Grant Closed

Foundations of Mathematical Understanding: Developing a Strategic Intervention on Whole Number Concepts

NCSER
Program: Special Education Research Grants
Program topic(s): Science, Technology, Engineering, and Mathematics
Award amount: $1,455,851
Principal investigator: Ben Clarke
Awardee:
University of Oregon
Year: 2009
Project type:
Development and Innovation
Award number: R324A090341

Purpose

The purpose of this project was to develop a core mathematics intervention for students in first grade who are at risk for mathematics difficulties and disabilities. The intervention, FUSION, is designed as a program for schools using a multi-tiered approach to instruction that provides increasingly intense levels of instruction based on the results of frequent progress monitoring of students. FUSION will be developed as a tier 2 program, most applicable in schools that rely on a response-to-intervention model for the identification of learning disabilities. This project aims to develop a 60-lesson intervention focusing on whole number concepts for students at risk for math learning difficulties and disabilities and assess the intervention's feasibility and potential for efficacy.

Project Activities

The project team planned to develop FUSION through multiple "design experiments," or iterative cycles of development, observation, analysis, and refinement. The plan included an extensive content analysis to determine scope and sequence of the lessons, build instructional templates, and complete lesson sets; two feasibility studies to determine teacher satisfaction with the intervention, delivery of lesson content, and student responsiveness; and a pilot study to determine if the intervention is operating as intended and the student learning outcomes.

Structured Abstract

Setting

The research takes place in elementary schools in Oregon.

Sample

Participants will include approximately 100 first grade students and 15 first grade teachers in Title I schools in two school districts. Students identified as at risk on a screening battery will participate in groups with sizes ranging from four to six students.
Intervention
Based on research that young children need to develop strong foundational knowledge and skills in early mathematics, the FUSION curriculum will combine two important features: (1) research-based instructional design and delivery, and (2) focused foundational knowledge on whole numbers. The intervention includes two major components. The first is mathematics content, which focuses on whole number concepts, and includes three major strands: (a) number sense, (b) base 10 and place value, and (c) number operations and related properties. The second component is research-based instructional design and delivery features. The intervention will be taught in small groups for 30 minutes per day, 4 to 5 days per week.

Research design and methods

The researchers will use design experiments in all phases of the project. Design experiments offer a methodological structure for developing instructional interventions through iterative cycles of development, observation, analysis, and refinement. The design experiments involve frequent observations of teaching and a range of measures to provide the structure necessary to determine the feasibility of the implementation of the intervention and to examine the potential promise of the intervention for increasing student mathematics achievement. Two experts in instructional design and mathematics instruction will conduct an extensive content analysis to determine scope and sequence of the lessons, build instructional templates, and complete lesson sets for the implementation phase. The project team will then conduct implementation studies to explore feasibility and potential efficacy. Two feasibility studies with first grade teachers will be conducted (with a revision phase in between) to determine teacher satisfaction with the intervention, delivery of lesson content, and student responsiveness. In the final year, the project team will conduct a pilot study in which all 60 lessons will be implemented by 12 teachers to determine if the intervention is operating as intended. Data collection will include surveys, focus groups, and direct observations as well as proximal and distal outcome measures of student learning. The project concludes with a final revision phase.

Control condition

There is no control condition.

Key measures

The researchers will use several measures to collective formative data as part of intervention development. They include the Number Knowledge Test and Early Numeracy-CBM as screeners, as well as the Number Identification Measure, Quantity Identification Measure, Missing Number Measure, Number Knowledge Test, Counting Knowledge, and Test of Early Mathematics Ability (TEMA). The researchers will also use teacher focus groups, teacher surveys, and a classroom observation system focusing on fidelity and instructional quality to inform revisions to the intervention.

Data analytic strategy

Descriptive analyses of data from teacher surveys, classroom observations, and teacher focus groups will be used to guide revisions to the intervention. Pre- to post-test gains on mathematics content measures will be examined to assess the promise of the intervention. The researchers will examine the degree to which an increase in students' procedural fluency and conceptual understanding during the intervention correlates with gains on the TEMA. In addition, the researchers will conduct correlation analyses to determine the nature of relationships between implementation fidelity, instructional quality (e.g., frequency and quality of teacher student interactions involving mathematics content) and mathematics achievement.

