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Using Rule Space and Poset-Based Adaptive Testing Methodologies to Identify Ability Patterns in Early Mathematics and Create a Comprehensive Mathematics Ability Test

This project will develop a new assessment for children ages 3-7 to provide teachers with diagnostic information on a child's development of mathematics facility on ten domains such as counting, sequencing, adding/subtracting, and measurement. The Comprehensive Research-based Mathematics Ability (CREMAT) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains.

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Award Number: 
1313695
Funding Period: 
Sat, 09/01/2012 to Wed, 02/28/2018
Full Description: 

A new assessment for children ages 3-7 is being developed to provide teachers with diagnostic information on a child's development of mathematics facility on ten domains such as counting, sequencing, adding/subtracting, and measurement. The Comprehensive Research-based Mathematics Assessment (CREMA) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains. The CREMA will produce information based on carefully developed learning trajectories in a relative short period of time by using computer adaptive testing. The project is guided by two goals: 1) to produce a cognitively diagnostic adaptive assessment that will yield more useful and detailed information about students' knowledge of mathematics than previously possible, and 2) subject the developmental progressions to close cognitive diagnosis using cutting-edge psychometric approaches. An item pool of about 350 items is being developed that can be used to identify the level of understanding children ages 3-7 have on the 10 domains that have been identified as foundational to further learning in mathematics. A research team headed by Dr. Douglas Clements at the University of Buffalo is conducting the development work while being assisted by Dr. Curtis Tatsuoka, a statistician at Case Western Reserve University.

The CREMA is being developed using leading-edge psychometric models based on Q-Matrix theory, rule-state models, and posets. The initial item pool includes items from the REMA, a previously developed instrument based on unidemensional IRT models. New items are being piloted with at least 200 students from a group of a total of 800 students evenly distributed among pre-K to grade 2. The successful items then are used to create the new CREMA. The new assessment is being field tested with 300 children, pre-K to grade 2. A random sample of 50 students (at least 10 from each grade) is being video taped as they work the items. Specific criteria of convergence are being used for feedback on how specific items are performing to meet the required specifications. An external evaluator is auditing the process and is doing spot checks of item codings and other analyses performed.

The main product will be the CREMA that will be made widely available. This instrument using computer adaptive testing will provide teachers with ready information on young children's understanding of critical mathematical ideas. The new psychometric models that will be used and developed to process multiple attributes from individual items will make large strives to move forward the field of mathematics assessment of young children. A publisher has expressed interest to make the assessment widely available that increases the likelihood the assessment will have large impact on early childhood mathematics learning.

This project was previously funded under award # 1019925.

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Award Number: 
1743356
Funding Period: 
Mon, 03/15/2010 to Fri, 06/30/2017
Full Description: 

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

This project was previously funded under award #0952415.

Supporting Staff Developers in the Implementation of Professional Development Programs to Improve Mathematics Education for Students with Disabilities

This project is (1) conducting a qualitative study on the way facilitators use Math for All (MFA), an NSF-supported set of professional development materials for teachers who teach elementary school students with disabilities; (2) developing resources based on that study for teacher leaders and other facilitators of professional development; and (3) conducting fieldtests of the resources to examine their usefulness and impact.

Award Number: 
0822313
Funding Period: 
Mon, 09/01/2008 to Fri, 08/31/2012
Project Evaluator: 
Teresa Duncan
Full Description: 

 

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