.

There is a canon of research on high performance, built over the last century, that suggests it goes way beyond tested intelligence. On top of that, research is clear that brains are malleable, new neural pathways can be forged, and IQ isn’t fixed. Just because you can read Harry Potter at five doesn’t mean you will still be ahead of your contemporaries in your teens.

According to my colleague, Prof Deborah Eyre, with whom I’ve collaborated on the book Great Minds and How to Grow Them, the latest neuroscience and psychological research suggests most people, unless they are cognitively impaired, can reach standards of performance associated in school with the gifted and talented. However, they must be taught the right attitudes and approaches to their learning and develop the attributes of high performers – curiosity, persistence and hard work, for example – an approach Eyre calls “high performance learning”. Critically, they need the right support in developing those approaches at home as well as at school.

So, is there even such a thing as a gifted child? It is a highly contested area. Prof Anders Ericsson, an eminent education psychologist at Florida State University, is the co-author of Peak: Secrets from the New Science of Expertise. After research going back to 1980 into diverse achievements, from music to memory to sport, he doesn’t think unique and innate talents are at the heart of performance. Deliberate practice, that stretches you every step of the way, and around 10,000 hours of it, is what produces the expert. It’s not a magic number – the highest performers move on to doing a whole lot more, of course, and, like Mirzakhani, often find their own unique perspective along the way.

Ericsson’s memory research is particularly interesting because random students, trained in memory techniques for the study, went on to outperform others thought to have innately superior memories – those you might call gifted.

He got into the idea of researching the effects of deliberate practice because of an incident at school, in which he was beaten at chess by someone who used to lose to him. His opponent had clearly practised.

But it is perhaps the work of Benjamin Bloom, another distinguished American educationist working in the 1980s, that gives the most pause for thought and underscores the idea that family is intrinsically important to the concept of high performance.

Bloom’s team looked at a group of extraordinarily high achieving people in disciplines as varied as ballet, swimming, piano, tennis, maths, sculpture and neurology, and interviewed not only the individuals but their parents, too.

He found a pattern of parents encouraging and supporting their children, in particular in areas they enjoyed themselves. Bloom’s outstanding adults had worked very hard and consistently at something they had become hooked on young, and their parents all emerged as having strong work ethics themselves.

While the jury is out on giftedness being innate and other factors potentially making the difference, what is certain is that the behaviours associated with high levels of performance are replicable and most can be taught – even traits such as curiosity.

Eyre says we know how high performers learn. From that she has developed a high performing learning approach that brings together in one package what she calls the advanced cognitive characteristics, and the values, attitudes and attributes of high performance. She is working on the package with a group of pioneer schools, both in Britain and abroad.

But the system needs to be adopted by families, too, to ensure widespread success across classes and cultures. Research in Britain shows the difference parents make if they take part in simple activities pre-school in the home, supporting reading for example. That support shows through years later in better A-level results, according to the Effective Pre-School, Primary and Secondary study, conducted over 15 years by a team from Oxford and London universities.

Eye-opening spin-off research, which looked in detail at 24 of the 3,000 individuals being studied who were succeeding against the odds, found something remarkable about what was going in at home. Half were on free school meals because of poverty, more than half were living with a single parent, and four in five were living in deprived areas.

The interviews uncovered strong evidence of an adult or adults in the child’s life who valued and supported education, either in the immediate or extended family or in the child’s wider community. Children talked about the need to work hard at school and to listen in class and keep trying. They referenced key adults who had encouraged those attitudes.

Einstein, the epitome of a genius, clearly had curiosity, character and determination. He struggled against rejection in early life but was undeterred. Did he think he was a genius or even gifted? No. He once wrote: “It’s not that I’m so smart, it’s just that I stay with problems longer. Most people say that it is the intellect which makes a great scientist. They are wrong: it is character.”

And what about Mirzakhani? Her published quotations show someone who was curious and excited by what she did and resilient. One comment sums it up. “Of course, the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.”

The trail took her to the heights of original research into mathematics in a cruelly short life. That sounds like unassailable character. Perhaps that was her gift."
sfsh  parenting  gifted  precocity  children  prodigies  2017  curiosity  rejection  resilience  maryammirzakhani  childhood  math  mathematics  reading  slowlearning  lewisterman  iq  iqtests  tests  testing  luisalvarez  williamshockley  learning  howwelearn  deboraheyre  wendyberliner  neuroscience  psychology  attitude  persistence  hardwork  workethic  andersericsson  performance  practice  benjaminbloom  education  ballet  swimming  piano  tennis  sculpture  neurology  encouragement  support  giftedness  behavior  mindset  genius  character  determination  alberteinstein
july 2017 by robertogreco
The Edgeless & Ever-Shifting Gradient: An Encyclopaedic and Evolving Spectrum of Gradient Knowledge
"A gradient, without restriction, is edgeless and ever-shifting. A gradient moves, transitions, progresses, defies being defined as one thing. It formalizes difference across a distance. It’s a spectrum. It’s a spectral smearing. It’s an optical phenomenon occurring in nature. It can be the gradual process of acquiring knowledge. It can be a concept. It can be a graphic expression. It can be all of the above, but likely it’s somewhere in between.

A gradient, in all of it’s varied forms, becomes a catalyst in it’s ability to seamlessly blend one distinct thing/idea/color, to the next distinct thing/idea/color, to the next, etc.

In this sense, it is the gradient and the way it performs that has become a model and an underlying ethos, naturally, for this online publishing initiative that we call The Gradient.

Similarly, it’s our hope that this post—an attempt to survey gradients of all forms and to expand our own understanding of gradients—will also be edgeless and ever-shifting. This post will evolve and be progressively added to in an effort to create, as the subtitle says, an encyclopaedic and evolving spectrum of gradient knowledge."
gradients  art  2017  ryangeraldnelson  color  blending  spectrums  nature  design  gender  genderfluidity  computers  music  photography  graphics  graphicdesign  thermography  iridescence  brids  animals  insects  snakes  cephlalopods  reptiles  chameleons  rainbows  sky  math  mathematics  taubaauerbach  science  tomássaraceno  vision  brycewilner  alruppersberg  germansermičs  glass  ignazschiffermüller  lizwest  markhagen  ombré  rawcolor  samfall
july 2017 by robertogreco
Stephanie Hurlburt on Twitter: "A bunch of people are asking what resources I recommend to start learning graphics programming. So you get a thread on it!"
"A bunch of people are asking what resources I recommend to start learning graphics programming. So you get a thread on it!

I really enjoy giving beginner-level workshops. Here are two that focus on graphics:
https://www.slideshare.net/StephanieHurlburt/graphics-programming-workshop

If you're a graphics coder reading this wondering how you can host a workshop too, I've written about that:
http://stephaniehurlburt.com/blog/2016/11/1/guide-to-running-technology-workshops

I also wrote my own little writeup on graphics, notes from when Rich & I were helping Sophia learn graphics.
http://stephaniehurlburt.com/blog/2016/10/28/casual-introduction-to-low-level-graphics-programming

One more graphics workshop-- this one includes a raytracing and particle demo for you to play with.

I love @baldurk 's blog series, "Graphics in Plain Language" https://renderdoc.org/blog/Graphics-in-Plain-Language/

For those ready to wade into advanced waters, "A trip through the graphics pipeline" by @rygorous is great
https://fgiesen.wordpress.com/2011/07/09/a-trip-through-the-graphics-pipeline-2011-index/

This online book is just an amazing introduction to shaders, by @patriciogv and @_jenlowe_ https://thebookofshaders.com/

Prepare yourself for a monster list of graphics resources on this site! My favorite is the SIGGRAPH papers. http://kesen.realtimerendering.com/

I'm a big fan of Cinder and OpenFramworks, both C++/graphics. They are what I started from.
https://libcinder.org/docs/guides/opengl/index.html
http://openframeworks.cc/learning/

BGFX is also great!

For a more beginner friendly library, Processing is simply lovely. https://processing.org/tutorials/

Shaders! GLSLSandbox is more beginner-friendly, Shadertoy if you want to see some crazy shit
http://glslsandbox.com/

Can't go without mentioning @CasualEffects 's Graphics Codex-- excellent and comprehensive graphics resource. http://graphicscodex.com/

I stand by this advice on how to approach learning graphics programming.
[image with screenshot of chat]

Since we're now on the topic of getting jobs, do mock interviews and get mentors and talk to people. https://twitter.com/sehurlburt/status/872919452718727168 ["Attn coders who struggle w these, or jr coders:

It is your homework to set up a mock interview w one of these folks"]

My mentor list is FULL of graphics programmers. They all love helping you. I do need to update it with more.
http://stephaniehurlburt.com/blog/2016/11/14/list-of-engineers-willing-to-mentor-you

People ask me about learning math and I point them to @EricLengyel 's book
https://www.amazon.com/Foundations-Game-Engine-Development-Mathematics/dp/0985811749/

GPU Performance for Game Artists by @keithoconor
http://fragmentbuffer.com/gpu-performance-for-game-artists/

There are more resources I didn't mention. Check out the last two slides of this https://www.slideshare.net/StephanieHurlburt/graphics-programming-workshop , and http://www.realtimerendering.com

This is a good little collection of resources on advanced GPU optimization and documentation.
https://github.com/g-truc/sdk/tree/master/documentation/hardware/amd/Southern%20Islands

An important point: The vast majority of graphics coders I know don't know math very well. Don't be scared away if you aren't a math person.

I say this as someone who adores math, was expecting to use it all the time, & only ever needed basic linear algebra for my graphics work.

Someone made a Slack chat for graphics programming learning/development! Both experienced folks + newbies welcome. https://twitter.com/iFeliLM/status/884801828696805377 ["Great idea. We have a Slack group here:

graphics  programming  howto  tutorials  stephaniehurlburt  via:datatelling  math  mathematics  coding
july 2017 by robertogreco
Pie charts did nothing to deserve how you’re treating them
"So if you want to complain about something, complain about the rampant misuse of charts instead. No chart type is good at everything, and charting tools can’t read our minds yet. Pick the chart type that tells your story best, and ameliorates the pitfalls that you want to avoid.

