If you've been reading my blog for a while, you know that I'm a big fan of geometric construction. I have written about it here more than once, and my Web site includes quite a bit of curriculum involving construction. See the end of the post for additional links. I have many reasons for this… Continue reading Geometric Construction for Middle School

# Tag: Technology

## Spirograph

## Geoboard Triangles

One way to discover or apply the formula for the area of a triangle is to explore area on the geoboard. The initial activities should be along the lines suggested in my Geometry Labs Lab 8.4. (Free download.)After that, one can zero in on triangles, by asking a question like: "Find triangles of area 15."… Continue reading Geoboard Triangles

## About Hints, the sequel

A few weeks ago, I wrote about the use of hints in the math classroom. I just reread that post, and stand by what I wrote. I admit that my very last sentence (in the PS) was perhaps a bit snarky, and I'll try to elaborate on it in this post.What is prompting me to… Continue reading About Hints, the sequel

## Constant Sums, Constant Products

I just cleaned up an existing page on my Web site: Constant Sums, Constant Products, "an untraditional approach to traditional topics". This is a mega-unit, spanning content from middle school, all the way to what one might call "teachers' mathematics." Take a look at it on a summer day when you have a little time… Continue reading Constant Sums, Constant Products

## Pruning the Curriculum

In my decades as math department chair, I learned that if you want to teach for understanding, you need to approach important topics repeatedly, and from different points of view. This includes different representations of concepts, and different learning tools to get at them. One reason for this is that since students have different backgrounds,… Continue reading Pruning the Curriculum

## Getting Help

In my last post, I described a problem I encountered more than twenty years ago, and my recent attempt at solving it. The problem: Partition the numbers from 1 to 2n into pairs, so that the sum of the numbers in each pair is a perfect square. For what numbers is this possible? I decided… Continue reading Getting Help

## I’ve Got a Problem!

Many, many years ago, I saw this problem somewhere:Arrange the whole numbers from 1 to 18 into nine pairs, so that the sum of the numbers in each pair is a perfect square.I liked the problem, and included it in a book I co-authored (Algebra: Themes, Tools, Concepts, following lesson 5.5). In the Teacher's Edition,… Continue reading I’ve Got a Problem!

## Geometry of the Parabola

Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the… Continue reading Geometry of the Parabola

## Summer Workshops, 2015

I'll be teaching four workshops this summer, in two new locations: Seattle, and Waltham, MA (which is a half-hour West of Boston.) If you've meant to attend my workshops in the past, but couldn't make it to San Francisco, New York, or DC, perhaps these venues are more convenient for you? There will be no… Continue reading Summer Workshops, 2015