# Tag Archives: Problem Solving

# Constructing Equal-Area Triangles

The origins of this week's Web Sketchpad model date back to the Connected Geometry curriculum from the mid 1990s. I was one of the co-authors of the curriculum, working at Education Development Center with a wonderful team of math educators (Al Cuoco, Paul Goldenberg, and June Mark, … Continue Reading ››

# Solving Simultaneous Equations with Common Sense

Simultaneous equations belong in elementary-school mathematics curricula. That's been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity.
When I say that elementary-age students should encounter simultaneous equations, I don't mean that they should be instructed in the standard algebraic procedure for solving pairs of equations … Continue Reading ››

# Pi Day 2015: Pieces of Pi

For this year’s Pi Day post, I thought I’d continue our Web Sketchpad (WSP) construction theme. But rather than adapting the visualizations from last year’s Pi Day post to the new construction capabilities, I decided to take a different approach. Some time ago, I built a set of custom tools for … Continue Reading ››

# WCYDWT: A Ball, a Trash Can, and Web Sketchpad

Dan Meyer has posted a number of "What Can You Do With This?" activities on his blog. (Activities is probably too prescriptive a word; they're more in the nature of prompts for student thinking, noticing, and wondering.) One of the first was the image below, which he made by superimposing frames from a … Continue Reading ››

# Moving Beyond Formulas When Investigating Triangle Area

For the past year, my blogging partner Scott and I have worked with the team of

*Everyday Mathematics*to build interactive Web Sketchpad models for their forthcoming new edition. It's been fun for both of us to find ways to insert dynamic mathematics into their K–6 curriculum. Last year, I shared an*… Continue Reading ››*

# Innovative Approaches to Computer-Based Assessment, Part Four

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 … Continue Reading ››

# Innovative Approaches to Computer-Based Assessment, Part Two

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 … Continue Reading ››

# Refutation in a Dynamic Geometry Context

*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 … Continue Reading ››*

# Isosceles Triangle Puzzles

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, but … Continue Reading ››