Several days ago, I was reminded of an interactive pattern block puzzle that I designed during the pandemic in collaboration with Toni Cameron of Reimagined. It provides an engaging opportunity to promote proportional reasoning in the context of geometry.
On page 1 of the websketch below (and Continue Reading ››
When I taught a geometry methods course at City College last fall, I devoted an entire class to investigating area. We focused on problems where triangles were sheared, transforming into new triangles, but maintaining their area. The two Web Sketchpad activities that follow introduce shearing and present a problem with a surprising result … Continue Reading ››
In the February 1954 issue of Mathematics Teacher, Paul C. Clifford describes an optimization problem from his trigonometry class. Of all isosceles triangles ABC with sides AB and BC of length 12, which one has the maximal area? Clifford told his class that an exact solution to the question required calculus. One student, … Continue Reading ››
In the fall of 2023, I taught a geometry methods course at City College here in New York. While my goal was to make use of Web Sketchpad throughout the semester, I knew that the most effective use of the software required activities that coupled it with hands-on modeling. Two such opportunities arose … Continue Reading ››
How might we help students connect the unit-circle representation of trigonometric functions with the graphs of these same functions? Below (and here) is a Web Sketchpad model that gives students the tools to construct the graphs of trigonometric functions by using the unit circle as the driving engine. To get started, … Continue Reading ››
With nothing but a compass, students can construct a lovely daisy design consisting of seven interlocking circles, all of the same size.
I was delighted to see that the U.S. postal service chose to feature … Continue Reading ››
Eleven years ago, I wrote a post titled What is All the Fuss About Lines? In it, I discussed the difficulties that students encounter when asked to determine the equation of a line. Faced with formulas for calculating slope, the point-slope form of a line, and the slope-intercept form, students lose … Continue Reading ››
What do you get when you cross geometry with the classic murder mystery game Clue? Why, the Mysteries of Polygon Flats, of course!
In my prior post, I offered examples of how Web Sketchpad can help students classify special quadrilaterals like squares, rectangles, kites, parallelograms, … Continue Reading ››
Ah geometry, how you suffer from a lack of attention in the elementary grades! Rare is the curriculum that doesn't stuff geometry into its final chapter, waiting patiently in line behind number and operation.
But the one geometry topic that does command attention is classifying two-dimensional shapes into … Continue Reading ››
While most numbers lead anonymous lives away from the mathematical spotlight, eiπ occupies hallowed ground. Douglas Hofstadter writes that when he first saw the statement eiπ = −1, “. . . perhaps at age 12 or so, it seemed truly magical, almost other-worldly.”
At the risk of deflating the celebrity status of … Continue Reading ››