Liz Caffrey is a master middle school math teacher in the Boston area. She is the author of last year’s Lab Gear, the Great Connector, a guest post on this blog. Today, she shares her big-picture thoughts about manipulatives. I inserted some links to pages on my website — you can find many more links… Continue reading Manipulatives
Author: hpicciotto
Functions from Tables
At some point, maybe thirty years ago, it became fashionable to emphasize functions and their multiple representations in secondary school math. This was in part driven by the newly available electronic graphing technology, and in part by the realization that important curricular ideas should be approached in more than one way. As is often the… Continue reading Functions from Tables
A Construction Unit
I have written about geometric construction a number of times on this blog, and on my website. I outlined my philosophical outlook on this topic here. Today I summarize some construction activities, a subset of the unit you can find on my website. —————————————————————————————————— Geometric construction with straightedge and compass is a standard topic in… Continue reading A Construction Unit
Teacher-Created Materials
In this post I would like to discuss the place of teacher-created materials in the big picture of math curriculum. In some ways, the topic is of limited importance. Teachers in the US do not have a lot of time and energy for this once they are done with lesson planning, paper grading, and assorted… Continue reading Teacher-Created Materials
Factoring Trinomials
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
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
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