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Stones and apples
A model of motion

To help us visualize the motion we are dealing with in this thought experiment, let’s draw a diagram that shows the position of an object at different points in time. A third object, which we’ll call Charlie, will join us for this part of the experiment.

If Charlie is initially at rest, and is acted upon by no forces, we observe the very unexciting timeline shown below.
math  Physics 
2 hours ago by euler
The Fair Game That's Totally Unfair - YouTube
How games can be non-transitive, which causes a bias. How RPS is a non-transitive game, and the fact that bacteria use it to create an equilibrium.
math  trick  boardGames 
2 hours ago by ixwt
Mathspace - Replace your math textbook with something better
Replace your math textbook with something better
Give your students step-by-step support online
Ayushi  School  Learning  Math  Education  Science 
2 hours ago by mfernando
Why Equity Has Been a Conservative Force in American Education—And How That Could Change - Next Gen Learning in Action - Education Week
"By Jal Mehta, an associate professor at the Harvard Graduate School of Education and the co-director of the Deeper Learning Dozen

Over the past 15 years, at least since the passage of No Child Left Behind, equity has been more of a conservative than a liberating force in American education.

It started with good intentions. The idea was that some students, particularly students of color and poor students, historically had been ill-served by our school system. When Ted Kennedy and George Miller joined their Republican colleagues in supporting No Child Left Behind, they did so out of a belief that it was a continuation of the civil rights movement—a way to use federal power to support an equity agenda.

But that's not how it played out. The consequence of holding everyone accountable to low level tests in reading and math, without building any of the supporting structures, climate, or culture that would enable those results, is that schools serving disadvantaged students narrowed the curriculum and focused disproportionately on test prep, whereas more advantaged public schools and private schools had flexibility to continue offering a richer and more holistic educational approach.

Even as the legal requirements for NCLB have ended, the mindset has persisted. Urban schools and districts continue to be run in more authoritarian ways than their suburban counterparts, and students in disadvantaged schools continue to be more subject to test-driven pressures. When we run institutes at the Harvard Graduate School of Education on "deeper learning," we tend to attract folks from more privileged public schools and private schools here and abroad. In contrast, when we offer institutes on data-driven instruction or school turnarounds, we tend to attract people serving students of color in high-poverty public schools.

The consequence is that equity has become, more often than not, a conservative force in American public education. The effort to close achievement gaps has in practice doubled down on the century-old industrial model of schooling, leaving in place all of the essential elements of its grammar: teaching as transmission, batch processing of students, conventional assessments, tracking and leveling, and all of the rest. Anything that moves away from those assumptions—like project-based learning, problem-based learning, interdisciplinary learning, authentic assessment, or constructivist pedagogy—is seen as "risky;" something that is "OK for the privileged kids" but somehow distracts from the real work of closing achievement gaps on state-sponsored tests.

I've come to think that the reality is close to the opposite. The existing system, for all of its warts, works well enough for the privileged kids. They know how to play the "game of school," and thus they learn what they need to learn to get the grades and credentials they need to head to college and beyond. It is the kids who are disaffected from school who are most in need of a new approach. For them, finding a way to make school more relevant, more student-centered, more connected to their purposes and passions, is not a luxury but a requirement. Ironically, the more we double down on closing achievement gaps within the existing grammar of schooling, the more difficult we make it for ourselves to transform schooling into a more purposeful, relevant, and engaging institution.

There is an alternative, well-developed in some circles, but just recently entering broader reform discussions.

Equity as liberation.

This approach has entered the mainstream education space over the past five years from places like the National Equity Project and equityXdesign. The roots of it are old, drawing on Paulo Freire's ideas of "problem-posing" education and education as a force for liberation, and they run through the writings of folks like Jeff Duncan-Andrade, Pedro Noguera, Gloria Ladson-Billings, Theresa Perry, and many others. The idea here is that equity is a lens, a way of seeing how power is distributed, whose voices are being heard, which ideas are being represented, and whose interests are being served. It relies more heavily on what Shane Safir calls "street data" (the lived experiences of students in schools) than "satellite data" (test scores). It sees diversity as an asset—where our different lived experiences and funds of knowledge create rich opportunities for mutual learning—which is a profoundly different stance from the deficit approaches that have become standard in these discussions. It takes seriously the idea that education should liberate, meaning create ways for students to take agency to transform their lives and the world around them.

Taking this stance also implies a different way of working. Fundamentally, many gap-closing approaches take a fundamentally old-style command and control orientation for granted. What is to be known is determined by the district or the state. Students don't know this knowledge when they start. Teachers don't know how to deliver this knowledge. The solution is tighter implementation chains—from districts into the heads of teachers and then into the heads of students. This prescription is compounded by urgency; we are told that students have no time to lose so vertical hierarchies are the most efficient way to get things done.

A better approach would start with a different set of assumptions. There is lots of knowledge in the system, held by both teachers and students. This knowledge is also more heterogeneous than what is known by the district: Older teachers may have wisdom about teaching practice, younger teachers may have learned non-Western history in college, and students may know things about their neighborhoods and communities that are invisible to teachers and administrators. Good leadership would tap into these centers of knowledge and connect and build upon them in ways that are likely to lead to mutual learning for everyone.

It also would imply a different approach to change. Much of the traditional literature assumes that the leader is the hero, the members of the organization are the resistance, and the central challenge is to achieve "buy-in" via "change management." A liberatory design approach, by contrast, assumes that teachers and students would like to develop engaging, meaningful learning experiences, and that the problem is not them but the institutional structures and culture of schools that constrains them. Such an approach would foreground the lived experiences of students and teachers and invite them to help redesign schools in ways that are more purposeful and humane. Rather than act on students, teachers, and communities, we would work with them.

Liberatory design would also create an attractive symmetry between adult learning and student learning. If we want classrooms where students are seen as capable meaning-makers and teachers are facilitators of that learning, then districts need to treat teachers as capable meaning-makers and themselves as facilitators of teacher learning. Taking this point seriously would require districts to rethink many of their assumptions, large and small, spurring a shift from a bureaucratic to a professional mode of social organization.

Engaging with the lived experiences of students would also force us to think harder about whether students' full selves are welcomed into schools. This is relevant for all students, but particularly for students of color. One of my favorite ethnographies of schooling is Angela Valenzuela's Subtractive Schooling, which shows in excruciating detail the ways in which the mostly Mexican-American students in her research have to forego critical parts of themselves to show up in school. Ta-Nehisi Coates' memoir similarly recounts how his inquisitive stance was not welcome in Baltimore schools that repressed questions and rewarded compliance.

We could create schools that reverse this cycle; many in the sector already have. They start from what should be an uncontroversial idea—that students learn best when they feel affirmed, recognized, and welcomed into the spaces in which they are learning. Diversifying the curriculum does not mean lessening the rigor of that curriculum; rather, it potentially enables more students to do rigorous work by creating subjects worth investing in. And when we do that, ironically, we have a much better chance of closing conventional achievement gaps, because we have created welcoming, inclusive spaces where students can do their best work.

Equity can be either a conservative or a liberating force. Which one is it in your school?"
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15 hours ago by robertogreco

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