A correspondent writes (I added the links): Our district is looking at revamping our year map and I would like to suggest a map that has the qualities of Algebra: Themes, Tools, Concepts (ATTC): particularly its ‘integratedness’ and how well it spirals through the topics. I’ve read on your blog about separating topics and lagging… Continue reading Mapping Out a Course
Author: hpicciotto
Online Collaboration
In 2008, I gave a talk about teacher collaboration at the Asilomar meeting of the California Math Council. It was well attended, and well received, but more than a few attendees told me that they had no one to collaborate with. They were the only math teacher at their school, or the only one teaching… Continue reading Online Collaboration
Pruning the Curriculum
In my decades as math department chair, I learned that if you want to teach for understanding, you need to approach important topics repeatedly, and from different points of view. This includes different representations of concepts, and different learning tools to get at them. One reason for this is that since students have different backgrounds,… Continue reading Pruning the Curriculum
The Thinking Classroom
In my last post, I summarized Peter Liljedahl's paper on "visibly random groups." That research confirmed many things I already knew from experience. Today, I will summarize another one of his papers, this one titled "Building Thinking Classrooms: Conditions for Problem Solving." (It is also available on ResearchGate.) I learned quite a bit from reading… Continue reading The Thinking Classroom
Random Groups
Peter Liljedahl is a math education professor at Simon Fraser University in British Columbia. He is interested in helping teachers create what he calls a "thinking classroom," as contrasted of course with a classroom where the main objective is memorization. I just read two phenomenal papers he wrote. Since his research confirms my beliefs, I… Continue reading Random Groups
NCTM wrap-up
I only attended a few sessions at NCTM-Boston, because I spent a fair amount of time promoting the Lab Gear. I already posted my report on Geoff Krall's strategies to improve the problems we find in standard textbooks. In this post, I'll go over some of the other worthwhile ideas I came across.- Scott Steketee… Continue reading NCTM wrap-up
About hints
A few days ago, I saw a raging debate on Twitter about hint-giving in math class. It was triggered by a short talk by Michael Pershan, a teacher in NYC. Michael argues that high school teachers need to share good hints with each other, and he proposes some guidelines as to what makes a good… Continue reading About hints
NCTM Report: Adaptation
I'm just back from the NCTM National Meeting in Boston, where I promoted the Lab Gear at the Didax booth, and attended a few sessions.One nice thing about NCTM was the opportunity to connect with friends and colleagues who I don't see often enough. Another is running into fans of my work, which happened with… Continue reading NCTM Report: Adaptation
Logarithms
A young teacher writes:I'm teaching exponential functions and just getting into logs. Everyone tells me that kids tend to struggle with this chapter, so I'd like to try something different than what my school has been doing (just teaching the rules, then practicing over and over again.) Is there a way to introduce logs that… Continue reading Logarithms
Getting Help
In my last post, I described a problem I encountered more than twenty years ago, and my recent attempt at solving it. The problem: Partition the numbers from 1 to 2n into pairs, so that the sum of the numbers in each pair is a perfect square. For what numbers is this possible? I decided… Continue reading Getting Help
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