Pie charts are OK. They existed before most of us, and they’ll probably outlive all of us. When we finally read the climate-driven death sentence of our planet in a 100-page report, it will probably have pie charts. So enjoy your artisanal donut charts and your home-baked square pie charts while you can, hipsters. Just kidding. Till then though, you can find me putting gold stars on every good little pie chart I encounter.

Lay off it, friends!"
piecharts  math  mathematics  data  datavisualization  visualization  classideas  2017  malakmanalp  charts  graphs
april 2017 by robertogreco
When I Heard the Learn’d Astronomer… – Arthur Chiaravalli – Medium
"As I reflect back on these experiences, however, I wonder if the standards-based approach gave me a warped view of teaching and learning mathematics. I had apparently done an excellent job equipping my students with dozens of facts, concepts, and algorithms they could put into practice…on the multiple-choice final exam.

Somewhere, I’m sure, teachers were teaching math in a rich, interconnected, contextualized way. But that wasn’t the way I taught it, and my students likely never came to understand it in that way.

Liberating Language Arts

Fast forward to the present. For the past five years I have been back teaching in my major of language arts. Here the shortcomings of the standards-based method are compounded even further.

One of the more commonly stated goals of standards-based learning and grading is accuracy. First and foremost, accuracy means that grades should reflect academic achievement alone — as opposed to punctuality, behavior, compliance, or speed of learning. By implementing assessment, grading, and reporting practices similar to those I’d used in mathematics, I was able to achieve this same sort of accuracy in my language arts classes.

Accuracy, however, also refers to the quality of the assessments. Tom Schimmer, author of Grading From the Inside Out: Bringing Accuracy to Student Assessment through a Standards-based Mindset, states
Low-quality assessments have the potential to produce inaccurate information about student learning. Inaccurate formative assessments can misinform teachers and students about what should come next in the learning. Inaccurate summative assessments may mislead students and parents (and others) about students’ level of proficiency. When a teacher knows the purpose of an assessment, what specific elements to assess…he or she will most likely see accurate assessment information.

Unfortunately, assessment accuracy in the language arts and humanities in general is notoriously elusive. In a 1912 study of inter-rater reliability, Starch and Elliot (cited in Schinske and Tanner) found that different teachers gave a single English paper scores ranging from 50 to 98%. Other studies have shown similar inconsistencies due to everything from penmanship and the order in which the papers are reviewed to the sex, ethnicity, and attractiveness of the author.

We might argue that this situation has improved due to common language, range-finding committees, rubrics, and other modern developments in assessment, but problems remain. In order to achieve a modicum of reliability, language arts teams must adopt highly prescriptive scoring guides or rubrics, which as Alfie Kohn, Linda Mabry, and Maya Wilson have pointed out, necessarily neglect the central values of risk taking, style, and original thought.

This is because, as Maya Wilson observes, measurable aspects can represent “only a sliver of…values about writing: voice, wording, sentence fluency, conventions, content, organization, and presentation.” Just as the proverbial blind men touching the elephant receive an incorrect impression, so too do rubrics provide a limited — and therefore inaccurate — picture of student writing.

As Linda Mabry puts it,
The standardization of a skill that is fundamentally self-expressive and individualistic obstructs its assessment. And rubrics standardize the teaching of writing, which jeopardizes the learning and understanding of writing.

The second part of Mabry’s statement is even more disturbing, namely, that these attempts at accuracy and reliability not only obstruct accurate assessment, but paradoxically jeopardize students’ understanding of writing, not to mention other language arts. I have witnessed this phenomenon as we have created common assessments over the years. Our pre- and post-tests are now overwhelmingly populated with knowledge-based questions — terminology, vocabulary, punctuation rules. Pair this with formulaic, algorithmic approaches to the teaching and assessment of writing and you have a recipe for a false positive: students who score well with little vision of what counts for deep thinking or good writing.

It’s clear what we’re doing here: we’re trying to do to writing and other language arts what we’ve already done to mathematics. We’re trying to turn something rich and interconnected into something discrete, objective and measurable. Furthermore, the fundamentally subjective nature of student performance in the language arts renders this task even more problematic. Jean-Paul Sartre’s definition of subjectivity seems especially apt:
The subjectivity which we thus postulate as the standard of truth is no narrowly individual subjectivism…we are attaining to ourselves in the presence of the other, and we are just as certain of the other as we are of ourselves.…Thus the man who discovers himself directly in the cogito also discovers all the others, and discovers them as the condition of his own existence. He recognises that he cannot be anything…unless others recognise him as such. I cannot obtain any truth whatsoever about myself, except through the mediation of another. The other is indispensable to my existence, and equally so to any knowledge I can have of myself…Thus, at once, we find ourselves in a world which is, let us say, that of “intersubjectivity.”

First and foremost, the language arts involve communication: articulating one’s own ideas and responding to those of others. Assigning a score on a student’s paper does not constitute recognition. While never ceding my professional judgment and expertise as an educator, I must also find ways to allow students and myself to encounter one another as individuals. I must, as Gert Biesta puts it, create an environment in which individuals “come into presence,” that is, “show who they are and where they stand, in relation to and, most importantly, in response to what and who is other and different”:
Coming into presence is not something that individuals can do alone and by themselves. To come into presence means to come into presence in a social and intersubjective world, a world we share with others who are not like us…This is first of all because it can be argued that the very structure of our subjectivity, the very structure of who we are is thoroughly social.

Coming to this encounter with a predetermined set of “specific elements to assess” may hinder and even prevent me from providing recognition, Sartre’s prerequisite to self-knowledge. But it also threatens to render me obsolete.

The way I taught mathematics five years ago was little more than, as Biesta puts it, “an exchange between a provider and a consumer.” That transaction is arguably better served by Khan Academy and other online learning platforms than by me. As schools transition toward so-called “personalized” and “student-directed” approaches to learning, is it any wonder that the math component is often farmed out to self-paced online modules — ones that more perfectly provide the discrete, sequential, standards-based approach I developed toward the end of my tenure as math teacher?

Any teacher still teaching math in this manner should expect to soon be demoted to the status of “learning coach.” I hope we can avoid this same fate in language arts, but we won’t if we give into the temptation to reduce the richness of our discipline to standards and progression points, charts and columns, means, medians, and modes.

What’s the alternative? I’m afraid I’m only beginning to answer that question now. Adopting the sensible reforms of standards-based learning and grading seems to have been a necessary first step. But is it the very clarity of its approach — clearing the ground of anything unrelated to teaching and learning — that now urges us onward toward an intersubjective future populated by human beings, not numbers?

Replacing grades with feedback seems to have moved my students and me closer toward this more human future. And although this transition has brought a kind of relief, it has also occasioned anxiety. As the comforting determinism of tables, graphs, charts, and diagrams fade from view, we are left with fewer numbers to add, divide, and measure. All that’s left is human beings and the relationships between them. What Simone de Beauvoir says of men and women is also true of us as educators and students:
When two human categories are together, each aspires to impose its sovereignty upon the other. If both are able to resist this imposition, there is created between them a reciprocal relation, sometimes in enmity, sometimes in amity, always in tension.

So much of this future resides in communication, in encounter, in a fragile reciprocity between people. Like that great soul Whitman, we find ourselves “unaccountable” — or as he says elsewhere, “untranslatable.” We will never fit ourselves into tables and columns. Instead, we discover ourselves in the presence of others who are unlike us. Learning, growth, and self-knowledge occur only within this dialectic of mutual recognition.

Here we are vulnerable, verging on a reality as rich and astonishing as the one Whitman witnessed."
arthurchiaravalli  2017  education  standards-basedassessments  assessment  teaching  math  mathematics  writing  learning  romschimmer  grading  grades  alfiekohn  lindamabry  gertbiesta  khanacademy  personalization  rubics  waltwhitman  simonedebeauvoir  canon  sfsh  howweteach  howwelearn  mutualrecognition  communication  reciprocity  feedback  cv  presence  tension  standards  standardization  jean-paulsartre  mayawilson  formativeassessment  summativeassessment  interconnection  intersubjectivity  subjectivity  objectivity  self-knowledge  humans  human  humanism
april 2017 by robertogreco
Welcome to the Mathematics Assessment Project
"The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students’ mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students' understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems."
math  mathematics  teaching  eduction  curriculum
february 2017 by robertogreco
Absolute Blast | Institute of Play
"A rocket-launching math board game to boost understanding of integers, operations and absolute value for grades 6 through 8"
games  math  mathematics  classideas
january 2017 by robertogreco
"http://Reebok.com/CountYourDays The average human lifespan is 71 years. That’s 25,915 days. 25,915 opportunities to make the most of our time, honoring the body you’ve been given through a commitment to physicality. So what are you waiting for? The clock, and your days, are ticking. Calculate yours at http://Reebok.com/CountYourDays. "
reebok  advertising  classideas  time  life  lifespan  math  mathematics  medialiteracy  2016  sfsh
january 2017 by robertogreco
PAVING SPACE on Vimeo
"An unconventional encounter between maths, art and skateboarding.

This film documents a series of performances at the Palais de Tokyo in Paris, as well as the Institute of Contemporary Art Singapore and Sainte-Croix Museum in Poitiers.

The project originated after Carhartt WIP approached Isle skateboards to work on a collaborative
collection.ISLE, which started in 2013, has always prided itself on artist led conceptually driven ideas. Carhartt WIP and ISLE could think of no one better than artist and fellow skateboarder, Raphaël Zarka to work with. When they approached Zarka, he had been researching the work of 19th Century mathematician Arthur Moritz Schoenflies.

Schoenflies was a master of geometry and crystallography. He had developed his own three dimensional models that specifically captivated Zarka’s attention, after he was inspired with their sculptural potential.

This film invites you to view Zarka’s large scale reconstructions of Schoenflies’ models, re-appropriated in a way never imagined before.

