The Math Education Blog
Function machines have long been a fixture of elementary and middle-school mathematics. Typically, the teacher enters an expression into a machine (for example f(x) = 3x + 2), hides the expression, and then runs the machine with a variety of inputs, with each yielding a single output. By examining the input-output pairs, students determine the...
Can it be only six months that I’ve been coding with Claude? In that short time, I’ve built 20+ apps, most of which you’ll find here. It began with a single app, Herding Sheep, that I described in a post back in March. I thought that my foray into A.I. coding would be brief, but...
Several weeks ago, I saw an online post from Matt Henderson describing a fractal construction that was new to me. Here is how to generate it: Start with a hexagon and a random point A inside it. Pick a side of the hexagon at random (for example, side GH below) and construct ∆AGH. Continue by...
This is hard to say, but I feel so…unfaithful. For 35 years, Sketchpad has been my tool of choice for designing interactive mathematical models. I’ve toyed with learning programming languages like Python, p5.js, and Snap, but a lack of motivation always got in my way. Why, I thought, spend months developing new coding skills when...
The websketch below (and here) provides tools to build six different pattern block shapes. To add a new pattern block to your design, tap its icon. A preview of the pattern block appears with one vertex glowing. Tap to place the pattern block in your design. You can then drag the pattern block wherever you...
For some time now, Scott and I have been thinking about how we might create a Web Sketchpad model of an open number line that could offer functionality not found in the typical hand-drawn variety. We’re finally ready to share our work. Below [and here] is our Web Sketchpad open number line. This video explains...
Great news statistics fans: A version 3 beta of the Common Online Data Analysis Platform (CODAP) is now available. To quote the CODAP website, “[The new CODAP] is a powerhouse under the hood, handling much larger datasets, drawing graphs and maps faster, animating more smoothly, and responding instantly.” CODAP is the successor to Fathom, both...
In my numerous blog posts about Exploring Conic Sections with The Geometer’s Sketchpad, I’ve featured an assortment of hands-on and virtual models for drawing conic sections, ranging from pins and string to paper folding to 17th-century linkages. But in order for students to understand why any of these approaches work, they must first grapple with...
In this lesson, one of my favorites from Exploring Algebra 1 with The Geometer’s Sketchpad, students model expressions with dynamic algebra tiles, using the areas of the tiles to see the equivalence of expressions in factored and expanded form. Down below (and here) is a Web Sketchpad model of algebra tiles. To model (x +...
Welcome to Algebra Mazes, my new early algebra puzzle that shares DNA with my earlier creation, Sneaky Sums. Both Algebra Mazes and Sneaky Sums puzzles present you with a grid of shapes. Each shape represents a secret numerical value for you to deduce. Whereas Sneaky Sums puzzles were generated randomly, Algebra Mazes are handcrafted and...