Revised Project Description - 2/28/05

School: The Lincoln School
Teacher: Connie Bryan
Audience: Third graders
Project: Understanding Multiplication Concepts

Motivation:
Mrs. Bryan would like a program which would help her students learn multiplication using animated models. Mrs. Bryan uses block arrays as a learning tool in her classroom to demonstrate multiplication as the addition of groups. Arrays are linear collections of unit cubes. Arrays of the same size can be grouped (added) together to represent multiplication (i.e. a collection of 6 arrays which are each 9 units long would represent 6 times 9). The girls in Mrs. Bryan's class seem to react positively to this paradigm, compared to the time they spend memorizing times tables. Sotware which used this visual model could give students individual practice with their multiplication skills, potentially adapting to their specific needs. It could also encourage supplimental skills and intuitions which Mrs. Bryan does not have the time to develop with the entire class.

Facilities:
The class has access to a computer lab outfitted with enough iMacs that each girl can have her own computer. There is a large television on the wall which is set up to display the activity on the teacher's eMac. The screen may be useful for sharing the students customized problems with the entire class, but our program should be intuitive enough to not require a walkthrough from the teacher.

Goals/Ambitions:
This project should provide an experience beyond simple repitious quizing of multiplication tables, advancing a more intuitive understanding of the properties of multiplication.

• The basic segment of the program will be multiplication problems companied by some visual element. There will be difficulty settings and some sort of performance/progress report. Additionally, the girls could create their own problems and take part in the illustration process.
• There should be additional exercises which will apply the topic lending an intuitive introduction to other topics: Prime Numbers, Permutations, and other related topics or challenging concepts. For example, the girls demonstrated some difficulty in understanding that multiplication is commutative (i.e. that 6 * 7 is the same as 7 * 6). So one exercise might show the arrays rotating the 90 degrees between X*Y and Y*X.
• We must also keep our audience in mind. While we hope our end product will be useful to a wider variety of students, we are tailoring it to the demands of a specific classroom of third grade girls. As such, there should be some investigation (i.e. additional reading) regarding the differences in the early math education of young girls and boys.

Tentative Schedule:
We shall have (but not be limited to) scheduled weekly meetings every Friday for general discussion and assessment.

Week of	Goal
March 7&14	Further meetings with students and teacher
March 21	Storyboards
March 28	Concrete Project Design
April 4	Prototype Completion
April 11&18	On-site Testing & Revising
April 18	Project Completion and Evaluation