Featured skaters :
Sylvain Tognelli / Nick Jensen / Casper Brooker / Jan Kliewer / Joseph Biais / Rémy Taveira / Josh Pall / Chris Jones / Armand Vaucher

Filmed, Edited and Directed by Dan Magee.
Technical motion design by Fabian Fuchs & Location intro animations by Andrew Khosravani.
Music composed and performed by Joel Curtis with contributing scoring by ADSL Camels."
skating  skateboarding  skateboards  danmagee  film  art  math  mathematics  arthurmoritzchoenflies  raphaëlzarka  sculpture  3d  tessellations  edg  video
january 2017 by robertogreco
Paper Models of Polyhedra
"Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia. On this site are a few hundred paper models available for free.

Make the models yourself.

Click on a picture to go to a page with a net of the model."
papercraft  via:dvsch  math  mathematics  geometry  art  classideas  polyhedra
january 2017 by robertogreco
Mathpix - Solve and graph math using pictures on the App Store
"Mathpix is the easiest way to create beautifully typeset mathematical documents. Simply take pictures of your equations and you instantly you get a digital document which you can export as a PDF, raw LaTeX file, or Overleaf link. "
applications  ios  math  mathematics
december 2016 by robertogreco
“All the time.”
"David Cox:
Yesterday, a student gave me step-by-step directions to solve a Rubik’s Cube. I finished it, but had no idea what I was doing. At times, I just watched what he did and copied his moves without even looking at the cube in my hands.

When we were finished, I exclaimed, “I did it!”, received a high-five from the student and some even applauded. For a moment, I felt like I had accomplished something. That feeling didn’t last long. I asked the class how often they experience what I just did.

They said, “All the time.”

Featured Comment

Lauren Beitel:
Is there an argument to be made that sometimes the conceptual understanding comes from repeating a procedure, then reflecting on it? Discovering/noticing patterns through repetition?

Great question. I wrote a comment [http://blog.mrmeyer.com/2016/all-the-time/#comment-2430188 ] in response."
math  teaching  education  danmeyer  learning  understanding  sfsh  repetition  mimicry  davidcox  laurenbeitel  via:lukeneff  howwelearn  howweteach  schools  meaningmaking
november 2016 by robertogreco
Maths Gear - Mathematical toys and curiosities - Mathematical curiosities, games and gifts
"We are Steve Mould, Matt Parker and James Grime.

We do maths shows, and people are always asking where they can buy the stuff from our shows. How disappointing to be told that it's all hand made and can't be bought! That's why we decided to start making things in bulk and selling them.

Matt and Steve started Maths Gear in 2011. James joined soon after and continues to feed the website will new toys like the Grime Dice and the Utilities Mug.

The shop is steadily growing as we add more hard-to-find mathematical curiosities, so if you have any ideas let us know:

contact@mathsgear.co.uk

And if you want to be kept up-to-date as we add new stuff, join the mailing list to the right.

If you're interested in our maths shows, take a look at these DVDs."

[previously: https://pinboard.in/u:robertogreco/b:702706055cb6 ]

[specifically:

"Shapes of constant width – set of 4"
https://mathsgear.co.uk/products/shapes-of-constant-width-in-acrylic-set-of-4?variant=290972516

"Solids of constant width"
https://mathsgear.co.uk/products/solids-of-constant-width

Dice:
https://mathsgear.co.uk/collections/dice

"Go First Dice"
https://mathsgear.co.uk/collections/games/products/go-first-dice

"Recast 2d6"
https://mathsgear.co.uk/collections/dice/products/recast-2d6

"Skew dice - d6"
https://mathsgear.co.uk/collections/dice/products/skew-dice

"Non transitive Grime dice"
https://mathsgear.co.uk/products/non-transitive-grime-dice

"D120 dice"
https://mathsgear.co.uk/collections/dice/products/d120-dice ]
math  mathematics  classideas  toys  curiosities  dice  sfsh
november 2016 by robertogreco
A Gadget for Every Need: Assistive Technology for Students | Edutopia
"Technology provides today’s students with an infinite number of distractions; mobile devices have literally put texting, Facebook, and addictive games at their fingertips. Although some educators might perceive this technology as a bane to classroom learning, it can actually be one of your most powerful educational tools.

All of your students can benefit from technology in the classroom, but new advancements have become particularly useful for those with special needs. Known as assistive technology (AT), these developments help level the playing field for students with special needs, giving them a greater chance at success in some of the more challenging areas.

Listening, Memory, and Organization

Listening and memorization are two difficult areas for many students. But there are many recording devices on the market that can help, including noise-canceling headphones and recording devices, such as tape recorders or students’ iPhones, that can be used to record lectures. Personal listening devices can also link students directly to their lecturers through a microphone and headset.

Even more specialized are AT devices like smartpens. These devices are used with special paper so students can write notes that correspond with verbal recordings. When students return to their written notes, they can touch the pen to the handwriting, and the pen will play back the corresponding recording. This eases the anxiety of having to listen intently while determining what’s most important to write down.

Enabling students to better organize their thoughts and assignments can significantly aid in comprehension, as well. Physical or digital color-coordinated daily planners are simple yet effective ways to get students organized. The advantage of digital organizers such as the iPhone organizer or software such as Info Select by Micro Logic is that students can set reminders with alarms and even add links to assignments to help them stay on track.

Math

Students struggling with math can also benefit from smartpens by linking their handwritten formulas and math problems with recorded instructions and tips.

Aligning math problems on paper is another challenge for some students with special needs, but putting those math problems on a computer screen with electronic math worksheets can alleviate that issue. Applications like MathPad allow students to write out problems on a tablet screen, and the program translates and aligns the writing into a more readable, solvable math problem. The student can also utilize the program’s special keyboard that includes clear mathematical symbols.

Calculators can also be difficult to handle, but with talking calculators such as Calc-U-Vue, students can double-check what they’ve entered and reiterate correct answers verbally, helping them focus on solving the problem rather than working the device.

Whether your students are visually impaired or struggle with comprehension, translating text into speech is a helpful function. There are many resources for audiobooks and publications, such as Audible, Bookshare, or your state library, where you can find a national database of audio publications via the National Library Service for the Blind and Physically Handicapped.

If you can’t find a specific book or publication in audio form, computer software or separate handheld devices with optical character recognition can scan documents and read them aloud using speech synthesizers or screen readers. These can also read text that users type or copy and paste from other resources.

Writing

Most word-processing programs include proofreading software for spelling and grammar, but students with special needs often require more comprehensive AT tools for writing.

For students with underdeveloped motor skills, speech recognition programs allow users to speak into a microphone, and the program will translate those spoken words into text. Many software programs have both speech recognition and speech synthesizers built in so students can verbalize what they want written, and the program reads the text back to them.

For students who struggle with writing by hand and prefer typing, small portable word processors allow them to type notes in class and take them home to add to or expand on for assignments without rekeying. This can be done on a tablet with word-processing software or with AT devices specific to this task, such as the Forte portable word processor.

Abbreviation expanders and word prediction software can help students with spelling and grammar by suggesting words or phrases they might mean to type while also speeding up their keying time. Similarly, alternative keyboards, such as IntelliKeys, help increase typing proficiency by grouping letters or symbols with customizable overlays, for example.

These AT tools and others can enhance the learning experience for all students and help them develop the self-confidence they need to succeed. You can find additional resources on the National Public Website on Assistive Technology, as well as games and websites for the classroom on Common Sense Education. AbleNet is a great resource for information on the most recent AT developments, such as SoundingBoard, an application that allows students with speech difficulties to communicate by touch screen.

Assistive technology can’t replace the vital human element of dedicated teachers, parents, and aides, but embracing these advancements will give both you and your students a leg up on learning."
assistivetechnology  technology  2015  rebeccadean  listening  memory  organization  math  mathematics  writing  reading  tools  teaching  education
november 2016 by robertogreco
Teaching is Compression
"Teaching itself comes in at least two forms. It's not just about broadcasting knowledge. No matter how many students you have, if that's all you're doing you aren't making as much progress as you could. The internet is a powerful tool for Type I teaching, but it can't help much with Type II. That is why it is not a satisfactory replacement.

The second type of teaching is a form of compression, making things easier to understand. I don't mean simply eliding details, or making your proofs more terse. I mean compression in the time it takes to explain an idea and its implications.

Computer science is hard. Logic is hard. And that's fine. But if we leave this world as complicated as we found it then we've failed to do our jobs. Think about it this way: if the next generation learns at the same speed as yours, they won't have time to move beyond you. Type II teaching is what enables Type I progress.

Physics went through a period of compression in the middle of the last century. Richard Feynman's reputation wasn't built on discovering new particles or laws of nature, but for discovering better ways to reason about what we already knew. [1] Mathematics has gone though several rebuilding periods. That's why you can pick up a child's math book today and find negative numbers, the square root of two, and many cheerful facts about the square of the hypotenuse. Every one of those mundane ideas was once the hardest problem in the world. My word, people died in arguments over the Pythagorean Theorem. Now we teach it to kids in a half hour. If that's not progress I don't know what is.

So how do we get there in computer science? How can we simplify what we already know so the next crop learns what they need to put our best efforts to shame?

The second form of progress is closely related to the second form of teaching. To my mind, understanding and explaining are just opposite ends of the same process. The only way to prove that you understand something is to explain it to somebody else. Not even using the knowledge is an airtight proof. That's why teachers are always telling you to show your work, to explain step-by-step how you got to the answer.

The most powerful way I know of to understand and explain is through story. Rendering a complex idea into a simple example, analogy, metaphor or allegory simultaneously achieves compression and a way to spread that idea far and wide. Making a good story also forces you to think hard about ways to drive home both the idea and its implications."
teaching  compression  howweteach  explanation  analogy  2012  carlosbueno  richardfeynman  math  mathematics
september 2016 by robertogreco
dy/dan » Blog Archive » Testify
"Karim Ani, the founder of Mathalicious, hassles me because I design problems about water tanks while Mathalicious tackles issues of greater sociological importance. Traditionalists like Barry Garelick see my 3-Act Math project as superficial multimedia whizbangery and wonder why we don’t just stick with thirty spiraled practice problems every night when that’s worked pretty well for the world so far. Basically everybody I follow on Twitter cast a disapproving eye at posts trying to turn Pokémon Go into the future of education, posts which no one will admit to having written in three months, once Pokémon Go has fallen farther out of the public eye than Angry Birds.

