The Math Education Blog
For the past month, I’ve focused this blog on the role that computers can play in assessing students’ mathematical knowledge. I’ve presented three Web Sketchpad-based examples of assessment with mathematical topics ranging from isosceles triangles, to the Pythagorean Theorem, to the slopes of perpendicular lines. Throughout, I’ve tried to show that the introduction of the computer...
Today there is no lack of outrage directed at the high-stakes standardized testing that has become so prevalent in the U.S. educational system. A recent opinion piece in The New York Times examines the backlash against the Common Core and lays the blame not on the standards themselves, but rather on the rise in testing that has accompanied their...
In my previous post, I shared Dan Meyer’s analysis of what’s wrong with computer-based mathematics assessments. Dan focuses his critique on the Khan Academy’s eighth-grade online mathematics course, identifying 74% of its assessment questions as focusing on numerical answers or multiple-choice items. This is a far cry from the constructing, analyzing, and arguing tasks advocated by the Smarter...
Several weeks ago, Dan Meyer described his experience of completing 88 practice sets in Khan Academy’s eighth-grade online mathematics course. His goal was to document the types of evidence the Khan Academy asked students to produce of their mathematical understanding. Dan’s findings were disappointing: He concludes that 74% of the Khan Academy’s eighth-grade questions were either multiple choice or required nothing more than a numerical response. By contrast, Dan...
This week, I’m going to describe one of my favorite activities for introducing young learners to multiplication and factors. It comes from Nathalie Sinclair, a professor of mathematics education at Simon Fraser University. In the interactive Web Sketchpad model below (and here), press Jump Along to watch the bunny take 2 jumps of 4 along...
Michael de Villiers teaches courses in mathematics and mathematics education at University of KwaZulu-Natal in South Africa. His website features a wealth of Dynamic Geometry-related books, articles, and sketches. He is the author of the Sketchpad activity module Rethinking Proof with The Geometer’s Sketchpad. This blog post is a condensed version of a longer article, “Conjecturing, Refuting and Proving...
The 17th-century Dutch mathematician Frans van Schooten developed “hands-on manipulatives” centuries before the term became popular in math education circles. Below are two images of ellipse-drawing linkages from van Schooten’s manuscript, Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus (A Treatise on Devices for Drawing Conic Sections). Building physical models of these devices isn’t hard....
As readers of this blog can probably tell, I like puzzles. I especially enjoy taking ordinary mathematical topics that might not seem puzzle worthy and finding ways to inject some challenge, excitement, and mystery into them. This week, I set my sights on isosceles triangles. It’s common to encounter isosceles triangles as supporting players in geometric proofs,...
When it comes to simultaneous equations, I like to push the bounds of conventional pedagogical wisdom. In an earlier post, I offered a puzzle in which elementary-age students solve for four unknowns given eight equations. Now, I’d like to present a puzzle that might sound even more audacious: Solving for ten unknowns. Oh, and did I mention that the unknowns are...
The study of multiples and factors is ripe with opportunities to engage students in intriguing mathematical puzzles. In prior posts (When Factoring Gets Personal, and Open the Safe), I’ve given some examples of what can be done. Now I’d like to introduce you to another puzzle of mine called Mystery Number that focuses on multiples. Here’s how the Web Sketchpad...