MATHSTEPS © 2000 Pre-Publication Research



MathSteps© 2000 is, in part, the republication of the Individualized Computational Skills Program (ICSP) published earlier by Houghton Mifflin Company. This brief describes the research trials by Bryce R. Shaw, a math educator in the Flint, Michigan, public schools. Shaw's research was funded by a grant from the Kellogg Foundation, and his work led him to develop ICSP for students who were underperforming in mathematics.

In Flint, Michigan, some 45,000 elementary and secondary school children were on average nearly one full year below national norms in performing basic arithmetic skills as measured by the Science Research Associates Arithmetic Test Battery. Although getting school children to add, subtract, multiply and divide is recognized as a perplexing national education problem, the Flint school system sought to reverse the local area trend in an effort to raise its elementary school arithmetic achievement.

Concerned administrators, teachers, and parents utilized the system's resources to develop materials to remedy the problem. Bryce R. Shaw was engaged to develop a program for individual students, classes, and the entire school system, to establish accountability and to halt the declining arithmetic skills level of most students. The materials in this program were designed to supplement the existing textbook program in the schools, and to fit into the multiple instruction organizations with minimal in-service teacher training.

Over a period of seven years, the design, development, implementation and statistical validation of the Individualized Computational Skills Program (the "Program") would involve roughly 90,000 elementary school students, 35,000 junior high school students and 3,400 teachers in the Flint Community Schools.

The objectives of the Program were to provide teachers with the materials to correctly assess and identify a student's grade level competence in computation skills in order to then prescribe effective and appropriate materials to correct specific weaknesses as they occurred. Students could rely on a validated program that had the overall effect of helping them to achieve grade-level proficiency in all computational skills areas. Progress would then be monitored by a functional record-keeping procedure to track the student's progress on a day-to-day basis, thereby eliminating "cumulative deficit knowledge."

The foundations upon which the Program rested were the "Skills Inventories," simple tests that contained problems representative of each grade level. Revised and refined, these tests consisted of a non-graded sequence of problems within each of the major computational skills areas (i.e., whole number operations, fractions, decimals and percents) which enabled the teacher to reliably and accurately determine what a student knew and what the student should be working to improve.

The items in the Skills Inventories formed the basis for the writing of the "Sequential Skills Outline," developed to provide each teacher with a complete overview of the non-graded sequential order of development of computational skills which were correlated with the specific grade levels. These components of the Program enabled teachers to determine the grade level in which each computational skill is usually taught and mastered; the corresponding material necessary to meet the individual needs of each student; and the skill area in which the student was in need of individualized instruction.

Correlation Guides were written to correlate the pages and/or chapters of textbooks and work texts with each skill in the Sequential Skills Outline, and to provide cross-referencing of all material in use to meet individual student needs. Additional supplementary materials were developed to enable teachers to provide more individualized instructional material than available through the Correlation Guides, which were keyed to the basal mathematics program used in the schools and to the Sequential Skills Outline. Skills and Practice sheets were written to teach, review and re-teach skills, and review tests were developed to measure retention or the need for further practice.

A simple, economical and effective record-keeping device was developed to show a student's placement based upon the outcome of the Skills Inventories and the Sequential Skills Outline. A record card noted placement and student progress, and was sent along as the student passed from grade to grade.

In order to provide a reliable, streamlined test instrument for grades 3-6 which enabled teachers to arrange groups for instruction and identify the need for further diagnostic testing, the Early Elementary Computation Test and Arithmetic Computation Test were developed. These "Computation Tests" also provided the local school district with statistical information necessary to analyze the effectiveness of their elementary program. Highly reliable and practical, the validated Computation Tests as pre- and post tests provided administrators, teachers and students with a foundation of responsibility, as well as an effective system for monitoring the elementary mathematics program. Materials were organized by mathematics skills strands, and by level (primary and intermediate) for easy access by educators.

As for results, a comparison of achievement as measured on the Computation Tests and the scores as measured by the Science Research Associates Standardized Achievement Tests showed a notably high correlation. Initial results from the SRA Standardized Achievement Tests indicated that students were eight months below grade level. However, following the introduction of the ICSP the SRA Standardized Achievement Test data clearly showed a steady increase in improved computation achievement to the extent that national norms were reached. That growth was maintained throughout the use of the program.

The fact that the average gain for students was 3.2 months above the expected gain and retention was 100 percent supported anecdotal reports of success from classroom teachers, students and parents. In 1999, renewed interest in the Individualized Computational Skills Program resulted in a slight revision to the kit, and the publication of several new components: Student Books (for Kindergarten through grade 7) that provide coverage of the entire mathematics curriculum for that grade, and Teacher Guides and Teaching Resources that include teaching support, assessments and home/school connections. The kit was also made available in CD-ROM format. The program was re-named, MathSteps, and is in use in regular classrooms, in summer school programs, and in Title I classrooms across the country. Currently, a research update is underway with approximately 10,000 students and 500 teachers using MathSteps. Published results of this research will be available in the summer of 2000.


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