So this 3-Act math task is bound to disappoint everybody above. It’s a trivial question about a piece of pop culture ephemera wrapped up in multimedia whizbangery.

But I had to testify. That’s what this has always been – a testimonial – where by “this” I mean this blog, these tasks, and my career in math education to date.

I don’t care about Pokémon Go. I don’t care about multimedia. I don’t care about the sociological importance of a question.

I care about math’s power to puzzle a person and then help that person unpuzzle herself. I want my work always to testify to that power.

So when I read this article about how people were tricking their smartphones into thinking they were walking (for the sake of achievements in Pokémon Go), I was puzzled. I was curious about other objects that spin, and then about ceiling fans, and then I wondered how long a ceiling fan would have to spin before it had “walked” a necessary number of kilometers. I couldn’t resist the question.

That doesn’t mean you’ll find the question irresistible, or that I think you should. But I feel an enormous burden to testify to my curiosity. That isn’t simple.

“Math is fun,” argues mathematics professor Robert Craigen. “It takes effort to make it otherwise.” But nothing is actually like that – intrinsically interesting or uninteresting. Every last thing – pure math, applied math, your favorite movie, everything – requires humans like ourselves to testify on its behalf.

In one kind of testimonial, I’d stand in front of a class and read the article word-for-word. Then I’d work out all of this math in front of students on the board. I would circle the answer and step back.

But everything I’ve read and experienced has taught me that this would be a lousy testimonial. My curiosity wouldn’t become anybody else’s.

Meanwhile, multimedia allows me to develop a question with students as I experienced it, to postpone helpful tools, information, and resources until they’re necessary, and to show the resolution of that question as it exists in the world itself.

I don’t care about the multimedia. I care about the testimonial. Curiosity is my project. Multimedia lets me testify on its behalf.

So why are you here? What is your project? I care much less about the specifics of your project than I care how you testify on its behalf.

I care about Talking Points much less than Elizabeth Statmore. I care about math mistakes much less than Michael Pershan. I care about elementary math education much less than Tracy Zager and Joe Schwartz. I care about equity much less than Danny Brown and identity much less than Ilana Horn. I care about pure mathematics much less than Sam Shah and Gordi Hamilton. I care about sociological importance much less than Mathalicious. I care about applications of math to art and creativity much less than Anna Weltman.

But I love how each one of them testifies on behalf of their project. When any of them takes the stand to testify, I’m locked in. They make their project my own.

Again:

Why are you here? What is your project? How do you testify on its behalf?"
danmeyer  2016  math  mathematics  teaching  interestedness  pokémongo  curiosity  mathalicious  testament  multimedia  howweteach  interest  wonder  wondering  askingquestions  questionasking  modeling  education  howwelearn  engagement
august 2016 by robertogreco
Research study: To do better in school, log out of Facebook (FB) and play videogames — Quartz
"Pokémon Go might offer more than mindless entertainment.

Since the dawn of videogames, parents across the world have complained that their kids spend too much time playing online contests like Nintendo’s recent hit and other best-selling games such as Grand Theft Auto, Mario Kart, and Call of Duty. Yet according to new research, gamers actually do better in school.

This isn’t proof that playing videogames causes academic success, but it sets up a strong link. Alberto Posso, a business professor at the Royal Melbourne Institute of Technology, looked at data from national surveys on 12,000 Australian high school students, studying how their academic scores connected with their personal interests and activities. His report—published in the International Journal of Communication—shows that the teens who made a near-daily habit of playing videogames scored roughly 15 points higher than average on math, reading, and science tests.

“Videogames potentially allow students to apply and sharpen skills learned in school,” Posso wrote. Gamers solve puzzles, often using deductive reasoning, science knowledge, or math, and they have to be completely focused on the task at hand.

No surprise, then, that Posso’s study also found students who heavily used social media, which requires only minimal focus and promotes superficial thinking, tended to score 4% lower than their peers. The more time kids spent on sites like Twitter and Facebook, the bigger the drop in their scores—a conclusion that echoes that of many prior studies on social media and academic performance.

The evidence on videogames isn’t conclusive. It may be that kids who are naturally gifted at math and reasoning also gravitate toward gaming; gamers might also have other shared interests that contribute to their sharpness in school.

Still, between time spent online on Minecraft or Facebook, parents might want to consider being more lenient on the former."
games  gming  videogames  school  education  learning  facebook  2016  albertoposso  socialmedia  minecraft  gaming  reasoning  math  mathematics
august 2016 by robertogreco
The Importance of Recreational Math - The New York Times
"Baltimore — IN 1975, a San Diego woman named Marjorie Rice read in her son’s Scientific American magazine that there were only eight known pentagonal shapes that could entirely tile, or tessellate, a plane. Despite having had no math beyond high school, she resolved to find another. By 1977, she’d discovered not just one but four new tessellations — a result noteworthy enough to be published the following year in a mathematics journal.

The article that turned Ms. Rice into an amateur researcher was by the legendary polymath Martin Gardner. His “Mathematical Games” series, which ran in Scientific American for more than 25 years, introduced millions worldwide to the joys of recreational mathematics. I read him in Mumbai as an undergraduate, and even dug up his original 1956 column on “hexaflexagons” (folded paper hexagons that can be flexed to reveal different flowerlike faces) to construct some myself.

“Recreational math” might sound like an oxymoron to some, but the term can broadly include such immensely popular puzzles as Sudoku and KenKen, in addition to various games and brain teasers. The qualifying characteristics are that no advanced mathematical knowledge like calculus be required, and the activity engage enough of the same logical and deductive skills used in mathematics.

Unlike Sudoku, which always has the same format and gets easier with practice, the disparate puzzles that Mr. Gardner favored required different, inventive techniques to crack. The solution in such puzzles usually pops up in its entirety, through a flash of insight, rather than emerging steadily via step-by-step deduction as in Sudoku. An example: How can you identify a single counterfeit penny, slightly lighter than the rest, from a group of nine, in only two weighings?

Mr. Gardner’s great genius lay in using such basic puzzles to lure readers into extensions requiring pattern recognition and generalization, where they were doing real math. For instance, once you solve the nine coin puzzle above, you should be able to figure it out for 27 coins, or 81, or any power of three, in fact. This is how math works, how recreational questions can quickly lead to research problems and striking, unexpected discoveries.

A famous illustration of this was a riddle posed by the citizens of Konigsberg, Germany, on whether there was a loop through their town traversing each of its seven bridges only once. In solving the problem, the mathematician Leonhard Euler abstracted the city map by representing each land mass by a node and each bridge by a line segment. Not only did his method generalize to any number of bridges, but it also laid the foundation for graph theory, a subject essential to web searches and other applications.

With the diversity of entertainment choices available nowadays, Mr. Gardner’s name may no longer ring a bell. The few students in my current batch who say they still do mathematical puzzles seem partial to a website called Project Euler, whose computational problems require not just mathematical insight but also programming skill.

This reflects a sea change in mathematics itself, where computationally intense fields have been gaining increasing prominence in the past few decades. Also, Sudoku-type puzzles, so addictive and easily generated by computers, have squeezed out one-of-a-kind “insight” puzzles, which are much harder to design — and solve. Yet Mr. Gardner’s work lives on, through websites that render it in the visual and animated forms favored by today’s audiences, through a constellation of his books that continue to sell, and through biannual “Gathering 4 Gardner” recreational math conferences.

In his final article for Scientific American, in 1998, Mr. Gardner lamented the “glacial” progress resulting from his efforts to have recreational math introduced into school curriculums “as a way to interest young students in the wonders of mathematics.” Indeed, a paper this year in the Journal of Humanistic Mathematics points out that recreational math can be used to awaken mathematics-related “joy,” “satisfaction,” “excitement” and “curiosity” in students, which the educational policies of several countries (including China, India, Finland, Sweden, England, Singapore and Japan) call for in writing. In contrast, the Common Core in the United States does not explicitly mention this emotional side of the subject, regarding mathematics only as a tool.

Of course, the Common Core lists only academic standards, and leaves the curriculum to individual districts — some of which are indeed incorporating recreational mathematics. For instance, math lesson plans in Baltimore County public schools now usually begin with computer-accessible game and puzzle suggestions that teachers can choose to adopt, to motivate their classes.

The body of recreational mathematics that Mr. Gardner tended to and augmented is a valuable resource for mankind. He would have wanted no greater tribute, surely, than to have it keep nourishing future generations."
math  mathematics  fun  recreationalmathematics  2016  1975  marjorierice  problemsolving  puzzles  martin  gardner  games  play
august 2016 by robertogreco
We’d be better at math if the U.S. borrowed these four ideas for training teachers from Finland, Japan and China
"1. Raise selectivity standards for future educators. The report notes that this looks differently across the four systems. While Finland maintains very high admissions standards for entry to teacher preparation programs, Japan instead has the checkpoint at the end of training programs, requiring teachers to sit for a tough licensure exam.

2. Require that elementary school teachers specialize in content areas. Most primary school teachers in the U.S. teach all subjects. In many top countries, teacher candidates specialize in either math and science or language and social studies.

3. Focus on content knowledge. Trainee teachers in these countries study the content they will actually be teaching, say fourth grade fractions, not advanced college math. The idea is to give them a deep understanding not just of the content but also how students learn it.

4. Create structured professional learning communities. Many top countries embrace career ladders where master teachers formally train teachers in their first few years in the classroom."
math  mathematics  education  teaching  japan  finland  howweteach  emmanuelfenton
july 2016 by robertogreco
Why San Francisco stopped teaching algebra in middle school - Business Insider
"As Ryan points out, the CCSS Math 8 course that eighth graders are now expected to take includes 60% of the material from the old Algebra I course. This includes linear equations, roots, exponents, and an introduction to functions. The new course also offers students a taste of geometry and statistics—hardly your typical middle school fare. According to Ryan, this helps students to understand the "why" and "what for" of pre-algebraic math.

Likewise, the course called "Algebra I" that students will now take in their first year of high school introduces a number of the concepts we all associate with introductory algebra (quadratic equations, say), but also delves deeper into modeling with functions and quantitative analysis. Call it what you want, in other words, but this is not your grandmother's Algebra I.

