**robertogreco : algebra**
38

Imaginary Numbers Are Real [Part 1: Introduction] - YouTube

may 2018 by robertogreco

[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
"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 ."

may 2018 by robertogreco

How Systemic Control Stunts Creative Growth – Rafranz Davis – Medium

november 2017 by robertogreco

"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.

I’m glad that we didn’t.

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
…for the sake of time and because it would’ve been much easier.

I’m glad that we didn’t.

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."

november 2017 by robertogreco

Why San Francisco stopped teaching algebra in middle school - Business Insider

july 2016 by robertogreco

"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.

Still, advanced eighth graders, prevented from skipping ahead in the course sequence, will be encouraged instead to delve deeper into the material."

[See also: http://www.sfusdmath.org/secondary-course-sequence.html ]

math
sanfrancisco
mathematics
algebra
schools
curriculum
education
2016
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.

Still, advanced eighth graders, prevented from skipping ahead in the course sequence, will be encouraged instead to delve deeper into the material."

[See also: http://www.sfusdmath.org/secondary-course-sequence.html ]

july 2016 by robertogreco

Algebra II has to go.

march 2016 by robertogreco

"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
…

"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. "

march 2016 by robertogreco

Beginning Algebra - Table of Contents

november 2015 by robertogreco

[via: http://2012books.lardbucket.org/ }

[See also: "Advanced Algebra"

http://2012books.lardbucket.org/books/advanced-algebra/ ]

textbooks
algebra
mathematics
math
[See also: "Advanced Algebra"

http://2012books.lardbucket.org/books/advanced-algebra/ ]

november 2015 by robertogreco

The Humane Representation of Thought on Vimeo

march 2015 by robertogreco

"Closing keynote at the UIST and SPLASH conferences, October 2014.

Preface: http://worrydream.com/TheHumaneRepresentationOfThought/note.html

References to baby-steps towards some of the concepts mentioned:

Dynamic reality (physical responsiveness):

- The primary work here is Hiroshi Ishii's "Radical Atoms": http://tangible.media.mit.edu/project/inform/

- but also relevant are the "Soft Robotics" projects at Harvard: http://softroboticstoolkit.com

- and at Otherlab: http://youtube.com/watch?v=gyMowPAJwqo

- and some of the more avant-garde corners of material science and 3D printing

Dynamic conversations and presentations:

- Ken Perlin's "Chalktalk" changes daily; here's a recent demo: http://bit.ly/1x5eCOX

Context-sensitive reading material:

- http://worrydream.com/MagicInk/

"Explore-the-model" reading material:

- http://worrydream.com/ExplorableExplanations/

- http://worrydream.com/LadderOfAbstraction/

- http://ncase.me/polygons/

- http://redblobgames.com/pathfinding/a-star/introduction.html

- http://earthprimer.com/

Evidence-backed models:

- http://worrydream.com/TenBrighterIdeas/

Direct-manipulation dynamic authoring:

- http://worrydream.com/StopDrawingDeadFish/

- http://worrydream.com/DrawingDynamicVisualizationsTalk/

- http://tobyschachman.com/Shadershop/

Modes of understanding:

- Jerome Bruner: http://amazon.com/dp/0674897013

- Howard Gardner: http://amazon.com/dp/0465024335

- Kieran Egan: http://amazon.com/dp/0226190390

Embodied thinking:

- Edwin Hutchins: http://amazon.com/dp/0262581469

- Andy Clark: http://amazon.com/dp/0262531569

- George Lakoff: http://amazon.com/dp/0465037712

- JJ Gibson: http://amazon.com/dp/0898599598

- among others: http://en.wikipedia.org/wiki/Embodied_cognition

I don't know what this is all about:

- http://worrydream.com/ABriefRantOnTheFutureOfInteractionDesign/

- http://worrydream.com/ABriefRantOnTheFutureOfInteractionDesign/responses.html

---

Abstract:

New representations of thought — written language, mathematical notation, information graphics, etc — have been responsible for some of the most significant leaps in the progress of civilization, by expanding humanity’s collectively-thinkable territory.

But at debilitating cost. These representations, having been invented for static media such as paper, tap into a small subset of human capabilities and neglect the rest. Knowledge work means sitting at a desk, interpreting and manipulating symbols. The human body is reduced to an eye staring at tiny rectangles and fingers on a pen or keyboard.

Like any severely unbalanced way of living, this is crippling to mind and body. But it is also enormously wasteful of the vast human potential. Human beings naturally have many powerful modes of thinking and understanding.

