I will present a workshop at the the Math Teachers' Circle in Palo Alto (at the American Institute of Mathematics.) The topic is area on a lattice, which we will explore on geoboards and dot paper. We will discuss "curricular" classroom applications (the Pythagorean theorem, simplifying radicals) as well as Pick's theorem and its proof,… Continue reading Saturday workshop
Tag: Teaching
The Common Core
Now that I'm a freelance math education consultant and curriculum developer, I need to pay attention to the Common Core State Standards as they affect everything I do in my professional life. Merely listening to talks about the standards, and reading angry posts about them did not provide a lot of information. On the other… Continue reading The Common Core
A Curriculum Model
The above map is an attempt at a curriculum development model. Traditional pedagogy stays at the top, as it is based on the belief that skills practice and teacher explanations are sufficient to build student understanding. Understanding acquired this way, plus the skills, allow the student to apply the ideas.Would that it were that simple.In… Continue reading A Curriculum Model
Geoboards and Dot Paper
If you are familiar with my curricular creations, you know that I often use the geoboard as a microworld to introduce interesting problems and important concepts. This is in line with my call for a tool-rich pedagogy. (A geoboard is a square lattice pegboard on which students use rubber bands to create and investigate geometric… Continue reading Geoboards and Dot Paper
"Enrichment"
During my first ten years as a teacher, I worked in elementary schools. In addition to team teaching my own class (grade 3, then 4, then 5) I was a math specialist for grades K-5. The basic idea was that there was "normal" math (a lot of arithmetic, textbook-based), and there was "enrichment" math. I… Continue reading "Enrichment"
Math and Art
Many years ago, I team-taught a class called "Math and Art" with my then-colleague Stephen Thomas, who was an art teacher at The Urban School. Like most such endeavors at any school, the class was short-lived — I believe we offered it twice. However it was not in vain: some of that curriculum found its… Continue reading Math and Art
NY Times special issue
The New York Times special issue on math and science education on September 2, 2013, included some worthwhile items."Cognitive Science Meets Pre-Algebra" reports on a recent study of "interleaving homework" in a middle school in Tampa. The idea was to compare the usual approach (homework is on the topic currently under study) with interleaving, which… Continue reading NY Times special issue
Extending Exposure
Not all students learn new math concepts at the same rate. Everyone knows this. Can anything be done about it?This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range. Most schools attempt to make the problem more manageable by tracking students into Honors, Regular,… Continue reading Extending Exposure
One Should Separate Related Topics!
This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.In a previous post, I discussed the benefits of "lagging homework". These included extending student exposure to new ideas, which benefits everyone: stronger students get the forward motion they want and need, and students who… Continue reading One Should Separate Related Topics!
"A New Algebra"
About twenty years ago, along with Anita Wah, I wrote "A New Algebra", a paper for the Journal of Mathematical Behavior (JMB). It was an attempt to address what I saw as a crucial issue in secondary math education: on the one hand, the traditional Algebra 1 course was the gateway to any further work… Continue reading "A New Algebra"
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