Elementary School

Measuring Early Mathematical Reasoning Skills: Developing Tests of Numeric Relational Reasoning and Spatial Reasoning

The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR).

Award Number: 
1721100
Funding Period: 
Fri, 09/15/2017 to Tue, 08/31/2021
Full Description: 

Numeric relational reasoning and spatial reasoning are critical to success in later mathematics coursework, including Algebra 1, a gatekeeper to success at the post-secondary level, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. Given the importance of these skills for later success, it is imperative that there are high-quality screening tools available to identify students at-risk for difficulty in these areas. The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). The measures will be intended for use by teachers and school systems to screen students to determine who is at-risk for difficulty in early mathematics, including students with disabilities. The measures will help provide important information about the intensity of support that may be needed for a given student. Three forms per grade level will be developed for both the T-NRR and T-SR with accompanying validity and reliability evidence collected. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The development of the T-NRR and T-SR measures will follow an iterative process across five phases. The phases include (1) refining the construct; (2) developing test specifications and item models; (3) developing items; (4) field testing the items; and (5) conducting validity studies. The evidence collected and evaluated during each phase will contribute to the overall evaluation of the reliability of the measures and the validity of the interpretations made using the measures. Item models, test specifications, and item development will be continuously evaluated and refined based on data from cognitive interviews, field tests, and reviews by mathematics educators, teachers of struggling students, teachers of culturally and linguistically diverse populations, and a Technical Advisory Board. In the final phase of development of the T-NRR and T-SR, reliability of the results will be estimated and multiple sources of validity evidence will be collected to examine the concurrent and predictive relation with other criterion measures, classification accuracy, and sensitivity to growth. Approximately 4,500 students in Grades K-2 will be involved in all phases of the research including field tests and cognitive interviews. Data will be analyzed using a two-parameter IRT model to ensure item and test form comparability.

Networking Urban Resources with Teachers and University to Enrich Early Childhood Science (NURTURES) Phase II: Expansion and Evaluation

Building on successful prior work, this project simultaneously targets young children's teachers and families/caregivers in an effort to build both parties' capacity to promote student interest in science, technology, engineering and mathematics (STEM) learning.

Lead Organization(s): 
Award Number: 
1721059
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

Building on successful prior work, this University of Toledo project, Networking Urban Resources with Teachers and University to enRich Early Childhood Science (NURTURES): Researching the impact of teacher professional development and family engagement on PreK-3 achievement, simultaneously targets young children's teachers and families/caregivers in an effort to build both parties' capacity to promote student interest in science, technology, engineering and mathematics (STEM) learning. Teachers participate in a two-week summer professional development program and receive support across the school year in the form of individualized coaching and participation in professional learning communities. Families receive science inquiry packets (sent home from school) four times a year and attend community STEM events throughout the year. Inquiry packets and community events encourage science inquiry, discourse, and further exploration of key science ideas. Project participants will include 120 teachers, 2,400 PreK-3 children and over 7,200 family members in Ohio and Michigan.

Extending the initial NURTURES project, developed with NSF Math and Science Partnership funding, this follow-up project aims to: 1) Transform early childhood science teaching based upon Next Generation Science Standards (NGSS) to measurably increase student science, literacy, and math achievement, and 2) Engage families of PreK-3 students in science inquiry practices to measurably improve student science, literacy, and math achievement. A particularly important facet of this follow-up project is the research effort to parse and understand how each component (teacher professional development versus family engagement) impacts student learning. The project will use a randomized control group research design (RCT) to compare student achievement outcomes among three groups: Children whose teachers received professional development and family engagement activities, children whose teachers received only professional development, and a control group. The project will use standardized tests (the TerraNova Complete Battery) to measure impact on learning gains in science, mathematics, reading, and early literacy for children in grades K- 3. The Lens on Science assessment will measure science learning in preschool children. This project will result in an NGSS-based program for teachers and families that has been systematically tested and may ultimately be scaled up to an impact study and dissemination at a broad level.