This may be cold comfort for anxious parents concerned about packing in Calculus before graduation. But Ryan insists that acceleration is still possible under the new system. The key difference is that numerically-inclined students aren't tracked ahead of their peers until high school. Last week, the district announced that it would allow freshmen to choose from an array of math courses ranging from Algebra to Geometry.

math  sanfrancisco  mathematics  algebra  schools  curriculum  education  2016
july 2016 by robertogreco
The Problem with Story Problems
"Here’s my story of a problem, and it began with Frank. Pressing the math picture book to his chest, Frank explained how delighted he was to be reunited with this fun, clever text from his childhood. Frank, the leader of the mathematics department for our school district, said he wished we could buy a copy of this sweet book for every teacher in the district. I was intrigued.

As soon as I started The Dot and the Line: A Romance in Lower Mathematics, I felt uneasy. The book—by Norton Juster—favored all the characteristics that Frank himself embodied. The main character was an intelligent male—white, English-speaking, heterosexual, and someone with power—just like Frank. The other two characters were a man of color and a woman—both thinly portrayed and framed as vapid, frivolous, inept, and marginal. The female character was described as physically attractive and her body measurements were presented as a form of mathematics humor. As a female math educator myself, I was disappointed and outraged at the portrayals in this book—and even more disappointed at how dearly Frank loved this text. What did this say to me and about me, and what did it say to and about all the K–12 students in our care?

This got me thinking about the values our math texts promote. Story problems are supposed to be the most humanizing part of math education. Although this is sometimes the case, too often the assumptions inherent in story problems perpetuate consumerism, reinforce racist and sexist stereotypes, and maintain classism and unsustainable approaches to the Earth.

Because I know my insights are limited by my life experiences, my curiosity drove me to start asking others—teachers and future teachers—to share examples of math problems that stood out as damaging or exploitative, or that put forward a worldview that privileged a certain way of thinking or kind of person. I also asked them how they have used these problematic problems to help their students think critically about textbooks and the world.

It turns out I wasn’t alone in my concern about the messages in word problems. We found poisonous examples all over the place, in materials from the elementary level right through calculus. Fortunately, I also learned about inspiring examples of how math teachers are working with students to recognize and subvert biased and negative messages hidden in supposedly neutral material."
anitabright  storyproblems  math  mathematics  teaching  howweteach  consumerism  lesiure  environment  bias  racism  sexism  stereotypes  clssism  sustainability  learning  values
june 2016 by robertogreco
The Remarkable Way We Eat Pizza – Numberphile | The Kid Should See This
"Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature.""

cliffordstoll  math  curvature  gauss  mathematics
june 2016 by robertogreco
"These problems are the best way for students to learn subtraction. They are essential in every classroom learning subtraction."
math  mathematics  subtraction  sfsh
june 2016 by robertogreco
dy/dan » Blog Archive » Your GPS Is Making You Dumber, and What That Means for Teaching
"Ann Shannon asks teachers to avoid “GPS-ing” their students:
When I talk about GPSing students in a mathematics class I am describing our tendency to tell students—step-by-step—how to arrive at the answer to a mathematics problem, just as a GPS device in a car tells us – step-by-step – how to arrive at some destination.

Shannon writes that when she used her GPS, “I usually arrived at my destination having learned little about my journey and with no overview of my entire route.”

True to the contested nature of education, we will now turn to someone who advocates exactly the opposite. Greg Ashman recommends novices learn new ideas and skills through explicit instruction, one facet of which is step-by-step worked examples. Ashman took up the GPS metaphor recently. He used his satellite navigation system in new environs and found himself able to re-create his route later without difficulty.

What can we do here? Shannon argues from intuition. Ashman’s study lacks a certain rigor. Luckily, researchers have actually studied what people learn and don’t learn when they use their GPS!

In a 2006 study, researchers compared two kinds of navigation. One set of participants used traditional, step-by-step GPS navigation to travel between two points in a zoo. Another group had to construct their route between those points using a map and then travel segments of that route from memory.

Afterwards, the researchers assessed the route knowledge and survey knowledge of their participants. Route knowledge helps people navigate between landmarks directly. Survey knowledge helps people understand spatial relationships between those landmarks and plan new routes. At the end of the study, the researchers found that map users had better survey knowledge than GPS users, which you might have expected, but map users outperformed the GPS users on measures of route knowledge as well.

So your GPS does an excellent job transporting you efficiently from one point to another, but a poor job helping you acquire the survey knowledge to understand the terrain and adapt to changes.

Similarly, our step-by-step instructions do an excellent job transporting students efficiently from a question to its answer, but a poor job helping them acquire the domain knowledge to understand the deep structure in a problem set and adapt old methods to new questions.

I’ll take that trade with my GPS, especially on a dull route that I travel infrequently, but that isn’t a good trade in the classroom.

The researchers explain their results from the perspective of active learning, arguing that travelers need to do something effortful and difficult while they learn in order to remember both route and survey knowledge. Designing learning for the right kind of effort and difficulty is one of the most interesting tasks in curriculum design. Too much effort and difficulty and you’ll see our travelers try to navigate a route without a GPS or a map. While blindfolded. But the GPS offers too little difficulty, with negative consequences for drivers and even worse ones for students."
education  teaching  gps  belesshelpful  instruction  math  mathematics  2016  annshannon  learning  howwelearn  navigation  attention  knowledge  curriculum  domainknowledge  problemsolving
june 2016 by robertogreco
When I Let Them Own the Problem
"There is essentially nothing left in this problem for students to explore and figure out on their own. If anything, all those labels with numbers and variables conspire to turn kids off to math. Ironically even when the problem tells kids what to do (use similar triangles), the first thing kids say when they see a problem like this is, “I don’t get it.”

They say they don’t get it because they never got to own the problem.

I wiped out the entire question and gave each student this mostly blank piece of paper and the following verbal instructions:"

"This lesson leaves me so full and proud. Their singing to the Stones while struggling in math makes me crazy in love with them."
math  teaching  mathematics  education  classideas  2013  geometry
april 2016 by robertogreco
Algebra II has to go.
"It drives dropout rates and is mostly useless in real life. Andrew Hacker has a plan for getting rid of it."

"So Hacker’s book is deeply comforting. I’m not alone, it tells me—lots of smart people hate math. The reason I hated math, was mediocre at it, and still managed to earn a bachelor’s degree was because I had upper-middle-class parents who paid for tutoring and eventually enrolled me in a college that doesn’t require math credits in order to graduate. For low-income students, math is often an impenetrable barrier to academic success. Algebra II, which includes polynomials and logarithms, and is required by the new Common Core curriculum standards used by 47 states and territories, drives dropouts at both the high school and college levels. The situation is most dire at public colleges, which are the most likely to require abstract algebra as a precondition for a degree in every field, including art and theater.

“We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can’t even get a community college degree,” Hacker told me in an interview. “I regard this math requirement as highly irrational.”

Unlike most professors who publicly opine about the education system, Hacker, though an eminent scholar, teaches at a low-prestige institution, Queens College, part of the City University of New York system. Most CUNY students come from low-income families, and a 2009 faculty report found that 57 percent fail the system’s required algebra course. A subsequent study showed that when students were allowed to take a statistics class instead, only 44 percent failed.

Such findings inspired Hacker, in 2013, to create a curriculum to test the ideas he presents in The Math Myth. For two years, he taught what is essentially a course in civic numeracy. Hacker asked students to investigate the gerrymandering of Pennsylvania congressional districts by calculating the number of actual votes Democrats and Republicans received in 2012. The students discovered that it took an average of 181,474 votes to win a Republican seat, but 271,970 votes to win a Democratic seat. In another lesson, Hacker distributed two Schedule C forms, which businesses use to declare their tax-deductible expenses, and asked students to figure out which form was fabricated. Then he introduced Benford’s Law, which holds that in any set of real-world numbers, ones, twos, and threes are more frequent initial digits than fours, fives, sixes, sevens, eights, and nines. By applying this rule, the students could identify the fake Schedule C. (The IRS uses the same technique.)

In his 19-person numeracy seminar, the lowest grade was a C, Hacker says. But he says that the math establishment—a group he calls “the Mandarins” in his book—doesn’t take kindly to a political scientist challenging disciplinary dogma, even at Queens College. The school has reclassified his class as a “special studies” course.

Hacker’s previous book, Higher Education? How Universities Are Wasting Our Money and Failing Our Kids, took a dim view of the tenured professoriate, and he extends that perspective in The Math Myth. Math professors, consumed by their esoteric, super-specialized research, simply don’t care very much about the typical undergraduate, Hacker contends. At universities with graduate programs, tenure-track faculty members teach only 10 percent of introductory math classes. At undergraduate colleges, tenure-track professors handle 42 percent of introductory classes. Graduate students and adjuncts shoulder the vast majority of the load, and they aren’t inspiring many students to continue their math education. In 2013, only 1 percent of all bachelor’s degrees awarded were in math.

“In a way, math departments throughout the country don’t worry,” Hacker says. “They have big budgets because their classes are required, so they keep on going.”

Hacker attacks not only algebra but the entire push for more rigorous STEM education—science, technology, engineering, and math—in K-12 schools, including the demand for high school classes in computer programming. He is skeptical of one of the foundational tenets of the standards-and-accountability education reform movement, that there is a quantitative “skills gap” between Americans and the 21st-century job market. He notes that between 2010 and 2012, 38 percent of computer science and math majors were unable to find a job in their field. During that same period, corporations like Microsoft were pushing for more H-1B visas for Indian programmers and more coding classes. Why? Hacker hypothesizes that tech companies want an over-supply of entry-level coders in order to drive wages down.