Most are incompatible with static media. In a culture that has contorted itself around the limitations of marks on paper, these modes are undeveloped, unrecognized, or scorned.

We are now seeing the start of a dynamic medium. To a large extent, people today are using this medium merely to emulate and extend static representations from the era of paper, and to further constrain the ways in which the human body can interact with external representations of thought.

But the dynamic medium offers the opportunity to deliberately invent a humane and empowering form of knowledge work. We can design dynamic representations which draw on the entire range of human capabilities — all senses, all forms of movement, all forms of understanding — instead of straining a few and atrophying the rest.

This talk suggests how each of the human activities in which thought is externalized (conversing, presenting, reading, writing, etc) can be redesigned around such representations.

---

Art by David Hellman.

Bret Victor -- http://worrydream.com "

[Some notes from Boris Anthony:

"Those of you who know my "book hack", Bret talks about exactly what motivates my explorations starting at 20:45 in https://vimeo.com/115154289 "

https://twitter.com/Bopuc/status/574339495274876928

"From a different angle, btwn 20:00-29:00 Bret explains how "IoT" is totally changing everything

https://vimeo.com/115154289

@timoreilly @moia"

https://twitter.com/Bopuc/status/574341875836043265 ]

bretvictor
towatch
interactiondesign
davidhellman
hiroshiishii
softrobotics
robots
robotics
kenperlin
jeromebruner
howardgardner
kieranegan
edwinhutchins
andyclark
jjgibson
embodiedcognition
cognition
writing
math
mathematics
infographic
visualization
communication
graphics
graphicdesign
design
representation
humans
understanding
howwelearn
howwethink
media
digital
dynamism
movement
conversation
presentation
reading
howweread
howwewrite
chalktalk
otherlab
3dprinting
3d
materials
physical
tangibility
depth
learning
canon
ui
informationdesign
infographics
maps
mapping
data
thinking
thoughts
numbers
algebra
arithmetic
notation
williamplayfair
cartography
gestures
placevalue
periodictable
michaelfaraday
jamesclerkmaxell
ideas
print
printing
leibniz
humanism
humanerepresentation
icons
visual
aural
kinesthetic
spatial
tactile
symbols
iot
internetofthings
programming
computers
screens
computation
computing
coding
modeling
exploration
via:robertogreco
reasoning
rhetoric
gerrysussman
environments
scale
virtualization
Preface: http://worrydream.com/TheHumaneRepresentationOfThought/note.html

References to baby-steps towards some of the concepts mentioned:

Dynamic reality (physical responsiveness):

- The primary work here is Hiroshi Ishii's "Radical Atoms": http://tangible.media.mit.edu/project/inform/

- but also relevant are the "Soft Robotics" projects at Harvard: http://softroboticstoolkit.com

- and at Otherlab: http://youtube.com/watch?v=gyMowPAJwqo

- and some of the more avant-garde corners of material science and 3D printing

Dynamic conversations and presentations:

- Ken Perlin's "Chalktalk" changes daily; here's a recent demo: http://bit.ly/1x5eCOX

Context-sensitive reading material:

- http://worrydream.com/MagicInk/

"Explore-the-model" reading material:

- http://worrydream.com/ExplorableExplanations/

- http://worrydream.com/LadderOfAbstraction/

- http://ncase.me/polygons/

- http://redblobgames.com/pathfinding/a-star/introduction.html

- http://earthprimer.com/

Evidence-backed models:

- http://worrydream.com/TenBrighterIdeas/

Direct-manipulation dynamic authoring:

- http://worrydream.com/StopDrawingDeadFish/

- http://worrydream.com/DrawingDynamicVisualizationsTalk/

- http://tobyschachman.com/Shadershop/

Modes of understanding:

- Jerome Bruner: http://amazon.com/dp/0674897013

- Howard Gardner: http://amazon.com/dp/0465024335

- Kieran Egan: http://amazon.com/dp/0226190390

Embodied thinking:

- Edwin Hutchins: http://amazon.com/dp/0262581469

- Andy Clark: http://amazon.com/dp/0262531569

- George Lakoff: http://amazon.com/dp/0465037712

- JJ Gibson: http://amazon.com/dp/0898599598

- among others: http://en.wikipedia.org/wiki/Embodied_cognition

I don't know what this is all about:

- http://worrydream.com/ABriefRantOnTheFutureOfInteractionDesign/

- http://worrydream.com/ABriefRantOnTheFutureOfInteractionDesign/responses.html

---

Abstract:

New representations of thought — written language, mathematical notation, information graphics, etc — have been responsible for some of the most significant leaps in the progress of civilization, by expanding humanity’s collectively-thinkable territory.

