Tag Archives: Geometry

Educational Technology, Geometry, Math Software

The Varied Paths to Constructing a Rhombus

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In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral. While the rhombus task works … 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 ››
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, Elementary Mathematics, Geometry, Math Software

Exploring Tessellations with Web Sketchpad

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Metamorphosis is a New York-based company that offers professional content coaching to transform the mindset and practice of both teachers and administrators. I recently had the pleasure to collaborate with Metamorphosis staff members Toni Cameron and Kara Levin as well as mathematics coach Ariel Dlugasch from P.S. 276 in a coaching learning community that … Continue Reading ››
Assessment, Educational Technology, Geometric Functions, Geometry, Math Software

Dilation Games: Assessment That’s Fun

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What does dilation feel like? I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what I call geometric functions). I got lots of good ideas for improving the activities not only by watching the students, but also but also from their suggestions and the … Continue Reading ››
Conic Sections, Educational Technology, Math Software

Constructing an Ellipse with Web Sketchpad Tools

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In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … Continue Reading ››
Educational Technology, Geometry, Math Software

Hello Spring!

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Today's blog post features a sketch from Anna Nguyen, who's a 9th grade student. Anna observes, "Math is one of my favorite subjects. I'm not a genius or the smartest in my class, but I do enjoy dealing with letters and numbers, which is also why I like chemistry. I think GSP is the most … Continue Reading ››
Educational Technology, Geometry, Math Software

Constructing Morley Triangles

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By Adrienne Barrett This post is by guest blogger Adrienne Barrett, who's a senior mathematics and education dual major at Rowan University. She is currently student teaching and upon graduation in May, she hopes to find a full-time position teaching high-school mathematics. She's always loved math, and studying it in college has given her … Continue Reading ››
Assessment, Educational Technology, Math Software

Innovative Approaches to Computer-Based Assessment, Part Three

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Today there is no lack of outrage directed at the high-stakes standardized testing that has become so prevalent in the U.S. educational system. A recent opinion piece in The New York Times examines the backlash against the Common Core and lays the blame not on the standards themselves, but rather on … Continue Reading ››