Activity Math Using Manipulative in the Classroom

A Proposal for a Thesis presented to The Faculty of the Department of Computer and Information Science, Brooklyn College

in Partial Fulfillment of the Requirement for the Degree Master of Science

by

Elkayal, Ali

Spring, 2003

Abstract

This thesis will address the problem of teaching Math to children in the elementary level.  Enhancing the mathematical understanding by students may be done by using traditional manipulative, or by using computer applications. I assume that computer applications will be helpful for children while they are learning their first mathematical lessons.

Introduction

Our vision of a high-quality mathematics education for every child demands that we find approaches for improving the mathematics content knowledge and pedagogy of all teachers, especially elementary school teachers.

Mathematical learning has many aspects, in the past, children's school mathematics experience was often dedicated by the content of standardized tests, and was largely based on memory of computational skills, vocabulary, formulas, etc.  however our modern world presents new challenges-complex problems requiring new and creative solutions. 

The use of manipulative to explore problems and represent mathematical ideas became very important, with many mathematicians who decided to favor it.

Anne implied that "the use of manipulative enhances concept formation when both the concrete and connecting stages are fully understood before moving to the abstract.  this fully understood before moving to the abstract.  their way of instructing students promotes understanding of the why as well as the how of mathematics". (Bloomer p21)

Furthermore; the use of computer educational software became widely accepted by many mathematic teachers to make the mathematical problem exploring more affordable and easy to view by many of students, in the elementary level.  There are many software programmers and many interactive applications dedicated to this goal.

Many mathematic teaching software are offered by non profit organizations or individuals.  most of the applications are offered for free.  the result teachers may gain from implementing them at classrooms has always been very promising.

Here is a list for some applications.  Files are either Java appletes, or Exe formats.

• www.arcytech.org A site that shows many applets you can use to teach math to children.

• www.math.utah.edu/~alfeld/math/polyhedra/polyhedra.html A site on regular, 3-dimensional polyhedra.

• http://info.lboro.ac.uk/departments/ma/gallery/hyper/index.html A site that shows a rotating 4-dimensional hypercube.

• http://www.math.bcit.ca/faculty/hiob/mathonweb/help/backgd3.htm Gauss - Jordan Elimination Program.  Purpose:  This program is useful for illustrating the Gauss - Jordan elimination method of solving a system of linear equations. It allows the user to focus on the method and not get bogged down by the arithmetic. It is also useful for:

  http://www.math.bcit.ca/faculty/hiob/mathonweb/alg_coach.htm The Algebra Coach In this program the user types in a mathematical expression or equation. In the case of an expression, the program shows step-by-step how to simplify it. In the case of an equation, the program shows step-by-step how to solve it. The output can be pasted into a word processor. Click here for more details.

The impact of using manipulative and software applications in classroom are very important to our new generations

It's time to make changes. Excellence in mathematics teaching and learning cannot wait. If we are to develop flexible and resourceful problem solvers for the future, we must eliminate the mathematics of exclusion in which only a few students gain access to the best we can offer. We must staff our classrooms at every grade level with well-prepared, knowledgeable mathematics teachers right now. And we must teach in ways that develop successful learners of mathematics. Our children deserve it.

Proposed approach

A software application to present different attractive ways of dealing with Cuisenaire rods will be created and tested.

There are many advantages related to the use of Cuisenaire rods.

Cuisenaire rods are an attractive and versatile tool for developing mathematical thinking.  in primary grades, rods are often used to develop the interpretation of addition as putting lengths together, leading eventually to understanding of the number line as a model for arithmetic.  in upper grades, they are useful as a model for fractions.  at all levels they are helpful in learning about metric units of length, area and volume, because the square base measures 1 cm on a side.  finally, they invite play, which is likely to involve spatial concepts.

the lengths are color-coded, and students who will work extensively with rods should learn this code.  note that the code corresponds to the first letter of most colors (white, red, light green, purple, yellow, dark green, orange), but for the 3 colors beginning with 'b', the last letters are used (brown, black, blue).  a nice challenge might be to have students figure out why the code is formed in this way.  some teachers have students memorize the number equivalents of the colors, however, others feel that this practice reduces the potential of the rods for later work with fractions and algebraic concepts.

