I recently added a guided inquiry worksheet on my website’s Pythagorean theorem page. It leads students along a proof of the theorem based on similarity. It is called The Three Triangles. This is a worksheet I used and honed over the years when I taught geometry. Upon rereading it, I thought it would make a… Continue reading The Three Triangles
Tag: Teaching
Fractions
Last weekend, I shared my thoughts about teaching fractions with teachers of grades 3-5 at the Asilomar meeting of the California Math Council. After decades of work in high school, and hundreds of presentations to teachers of grades 7-12, this was a bit of a departure from my normal routine, and somewhat anxiety-provoking. The reason… Continue reading Fractions
Manipulatives
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
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
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?
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
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
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
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