But at debilitating cost. These representations, having been invented for static media such as paper, tap into a small subset of human capabilities and neglect the rest. Knowledge work means sitting at a desk, interpreting and manipulating symbols. The human body is reduced to an eye staring at tiny rectangles and fingers on a pen or keyboard.

Like any severely unbalanced way of living, this is crippling to mind and body. But it is also enormously wasteful of the vast human potential. Human beings naturally have many powerful modes of thinking and understanding.

Most are incompatible with static media. In a culture that has contorted itself around the limitations of marks on paper, these modes are undeveloped, unrecognized, or scorned.

We are now seeing the start of a dynamic medium. To a large extent, people today are using this medium merely to emulate and extend static representations from the era of paper, and to further constrain the ways in which the human body can interact with external representations of thought.

But the dynamic medium offers the opportunity to deliberately invent a humane and empowering form of knowledge work. We can design dynamic representations which draw on the entire range of human capabilities — all senses, all forms of movement, all forms of understanding — instead of straining a few and atrophying the rest.

This talk suggests how each of the human activities in which thought is externalized (conversing, presenting, reading, writing, etc) can be redesigned around such representations.

---

Art by David Hellman.

Bret Victor -- http://worrydream.com "

[Some notes from Boris Anthony:

"Those of you who know my "book hack", Bret talks about exactly what motivates my explorations starting at 20:45 in https://vimeo.com/115154289 "

https://twitter.com/Bopuc/status/574339495274876928

"From a different angle, btwn 20:00-29:00 Bret explains how "IoT" is totally changing everything

https://vimeo.com/115154289

@timoreilly @moia"

https://twitter.com/Bopuc/status/574341875836043265 ]

march 2015 by robertogreco

California Study Finds Harm for Some in Repeating Algebra, Questions Whether it Benefits Anyone by Jill Barshay | College Guide | The Washington Monthly

december 2014 by robertogreco

"Among the higher performing students (C or better) who repeated, half saw their scores on the algebra state assessment fall by an entire performance level from “proficient” to “basic”. Fong’s data analysis doesn’t explain why the higher performing students do worse the second time around, but he suspects that these students were demoralized by being held back in math and lost their motivation.

You might question why teachers are holding kids back in algebra if their grades are decent. It’s a bit of a mystery. In informal conversations, Fong learned that teachers were concerned that some students with passing grades weren’t ready to move on. For example, some teachers give high grades to students who try hard and hand their homework in even if their calculations are consistently wrong. Also, the California State Test scores were often not available until the end of summer or after school started and couldn’t be used by teachers to help them make placement decisions.

The purpose of the study is to provide guidance to schools on whether students should repeat algebra. “If you have a kid who’s on the borderline of repeating algebra or moving on, if you’re in doubt, it seems like it’s better to move on,” said Fong.

As for the majority of struggling math students, Fong said this study doesn’t definitively conclude whether students should or shouldn’t take algebra again. They tend to improve slightly, but not as much might be hoped.

This study confirms an earlier 2012 California study that struggling students aren’t mastering algebra by repeating it. That study looked at only ninth graders across 24 school districts in California, but also found that students who took algebra a second time were unlikely to score “proficient” on the state exam following the second attempt."

education
california
math
algebra
mathematics
2014
schools
policy
You might question why teachers are holding kids back in algebra if their grades are decent. It’s a bit of a mystery. In informal conversations, Fong learned that teachers were concerned that some students with passing grades weren’t ready to move on. For example, some teachers give high grades to students who try hard and hand their homework in even if their calculations are consistently wrong. Also, the California State Test scores were often not available until the end of summer or after school started and couldn’t be used by teachers to help them make placement decisions.

The purpose of the study is to provide guidance to schools on whether students should repeat algebra. “If you have a kid who’s on the borderline of repeating algebra or moving on, if you’re in doubt, it seems like it’s better to move on,” said Fong.

As for the majority of struggling math students, Fong said this study doesn’t definitively conclude whether students should or shouldn’t take algebra again. They tend to improve slightly, but not as much might be hoped.

