A recent online conversation got me thinking about the factoring of trinomials. To start with, I would like to step back, and think about why this topic is prominent in the teaching of algebra. In the age of computer algebra systems (CAS), factoring trinomials is not an important skill, except of course for the purposes… Continue reading Factoring Trinomials
Author: hpicciotto
Simplify?
We ask students to simplify expressions in various arenas: fractions, order of operations, radicals, and no doubt other topics I’m not recalling right now. What is the purpose of this? When is it appropriate? How much is too much? In my in-depth analysis of the Common Core Standards for Mathematics (CCSSM), I wrote approvingly of… Continue reading Simplify?
Geometry Labs Notes
In this post, I share thoughts about my Geometry Labs (free download), and complement some of Mimi Yang's notes about it. (In fact, this post was suggested by the existence of Mimi’s notes. You may find those useful, as she lists which topics are supported by various labs.) First, big-picture thoughts. The book includes obviously… Continue reading Geometry Labs Notes
Order of Operations
A guest post by Rachel Chou I recently saw this in my Facebook feed: I had many questions: Why is this posted in a facebook group called “Grandma’s recipes?!” 462,000 people cared enough to leave a comment? 6,900 people cared enough to re-share it? Most importantly: I hope no one is posing this question to… Continue reading Order of Operations
Matrices
As a high school teacher, my first attempts at teaching about matrices were not successful. I tried to sell them as a way to solve systems of linear equations with three or more unknowns. This was a highly technical approach to something my students were not particularly interested in. It was not a hit, and… Continue reading Matrices
Supertangrams
Many years ago, in the exhibits area at an NCTM national meeting (in New Orleans?), I saw math teachers standing in an insanely long line. I had never seen anything like it, and never saw anything like it since. They were waiting to have a book signed by Martin Gardner, the author of the “Mathematical… Continue reading Supertangrams
Convex Tangram Polygons
If you’re a regular reader of this blog, or visitor to my website, you probably know of my long-standing interest in geometric puzzles. Among those, tangrams are probably the most well-known and widely available. Thus I included them in Geometry Labs (free download) where they are the subject of Section 2, and Lab 10.6. In this… Continue reading Convex Tangram Polygons
An Assessment Conundrum
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
Teachers’ Mathematics
I recently came across an interesting and humorous lesson, intended to generate discussion and reflection about the properties of our number system. It is based on the idea of a fictional cashier who knows absolutely nothing about numbers. The worksheets (Tarzan 1 | Tarzan 2) were created by mathematician Robin Pemantle for use in a… Continue reading Teachers’ Mathematics
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
Henri's Math Education Blog 