A Double Spiral from David Henderson

March 10, 2019 Daniel Scher 7 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 ››

Elementary Mathematics, Math Software

Find the Secret Number

October 19, 2018 Daniel Scher 2 Comments

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 ››

Educational Technology, Geometry

A Dynamic Approach to Finding Pirate Treasure

September 25, 2018 Daniel Scher 1 Comment

In his 1947 book, One, Two, Three...Infinity, physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle.

Among a pirate's belongings you find the following note: The island where I buried my treasure contains a single palm tree. Find the tree. From the palm tree, … Continue Reading ››

Educational Technology, Geometry, Math Software

The Scaled Maps Problem

August 29, 2018 Daniel Scher Leave a comment

Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other. Believe it or not, you can stick a pin straight through both maps … Continue Reading ››

Algebra, Educational Technology, Elementary Mathematics, Math Software

Adding and Subtracting Integers

July 26, 2018 Scott Steketee Leave a comment

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers. I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››

Educational Technology, Elementary Mathematics, Math Software

Interactive Array Explorations

July 23, 2018 Daniel Scher Leave a comment

Arrays can be enormously helpful tools for helping young learners to visualize multiplication. Early work with arrays also sets the stage for more advanced mathematics, like binomial multiplication. In this blog post, I present several interactive arrays built with Web Sketchpad as part of the Dynamic Number project. The interactive array model below (and … Continue Reading ››

Educational Technology, Elementary Mathematics, Math Software

Fifth Graders Investigate a Mathematical Code

June 19, 2018 Daniel Scher Leave a comment

How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown? For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››

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