This study confirms an earlier 2012 California study that struggling students aren’t mastering algebra by repeating it. That study looked at only ninth graders across 24 school districts in California, but also found that students who took algebra a second time were unlikely to score “proficient” on the state exam following the second attempt."

december 2014 by robertogreco

Education Outrage: Music, Golf, Humanities, or Algebra: why we must make students study stuff that some adult likes

october 2014 by robertogreco

[via: https://twitter.com/garystager/status/518910182873894912 ]

"We are constantly being told why kids must take subjects in school that they obviously dislike. Someone is always promoting the benefits of forcing kids to do what they hate. So, for fun, I found some lists. I start with things very few kids are being forced to study which apparently would be very good for them, and end with things kids are also forced to study because they are also very good for them. See if you can tell who is right (and what we should make kids do even if they hate it.) (Hint: the last one is the best (or anyway, the funniest.))"

…

18 Benefits of Playing a Musical Instrument

http://www.effectivemusicteaching.com/articles/directors/18-benefits-of-playing-a-musical-instrument/

…

The Top 10 Life Lessons Your Child Can Learn from Playing Golf

http://www.streetdirectory.com/travel_guide/4807/golf_guide/the_top_10_life_lessons_your_child_can_learn_from_playing_golf.html

…

Why do the humanities matter?

http://shc.stanford.edu/why-do-humanities-matter

…

Ten Reasons to Study the Humanities

http://www.clayton.edu/humanities/Top-Ten

…

10 Everyday Reasons Why Algebra is Important in your Life

http://www.mathworksheetscenter.com/mathtips/algebra.html

…

So, algebra teaches you everything and you can’t function without it. But there are all those people who can buy cell phones without it. What do I know?

What subjects should be required then? My vote is for golf. It teaches quiet and graciousness which is better than interconnectedness and data entry any day.

Oh wait. Here is an idea. Stop telling kids what to study and let them follow their own interests. Nah. Too radical.

rogerschank
curriculum
compulsory
2014
algebra
music
forcefeeding
unschooling
deschooling
teaching
howweteach
howwelearn
requirements
humanities
math
mathematics
golf
humor
"We are constantly being told why kids must take subjects in school that they obviously dislike. Someone is always promoting the benefits of forcing kids to do what they hate. So, for fun, I found some lists. I start with things very few kids are being forced to study which apparently would be very good for them, and end with things kids are also forced to study because they are also very good for them. See if you can tell who is right (and what we should make kids do even if they hate it.) (Hint: the last one is the best (or anyway, the funniest.))"

…

18 Benefits of Playing a Musical Instrument

http://www.effectivemusicteaching.com/articles/directors/18-benefits-of-playing-a-musical-instrument/

…

The Top 10 Life Lessons Your Child Can Learn from Playing Golf

http://www.streetdirectory.com/travel_guide/4807/golf_guide/the_top_10_life_lessons_your_child_can_learn_from_playing_golf.html

…

Why do the humanities matter?

http://shc.stanford.edu/why-do-humanities-matter

…

Ten Reasons to Study the Humanities

http://www.clayton.edu/humanities/Top-Ten

…

10 Everyday Reasons Why Algebra is Important in your Life

http://www.mathworksheetscenter.com/mathtips/algebra.html

…

So, algebra teaches you everything and you can’t function without it. But there are all those people who can buy cell phones without it. What do I know?

What subjects should be required then? My vote is for golf. It teaches quiet and graciousness which is better than interconnectedness and data entry any day.

Oh wait. Here is an idea. Stop telling kids what to study and let them follow their own interests. Nah. Too radical.

october 2014 by robertogreco

A Conversation With Ted Nelson - YouTube

july 2014 by robertogreco

"The event is part of Virginia Commonwealth University's UNIV 200 cMOOC, "Living The Dreams: Digital Investigation and Unfettered Minds." We'll be talking about a wide range of topics, beginning with Dr. Nelson's seminal new media manifesto: Computer Lib / Dream Machines."

2014
tednelson
gardnercampbell
education
policy
unschooling
deschooling
technology
edtech
learning
howwelearn
curriculum
training
dreammachines
internet
computing
freedom
1974
marshallmcluhan
content
media
documents
xanadu
projectxanadu
hypertext
math
mathematics
algebra
schools
filmmaking
film
howwework
making
dougengelbart
hierarchy
hierarchies
aristotle
plato
intertwingularity
depth
richness
clarity
composition
arbitrary
systemsthinking
generalization
text
franklloydwright
leonardodavinci
coding
programming
teaching
structure
rules
academia
publishing
self-publishing
headstart
preschool
language
languageacquisition
poverty
vocabulary
alankay
multicontextuality
wikipedia
youtube
curiosity
raspberrypi
anarchy
anarchism
collectivism
interdependence
mutualaid
society
generalists
selfpublishing
july 2014 by robertogreco

