The Math Education Blog
One of the aspects I like best about Dynamic Geometry software like Web Sketchpad is its ability to illustrate concepts that cannot effectively be represented with static media. Take, for example, a number line that we draw on a white board. Showing the number line labeled with integers is easy. Adding tenth-mark divisions to the...
With Web Sketchpad, it’s easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics. My goal was to design a lesson focusing on the triangle area formula, A = bh/2. In particular,...
In my prior posts ( When Factoring Gets Personal, Open the Safe, and Reasoning with Multiples to Find the Mystery Number), I’ve given examples of how learning about multiples and factors can be made more engaging through the use of puzzles. Now, to add to this collection, is the lock puzzle below (and here). The first page of...
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, among others) to develop a habits of mind approach...
This Thursday, Scott Steketee and I will be presenting two sessions at the NCTM 2015 Annual Meting in Boston: Functions as Dances: Experience Variation and Relative Rate of Change Session 52 on Thursday, April 16, 2015: 8:00 AM-9:15 AM in 157 B/C (BCEC) How better to explore rate of change than as independent and dependent...
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...
In my prior blog posts, I’ve described how to construct ellipses using linkages, concentric circles, congruent triangles, and tangent circles. These are all great methods, but I think I got ahead of myself: There’s a simple ellipse construction technique described in nearly every precalculus book that I’ve bypassed in my excitement to show you the more exotic approaches. Say hello to...
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 Everyday Mathematics isosceles triangle investigation that...
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...