Advanced Mathematics, Educational Technology, Math Software

An Interactive Approach to Finding nth Roots

September 25, 2019 Daniel Scher Leave a comment

When students find the nth roots of a complex number, they use de Moivre's Theorem and a fair bit of calculation and trigonometry. In this blog post, I'm going to approach the topic from a more visual perspective and make use of the following geometric way to think about complex number multiplication: To multiply two complex … Continue Reading ››

Educational Technology, Elementary Mathematics, Math Software

Beam of Light

September 3, 2019 Daniel Scher Leave a comment

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

August 6, 2019 Daniel Scher Leave a comment

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

June 19, 2019 Daniel Scher 1 Comment

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

May 28, 2019 Daniel Scher Leave a comment

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 ››

Geometry, Math Software

Circle Tracer Challenges

April 18, 2019 Daniel Scher Leave a comment

Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.

On page 1 of the websketch below (and here), begin by asking students to drag point … Continue Reading ››

Educational Technology, Geometry

A Double Spiral from David Henderson

March 10, 2019 Daniel Scher 8 Comments

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 ››

Algebra, Geometry

The Perimeter Problem

February 7, 2019 Daniel Scher 4 Comments

When the Metamorphosis team of content coaches meet at their New York office, the day is filled with Qi Gong, video case analysis, good food, and—best of all—a mathematical challenge for everyone to investigate and discuss. These problems are chosen to be accessible across a wide range of grade levels and to allow for a variety … Continue Reading ››

Educational Technology, Math Software

What’s New with Web Sketchpad in 2019

January 2, 2019 Daniel Scher Leave a comment

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

November 12, 2018 Scott Steketee 4 Comments

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 ››

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