5-Year-Olds Can Learn Calculus - Luba Vangelova - The Atlantic

march 2014 by robertogreco

"Why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to mat"

math
mathematics
learning
education
teaching
children
algebra
calculus
arithmetic
2014
lubavangelova
mariadroujkova
howweteach
march 2014 by robertogreco

...Only two things wrong with education: 1) What we teach; 2) How we teach

november 2012 by robertogreco

"school he thinks, has turned into a funnelling process for Universities. This is a big mistake. His solution is to have lots of curricula and allow people to follow their curiosity and interests, as this is what drives real, meaningful and useful learning, as opposed to memorisation and hoop jumping. Organise school, not around subjects, but cognitive processes that match what we do in the real world."

"Schank things Higher Education is a con. You pay through the nose for not very much more than a three or four year vacation and a good social life. The courses are poor and the system designed to select researchers."

"Schank has a strongly libertarian view in that he wants to abandon lectures, memorisation and tests. Start to learn by doing and practice, not theory. Stop lecturing and delivering dollops of theory. Stop building and sitting in classrooms. We need to teach cognitive processes and acquire skills through the application of these processes, not fearing failure."

"Based on an examination of language and memory, Schank explored the idea of personalised scripts in learning. This personalised, episodic model of memory led to a theory of instruction that exposed learners to model scripts by allowing them to experience the process of building their own scripts. We need scripts for handling meetings, dealing with customers, selling to others and so on. Knowledge is not a set of facts, it’s a set of experiences. This is not taught by telling, it is taught by doing, ‘there really is no learning without doing’. Interestingly, recent memory research confirms this view."

"He rejects the idea that we have to fill people up with knowledge they’ll never use. Too much education and training tries, and fails, to do this. We need to identify why someone wants to learn then teach it. In this sense he puts motivation and skills before factual knowledge. One can pull in knowledge when required."

[via Taryn, whose notes and quotes follow]

[not sure why anyone wants to make up problems when there is already so much work to do, Internet makes more of it more accessible to more of us; also "evaluate" for what, exactly, and why]

[Schank] prefers to deliver learning from mentored experience, not from direct instruction presented out of context. Fictional situations are set up in which students must play a role. They need to produce documents, software, plans, presentations and such within a story describing the situation. Deliverables produced by the student are evaluated by team members and by mentors. The virtual experiential curricula are story centred. Story-Centred Curricula are carefully designed apprenticeship-style learning experiences in which the student encounters a planned sequence of real-world situations constructed to motivate the development and application of knowledge and skills in an integrated fashion.

learning
storytelling
rogerschank
2012
unschooling
deschooling
curriclum
self-directedlearning
education
schools
schooling
highered
highereducation
colleges
universities
learningby
doing
math
science
algebra
change
apprenticeships
via:Taryn
"Schank things Higher Education is a con. You pay through the nose for not very much more than a three or four year vacation and a good social life. The courses are poor and the system designed to select researchers."

"Schank has a strongly libertarian view in that he wants to abandon lectures, memorisation and tests. Start to learn by doing and practice, not theory. Stop lecturing and delivering dollops of theory. Stop building and sitting in classrooms. We need to teach cognitive processes and acquire skills through the application of these processes, not fearing failure."

"Based on an examination of language and memory, Schank explored the idea of personalised scripts in learning. This personalised, episodic model of memory led to a theory of instruction that exposed learners to model scripts by allowing them to experience the process of building their own scripts. We need scripts for handling meetings, dealing with customers, selling to others and so on. Knowledge is not a set of facts, it’s a set of experiences. This is not taught by telling, it is taught by doing, ‘there really is no learning without doing’. Interestingly, recent memory research confirms this view."

"He rejects the idea that we have to fill people up with knowledge they’ll never use. Too much education and training tries, and fails, to do this. We need to identify why someone wants to learn then teach it. In this sense he puts motivation and skills before factual knowledge. One can pull in knowledge when required."

