Both in person and online, a common topic of discussion among math teachers is the question of “retakes”. Under what conditions should students be allowed to have another chance at taking a test? How does the retake affect the grade? This is an important conversation. Different opinions reflect different values, different attitudes towards assessment, and different… Continue reading Retakes vs. Test Corrections vs. Neither
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Learning from Teaching (cont.)
For the second time this summer, I taught a version of my Visual Algebra workshop, this time as part of a summer institute at the Atrium School near Boston. (Earlier in the summer, I did this at Synapse School, in Silicon Valley, and wrote about it here.) Once again, I walked away from the workshop… Continue reading Learning from Teaching (cont.)
Taking Notes vs. Doing Math
Some time ago, during a professional development workshop, a participant asked how I teach students to take notes in math class. I explained that I didn’t think students can simultaneously do math, and take notes. It’s really one or the other. The teacher gave me a contemptuous look that made clear she disapproved of my answer. Later in the… Continue reading Taking Notes vs. Doing Math
Learning from Teaching
Now that I’m retired from the classroom, summer tends to be my busy time. I just taught the grades 6-9 version of my Visual Algebra workshop. There were quite a few familiar faces among the participants. Some had seen me present at the Asilomar (California Math Council) conference, others at NCTM, yet others at a… Continue reading Learning from Teaching
Geometry: A Guided Inquiry
In my last post, I discussed Every Minute Counts, a book that influenced me early in my career as a high school teacher in the 1980’s. It was mostly useful because of David R. Johnson’s suggestions on how to run a class discussion, and his insistence that the teacher needs to hear from every student, not just the… Continue reading Geometry: A Guided Inquiry
Every Minute Counts
I’ve learned much of what I know about teaching from colleagues, but when I started teaching high school, there is one book that I found extremely helpful: Every Minute Counts, by David R. Johnson (1982, Dale Seymour Publications, with great illustrations by cartoonist John Johnson). In the 37 years since the book's publication, society has… Continue reading Every Minute Counts
In Defense of Geometry: Part II
In my last post, I complained about the shrinkage of geometry, a decades-long trend in US math education. Some of the reasons I suggested for this state of affairs is the offering of a substantial amount of algebra to a much broader population, the growth of calculus as a high school subject, and the increasing place given to… Continue reading In Defense of Geometry: Part II
In Defense of Geometry: Part I
In 2016, I wrote In Defense of Algebra 2, a blog post addressed to math educators who do not see that Algebra 2 can be engaging and worth teaching to all students. In this post and the next, I defend geometry. This is a different sort of argument. Algebra 2 has been offered to more and… Continue reading In Defense of Geometry: Part I
Story Tables in Middle School
In a recent post, I discussed story tables, mostly in the context of teaching about functions in high school, and as a springboard to discuss priorities in tool selection. I first heard about story tables from Shira Helft, who I believe was the first to fully appreciate the power of that representation. Today, a conversation with… Continue reading Story Tables in Middle School
Teaching Trig
I taught high school math for 32 years, Algebra 1 to Calculus, plus a few electives. In this post, I will summarize my department's approach to trigonometry. When I started there, we had a one-term trigonometry course, which became more engaging and comprehensible when we started using the now out-of-print Trigonometry: A Guided Inquiry by Chakerian,… Continue reading Teaching Trig
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