Developing and Evaluating Assessments of Problem Solving (Collaborative Research: Sondergeld)

This project builds upon the prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1720661
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

Current state standards in mathematics are strategically focused on problem-solving skills in both content standards and practice standards. Content standards describe what math students are expected to learn at each grade level while practice standards characterize math behaviors that all students should experience (e.g., perseverance while problem solving and reasoning effectively about real-world situations). Problem solving is found at every grade level. If math teachers are expected to engage students in problem solving during everyday instruction, then students' problem-solving performance must be assessed in a manner that produces meaningful, valid, and reliable scores, without unduly burdening teachers or students. Unfortunately, most problem-solving assessments are generally framed by a set of mathematics expectations that differ from state standards. Thus, results from those assessments are disconnected from the mathematics content that students learn in the classroom. Previously, this research team has built problem-solving measures for grades 6-8, which address this gap in framing and generates meaningful, valid, and reliable scores, and do not have unintended negative consequences on students. The current project, titled Developing and Evaluating Assessments of Problem Solving (DEAP), builds upon the team's prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

Broadly speaking, the aims of DEAP are to (a) create three new mathematical problem-solving assessments and gather validity evidence for their use, (b) link the problem-solving measures (PSMs) with prior problem-solving measures (i.e., PSM6, PSM7, and PSM8), and (c) develop a meaningful reporting system for the PSMs. The research questions are: (a) What are the psychometric properties of the PSM3, PSM4, and PSM5 as they relate to students' problem-solving performance? (b) How does the evidence support vertical equating (linking) of the PSM3, PSM4, PSM5, PSM6, PSM7, and PSM8? (c) How do the PSM3, PSM4, and PSM5, and their related reporting systems impact teachers' instructional decision making when used formatively? Year 1 focuses on item and test development. The study will conduct cognitive interviews and administer tests with a small group of students to explore how items and tests function. Rasch (1-PL) measurement will be employed, similar to prior PSM development. Year 2 includes further pilot testing and gathering validity evidence through cognitive interviews and test administration. Year 3 has a final round of pilot testing and selection of linking items for vertical equating. Year 4 involves pilot testing the PSM series with linking items and developing a reporting system. DEAP's potential contributions to the field are three-fold. (1) Assessments will be available for use by the public. (2) A set of vertically equated problem-solving measures will allow users the opportunity to explore students' problem-solving performance as they matriculate across grade levels, which is currently not possible at the state or national level. (3) This project fills a need in the field as no set of measures uses vertical equating to assess elementary students' problem-solving performance in a rigorous fashion within the context of state testing.

Developing and Evaluating Assessments of Problem Solving (Collaborative Research: Bostic)

This project builds upon the prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1720646
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

Current state standards in mathematics are strategically focused on problem-solving skills in both content standards and practice standards. Content standards describe what math students are expected to learn at each grade level while practice standards characterize math behaviors that all students should experience (e.g., perseverance while problem solving and reasoning effectively about real-world situations). Problem solving is found at every grade level. If math teachers are expected to engage students in problem solving during everyday instruction, then students' problem-solving performance must be assessed in a manner that produces meaningful, valid, and reliable scores, without unduly burdening teachers or students. Unfortunately, most problem-solving assessments are generally framed by a set of mathematics expectations that differ from state standards. Thus, results from those assessments are disconnected from the mathematics content that students learn in the classroom. Previously, this research team has built problem-solving measures for grades 6-8, which address this gap in framing and generates meaningful, valid, and reliable scores, and do not have unintended negative consequences on students. The current project, titled Developing and Evaluating Assessments of Problem Solving (DEAP), builds upon the team's prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Broadly speaking, the aims of DEAP are to (a) create three new mathematical problem-solving assessments and gather validity evidence for their use, (b) link the problem-solving measures (PSMs) with prior problem-solving measures (i.e., PSM6, PSM7, and PSM8), and (c) develop a meaningful reporting system for the PSMs. The research questions are: (a) What are the psychometric properties of the PSM3, PSM4, and PSM5 as they relate to students' problem-solving performance? (b) How does the evidence support vertical equating (linking) of the PSM3, PSM4, PSM5, PSM6, PSM7, and PSM8? (c) How do the PSM3, PSM4, and PSM5, and their related reporting systems impact teachers' instructional decision making when used formatively? Year 1 focuses on item and test development. The study will conduct cognitive interviews and administer tests with a small group of students to explore how items and tests function. Rasch (1-PL) measurement will be employed, similar to prior PSM development. Year 2 includes further pilot testing and gathering validity evidence through cognitive interviews and test administration. Year 3 has a final round of pilot testing and selection of linking items for vertical equating. Year 4 involves pilot testing the PSM series with linking items and developing a reporting system. DEAP's potential contributions to the field are three-fold. (1) Assessments will be available for use by the public. (2) A set of vertically equated problem-solving measures will allow users the opportunity to explore students' problem-solving performance as they matriculate across grade levels, which is currently not possible at the state or national level. (3) This project fills a need in the field as no set of measures uses vertical equating to assess elementary students' problem-solving performance in a rigorous fashion within the context of state testing.

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