They can write their own mathematical compositions. With Sketchpad, as with a word processor, students can start with a blank screen and combine the software’s basic objects to assemble, manipulate, review, share, and revise a complex creation. Even as I agreed with Wolfram’s analogy, I couldn’t help but think of another analogy that is, I think, both more accessible to students and more closely related to their math class: Dynamic geometry construction is to mathematics as composition is to English.

A few students (predominantly boys) take to it enthusiastically, but others find it too solitary, too impersonal, or too difficult, and most students have neither inclination nor opportunity to undertake interesting and satisfying projects. The Logo program here, for instance, uses a recursive procedure called inspi to define the on-screen path of an imaginary turtle.īut programming isn’t available-or of interest-to many of our students. It has explicit built-in support for conceptual abstraction ( procedures and functions) and mathematical iteration ( while and for loops as well as recursive procedures). It’s profoundly logical in nature, resting on a well-defined set of rules and the combining of elements in carefully thought-out ways to build up more and more complex structures on the way to a finished program. Programming is an excellent vehicle for mathematical activities. Recursive Logo program and sample output (see note below) I wanted students to take pride in the logical process of doing a project, and joy in having created something new and useful and even beautiful. Creativity was a major objective when I taught AP Computer Science. Mathematics should be to them more than received wisdom it should be a creative process. Wolfram is on the right track-to deeply understand and appreciate mathematics, students should not only read mathematics, but write it as well. By composing their own stories, poems, and essays, students come to appreciate the beauty of a well-crafted sentence, the emotional impact of alliteration, the convincing nature of a closely-reasoned argument. In English class, students read books, poems, short stories, essays, and articles-but to gain a deep appreciation for literature, they must write as well. I’ve taught programming and written a lot of Sketchpad code, and I appreciate Wolfram’s analogy. NOTE: A basic understanding of the mathematical terminology and concepts prior to using Geometer’s Sketchpad is essential in order to properly follow and understand the commands used in the program.In a recent blog post, Karen Coe referred to Conrad Wolfram’s opinion that programming is to mathematics what composition is to English. This will help educators determine the level students are performing at.

However, it is recommended that educators guide students through the first couple of lessons in each chapter to perform diagnostic testing of the material and the recollection of Geometer’s Sketchpad commands previously taught. Prior to examining each lesson, it is imperative to note that educators may use both teacher-direct and student-direct approaches to using Geometer’s Sketchpad. Along with mathematical terminology and concepts, students will gain a solid understanding of the various commands and functions within the Geometer’s Sketchpad program.

The different geometric concepts that are investigated in this compilation include: Points, Lines and Angles, Triangles, Ratio and Proportion, Transformations, Symmetry, Area, and Volume. The specific and overall expectations for grades seven and eight will be sufficiently met throughout the various chapters in this GSP package.

Each lesson is specifically tailored to meet the Ontario Curriculum guidelines. This compilation of lessons for grades seven and eight will aid intermediate educators in teaching the mathematics unit, Geometry and Spatial Sense. Geometer’s Sketchpad is a computer application designed to integrate mathematics with technology to produce visual representations of math created by the students.

Online math sketchpad