During the 1950s, Americans continued to adopt teaching apparatus developed overseas. Emile-Georges Cuisenaire (1891-1976), a Belgian schoolteacher, developed a colorful set of rods for teaching students basic properties of numbers and rules of arithmetic. Cuisenaire published an account of his rods in French in 1953 and attracted the attention of Egyptian-born educator Caleb Gattegno (1910-1988). 

Cuisenaire and Gattegno soon published an account of the rods in English. The rods came to be used in the United States and in many other countries.

 This set was used by an American teacher in the South Pacific.

( see appendix A )

The Project Phases

The work will be completed in four phases, which will overlap with each other, I'll create the software application, and make it a part of the project, to test the impact of using software application in mathematical teaching.

The focus throughout this entire project will be to discover the features that are significant or meaningful during using different mathematical teaching approaches and finding ways to make them more effective using computer application.

Phase I – Investigation and Task Analysis

During the first stage, a Public School will Be chosen as site to do our research.  Interviews will be hold with many of the math staff and also with the school consultants.  The research project will be using two groups of candidates.  The 1st group will be the control group, is a group of students who are receiving traditional educating course in mathematics, they are also using manipulative as a part of their class.  The 2nd group is a group of students who will be receiving mathematic education, using computer applications as a basic part of their study.  The Selection of  the most suitable candidates for this project will be done during this phase.

Phase II – Software Creation

This second phase, consists of processing and analyzing the data that was collected from the data collection.  There are essentially four ways to do this: visualization, filtering, segmentation, and automatic recognition.  The visualization, which will involve watching and picking out the significant features by eye. 

The filtering will consist of running a series of algorithms on the data to make it more usable and expose its underlying structure

The automatic recognition task will involve the implementation of a real-time improvement detection system.

Progress in this phase will be driven by the need for investigating every improvement during the ongoing process, for the etudes; I plan to pick one feature at a time, do an analysis of it, and then go on to write an etude for it. 

The final deliverables from this phase will be a chapter in the dissertation in which I focus on a few data segments and compare the success of different methods along various axes. 

Phase III – Testing

This phase, while it may requiring much time, it may be the crucial piece of all this work.  During this phase I will be using  my software in teaching many of the students (the 1st group) mathematical thinking, and methods to find solutions to mathematical problems, while the 2nd group of students will be learning mathematical thinking using traditional approach.  This will be my opportunity to decide how important software applications are, afterward during the Analysis Phase. 

Also, which approach of the two approaches is more useful and practical to implement.  More explicitly, I hope to use this phase to identify the most significant time-varying features in the set of methods that I’ve analyzed. 

As part of this work, it might be good to:

• Interview teachers
• Modify the original software and build a new features to responding to the performance improvements, of group (the candidates in the 1st group are using software applications, they may demand certain features to be added to the software).

Phase IV – Analysis

This phase is the main output of the whole project; it will be the final result of all the work leading up to it.  It will consist of the testing of the students and analyzing the result.  testing will be taking place to basically two kinds of students.

1) Students who were receiving traditional mathematical course.

2) Students who were using computer applications as a part of their mathematical course.

Expected Results

The results of this thesis project will be presented in the form of full detailed results, to best mathematical thinking improvement technique, for elementary school students.  During and after the project, math software application to represent the idea of using Cuisenaire rods thinking strategies, will be created, modified, and used.

Time-Line

February 2003

•  submit a thesis proposal
•  Start Phase 1
•  Begin working on finding the best Public School and conduct series of meetings with district consultants and obtain all the necessary approvals

March 2003

• Start meeting with, and interviewing the public school consultants, and math teachers.
• Conduct a series of interviews with a many of students in the age 6-8, to determine their acceptance, and enthusiasm to anticipate in the project.
• Start the creation of the software.

April 2003

•  Demonstrate a second round of results to Prof. Lori Scarlatos
•  Finish the creation of the software application

May 2003

•  Continue the research project at the public school
•  Finish any further modifications to the software application

June 2003

•  Begin Phase 3 (Testing)
• Continue with Phase 2(Software Modification)

July 2003

•  finish Phase 3
•  Demonstrate second round of results to Prof. Lori Scarlatos
• If the work was approved by My Thesis Advisor, there will be a starting date for Phase 4 (Final Analysis)

August 2003

• Beginning to work on phase 4
• Demonstrate another round of results to Prof. Lori Scarlatos
• If Phase 4 was properly completed, and approved by the Thesis Advisor, there will be final round of analysis.
•  Proper Documentation of the Analysis results
•  Begin dissertation
•  Thesis defense