Research-Based Mathematics Intervention from Houghton Mifflin

MathSteps is an intervention program for students in kindergarten through middle school, reflecting current and confirmed research in the area of direct instruction and experimental research.

The program was developed following 10 years of research involving roughly 90,000 elementary school students, 35,000 junior high school students, and 3,400 teachers in Flint, Michigan. The teaching approaches, amounts and kinds of practice, and assessment tools presently in MathSteps are directly linked to the approaches and materials prototypes that produced the most growth in preliminary studies.

When the study was initiated, some 45,000 elementary and secondary school children in Flint, Michigan were an average of one full year below national norms in mathematics 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 achievement.

Math educator Dr. 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 skills level of most students. The materials in this program–later renamed MathSteps–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.

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 achieve grade-level proficiency in all computational skills areas. Progress would then be monitored by a functional record-keeping procedure to track the students' progress on a day-to-day basis, thereby eliminating "cumulative deficit knowledge."

The key elements of the Program were:

  • Skills Inventories tests containing problems representative of each grade level that enabled the teacher to reliably and accurately determine what a student knew and what the student should be working to improve
  • Sequential Skills Outlines based on the items in the Skills Inventories to provide each teacher with a complete over-view of the non-graded, sequential order of development of computational skills correlated with specific grade levels
  • Correlation Guides 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
  • Skills and Practice sheets and Review tests to teach, review, and reteach skills, and measure retention or the need for further practice.

In order to provide a reliable, streamlined test instrument for Grades 36 that 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.

A comparison of achievement as measured on the Computation Tests and the scores measured by the Science Research Associates Standardized Achievement Tests showed a notably high correlation. Following the introduction of the Program, 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 gains and retention was 100 percent, supported anecdotal reports of success from classroom teachers, students, and parents.

In 1999, as a follow-up to the initial research, Houghton Mifflin Company commissioned an independent social science research firm to evaluate the effectiveness of MathSteps. A total of 21 schools in five districts, both urban and suburban, were involved in the study: 6,567 students and 201 teachers. Effectiveness was evaluated using two measures: extant mathematics achievement data from the Standford-9 (SAT-9) mathematics achievement test scores for 1999 and 2000, and teacher surveys administered in Spring 2000.

In a sample of second-graders to sixth-graders, scaled scores ranged from approximately 400 to approximately 800, and the mean gain over the course of one grade for students using MathSteps was approximately 30 points. There are, however, greater gains under certain conditions:

  1. The students taught by experienced teachers had greater gains than students taught by new teachers.
  2. Students who were identified by their teachers as being at the highest risk had gains greater than 30 points.

The teacher survey indicated that:

  • MathSteps teachers were either satisfied or very satisfied with the overall MathSteps curriculum: their mean level of satisfaction with the curriculum was 4.1 on a 5-point scale.
  • Over three-quarters of MathSteps teachers believe that the MathSteps curriculum is either effective or very effective at increasing their students' mathematics achievement.

MathSteps is an effective intervention program, as determined by the results of the earlier Flint study and the more recent results using the SAT-9 and teacher surveys. In response to the most recent study, the authors and development team, along with national mathematics consultants, have developed a comprehensive in-service plan and resource materials–including a training video–that are now used as part of the training for MathSteps.


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