After Hacker previewed the ideas in The Math Myth in a 2012 New York Times op-ed, the Internet lit up with responses accusing him of anti-intellectualism. At book length, it’s harder to dismiss his ideas. He has a deep respect for what he calls the “truth and beauty” of math; his discussion of the discovery and immutability of pi taught me more about the meaning of 3.14 than any class I’ve ever taken. He’s careful to address almost every counterargument a math traditionalist could throw at him. For example, he writes that students will probably learn little about concepts of proof that are relevant to their lives, such as legal proof, by studying abstract math proofs; they’d be better served by spending time studying how juries consider reasonable doubt. More controversially, he points out that many of the nations with excellent math performance, such as China, Russia, and North Korea, are repressive. “So what can we conclude about mathematics, when its brand of brilliance can thrive amid onerous oppression?” he writes. “One response may be that the subject, by its very nature, is so aloof from political and social reality that its discoveries give rulers no causes for concern. If mathematics had the power to move minds toward controversial terrain, it would be viewed as a threat by wary states.”

I found Hacker overall to be pretty convincing. But after finishing The Math Myth, I kept thinking back to how my husband talked about derivatives, how he helped me connect the abstract to the concrete. As a longtime education reporter, I know that American teachers, especially those in the elementary grades, have taken few math courses themselves, and often actively dislike the subject. Maybe I would have found abstract math more enjoyable if my teachers had been able to explain it better, perhaps by connecting it somehow to the real world. And if that happened in every school, maybe lots more American kids, even low-income ones, would be able to make the leap from arithmetic to the conceptual mathematics of algebra II and beyond.

I called Daniel Willingham, a cognitive psychologist at the University of Virginia who studies how students learn. He is worried about any call to make math—or any other subject—less abstract. I told him that even though I once passed a calculus class, my husband had to explain to me what a derivative was, as opposed to how to find it using an equation; Willingham replied, “This is very common. There are three legs on which math rests: math fact, math algorithm, and conceptual understanding. American kids are OK on facts, OK on algorithm, and near zero on conceptual understanding. It goes back to preschool. And this is what countries like Singapore do so well. They start with the conceptual business very, very early.” Willingham believes substituting statistics for algebra II might not solve the problem of high school math as a stumbling block. After all, basic statistical concepts—such as effect size or causality—also require conceptual understanding.

Of course, if math teachers are to help students understand how abstract concepts function in the real world, they will have to understand those abstractions themselves. So it’s not reassuring that American teachers are a product of the same sub-par math education system they work in, or that we hire 100,000 to 200,000 new teachers each year at a time when less than 20,000 people are majoring in math annually.

Could better teachers help more students pass algebra II? Given high student debt, low teacher pay, and the historically low status of the American teaching profession, it would be a tough road. In the meantime, it’s probably a good idea to give students multiple math pathways toward high school and college graduation—some less challenging than others. If we don’t, we’ll be punishing kids for the failures of an entire system. "
danagoldstein  math  mathematics  education  teaching  algebra  algebraii  andrewhacker  statistics  danielwillingham  stem
march 2016 by robertogreco
Readers Respond to Redesigned, and Wordier, SAT - The New York Times
"A commenter under the handle R-son from Glen Allen, Va., said his stepson, who is better in math than reading, would soon be taking the test. “The new SAT will be hard for him, but he has an advantage over other students — an \$800 Kaplan prep course. So it boils down to this — he’ll score better on the SAT than a lower-income student with the same abilities whose family can’t afford to fork out close to 1K to prep for and take this test. So how is this test, in any form, fair?”

Another reader cautioned against assuming only immigrant and lower-income students would find the test harder. “The biggest enemy of reading proficiency among even privileged children and adolescents today is technology, particularly the iPhone,” said Katonah from New York. “That phone is always in hand, beckoning — an addictive drug that demands little of its user. … I have seen the effects of this drug on my own (privileged) adolescent children. My attempted solutions have been only partially, intermittently helpful. It’s obvious to me that none of my children will grow up to be anywhere near as well-read as I am.”

Several commenters raised broader questions on why the SAT needed revamping. A commenter named Vince, who said he worked in the international admissions office of a New York state college, cited an “exponential increase in the number of international applicants” to American universities in recent years. “It has become increasingly difficult to evaluate these candidates and verify their test scores,” he wrote. “If we were to consider mainland Chinese applicants — who travel by the thousands to Hong Kong to take the SAT in convention-hall-sized test centers and support an entire industry of tutoring centers that specialize in teaching students how to deduce answers from a handful of question formats — this could be viewed as a defensive move by the College Board to crack down on inflated international student SAT scores.”

A few commenters critiqued the sample of five math SAT questions that accompanied the article. Ninety-three percent of readers answered the first question in the quiz correctly; 57 percent answered the fourth question correctly. Of an algebra problem about a phone repair technician, a reader using the name Kathy, WastingTime in DC wondered, “Who gets a phone fixed these days?”

One reader, who admitted she answered only one of the five problems correctly, pointed to a question about a pear tree. Gabrielle from Los Angeles wrote: “I am a horticultural therapist who designed and built a therapeutic garden. Here’s the answer to figure out which pear tree to buy: use your relationships. Ask your friends what they’ve had success with. Call me crazy but after I left high school, I never took another math class, and it’s never held me back.”"
2016  sat  testing  standardizedtesting  math  mathematics  education
february 2016 by robertogreco
PatrickJMT
"I have been teaching mathematics for over 8 years at the college/university level and tutoring for over 15 years. Currently I teach part time at Austin Community College, but have also taught at Vanderbilt University (a top 20 ranked university) and at the University of Louisville.

Often times, people are nervous about getting help in math: don’t be! I tell my students all the time that math is challenging for all of us at one point or another. My intent is to provide clear and thorough explanations, and to present them in an environment in which the student is comfortable. mannequinAlthough I do not promise to make someone into an A+ student overnight, with regular help just about every student I have encountered makes significant improvements over time. Think about learning math in the same way you would learn to play piano or learn another language: it takes time, patience, and LOTS of practice."
math  tutorials  mathematics
february 2016 by robertogreco
Building Better Teachers
"BaBT's thesis is simple. Most people assume that great teachers are born, not made. From politicians to researchers and teachers themselves, most of us speak and act as if there's a gene for teaching that someone either has or doesn't. Most reforms are therefore designed to find and promote those who can and eliminate those who can't. The problem is, this assumption is wrong, so educational reforms based on it are (mostly) destined to fail. Reforms based on changing the culture of teaching would have a greater chance of succeeding, but as with any cultural change, they would require the kind of long-term commitment that our society doesn't seem to be very good at.

The book is written as a history of the people who have put that puzzle together in the US, including Nate Gage and Lee Shulman in the 1960s and 1970s, Deborah Ball, Magdalene Lampert, and others at Michigan State in the 1980s and 1990s, and educational entrepreneurs like Doug Lemov today. Its core begins with a discussion of what James Stigler discovered during a visit to Japan in the early 1990s:
Some American teachers called their pattern "I, We, You": After checking homework, teachers announced the day's topic, demonstrating a new procedure (I)... Then they led the class in trying out a sample problem together (We)... Finally, they let students work through similar problems on their own, usually by silently making their way through a worksheet (You)... The Japanese teachers, meanwhile, turned "I, We, You" inside out. You might call their version "You, Y'all, We." They began not with an introduction, but a single problem that students spent ten or twenty minutes working through alone (You)... While the students worked, the teacher wove through the students' desks, studying what they came up with and taking notes to remember who had which idea. Sometimes the teacher then deployed the students to discuss the problem in small groups (Y'all). Next, the teacher brought them back to the whole group, asking students to present their different ideas for how to solve the problem on the chalkboard... Finally, the teacher led a discussion, guiding students to a shared conclusion (We).

It's tempting to think that this particular teaching technique is Japan's secret sauce: tempting, but wrong. The actual key is revealed in the description of Akihiko Takahashi's work. In 1991, he visited the United States in a vain attempt to find the classrooms described a decade earlier in a report by the National Council of Teachers of Mathematics (NCTM). He couldn't find them. Instead, he found that American teachers met once a year (if that) to exchange ideas about teaching, compared to the weekly or even daily meetings he was used to. What was worse:
The teachers described lessons they gave and things students said, but they did not see the practices. When it came to observing actual lessons‐watching each other teach—they simply had no opportunity... They had, he realized, no jugyokenkyu. Translated literally as "lesson study", jugyokenkyu is a bucket of practices that Japanese teachers use to hone their craft, from observing each other at work to discussing the lesson afterward to studying curriculum materials with colleagues. The practice is so pervasive in Japanese schools that it is...effectively invisible. And here lay the answer to [Akihiko's] puzzle. Of course the American teachers' work fell short of the model set by their best thinkers... Without jugyokenkyu, his own classes would have been equally drab. Without jugyokenkyu, how could you even teach?

So what does jugyokenkyu look like in practice?

Putting work under a microscope in order to improve it is commonplace in sports and music. A professional musician, for example, would dissect half a dozen different recordings of "Body and Soul" or "Yesterday" before performing it. They would also expect to get feedback from fellow musicians during practice and after performances. Many other disciplines work this way too. The Japanese drew inspiration from Deming's ideas on continuous improvement in manufacturing, while the adoption of code review over the last 15 years has, in my opinion, done more to improve everyday programming than any number of books or websites.
education  books  teaching  howweteach  japan  us  nctm  math  mathematics  matheducation  2014  teachereducation  jugyokenkyu
february 2016 by robertogreco
When Television Is More Than an “Idiot Box” — The Development Set — Medium
"Around the world, TV educates while it entertains. It can teach the internet a few things, too."

"When it comes to education and technology, it is not television but the internet that is hot and wired. The United Nation’s Broadband Commission, packed with luminaries from Mexico’s Carlos Slim to Rwanda’s President Paul Kagame, suggests that the internet can “enhance learning opportunities, transform the teaching and learning environment… and ultimately rethink and transform” education systems.

At first glance, the internet could be a very attractive tool to overcome a global learning crisis. At the turn of the 21st century, the World Bank reported that about seven percent of the world’s population was online. Last year, it had reached 41 percent.

But it turns out just giving kids access to the web doesn’t do much for educational outcomes. Across countries that take part in the Programme of International Student Assessment (PISA), children who use computers more intensively do worse on tests. One Laptop Per Child, which distributes cheap computers in developing countries, has been beset by failure. In Peru, they had no impact on math and language test scores. Similar findings emerged in Nepal. Likewise, extending access to broadband in schools in Portugal led to lower grades — although the impact was reduced if YouTube was blocked.

