The Math Education Blog
Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the article* where I found...
In my recent posts, I’ve introduced interactive models for comparing fractions and multiplying fractions. To continue the fraction theme, below (and here) is a Web Sketchpad model in which the need for equivalent fractions arises naturally through the rules of a game. The model displays two arrays. Dragging the four points changes the arrays’ dimensions. The goal is to drag blue squares into the...
In my previous post, I presented an interactive Web Sketchpad model for visualizing and solving fraction multiplication problems. This week, I’d like to back up a step and focus on the more fundamental skill of visualizing and reasoning about the size of fractions. The fraction game below (and here) presents two random fractions at a time and challenges...
Last week, Scott and I attended a fraction symposium at NYU, and it made me realize how long it’s been since I’ve written about our Sketchpad work with fractions. Below is a Web Sketchpad model for displaying and solving fraction multiplication problems. Representing fraction multiplication with an area model is a common approach, but it’s challenging to sort...
For the past few years, Scott Steketee and I have collaborated with the author team of Everyday Mathematics to integrate Web Sketchpad deeply into their curriculum. As part of that work, I just completed a websketch that nicely mixes practice with logical reasoning. Students are challenged to find a hidden treasure on the coordinate plane by...
Four years ago, my colleague Scott Steketee and I set out to develop an interactive game to help students develop strategies for thinking about and solving multiplication problems. As we examined the existing apps on the market, we discovered that most focused on the drill aspect of learning one’s multiplication facts. We set our goals higher. We...
The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points...
March 2023 UPDATE: If the dilation games below whet your appetite for challenges based on transformations, check out these Reflection and Rotation games as well. What does dilation feel like? I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what I call geometric...
Can mathematical curves be beautiful? Most certainly! Precalculus students glimpse the connection between mathematics and art when they graph roses, cardioids, limaçons, and lemniscates. But these curves give just a taste of the beauty that can be achieved when graphing equations. In a recent article from the online science magazine Quanta, Pradeep Mutalik reviews a gorgeous new math book, Creating Symmetry:...
In a prior blog post, I introduced my new puzzle, Arranging Addends, that mixes arithmetic with logical thinking to create an engaging playground for mathematical discovery. Let’s revisit this puzzle and introduce some new variations. Take a look at the puzzle below (and here), built with Web Sketchpad. Your goal is to arrange the circles...