On Twitter, Nick Corley writes: Students were SUPPOSED to use the distance formula, but look at the response in the pic. How do you grade????? This is a great discussion starter! Here are my thoughts. Assessment Should the student be penalized for finding the correct answer, using a correct method? That would be particularly egregious… Continue reading An Assessment Conundrum
Math as Literacy
This may be the only country where there is an ongoing campaign against high school math — in the media, in the overall culture, and even within the profession. I have written a number of posts in response to that state of siege, and I link to them below. Here is the ninth installment in… Continue reading Math as Literacy
Rate of Change
I often promote the idea that if a concept is important, we should teach it more than once, and preferably in more than one way. Rate of change is one such concept. It can be approached in various ways from middle school to calculus. Is there anything to add to the oft-repeated “rise over run”… Continue reading Rate of Change
Today, I share some materials not from my website — though not unrelated! Robert Wirtz As a young elementary school teacher and math specialist in the 1970’s I came across Robert Wirtz’s materials, and was inspired by them. Here is an example, the one I call “Wirtz’s flags": The idea is to draw vertical lines,… Continue reading Seen Elsewhere
I’ve written at length about assessment — the assessment of students by teachers. Today, I turn around and focus on how to maximize the benefits of student feedback in course evaluations. Early in my high school teaching career, I was given a form that my students were supposed to fill out. It had a long… Continue reading Course Evaluations
Last January, I addressed a blog post to a “young teacher”. Actually, it applied to beginners — whether young or not so young. The post was largely about big-picture thoughts on becoming a math teacher. It generated a thoughtful and heartfelt response from another veteran educator. If you’re a beginner, I encourage you to check… Continue reading Classroom Basics
The Atlantic published an excerpt from Temple Grandin’s latest book (Visual Thinking). They titled it “Against Algebra”, which puts it in a tradition of anti-algebra pieces in various magazines and radio programs (!). Alas, anti-algebra ideas are also present among some math educators. I have written about this repeatedly: Technology in Math Education (2022) My… Continue reading For Algebra
Technology in Math Education
Technology influences both the content and the methods of math education, but the impact is slow and gradual, not sudden and dramatic. This is in part because it takes time for technology to reach the classroom, but it is especially because school and societal culture develops unevenly. In this post, I think about some specific… Continue reading Technology in Math Education
We need to review!
It is a serious mistake to present important concepts only once, and move on. Most students need extended and repeated exposure to challenging ideas before those sink in. As I became more and more aware of this in the course of my decades in the classroom, I started to think in terms of a “preview… Continue reading We need to review!
Polyarcs in the Classroom
You may be familiar with polyominoes, the figures that can be made by connecting unit squares, edge to edge. For example, these are the tetrominoes, each one made of four unit squares: Polyominoes are an example of polyforms. I discussed polyforms in this article: Geometric Puzzles in the Classroom. In particular, this is where I… Continue reading Polyarcs in the Classroom