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IES Grant

Title: Foundations of Mathematical Understanding: Developing a Strategic Intervention on Whole Number Concepts
Center: NCSER Year: 2009
Principal Investigator: Clarke, Ben Awardee: University of Oregon
Program: Science, Technology, Engineering, and Mathematics      [Program Details]
Award Period: 06/01/2009 – 05/31/2012 Award Amount: $1,455,851
Type: Development and Innovation Award Number: R324A090341

Purpose: The purpose of this project is 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 that use 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 II program, and will be most applicable in schools that rely on a Response to Intervention model for the identification of learning disabilities. There are two major aims of the project: (a) develop a 60-lesson intervention focusing on whole number concepts for students at risk for math learning difficulties and disabilities, and (b) assess the feasibility and potential for efficacy of the intervention.

Project Activities: The project team will develop the 60-lesson FUSION intervention program through multiple "design experiments," which are iterative cycles of development, observation, analysis, and refinement. 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 eight 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 and focus groups, direct observations as well as proximal and distal outcome measures of student learning. The project concludes with a final revision phase.

Products: The products of this project include a fully developed FUSION intervention on 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 project team will also present findings in published reports and presentations.

Setting: The research takes place in elementary schools in Oregon.

Population: Participants are 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 4–6 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 number. 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, 4–5 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.

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, the Number Identification Measure, the Quantity Identification Measure, the Missing Number Measure, the Number Knowledge Test, Counting Knowledge, and the Test of Early Mathematics Ability. 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. Pretest — posttest gains on mathematics content measures will be examined to assess 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 Test of Early Mathematics Ability. 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 as measured by the instruments listed in the Key Measures section above.


Book chapter

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. doi:10.1037/14316–008

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.

Book chapter, edition specified

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 article, monograph, or newsletter

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. Full text

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. doi:10.1177/1534508411414153

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. doi:10.1177/1053451212473151

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. doi:10.1177/0731948713520555

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. doi:10.1177/1534508413511848

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: 200–209. doi:10.1177/1534508411414154