All posts by Daniel Scher

Daniel Scher, Ph.D., is a senior academic designer at McGraw-Hill Education. He has co-directed two NSF-funded projects: the Dynamic Number project and the Forging Connections project.

The Broken Stick Puzzle

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 to … Continue Reading ››

A Double Dissection from The New York Times

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 … Continue Reading ››

Zooming Integers: Magnifying the Number Line

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 … Continue Reading ››

Exploring Triangle Area with Custom-Built Tools

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, AContinue Reading ››

Constructing Equal-Area Triangles

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, … Continue Reading ››

Reflecting on the Annual NCTM Meeting

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 … Continue Reading ››

Solving Simultaneous Equations with Common Sense

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 equations … Continue Reading ››