There is a simple explanation. When you give kids a computer, they’re not suddenly more excited by math and social studies. Children are, for the most part, more interested in the medium’s entertainment capabilities."

"Under some circumstances, television can be at least as effective as traditional instruction. Mexico’s Telesecundaria programming broadcasts six hours of lessons a day to children in remote areas of the country where there is no secondary school.

For the most part, though, television has remained an adjunct in the classroom, rather than a replacement for teachers. But as a more holistic tool for learning outside the classroom, it has had a massive impact — particularly when it serves its primary function to entertain and not educate.

Recent research suggests there can be a considerable upside to hours “wasting time” in front of the television screen. Take Chitrahaar and Rangoli. Illiterate school kids who watched the shows were more than twice as likely to be functionally literate five years later than kids who didn’t watch the shows. The effect was particularly noticeable for girls. Given the reach of these two programs, it’s possible that millions of Indian kids became literate largely thanks to the simple and very cheap approach of same-language subtitling.

Perhaps the most well known form of educational entertainment, or “edutainment,” for children is Sesame Street, which is now broadcast in more than thirty countries around the world. In the US, children who grew up in areas where the television signal was stronger — and so had better access to Sesame Street — were much less likely to have to repeat a grade in school. In Mexico, viewers of Plaza Sesamo do better in literacy and mathematics tests. The results are the same in Turkey (Susam Sokagi), Portugal (Rua Sesamo), Russia (Ulitsa Sezam) and Bangladesh (Sisimpur), to name but a few.

elevision’s educational power extends beyond childhood, and beyond skills traditionally learned in a classroom. As cable access rolled out across India, for example, viewers of all ages started watching shows where comparatively strong women characters had financial and social independence. Women in villages with cable access reported more power over making decisions and less acceptance of wife beating. These villages also began to see declining birth rates and rapidly rising school enrollment for girls.

Similar effects have been observed around the world. In Brazil, as the Rede Globo channel extended across the country in the 1970s and 1980s, parents began to have fewer children, perhaps mimicking the characters on their favorite soaps. Recent research in Nigeria finds that areas where the TV signal is stronger see parents wanting fewer children and using contraceptives more, alongside lower rates of female genital cutting. In South Africa, World Bank researchers found that viewers of one locally produced soap opera, “Scandal”, which was specifically developed to incorporate plot lines dealing with financial responsibility, were almost twice as likely to borrow from formal sources of credit like banks rather than informal sources. They were also less likely to engage in gambling.

When soap opera characters are relatable and believable, audiences begin to associate with them. If a beloved character stands up for herself in front of her husband, or gets in over their head in debt, or gets pregnant by accident, viewers learn from that experience. And that knowledge translates into changed behavior: more control within the household, less informal debt, fewer children.

Heavy-handed public service messages on television, like condescending “the more you know” spots, may impart information but rarely engage viewers. The same may well be true of the internet. For most children in particular, it is primarily used as a source of fun and not education.

Pioneers around the world are already experimenting with internet-based edutainment for kids. Sites like ABC Mouse, among countless others, produce educational games for children. Pratham, an Indian NGO, has developed a program combining math questions with an arcade game. Children who used it for two hours a week saw their math test scores considerably improve. Given the internet’s interactive nature, perhaps the impact of well-designed web edutainment will end up being even greater than the broadcast variety.

Edutainment will never be able to replace teachers in a classroom. But well-designed programming — whether it arrives by broadcast or broadband — can have a dramatic impact at low cost."
charleskenny  television  tv  education  learning  howwelearn  2016  olpc  entertainment  mexico  turkey  russia  portugal  bangladesh  india  sesamestreet  literacy  math  mathematics
january 2016 by robertogreco
Inspiring Students to Math Success and a Growth Mindset
"Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.
We know from research how to teach math well and how to bring about high levels of student engagement and achievement but research has not previously been made accessible to teachers. All students can learn mathematics to high levels and teaching that is based upon this principle dramatically increases students’ mathematics achievement. The need to make research widely available is particularly pressing now as new science on the brain and learning is giving important insights into mathematics learning.

Mathematics is often the reason that students leave STEM, particularly girls and some students of color. We aim to change this by communicating the sources of math inequality in the US and by teaching the classroom methods that are needed for 21st century learning. By providing research based teaching methods, math tasks, videos, and ideas we intend to significantly reduce math failure and inequality in the United States and beyond, inspiring teachers and empowering all students to success."
joboaler  math  mathematics  education  teaching
january 2016 by robertogreco
Why Growth Mindsets Are Necessary to Save Math Class - The Atlantic
“The fact that a narrow and impoverished version of mathematics is taught in many school classrooms cannot be blamed on teachers. Teachers are usually given long lists of content to teach, with hundreds of topics and no time to go into depth on any ideas. When teachers are given these lists, they see a subject that has been stripped down to its bare parts—like a dismantled bike—a collection of nuts and bolts that students are meant to shine and polish all year. Such lists not only take away the connections that weave all through mathematics, but present math as though the connections do not even exist.

I don’t want students polishing disconnected bike parts all day. I want them to get onto the bikes and ride freely, experiencing the pleasure of math, the joy of making connections, the euphoria of real mathematical thinking.

When teachers open up mathematics and teach broad, visual, creative math, then they teach math as a learning subject, instead of a performance subject. It is very hard for students to develop a growth mindset if they are only ever answering short questions with right and wrong answers. Such questions themselves transmit fixed messages about math: that you can do it or you cannot. When educators teach open math and ask questions that have many solutions or pathways through them, and give students the opportunity to discuss different mathematical ideas, then students see that learning is possible. To put it simply, math questions should have space inside them for learning, for students to discuss and think about ideas; questions should not simply ask for answers that often require calculations or procedures with no encouragement for broader, engaging thought.”

[Also here with the title “Stop all the testing in math, and set free a generation of American mathematicians”
http://hechingerreport.org/save-american-mathematics-and-set-students-free/ ]
joboaler  math  mathematics  education  teaching  schools  2015  pedagogy  howweteach  howwelearn  learning
january 2016 by robertogreco
Contrasts in Number Theory - Scientific American Blog Network
"“Respected research math is dominated by men of a certain attitude.” So starts the prologue to The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: an Artist’s Rendering (pdf), mathematician Piper Harron’s thesis.

The entire prologue is fantastic, so instead of trying to describe it, I might as well quote it.
“Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success. As any good grad student would do, I tried to fit in, mathematically. I absorbed the atmosphere and took attitudes to heart. I was miserable, and on the verge of failure. The problem was not individuals, but a system of self-preservation that, from the outside, feels like a long string of betrayals, some big, some small, perpetrated by your only support system. When I physically removed myself from the situation, I did not know where I was or what to do. First thought: FREEDOM!!!! Second thought: but what about the others like me, who don’t do math the “right way” but could still greatly contribute to the community? I combined those two thoughts and started from zero on my thesis. People who, for instance, try to read a math paper and think, “Oh my goodness what on earth does any of this mean why can’t they just say what they mean????” rather than, “Ah, what lovely results!” (I can’t even pretend to know how “normal” mathematicians feel when they read math, but I know it’s not how I feel.) My thesis is, in many ways, not very serious, sometimes sarcastic, brutally honest, and very me. It is my art. It is myself. It is also as mathematically complete as I could honestly make it.

“I’m unwilling to pretend that all manner of ways of thinking are equally encouraged, or that there aren’t very real issues of lack of diversity. It is not my place to make the system comfortable with itself. This may be challenging for happy mathematicians to read through; my only hope is that the challenge is accepted.”

What follows is a math paper, filled with real number theory but written in an informal style, with clearly labeled sections for laypeople, mathematicians who want a general overview of the ideas, and people who want to see some of the gory details. She explains concepts using unicycles and groups of well-behaved children. There are comics about going into labor while writing a thesis. The content of the paper is not easy, but the presentation is entertaining and refreshing.

Harron, whose website is called The Liberated Mathematician, writes, “My view of mathematics is that it is an absolute mess which actively pushes out the sort of people who might make it better. I have no patience for genius pretenders. I want to empower the people.”

Harron has a reluctant maybe blog on her website and has written a great post on mathbabe.org. In both places, she says things a lot of us are afraid to say about the attitudes we feel like we have to pick up in order to fit into the mathematical community. Based on the way her thesis and blog posts have gone through my Facebook and Twitter, I think I’m not alone in identifying with many of the feelings she describes. I certainly felt the same pressure to conform that she felt as a beginning graduate student. As she puts it: “Please tell me the rules I must abide by in order to make no waves!”"

"This is why Harron’s work is all the more necessary. As she writes in her thesis, she wishes to relay to students that “1) you are not expected to understand every word as you read it, 2) you can successfully use math before you’ve successfully understood it, and 3) it has to be okay to be honest about your understanding.” I wish more young mathematicians learned these lessons and weren't afraid to reveal their ignorance.

Another thing I thought was interesting about these two stories is who reported and shared them. My math friends shared the heck out of Harron’s thesis, and I saw more about the abc conjecture from nonmathematicians who follow popular science. This wasn’t a binary thing; mathematicians shared articles about the abc conjecture, and nonmathematicians wrote about Harron's thesis, but for the most part, it was the other way around, at least in what I saw.

I’m not quite sure what conclusions to draw from the way the stories were shared, but it feels important. I think it says something about how mathematicians present themselves allow others to present them. On some level, we want others to put us on a pedestal. We don’t really mind it when someone gets the message “oh, it's too complicated—you wouldn’t understand.”

On the other hand, the strong positive reaction to Harron’s work within mathematics shows that many in the mathematical community are hungry for something different. Even people for whom the status quo has worked (after all, they’re still there) recognize that mathematics loses when we build barriers for some groups of people or encourage people to adopt the “certain attitude” Harron writes about in her thesis.

