Tag Archives: Use Appropriate Tools Strategically

Educational Technology, Geometry, Math Software

Digging Deep Into Varignon’s Theorem

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In the interactive websketch below (and here on its own page), ABCD is an arbitrary quadrilateral whose midpoints form quadrilateral EFGH. Drag any vertex of ABCD. What do you notice about EFGH? The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics educator Chris Pritchard … Continue Reading ››
Conferences, Educational Technology, Geometry, Math Software

Function Dances at NCTM

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At the 2017 NCTM Annual Meeting I was invited to do a short Wednesday-afternoon presentation on Function Dances in the NCTM Networking Lounge. (Here's the handout from the presentation.) The idea of function dances is to get students (or in this case teachers) moving around, acting as the independent and dependent … Continue Reading ››
Educational Technology, Geometry, Math Software

Revisiting the Isosceles Triangle Challenge

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In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››
Educational Technology, Geometry, Math Software, Uncategorized

A Geometry Challenge from Japan

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Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square? I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››
Educational Technology, Geometry, Math Software

Pythagoras Plugged In

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If there were an award for 'Mathematical Theorem Most Amenable to a Visual Proof,'  the Pythagorean Theorem would surely win. The title of this post is a nod to the Sketchpad activity module Pythagoras Plugged In by Dan Bennett. Dan's book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more:  The Pythagorean … Continue Reading ››
Conferences, Educational Technology, Geometric Functions, Math Software

International Congress for Mathematics Education Part 2

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I began this post on Friday night in Hamburg Germany, near the end of ICME, the quadrennial international math-education conference that's been both exhilarating and exhausting. I’m now finishing it on the airplane headed back home. ICME-paper As interesting as many of the presentations have been, they've also been … Continue Reading ››
Advanced Mathematics, Educational Technology, Math Software

A Mathematical Mystery Story with Web Sketchpad

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Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the article* where … Continue Reading ››
Educational Technology, Geometry, Math Software

Putting the Power of a Point Theorem to Work

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The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points … Continue Reading ››
Educational Technology, Geometry, Math Software

Tailoring Tools to the Task

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In years past, my colleagues and I at Key Curriculum conducted Sketchpad professional development workshops for teachers. One of our favorite activities challenged participants to  construct a rhombus in as many different ways as possible. This assignment invariably led to great discussions because there are a multitude of ways to build a rhombus, and each method highlights its … Continue Reading ››
Educational Technology, Geometry, Math Software

Creating Mosaics Inspired by a Pattern from Sultan Ahmed Mosque

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Mirek Majewski was born in Poland and studied mathematics at the Nicholas Copernicus University in Poland with an M.S. and Ph.D. in non-classical geometries. He is a professor of mathematics and computer science at several universities – PNG University of Technology, Inter-University of Macau (now Saint Joseph University), Zayed University in United Arab Emirates, and New York … Continue Reading ››