Measuring Early Mathematical Reasoning Skills

**Overview**

The project will develop and evaluate the validity of universal screening assessment tools for Grades K-2 focused on two foundational and predictive early mathematics constructs, numeric relational reasoning and spatial reasoning. The primary goal of the Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR) within the Measures of Mathematical Reasoning Skills system is to help teachers determine students who are at-risk for difficulty in these constructs that they can provide early intervention and prevent later difficulties. Three universal screeners for numeric relational reasoning and spatial reasoning per grade will be developed with accompanying electronic test administration procedures to facilitate efficient delivery.

**Funder**

This project, Award Number 1721100, is funded by the National Science Foundation's Discovery Research Pre-K-12 Program, which funds research and development of STEM innovations and approaches in assessment, teaching, and learning.

**Partner(s)**

NA

**Principal Investigator**

PI: Dr. Leanne Ketterlin Geller

Co-PI: Dr. Lindsey Perry

**Purpose**

The primary purpose of this study is to develop the Measures of Mathematical Reasoning Skills system comprised of two universal screening tools: Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). These screeners will measure students' abilities in two foundational and predictive mathematics constructs, numeric relational reasoning and spatial reasoning, in Grades K-2. Numeric relational reasoning and spatial reasoning are constructs critical to success in future mathematics coursework, including Algebra 1, a gatekeeper to success in post-secondary efforts, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. These screeners will assist teachers in understanding and monitoring their students' numeric relational reasoning and spatial reasoning abilities, leading to informed instructional decisions and curricular interventions.

The Measures of Mathematical Reasoning Skills will provide teachers with a tier classification for (1) numeric relational reasoning using the T-NRR and (2) for spatial reasoning using the T-SR. Following the typical schedule for screening, three screeners will be developed for each grade level (K-2) for administration at the beginning, middle, and end of the year to monitor students' learning and design appropriate instruction. At the end of the project, the prototype Measures of Mathematical Reasoning Skills systems will be ready for use and for extended usability and feasibility research.

The Measures of Mathematical Reasoning Skills system has the potential to improve mathematics achievement in the short- and long-term and STEM outcomes. Evidence indicates that early intervention in preschool and the early elementary grades can significantly improve mathematics achievement (Clements & Sarama, 2007; Fuchs et al., 2005). However, in order to provide quality interventions and identify students who need additional support, teachers and schools systems must have access to high-quality data (Datnow, Park, & Kennedy-Lewis, 2012). The Measures of Mathematical Reasoning Skills system will assist in early intervention efforts by providing teachers and school systems with easy-to-administer screening tools that are reliable and provide valid interpretations about students' numeric relational reasoning and spatial reasoning skills. This system of screening tools will support schools in implementing RTI.

**Methodology**

We will follow a 5-phase iterative process to develop and evaluate the Measures of Mathematical Reasoning Skills system (see Figure 1). This system will contain two tests for students in Grades K-2: Tests of Numerical Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). These development phases conform to and follow the Standards for Educational and Psychological Testing (AERA, APA, NCME, 2014).

Phase 1, in Year 1, will include a thorough review and examination of the constructs under investigation. During this phase, we will work with experts in early mathematics learning and assessment to build on the existing literature and fully operationalize the constructs of numeric relational reasoning and spatial reasoning. In addition, we will review the psychometric analyses obtained from a field test of experimental measures to examine the content and item features that may or may not be suitable for measuring these constructs. Results from Phase 1 will inform development of the test specifications and Item Models for the T-NRR and T-SR.

Phase 2, in Years 1-2, will include an iterative process of developing test specifications and item models that adequately measure students' numeric relational reasoning and spatial reasoning abilities. The item models will be rigorously studied in Phase 2 using experts' input, cognitive interviews, and review panels. In Phase 3, in Years 2-3, we will write items for the T-NRR and T-SR. Items will be written for each grade (K-2) for both targeted constructs: numeric relational reasoning and spatial reasoning. Phase 4, in Year 3 of development, includes a large-scale field test of the items with students in Grades K-2. Analyses include calibration of item parameters and differential item functioning. In Phase 5, in Year 4, we will conduct validity studies with the Measures of Mathematical Reasoning Skills system including examining the relation with other measures of early numeracy and the sensitivity to growth. This development process will be iterative; evidence collected from each phase will be used to continuously refine the design of the T-NRR and T-SR.

**Outcomes**

This project will develop the Tests of Numeric Relational Reasoning and Tests of Spatial Reasoning within the Measures of Mathematical Reasoning Skills system. Three universal screeners for numeric relational reasoning and spatial reasoning per grade for grades K-2 will be developed with accompanying electronic test administration procedures to facilitate efficient delivery.

**News and Related Articles**

$2.5 million NSF grant gives teachers a math assessment tool to help students

**References**

** **American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). *Standards for educational and psychological testing. *Washington, DC: American Educational Research Association.

Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. *Journal for Research in Mathematics Education*, *38*(2), 136-163.

Datnow, A., Park, V., & Kennedy-Lewis, B. L. (2012). High school teachers’ use of data to inform instruction. *Journal of Education for Students Placed At Risk, 17*(4), 247-265.

Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. *Journal of Educational Psychology*, *97*, 493–513.