For most of you, school started recently, or will start soon. For me, this is the beginning of the third year of my retirement, and I'm starting to get used to the weirdness of my new life.It turns out that August is by far the most intense work month for me, because that's when I… Continue reading First Day of School
Tag: Teaching
Themed courses?
This is the third in a series of summer posts on big-picture planning for a math department. Previous installments: Pruning the Curriculum, and Mapping Out a Course. Today's post represents a further zooming out, to discuss my thoughts about how to organize content across courses. Of course, many if not most teachers are not consulted… Continue reading Themed courses?
About Hints, the sequel
A few weeks ago, I wrote about the use of hints in the math classroom. I just reread that post, and stand by what I wrote. I admit that my very last sentence (in the PS) was perhaps a bit snarky, and I'll try to elaborate on it in this post.What is prompting me to… Continue reading About Hints, the sequel
Constant Sums, Constant Products
I just cleaned up an existing page on my Web site: Constant Sums, Constant Products, "an untraditional approach to traditional topics". This is a mega-unit, spanning content from middle school, all the way to what one might call "teachers' mathematics." Take a look at it on a summer day when you have a little time… Continue reading Constant Sums, Constant Products
Mapping Out a Course
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
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
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
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