[via Taryn, whose notes and quotes follow]

[not sure why anyone wants to make up problems when there is already so much work to do, Internet makes more of it more accessible to more of us; also "evaluate" for what, exactly, and why]

[Schank] prefers to deliver learning from mentored experience, not from direct instruction presented out of context. Fictional situations are set up in which students must play a role. They need to produce documents, software, plans, presentations and such within a story describing the situation. Deliverables produced by the student are evaluated by team members and by mentors. The virtual experiential curricula are story centred. Story-Centred Curricula are carefully designed apprenticeship-style learning experiences in which the student encounters a planned sequence of real-world situations constructed to motivate the development and application of knowledge and skills in an integrated fashion.

november 2012 by robertogreco

dy/dan » On iBooks 2 And iBooks Author

february 2012 by robertogreco

"Algebra, as designed by McGraw-Hill for iBooks 2, is lighter by pounds. It's indexed for search. It's quick. You can highlight the text and insert notes. It removes one layer of abstraction between students and tools that already existed. Rather than accessing quizzes, tutorials, and enrichment videos by loading a CD-ROM into a computer or entering a password into a website, they're a tap away.

That's where the differences end. Students still interact with mathematics as they always have…

What I'm saying, basically, is that I'd have to modify, adapt, and extend the McGraw-Hill iBook in all the same ways that I modified, adapted, and extended the McGraw-Hill print textbook. We'd pull out the iBook just as infrequently as its printed sibling."

2012
algebra
learning
education
textbooks
ibooks
danmeyer
teaching
math
ibooksauthor
That's where the differences end. Students still interact with mathematics as they always have…

What I'm saying, basically, is that I'd have to modify, adapt, and extend the McGraw-Hill iBook in all the same ways that I modified, adapted, and extended the McGraw-Hill print textbook. We'd pull out the iBook just as infrequently as its printed sibling."

february 2012 by robertogreco

The Way You Learned Math Is So Old School : NPR

march 2011 by robertogreco

"there's a reason elementary schools are teaching arithmetic in a new way.

"…largely to reflect the different needs of society. No one ever in their real life anymore needs to — & in most cases never does — do the calculations themselves."

Computers do arithmetic for us…but making computers do the things we want them to do requires algebraic thinking. For instance, take a computer spreadsheet. The computer does all the calculations for you automatically. But you have to write the macros that tell it what calculations to do —& that is algebraic thinking.

"You cannot become good at algebra w/out a mastery of arithmetic, but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.

That doesn't mean that kids can skip learning their multiplications tables. "But the way it's taught now is you get to multiplication tables by understanding number system & what numbers mean"

education
math
teaching
learning
algebra
algebraicthinking
criticalthinking
mathematics
change
algorithms
parenting
tcsnmy
deschooling
"…largely to reflect the different needs of society. No one ever in their real life anymore needs to — & in most cases never does — do the calculations themselves."

Computers do arithmetic for us…but making computers do the things we want them to do requires algebraic thinking. For instance, take a computer spreadsheet. The computer does all the calculations for you automatically. But you have to write the macros that tell it what calculations to do —& that is algebraic thinking.

"You cannot become good at algebra w/out a mastery of arithmetic, but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.

That doesn't mean that kids can skip learning their multiplications tables. "But the way it's taught now is you get to multiplication tables by understanding number system & what numbers mean"

march 2011 by robertogreco

The 7 Fascinating Education Ideas of the Year - voiceofsandiego.org: Schooled: The Education Blog

december 2010 by robertogreco

"Solving Einstein's Algebra Problem [Einstein Academy], Letting the Kids Make the Rules [Innovations Academy], English Learners Who Seem to Know English [Pacific Beach Middle School], Small (Change) Is Beautiful [Euclid Elementary], The Data War [SDUSD in opposition to RttT], Wording Up Without the Dictionary [Grant Barrett, SDUSD], One Class Fits All [Correia Middle School in Point Loma drops tracking]"

sandiego
2010
emilyalpert
einsteinacademy
innovationsacademy
algebra
math
teaching
learning
sdusd
language
languageacquisition
change
euclidelementary
data
rttt
vocabulary
tracking
democracy
democratic
schools
biliteracy
assessment
collaboration
teacherretention
december 2010 by robertogreco

Education Week: Is There an Algebra Overkill?

november 2010 by robertogreco

"No doubt, algebra is a steppingstone to higher mathematics and quite necessary in professions that require extensive knowledge of math. Too, it offers insights not only into numbers, but also into general problem-solving separately. It is also reasonable for most students to have some experience with it before they leave school.

The difficulty, however, is assuming that algebra, in itself, will greatly increase everyone's ability to do the kind of mathematics that most people do in ordinary life."

math
education
algebra
teaching
schools
curriculum
The difficulty, however, is assuming that algebra, in itself, will greatly increase everyone's ability to do the kind of mathematics that most people do in ordinary life."

november 2010 by robertogreco

Google: Exploring Computational Thinking

november 2010 by robertogreco

"Easily incorporate computational thinking into your curriculum with these classroom-ready lessons, examples, and programs. For more resources, including discussion forums and news, visit our ECT Discussion Forums."