Does the abc conjecture represent a dying old guard, and does Piper Harron represent the way of the future? I'd guess nothing that dramatic is going on. But mathematicians should think about how they want to explain mathematics and who they are inviting in or leaving out in the process."
math  mathematics  piperharron  2015  thesis  accessibility  gender  approachability
december 2015 by robertogreco
The Jacob’s Ladder of coding — Medium
"Anecdotes and questions about climbing up and down the ladder of abstraction: Atari, ARM, demoscene, education, creative coding, community, seeking lightness, enlightenment & strange languages"

"With only an hour or two of computer time a week, our learning and progress was largely down to intensive trial & error, daily homework and learning to code and debug with only pencil and paper, whilst trying to be the machine yourself: Playing every step through in our heads (and on paper) over and over until we were confident, the code did as we’d expect, yet, often still failing because of wrong intuitions. Learning this analytical thinking is essential to successful debugging, even today, specifically in languages / environments where no GUI debugger is available. In the late 90s, John Maeda did similar exercises at MIT Media Lab, with students role-playing different parts of a CPU or a whole computer executing a simple process. Later at college, my own CS prof too would often quote Alan Perlis:
“To understand a program you must become both the machine and the program.” — Alan Perlis

Initially we’d only be using the machine largely to just verify our ideas prepared at home (spending the majority of the time typing in/correcting numbers from paper). Through this monastic style of working, we also learned the importance of having the right tools and balance of skills within the group and were responsible to create them ourselves in order to achieve our vision. This important lesson stayed with me throughout (maybe even became) my career so far… Most projects I worked on, especially in the past 15 years, almost exclusively relied on custom-made tooling, which was as much part of the final outcome as the main deliverable to clients. Often times it even was the main deliverable. On the other hand, I’ve also had to learn the hard way that being a largely self-sufficient generalist often is undesired in the modern workplace, which frequently still encourages narrow expertise above all else…

After a few months of convincing my parents to invest all of their saved up and invaluable West-german money to purchase a piece of “Power Without the Price” (a much beloved Atari 800XL) a year before the Wall came down in Berlin, I finally gained daily access to a computer, but was still in a similar situation as before: No more hard west money left to buy a tape nor disk drive from the Intershop, I wasn’t able to save any work (apart from creating paper copies) and so the Atari was largely kept switched on until November 10, 1989, the day after the Berlin Wall was opened and I could buy an XC-12 tape recorder. I too had to choose whether to go the usual route of working with the built-in BASIC language or stick with what I’d learned/taught myself so far, Assembly… In hindsight, am glad I chose the latter, since it proved to be far more useful and transportable knowledge, even today!"

"Lesson learned: Language skills, natural and coded ones, are gateways, opening paths not just for more expression, but also to paths in life.

As is the case today, so it was back then: People tend to organize around specific technological interests, languages and platforms and then stick with them for a long time, for better or worse. Over the years I’ve been part of many such tool-based communities (chronologically: Asm, C, TurboPascal, Director, JS, Flash, Java, Processing, Clojure) and have somewhat turned into a nomad, not being able to ever find a true home in most of them. This might sound judgemental and negative, but really isn’t meant to and these travels through the land of languages and toolkits has given me much food for thought. Having slowly climbed up the ladder of abstraction and spent many years both with low & high level languages, has shown me how much each side of the spectrum can inform and learn from the other (and they really should do more so!). It’s an experience I can highly recommend to anyone attempting to better understand these machines some of us are working with for many hours a day and which impact so much of all our lives. So am extremely grateful to all the kind souls & learning encountered on the way!"

"In the vastly larger open source creative computing demographic of today, the by far biggest groups are tight-knit communities around individual frameworks and languages. There is much these platforms have achieved in terms of output, increasing overall code literacy and turning thousands of people from mere computer users into authors. This is a feat not be underestimated and a Good Thing™! Yet my issue with this siloed general state of affairs is that, apart from a few notable exceptions (especially the more recent arrivals), there’s unfortunately a) not much cross-fertilizing with fundamentally different and/or new ideas in computing going on and b) over time only incremental progress is happening, business as usual, rather than a will to continuously challenge core assumptions among these largest communities about how we talk to machines and how we can do so better. I find it truly sad that many of these popular frameworks rely only on the same old imperative programming language family, philosophy and process, which has been pre-dominant and largely unchanged for the past 30+ years, and their communities also happily avoid or actively reject alternative solutions, which might require fundamental changes to their tools, but which actually could be more suitable and/or powerful to their aims and reach. Some of these platforms have become and act as institutions in their own right and as such also tend to espouse an inward looking approach & philosophy to further cement their status (as owners or pillars?) in their field. This often includes a no-skills-neccessary, we-cater-all-problems promise to their new users, with each community re-inventing the same old wheels in their own image along the way. It’s Not-Invented-Here on a community level: A reliance on insular support ecosystems, libraries & tooling is typical, reducing overall code re-use (at least between communities sharing the same underlying language) and increasing fragmentation. More often than not these platforms equate simplicity with ease (go watch Rich Hickey taking this argument eloquently apart!). The popular prioritization of no pre-requisite knowledge, super shallow learning curves and quick results eventually becomes the main obstacle to later achieve systemic changes, not just in these tools themselves, but also for (creative) coding as discipline at large. Bloatware emerges. Please do forgive if that all sounds harsh, but I simply do believe we can do better!

Every time I talk with others about this topic, I can’t help but think about Snow Crash’s idea of “Language is a virus”. I sometimes do wonder what makes us modern humans, especially those working with computing technology, so fundamentalist and brand-loyal to these often flawed platforms we happen to use? Is it really that we believe there’s no better way? Are we really always only pressed for time? Are we mostly content with Good Enough? Are we just doing what everyone else seems to be doing? Is it status anxiety, a feeling we have to use X to make a living? Are we afraid of unlearning? Is it that learning tech/coding is (still) too hard, too much of an effort, which can only be justified a few times per lifetime? For people who have been in the game long enough and maybe made a name for themselves in their community, is it pride, sentimentality or fear of becoming a complete beginner again? Is it maybe a sign that the way we teach computing and focus on concrete tools too early in order to obtain quick, unrealistically complex results, rather than fundamental (“boring”) knowledge, which is somewhat flawed? Is it our addiction to largely focus on things we can document/celebrate every minor learning step as an achievement in public? This is no stab at educators — much of this systemic behavior is driven by the sheer explosion of (too often similar) choices, demands made by students and policy makers. But I do think we should ask ourselves these questions more often."

coding  via:tealtan  2015  abstraction  demoscene  education  creativecoding  math  mathematics  howwelearn  typography  design  dennocoil  alanperlis  johnmaeda  criticalthinking  analyticalthinking  basic  programming  assembly  hexcode  georgedyson  computing  computers  atari  amiga  commodore  sinclair  identity  opensource  insularity  simplicity  ease  language  languages  community  communities  processing  flexibility  unschooling  deschooling  pedagogy  teaching  howweteach  understanding  bottomup  topdown  karstenschmidt
december 2015 by robertogreco
The Man Who Will Save Math | New Republic
"Today, Meyer is the Chief Academic Officer at Desmos, a San Francisco startup that offers an online graphing calculator. The company is now building on that tool by offering complete, interactive lesson plans. Like the calculator, the lessons are free to the masses; Desmos plans to profit by selling the product to corporate entities.

The lessons use interactive technology to help students begin with the concrete: One lesson starts with a slab of pavement that must be divided into equally sized parking spaces; another asks students to recreate an animation in graph form. The emphasis is slightly different than Meyer’s old “Three-Act Tasks”: exploration and communication are now privileged over stories. In the parking lot lesson, students draw and redraw their dividers, getting immediate feedback as cars try to pull into their spaces; only gradually do they begin to work with numbers and variables. Other modules ask students to share their models with the class, which allows them to revise their thinking based on the ideas of their peers. Desmos’s lessons are based on the idea of constructivism, a theory that views knowledge as something that must be built by learners themselves.

This is a progressive and rather controversial notion. Developed from the ideas of Swiss psychologist Jean Piaget and American philosopher John Dewey in the twentieth century, it was popularized by reform-minded educators starting in the 1960s. In mathematics, constructivism and other “student-centered” forms of teaching have come under particular fire in mathematics: Are kids really supposed to discover 10,000 years of math all on their own? Meyer’s advisor at Stanford, Jo Boaler, well known for her efforts to make math more widely accessible, has described a concerted effort to discredit her work.

Meyer dismisses his own critics as ideologues. If they see anything that deviates from clear, straightforward explanation, he says, “they have a fuse that is tripped, a certain surge goes through their brain,” he said. “The question is not should we explain, but when should we explain.” Meyer believes we need to provide certain experiences to students before we lecture: showing why a tool is needed, for example, or provoking cognitive conflict, or providing an opportunity to create informal algorithms before the standard algorithms are taught.

I’m a former high school math teacher, and I worked for five years coaching teachers in Mississippi. The students in the schools where I worked were nearly all African American, and many faced the steep challenges of rural poverty. When I first encountered Meyer’s TED Talk in 2010, I was skeptical. But over time I saw too many students who were doing math just because they were told they had to; I began incorporating the ideas of constructivism into the lessons I developed for teachers. The few I could compel to try these lessons found their students’ perceptions of the subject transformed.

But my initial skepticism—and the skepticism of the teachers I coached—is telling. Constructivism is now an old theory, but it’s still uncommon, often associated with privileged private schools. (Meyer says he and his team test all their lessons in classrooms around the Bay Area, and aim to include a range of economic backgrounds and previous experiences with mathematics.) It’s is an ambitious form of teaching, putting high demands on a teachers—who must respond in the moment to each student’s developing ideas. That goes against the cut-the-workload-with-technology mentality pursued by Meyer’s competitors, and it’s a hard sell to administrators at struggling schools, who are often asked to make quick changes in test scores.

Which means Meyer’s quest can’t end with the creation of a few lesson plans, or even an entire textbook. He sees this as a generational project. “You really need the students in these classrooms to grow up and become teachers,” he says. “At that point a cycle begins.” The alien abductions will be over; math will be something that students do, rather than something that’s done to them."
danmeyer  digitalstorytelling  education  immersion  math  mathematics  howweteach  guershonharel  constructivism  piaget  johndewey  joboaler  desmos  boyceupholt  jeanpiaget
december 2015 by robertogreco
per page:    204080120160

Copy this bookmark: