Much can be said in defense of practice exercises, but when all is said and done, very few students develop deep understanding from routine practice. For example, compare these two approaches to the area of a trapezoid. Approach 1The teacher says: ”The area of a trapezoid is given by the formula h(b1+b2)/2, where h is… Continue reading Comparing two approaches
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Algebra Manipulatives
A middle school teacher writes: Just a little note and question about Lab Gear. I have been having so much fun with my students using Lab Gear again this year. The 3D-ness of it totally blows the other (cheaper) algebra tiles that I used last year out of the water! I have heard this often… Continue reading Algebra Manipulatives
Yet More on Homework
This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.A correspondent writes, presumably in response to my lagging homework concept:I love your approach and a lot of the details. I guess my only immediate reservation would be the necessity for homework. A lot of U.S.… Continue reading Yet More on Homework
Time and Tide
This is my yearly report on the Asilomar conference of the California Math Council, Northern Section. Because I was presenting three times, I didn't end up attending as many sessions as I would have liked. As always at Asilomar, I enjoyed hanging out with my ex-colleagues, running into friends, and meeting the occasional fan of… Continue reading Time and Tide
Upcoming presentations
I have a bunch of presentations coming up. That will be your last chance to hear me for a while, as my NCTM San Antonio talk was rejected†. Who knows, maybe retirement will finally kick in!Online Webinar: Reaching the Full RangeAs everyone knows, students learn math at different rates. What should we do about it?… Continue reading Upcoming presentations
More Notes from NCTM Phoenix
See Part 1 of my notes from Phoenix: A Brief History of Math Education (NCTM President Matt Larson's presentation.)Here is Part 2.Growth Mindset: telling is not teachingIn his short session, Dylan Kane pointed out that talking about growth mindset may be helpful to students "in the middle". But there are students in our classes who… Continue reading More Notes from NCTM Phoenix
NCTM Phoenix notes: History of Math Education
I attended the NCTM regional meeting in Phoenix. Here are some notes. A Brief History of Math EducationNCTM President Matt Larson talked about the history of the math wars, which as it turns out started in the early 1800's. A previous version of his presentation can be found on his page on the NCTM site.… Continue reading NCTM Phoenix notes: History of Math Education
Reading Algebra
Symbol sense is an essential part of mathematical literacy. It is the understanding that undergirds effective symbol manipulation, and perhaps more basically the ability to interpret and create algebraic expressions. Symbol sense, like number sense and operation sense, is not learned so much through listening to a teacher. Rather, it grows as one gets practice… Continue reading Reading Algebra
Technical Writing
It is difficult to learn something new and challenging without ever putting it into words. This is just as true when learning math as it is when learning anything else. Thus, it is a good idea to make time for students to discuss their ideas with their classmates in pairs, groups, and as a whole… Continue reading Technical Writing
Partitions
In this post, I will outline my approach to this partition problem:How many ways can you write a positive integer n as a sum of three or fewer positive integers? Partitions are a standard topic in number theory, but I will limit myself to this specific question. I started trying to figure it out after… Continue reading Partitions
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