Description:

Co-Principal Investigator: Paul Horwitz, Educational Network Services

Purpose: The purpose of this project is to develop and evaluate the promise of a software system, MathemAntics, designed to present a supplementary mathematics curriculum for children ranging from preschool to Grade 3. This software system will focus on a number of topics ranging from basic ideas about cardinal numbers to negative integers. A single system that covers such a broad range of topics has the advantage of a consistent look, feel, and use so that students need not become acquainted with a new system each time they advance to a new topic. The software system is intended to be an attractive, enjoyable yet challenging virtual world where children will receive mathematics instruction. Graphical tools will allow students to operate virtual objects in ways not possible with physical manipulatives and an avatar will provide instruction, feedback, and support. Additionally, a powerful information processing capability will provide assessment data to teachers.

Project Activities: The project will include the development of a software system, a formative evaluation of student use of the system, and a survey of teacher attitudes toward and use of the system. The development process will proceed iteratively and findings from the formative evaluation and survey will inform the refinement and further development of the system and supporting materials. Additionally, there will be a small pilot study to test whether student achievement improves with use of the system.

Products: The products of this project will include a fully developed software system, MathemAntics, a set of preliminary data about the promise of this intervention to improve student mathematics achievement, and published articles.

Structured Abstract

Setting: The software system will be developed at Teachers College, Columbia University. The field-testing, formative evaluation, and pilot achievement study will be conducted in local elementary schools in New York City.

Population: The participants include students in preschool through Grade 3, most of whom are African American and Latino students from low socioeconomic backgrounds.

Intervention: The intervention will be a game-like, whimsical computer environment where mathematical activities (e.g., counting, addition) can be performed. The activities will be presented to the students as games. The intervention will have three major components: a special world consisting of posichicks and negacylces (allowing for the representation of positive and negative numbers); various mathematical tools (e.g., boxes for grouping numbers, number lines, virtual manipulatives); and formal mathematical symbols (e.g., standard algorithms). Additionally, an avatar (e.g., an animated fairy godmother in the Kindergarten version) will provide real-time instruction, assistance, and feedback to the student, both visually and auditorily. As children work through each game, the computer will keep track of how well they are doing and will use this information to update their individual learning profiles as well as to make real time decisions regarding level changes within a game or promotions to more complex games in a sequence. The system will allow for both individual and small group use, and teachers will receive assessment data from the system. This data will include (but not be limited to)information regarding accuracy of student responses and various strategies (including erroneous ones) that were used in problem solving. This information will enable teachers to track their students' progress and to fine-tune the game sequence for each child.

Control Condition: In order to equate the time spent using software, the control students will spend an equivalent amount of time interacting with a reading software intervention in addition to their standard instruction in mathematics. This would equate the amount of exposure to software in general while varying the amount of exposure to the math content.

Research Design and Method: The development of the software will follow an iterative design, where the results of the Year 1 formative evaluation will inform the redesign carried out in Year 2. The pilot study in Year 3 will employ a between-subjects design where students assigned to the treatment will receive the to-be-designed intervention and students assigned to the control condition will receive a software intervention for reading. This will hold constant student exposure to software and time spent in instruction and practice, but varying the content being taught via the software.

Key Measures: The key measures used during the development of the software system include observational data from video recordings and software records of accuracy and speed. Survey data pertaining to teachers' attitudes toward use of the software will also be collected and analyzed. For the pilot testing of learning (i.e., achievement), the researchers will use the Test of Early Mathematics Ability-3 (TEMA-3) and an experiment-designed assessment instrument.

Data Analytic Strategy: Descriptive statistics will be used to analyze qualitative data of the formative evaluation (e.g., strategy, verbalization) and quantitative data (e.g., accuracy, speed). The pilot achievement data will be analyzed using Analysis of Variance (ANOVA) techniques.

Project Websites: For information about the prototype MathemAntics software, please visit: http://www.ednetserve.com/mathemantics.html.

Publications

Book chapter

Ginsburg, H. P., Labrecque, R., Carpenter, K., and Pager, D. (2015). New Possibilities for Early Mathematics Education: Cognitive Guidelines for Designing High-Quality Software to Promote Young Children's Meaningful Mathematics Learning. In A. Dowker, and R.C. Kadosh (Eds.), The Oxford Handbook of Numerical Cognition (pp. 1055–1078). Oxford, England: Oxford University Press.

Ginsburg, H.P., Azadeh, J., and Creighan, S. (2013). Cognitive Guidelines for the Design and Evaluation of Early Mathematics Software: The Example of MathemAntics. In L.D. English, and J.T. Mulligan (Eds.), Reconceptualizing Early Mathematics Learning, Advances in Mathematics Education (pp. 83–120). Netherlands: Springer.