[See also: http://googleresearch.blogspot.com/2010/10/exploring-computational-thinking.html ]

computerscience
computationalthinking
via:lukeneff
algebra
biology
calculus
compsci
geometry
python
programming
math
lessons
teaching
thinking
edtech
education
elearning
danmeyer
google
science
learning
glvo
edg
srg
[See also: http://googleresearch.blogspot.com/2010/10/exploring-computational-thinking.html ]

november 2010 by robertogreco

Karl Fisch: Do you Believe in Algebra? (VIDEO)

october 2010 by robertogreco

"But it still begs the question of whether all students need these 118 standards. For example, do you believe that all students (scratch, that, all people) need to know that "there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real?" (CCSS, N-CN 1). Or how about "prove the Pythagorean identity sin2(x) + cos2(x) = 1 and use it to find sin(x), cos (x), or tan(x) and the quadrant of the angle?" (CCSS, F-TF 8).

(My not-so-modest proposal is that no state legislature is allowed to require standards that they couldn't demonstrate proficiency on themselves. Since they are clearly successful adults and they are saying that these standards are necessary for all students to be successful, surely they'd be able to demonstrate proficiency by taking the same tests our students do. But I digress.)"

karlfisch
math
algebra
curriculum
education
teaching
learning
schools
deschooling
unschooling
policy
standardization
deanshareski
standards
(My not-so-modest proposal is that no state legislature is allowed to require standards that they couldn't demonstrate proficiency on themselves. Since they are clearly successful adults and they are saying that these standards are necessary for all students to be successful, surely they'd be able to demonstrate proficiency by taking the same tests our students do. But I digress.)"

october 2010 by robertogreco

Fisch Algebra 2010-11: Skill List

august 2010 by robertogreco

"These are the skills that are important enough to assess individually. Some skills will include sub-skills that aren’t assessed individually. This is not necessarily the order the skills will be assessed in." [More at: http://fischalgebra1011.blogspot.com/p/course-expectations.html]

algebra
math
assessment
conceptchecklists
mathematics
teaching
august 2010 by robertogreco

dy/dan » Blog Archive » (One Of Many Reasons) Why Students Hate Algebra

january 2010 by robertogreco

"Would a real person need to solve this problem?...the solution realistic?...using a system of 2 equations?...in what ways does this problem help our students become better problem solvers?"...problem you will only find in a textbook...bizarre...how many different ways just 50 words can fail to square with reality. Why does each chaperone have to drive? Why can't we take 5 vans? Why do our vehicles have to seat the exact number of people in our group & no more?...Algebra teachers sell students a cheap distortion of the real world while insisting at the same time that it really is the real world. The cognitive dissonance is obvious & terrible. Students know the difference. It cheapens my relationship to them & their relationship to mathematics when you ask me to lie to them...Not only are the short-term consequences devastating but it makes that person distrustful or wary of the real thing. Make no mistake. We are making an alien of algebra. We are doing real damage here."

math
algebra
education
tcsnmy
teaching
learning
reality
disservice
realworld
realism
distortion
schools
schooling
textbooks
cognitivedissonance
deschooling
unschooling
authenticity
danmeyer
january 2010 by robertogreco

dy/dan » Blog Archive » Asilomar #1: What Do We Do With Algebra II

december 2009 by robertogreco

"Leinwand opened his talk: "The great divider of our time is the Algebra II final exam. Algebra II squeezes off options for so many kids. Algebra II is anathema to all but the top 20% of the population. My premise: as currently implemented, high school algebra I and II are not working and not meeting either societal or student needs."

education
schools
schooling
math
algebra
algebraii
danmeyer
learning
change
reform
december 2009 by robertogreco

Khan Academy

september 2009 by robertogreco

"The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere.

We have 900+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by Salman Khan.

He has also developed a free, adaptive math program available here. ( Keep in mind that the web application is not fully supported and may not work properly with certain browser and/or network configurations)

To keep abreast of new videos as we add them, subscribe to the Khan Academy channel on YouTube.

The entire video library is shown below. Just click on a category or video title to start learning from the Khan Academy!"

