Educational Technology, Elementary Mathematics, Math Software

Beam of Light

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This month's post is based on a problem that appears in Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American. Below (and here) is a Web Sketchpad model of an orderly forest. There is a tree at every point whose x- and y-coordinates are both integers. These are the green points. You … Continue Reading ››
Educational Technology, Geometry, Math Software

Catching Up with New Web Sketchpad Functionality

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This past January, we introduced the Web Sketchpad Tool Library and  Viewer. The Tool Library is a collection of over 60 mathematical tools for customizing a Web Sketchpad model, making it possible for teachers to decide which tools students have available to them on an activity-by-activity basis. The Viewer is a site … Continue Reading ››
Conic Sections, Educational Technology, Math Software

The Folded Circle Construction

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Of all the conic section construction techniques, my favorite is undoubtedly the approach that requires nothing more than a paper circle. Here's what to do: Draw or print a circle and its center, point A, on a sheet of paper. Cut out the circle. Mark a random point B anywhere on the circle. Then, fold … Continue Reading ››
Educational Technology, Elementary Mathematics, Math Software

Dividing and Subdividing

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Given a strip of paper, how might you divide it into fourths without using a ruler?  Undoubtedly, you'd fold the strip in half and then in half again to locate the quarter marks. Now suppose that your goal is to divide a strip into sixths. You might start by folding the strip into thirds and … Continue Reading ››
Educational Technology, Geometry

A Double Spiral from David Henderson

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David Henderson, one of my two Cornell master's thesis advisors, died this past December. I wrote about David in a prior post, and in particular, his approach of asking us  to grapple with a small number of  rich problems, allowing us  to find our own, often non-traditional, … Continue Reading ››
Educational Technology, Math Software

What’s New with Web Sketchpad in 2019

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For the past five years, Scott and I have featured interactive Web Sketchpad models in nearly all our Sine of the Times blog posts.  As much fun as it's been to build "websketches" to share with you, we've really wanted to put the creative power of Web Sketchpad into your hands. And now, finally, that's possible. Today … Continue Reading ››
Educational Technology, Elementary Mathematics, Math Software

Multiplication Is Not Repeated Addition

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On the NCTM discussion site myNCTM, there's currently an extended discussion about "Division and multiplication of fractions." As the discussion has continued, I've grown concerned with what I see as a fundamental problem with the way we often introduce multiplication as repeated addition: "Multiplying 4 by 5 means we're combining five groups of four items. … Continue Reading ››
Elementary Mathematics, Math Software

Find the Secret Number

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We created the Web Sketchpad game below (and here)  as part of our Dynamic Number project. It challenges elementary-age students to uncover the value of a secret number by collecting and analyzing clues that narrow its range of possible values. The game familiarizes students with inequality signs, introduces the use of x to … Continue Reading ››

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