Sketchpad Activities for Young Learners: Grades 3-5*
Michigan State University
Over the past decade, The Geometer's Sketchpad has had tremendous impact on secondary school classrooms around the globe. Recognising its potential for impacting mathematics learning and teaching in the earlier grades, the NCTM explicitly recommends Dynamic Geometry technology in Grades 3-5. Innovative elementary school teachers have already started exploring the exciting possibilities that open up through the use of this technology.
This collection of activities for grades 3-5 offers examples of the ways in which Sketchpad can be used productively across the range of mathematical subject areas in the elementary curriculum. In addition to geometry activities, there are many activities that touch on various parts of the Measurement, Algebra, and Number & Operations content standards of the NCTM Standards.
In the NCTM Standards, the process standards are taken to be as important as the content standards, yet they are often sacrificed in the classroom. In contrast, in addition to representing the range of content standards, this collection of activities for young learners also offers examples across the process standards, focusing particularly on Problem solving, Reasoning & Proof, and Communication. For example, in the Lulu activity, students learn to communicate mathematics through Sketchpad's interface using the language of coordinate geometry by solving problems involving movement on a coordinate grid. In the Balance activity, students use mathematical reasoning in order to determine the relative weights of different shapes, and so explore the use and effectiveness of various problem-solving strategies.
This collection of activities is meant for teachers who have never before used Sketchpad, and who are interested in learning about the many ways they can use Sketchpad in their classrooms effectively, to help their students develop deep understandings of mathematical concepts. Many of the activities include pre-authored sketches, which require very little Sketchpad background; they can be used in the classroom immediately and productively. That said, of the teachers who have use Sketchpad in their own classrooms, most agree that some of the richest and effective activities involve students creating their own designs and models from scratch--starting with blank rather than pre-authored sketches. While such activities require more Sketchpad skills, they also give students the opportunity to express their mathematical understandings in personally meaningful ways. In order to give teachers a glimpse of this potential, the collection includes three such activities. For example, a transformation activity involves students using rotation and reflection to create an attractive Making a Kaleidoscope. In another activity, Similarity, students create their own logos using Sketchpad's custom tools functionality, logos that can be used to explore various mathematical ideas, but that also link students' mathematical activity to their more personal interests.
Each of the activities included in the collection has been tested with students in grades 3-5, and refined to suit the physical, social, and intellectual needs of young learners. Most of the activities have also been tested by elementary school teachers. Each activity includes Teacher Notes to help you use the sketches effectively in your classroom. These notes suggest ways of introducing the activities, offer prompts that can help you probe your students' thinking, and provide strategies to help you develop your students' mathematical understanding.
In February 2003, a group of some 40 educators convened at the University of Chicago for a two-day conference on Dynamic Visualization for Young Learners: Sketchpad in Grades 3-8. Classroom teachers, Dynamic Geometry software and curriculum authors and researchers, and representatives of several NSF reform elementary curriculum projects gathered to discuss how Sketchpad could be used in elementary and middle school mathematics classrooms. Many of these people, from across the country and around the globe, have contributed to the creation of this collection: Piet Human from South Africa, Spario Soon from Singapore, and Judy Dussiaume from Canada, as well as Daniel Scher (New York), Jeff Barrett (Illinois), Steven Chanan (California), and Nicholas Jackiw (California). I am especially grateful to Steven Chanan for helping to make all the activity notes more readable and informative, and for helping to make all the sketches consistent, attractive, and easy-to-use. I am also grateful to Nicholas, the creator of Sketchpad, who helped solve many sketch design problems, and who has inspired the kinds of activities that can mathematically motivate young learners.
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*Portions of the work described here were funded under National Science Foundation grant ESI 02-43196. Opinions expressed here are those of the authors and not necessarily those of the foundation.