[YouTube channel here: http://www.youtube.com/user/khanacademy ]

[via: http://smartpei.typepad.com/robert_patersons_weblog/2009/09/khan-academy---your-next-high-school---free-on-your-terms.html ]

education
learning
free
homeschool
economics
teaching
science
math
algebra
mathematics
geometry
trigonometry
physics
tutorials
youtube
calculus
online
finance
lectures
khanacademy
tcsnmy
arithmetic
We have 900+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by Salman Khan.

He has also developed a free, adaptive math program available here. ( Keep in mind that the web application is not fully supported and may not work properly with certain browser and/or network configurations)

To keep abreast of new videos as we add them, subscribe to the Khan Academy channel on YouTube.

The entire video library is shown below. Just click on a category or video title to start learning from the Khan Academy!"

[YouTube channel here: http://www.youtube.com/user/khanacademy ]

[via: http://smartpei.typepad.com/robert_patersons_weblog/2009/09/khan-academy---your-next-high-school---free-on-your-terms.html ]

september 2009 by robertogreco

How We Know § SEEDMAGAZINE.COM

september 2009 by robertogreco

"Moses spent the next five years developing a completely new curriculum. He called it the Algebra Project. Instead of confronting students with abstract equations, Moses took them out into the real world, traveling around Boston in search of experiences that could demonstrate the practical uses of math. A ride on the T became a lesson in coordinate graphing and negative numbers. Neighborhood landmarks stood in for integers. When Moses taught students about displacement, he had them measure the dimensions of their own bodies. The first rule of Moses’ math class was that students always had to “participate in a physical event.”

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september 2009 by robertogreco

Connecticut District Tosses Algebra Textbooks and Goes Online - NYTimes.com

june 2009 by robertogreco

"Math students in high-performing school district used to rush through their Algebra I textbooks only to spend the first few months of Algebra II relearning everything they forgot or failed to grasp the 1st time...district’s frustrated math teachers decided to rewrite algebra curriculum, limiting it to about 1/2 of the 90 concepts typically covered in a high school course in hopes of developing a deeper understanding of key topics...replacing 1,000+ page math textbooks with their own custom-designed online curriculum...“In America, we run through chapters like a speeding train. Schools in Singapore & India spend more time on each topic & their kids do better. We’re boiling down math to the essentials.”...students focus only on linear functions in Algebra I, taught in 7th, 8th or 9th grade depending on student ability & leave quadratics & exponents to Algebra II, eliminating overlap & repetition typical of most textbooks & curriculum guidelines...result=less review+higher test scores"

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june 2009 by robertogreco

Algebra Math Games

september 2008 by robertogreco

"Our directory of Free Algebra Math Games available on the Internet - games that teach, build or strengthen your algebra math skills and concepts while having fun. We categorise and review the games listed here to help you find the math games you are looking for."

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algebra
tcsnmy
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september 2008 by robertogreco

NROC Algebra IA [Algebra IB here: http://www.montereyinstitute.org/courses/Algebra%20IB/nroc%20prototype%20files/coursestartc.html]

september 2008 by robertogreco

"This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course include understanding, writing, solving, and graphing linear equations, systems of linear equations and inequalities, quadratic equations, and rational equations."

math
tcsnmy
algebra
september 2008 by robertogreco

Algebra.help -- Calculators, Lessons, and Worksheets

september 2008 by robertogreco

"Algebrahelp.com is a collection of lessons, calculators, and worksheets created to assist students and teachers of algebra. "

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september 2008 by robertogreco

Understanding Algebra by James Brennan

september 2008 by robertogreco

"The complete contents of this algebra textbook are available here online. This text is suitable for high-school Algebra I, preparing for the GED, a refresher for college students who need help preparing for college-level mathematics, or for anyone who wants to learn introductory algebra. I am especially pleased to help homeschoolers."

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tutorials
algebra
free
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september 2008 by robertogreco

GeoGebra

august 2008 by robertogreco

"GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus. It received several international awards including the European and German educational software awards."

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math
geometry
algebra
calculus
education
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technology
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freeware
august 2008 by robertogreco

Dimension M - Where there's power in numbers

august 2008 by robertogreco

"DimensionM™is an immersive video game world that engages students in the instruction and learning of mathematics. Pre-algebra and algebra objectives are covered through a series of missions that bring math into a world that today's students understand. Students become so captivated in solving problems that they forget they're learning but they don't forget what they've learned."

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august 2008 by robertogreco

HippoCampus - Homework and Study Help - Free help with your algebra, biology, environmental science, American government, US history, physics and religion homework

november 2007 by robertogreco

"We are dedicated to bringing you great multimedia and course materials that can help you with your homework and studies."

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november 2007 by robertogreco

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