Sketchpad EndlessPossibilities

7/31/2019 Sketchpad EndlessPossibilities

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In a third-grade classroom in Philadelphia, students construct ractions along a number line. Down thehall, eighth graders build a visual proo o the Pythagorean Theorem. Down the street, twelth gradersinvestigate the Fundamental Theorem o Calculus. What do these Philadelphia students and theirteachers have in common? Like students and teachers in classrooms all over the world, they are usingThe Geometers Sketchpad.

Sketchpads logical, elegant, and simple design makes it a powerul learning technology. From

the very rst day that students use Sketchpad, they can begin doing meaningul mathematics.Sketchpads tools behave in expectedand oten delightulways that enable students to explore andconstruct mathematical models, build connections among mathematical concepts, and communicate

mathematically.

This document demonstrates a ew o the ways in which Sketchpad oers a clear advantage over theopen-source sotware GeoGebra in everything rom mathematical coherence to ease of mathematicalcommunication to support for teachers and students.

Mathematical Coherence

John Dewey observed in the early part o the 20 th century that how an idea is represented is part othe idea, not merely its conveyance. Deweys insight is more relevant today than ever, as sotware and

technology become the means by which we represent mathematics to our students. Sketchpad is the most

widely used math sotware in American high schools not only because o its mathematical power, butalso because its mathematical representations are consistent with all other classroom representations.

Take, or example, this undamental postulate ohigh school geometry: You can construct exactlyone line through any two points. This is certainlythe case in Sketchpad, but what about

in GeoGebra?

In Sketchpad, you construct a line by clickingrst on point A and then point B. I you tried to

use the same points to make another line and youclicked on point B rst, then point A, Sketchpadwould present a single line, with one equation, asshown at let.

ENDLESS POSSIBILITIES WITH

THE GEOMETERS SKETCHPAD

How the Worlds Leading Mathematics

Education Software Surpasses GeoGebra


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In GeoGebra, the line

constructed through point Aand then B is represented asa different linethan the oneconstructed through point B

and then A. Moreover, eacho these lines is representedby a dierent equation.Imagine the conusion andincorrect suppositions that

students will make rom theserepresentations.

This is just one example ohow the open-source sotwares

representation o mathematics can lead students to unsound conclusions. Sketchpads representations

make mathematical sense and are consistent with school curriculum and best practices.

Ease of Mathematical Communication

Sketchpad is a powerul tool or exploring mathematics, and its grounded in pedagogy.Students not only see and interact with the mathematics represented by the sotware, they also make

sense o the explorations by communicating their understanding. As they develop their ability tocommunicate what they have learned, their understanding is deepened and enhanced.

Through its ease o use, Sketchpad acilitates student exploration and discussion. Students immediatelyconnect to the mathematics in Sketchpad because the mathematics on the screen is represented in the

same nomenclature that is used in their classroom and textbook.

Consider the investigation o thesum o the measures o the interior

angles o a triangle. Sketchpad allowsstudents to calculate the sum o theangle measures by clicking directly oneach measure in the sketch. The anglemeasures and the sum are displayed instandard classroom notation, clearlycommunicating the mathematicalresults. Students can easily manipulate

the triangle to reinorce the conceptthat or every triangle, the sum o theinterior angles is equal to 180 degrees.

Endless Possibilities with The Geometers Sketchpad page 2


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To accomplish this same task in GeoGebra, students must enter instructions in a command-lineorm, which means that they must decipher the commands and syntax beore they can engage withthe mathematics. In the example below, GeoGebra assigned the Greek letters d, e, and z or the anglemeasures, and the student used the command-line menu to sum the measures. This example revealsadditional barriers to learning: Not only is the result buried in the list o Dependent Objects in the letpanel, but the calculation that produced the sum is hidden, making this document an ineective tool

or communicating the geometric property it is supposed to illuminate.

Furthermore, manipulating the triangle toreinorce a concept can lead to inconsistentand conusing results in the open-sourcesotware, such as fipping the measuredangles rom interior to refex angles, as

shown at let.

GeoGebras use o Greek letters, reliance

on a command-line interace, hiddencalculations, and unexpected dynamicbehavior distance students rom themathematics and could easily detractrom their ability to synthesize andcommunicate their conclusions.

With Sketchpad, students are not so encumbered. Sketchpad users interact directly with the mathematics.Sketchpads clear representations acilitate student exploration and enable students to communicate their

observations.



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The two screen captures below provide another example o how Sketchpad and the open-source sotwaredier in their approaches to instruction and the development o a mathematical vocabulary.

When a student selects a circle inSketchpad, only those commandsapplicable to a circle are available.This interace supports the students

exploration o mathematical objectsand their properties.

In the open-source sotware, thestudent must search through the ull

list o commands rom the pull-downmenu, including commands that haveno applicability to the circle.

Students exploration should be scaolded in a way that leverages their curiosity yet ocuses their eorton correct suppositions. Sketchpad structures student interaction so that it reinorces correct conceptdevelopment and appropriate use o vocabulary.



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Support for Teachers and Students

Educational curriculum and tools have value only when students are interacting with the materials.Support or Sketchpad users, both teachers and students, includes integrated curriculum, extensiveproessional development oerings, technical support, a dedicated website, and an active user base.This type o support assures regular use o Sketchpad by students and has helped to make Sketchpadthe worlds leading educational mathematics sotware.

To highlight just three o these support services:

The Sketchpad Learning Centerembedded in the sotwareprovides introductory tutorialswith video, tool tips, sample activities, and inormation on how to use Sketchpad in a variety ograde levels and classroom settings.

Sketchpad Professional Development includes ace-to-ace workshops, moderated onlinecourses, and webinars, all o which consistently get outstanding reviews rom Sketchpad users.This type o ongoing support is both mathematically and pedagogically rich and acilitates growth

among teachers as well as their students. Sketchpad LessonLinkis a searchable online library o more than 500 Sketchpad lessons and

activities, aligned to textbooks and standards, or grades 3 to 12. Classroom-ready worksheets,

pre-built sketches, and teaching notes streamline lesson planning. Sketchpad LessonLink acilitatesstudent engagement without requiring teachers to create lessons rom scratch.



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GeoGebras community maintains a wiki where teachers contribute activities and a orum where teacherscan ask or technical support rom other users. The activities on this site are not vetted and can varywidely in quality and usability. Furthermore, GeoGebra lacks curriculum, proessional development, andauthentic technical support. In contrast, Key Curriculum Press, the education company that publishesSketchpad, is dedicated to the development o quality teaching materials and provides integratedcurriculum, ully vetted activities, extensive proessional development, and technical support or

Sketchpad.

Endless Possibilities for Student Growth with Sketchpad

John Dewey believed that good teachers were those who could create genuine intellectual curiosity. Heargued that the methods o such activity were the product o human curiosity, inquiry, and the search ortruth. Thereore, we think the tools our students use should acilitate and encourage this behavior.

Sketchpad grows with students in their mathematical journey because its oundation is built upon

mathematical principles. GeoGebra, because it is an assemblage o representation tools, cannot allowor the depth o inquiry Dewey envisioned. Students can explore their curiosity only to the depth that aspecic tool will represent.

In Sketchpad, students may begin their mathematical journey by constructing a triangle and measuringand summing its angles, move into more complex sketches, such as using the locus denition toconstruct a parabola, and continue their mathematical education by using Sketchpad to explorederivatives o unctions. Through this growth, the consistent and predictable mathematical behavior andthe clear mathematical notation o Sketchpad allow students to ocus on mathematical concepts and

develop their understanding as deeply as their curiosity takes them.


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