People and institutions involved

IES program contact(s)

Sarah Brasiel

Education Research Analyst
NCSER

Products and publications

ERIC Citations: Find available citations in ERIC for this award here.

WWC Review: Clarke, B., Doabler, C. T., Strand Cary, M., Kosty, D. B., Baker, S. K., Fien, H., and Smolkowski, K. (2014). Preliminary evaluation of a tier 2 mathematics intervention for first grade students: Utilizing a theory of change to guide formative evaluation activities. School Psychology Review, 43(2), 160-177 [WWC Review]

Selected Publications:

Book chapters

Clarke, B., Haymond, K., and Gersten, R. M. (2014). Mathematics screening measures for the primary grades. In R. J. Kettler, T. A. Glover, C. A. Albers, and K. A. Feeney-Kettler (Eds.), Universal screening in educational settings: Evidence-based decision making for schools (pp. 199-221). Washington, DC: American Psychological Association.

Clarke, B., Lemke, E., Hampton, D., and Hendricker, E. (2011). Understanding the R in RtI: What we know and what we need to know about measuring student response in mathematics. In R. Gersten, and R. Newman-Gonchar (Eds.), Response to intervention in mathematics (pp. 35-48). Baltimore: Paul H. Brookes.

Clarke, B., Nelson-Walker, N. J., and Shanley, L. (2016). Mathematics fluency: More than the weekly timed test. In K. D. Cummings, and Y. Petscher (Eds.), The fluency construct (pp. 67-89). New York: Springer.

Clarke, B., Doabler, C. T., and Nelson, N. J. (2014). Best practices in mathematics assessment and intervention with elementary students. In A. Thomas, and P. Harrison (Eds.), Best practices in school psychology (6th ed., pp. 219-232). Bethesda, MD: National Association of School Psychologists.

Journal articles

Clarke, B., Doabler, C. T., Strand Cary, M., Kosty, D. B., Baker, S. K., Fien, H., and Smolkowski, K. (2014). Preliminary evaluation of a tier 2 mathematics intervention for first grade students: Utilizing a theory of change to guide formative evaluation activities. School Psychology Review, 43(2), 160-177.

Clarke, B., Doabler, C. T., Nelson, N. J., and Shanley, C. (2015). Effective instructional strategies for kindergarten and first-grade students at risk in mathematics. Intervention in School and Clinic, 50(5), 257-265.

Clarke, B., Nese, J. F. T., Alonzo, J., Smith, J. L. M., Tindal, G., Kame'enui, E., and Baker, S. K. (2011). Classification accuracy of EasyCBM first-grade mathematics measures: Findings and implications for the field. Assessment for Effective Intervention, 36(4), 243-255.

Doabler, C., and Fien, H. (2013). Explicit mathematics instruction: What teachers can do for mathematics difficulties. Intervention in School and Clinic, 48(5), 276-285.

Doabler, C. T., Clarke, B., Fien, H., Baker, S. K., Kosty, D.B., and Cary, M. S. (2014). The science behind curriculum development and evaluation: Taking a design science approach in the production of a tier 2 mathematics curriculum. Learning Disability Quarterly, 38(2), 97-111.

Doabler, C. T., Nelson, N. J., Kosty, D. B., Fien, H., Baker, S. K., Smolkowski, K., and Clarke, B. (2014). Examining teachers' use of evidence-based practices during core mathematics instruction. Assessment for Effective Intervention, 39(2), 99-11.

Gersten, R. M., Clarke, B., Jordan, N., Newman-Gonchar, R., Haymond, K., and Wilkins, C. (2012). Universal screening in mathematics for the primary grades: Beginnings of a research base. Exceptional Children, 78(4), 423-445.

Methe, S. A., Hojonski, R., Clarke, B., Owen, B. B., Lilley, P.K., Politylo, B. C., White, K. M. and Marcotte, A. M. (2011). Innovations and future directions for early numeracy curriculum-based measurement: Commentary on the special series. Assessment for Effective Intervention, 36(4), 200-209.

Questions about this project?

To answer additional questions about this project or provide feedback, please contact the program officer.

 

Questions about this project?

To answer additional questions about this project or provide feedback, please contact the program officer.

 

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