The Math Education Blog
In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip’s path as you pull the pencil around the taut string. Guaranteeing that the traced path...
Several weeks ago, my friend Martin shared the following probability puzzle with me: Two points are chosen independently and at a random on a stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle? This is a classic problem, dating back...
Did you know that aside from being a source of news, The New York Times is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum editor, Dan...
In my prior post, I presented a “zooming” number line model that allowed students to estimate the location of a point along a number line and then repeatedly magnify that portion of the number line to obtain ever-finer estimates, accurate to tenths, hundredths, thousandths, and beyond. In a sense I got ahead of myself because I...
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...