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Cognitively Guided Instruction (CGI) is a teacher PD program that has been found to have a potentially positive impact on student learning in mathematics through randomized controlled trials. Through a series of grant-funded projects led by FSU, approximately 2,000 Florida teachers have participated in CGI-based professional development in the past 8 years. This paper describes the core features of the CGI-based PD programs that were implemented in Florida during that time period. We provide this information to help researchers and practitioners to understand the context in which the associated research studies occurred and interpret the available and forthcoming findings related to the impacts of the interventions.

This report provides evidence of the substantive and structural validity of the Knowledge for Teaching Elementary Fractions Test. Field-test data were gathered with a sample of 241 elementary educators, including teachers, administrators, and instructional support personnel, in spring 2017, as part of a larger study involving a multisite cluster-randomized trial evaluation design to investigate the effects of lesson study and a fractions resource toolkit on classroom instruction and student achievement in fractions. The web-based test was designed to measure mathematical knowledge for teaching (MKT) in the domain of fractions at the elementary level. We found that the Knowledge for Teaching Elementary Fractions test measures a dominant factor, supporting unidimensionality in the data. The purpose, or intended use, of the Knowledge for Teaching Elementary Fractions (K-TEF) test data gathered in spring 2017 is to produce ability estimates that can be used to serve as the dependent variable in models estimating the effect of the intervention on teacher MKT, as well as to investigate MKT as a potential mediator of the effect of the program on students. Reliability, test-information, and item-discrimination estimates appear to fit the intended purpose of the test.

This report provides a description of the development process, field testing, and psychometric properties of the fall 2015 grades 3-5 Elementary Mathematics Student Assessment (EMSA), a student mathematics test designed to be administered in a whole-group setting to students in grades 3, 4, and 5. The test was administered to 2,614 participating grade 3, 4, and 5 students in 266 classrooms located in 10 public school districts in Florida during fall 2015. Focused on number (including whole number and fractions), operations, and algebraic thinking, the student assessment was designed to serve as a baseline measure of student achievement for use as a covariate in a randomized controlled trial evaluating the impact of a teacher professional development program on student learning. [This report was prepared by the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) within the Learning Systems Institute.]

This report provides evidence of the substantive and structural validity of the Knowledge for Teaching Elementary Fractions Test. Field-test data were gathered with a sample of 277 elementary educators, including teachers, administrators, and instructional support personnel, in fall 2016, as part of a larger study involving a multisite cluster-randomized trial evaluation design to investigate the effects of lesson study and a fractions resource toolkit on classroom instruction and student achievement in fractions. The web-based test was designed to measure mathematical knowledge for teaching (MKT) in the domain of fractions at the elementary level. we found that the Knowledge for Teaching Elementary Fractions test measures a dominant factor, supporting unidimensionality in the data. The purpose, or intended use, of the Knowledge for Teaching Elementary Fractions test is to produce ability estimates that can be used to investigate baseline equivalence of groups of educators in four treatment conditions, to serve as a covariate in models estimating the effect of the intervention on MKT, as well as to investigate MKT as a potential moderator of the effect of the program on teachers and students. Reliability, test-information, and item-discrimination estimates appear to fit the intended purpose of the test, although further validation will be necessary to determine whether the test is well suited for its intended use.

Mathematics teacher professional-development (PD) programs based on Cognitively Guided Instruction (CGI) have been developed and implemented with tens of thousands of elementary mathematics teachers worldwide since the 1980s. Starting with a focus on addition and subtraction on whole numbers in the first CGI PD program, the content of these courses has expanded over time. In this study, we used a multisite cluster-randomized trial to estimate the impact of the first year of a three-year CGI teacher professional-development program. This CGI PD program designed for grades three, four, and five teachers. The content of the program focused on fractions concepts and operations on fractions, multiplication and division on whole numbers, and algebraic thinking. The randomized sample included 149 teachers and their students, representing 32 schools in nine public school districts in Florida. Student outcomes were measured by the Elementary Mathematics Student Assessment (EMSA). The CGI 3-5 PD program was found to significantly impact student performance on the EMSA test (p = 0.007) in the first year of the three-year program. The point estimate of the main effect of the CGI program on student achievement (g = 0.18) was greater than many of the most effective teacher professional-development programs that have been subjected to rigorous evaluation.

The Early Fractions Test v2.2 is a paper-pencil test designed to measure mathematics achievement of third- and fourth-grade students in the domain of fractions. The purpose, or intended use, of the Early Fractions Test v2.2 is to serve as a measure of student outcomes in a randomized trial designed to estimate the effect of an educational intervention on student understanding and ability in the domain of early fractions concepts. In this report, we discuss our exploration of options for scoring and data modeling and make recommendations for optimal scoring and data modeling procedures. We also report on the results of data modeling, including analyses of dimensionality, scale reliability estimates, item difficult estimates, test information, and the distribution of student ability estimates. The results of these analyses are largely consistent with the findings from the analysis of data from the previous version of the Early Fractions Test (Schoen, Liu, Yang, & Paek, 2017).

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather information about students' cognitive processes while they solved mathematics problems. The current report focuses on the content of the 2015 MPAC interview, interview protocol, scoring procedures, and psychometric properties for the achievement focus of the MPAC Interview. The 2015 MPAC interview was administered to 856 students in spring 2015 in 22 schools located in two public school districts in a single state in the southeastern U.S for the purpose of evaluating the impact of a teacher professional development program on student achievement, cognition, and understanding in the domain of number, operations, and algebraic thinking in mathematics. Nonetheless, we expect the interview data and protocol to be usable in other ways to make a broader contribution in various aspects of mathematics education research. [For the previous report, "Mathematics Performance and Cognition (MPAC) Interview: Measuring First- and Second-Grade Student Achievement in Number, Operations, and Equality in Spring 2014. Research Report No. 2016-01," see ED577242.]

The Early Fractions Test is a paper-pencil test designed to measure mathematics achievement of third- and fourth-grade students in the domain of fractions. The purpose, or intended use, of the Early Fractions Test is to serve as a student pretest covariate and a test of baseline equivalence in the larger study. In this report, we discuss our exploration of options for scoring and data modeling and make recommendations for optimal scoring and data modeling procedures. We also report on the results of data modeling, including analyses of dimensionality, scale reliability estimates, the intraclass correlation coefficient for the 66 schools represented in the sample, and the percentage of the variance in student achievement as measured by the end-of-year mathematics test that is explained by their scores on this beginning-of-year test.

This report describes efforts to measure teachers' knowledge of their own students' abilities in mathematics and offers preliminary findings. It provides a description of the sample, a description of the study design and its realization, and descriptive statistics for teacher judgment accuracy. The work described here was completed as part of a randomized controlled trial evaluating the implementation and impact of a teacher professional-development program called Cognitively Guided Instruction (CGI). The analytic sample for the spring 2014 wave of data collection involved grade 1 and grade 2 students (n = 504) and their mathematics teachers (n = 146). The analytic sample for the 2015 wave of data collection included a larger sample of students (n = 785) and their teachers (n = 200). During each wave of data collection, teachers were shown a set of problems from the interview and were told which students would be attempting to solve the problems. For each student and item, the teachers predicted whether the student would solve the item correctly. Overall, teachers accurately predicted their students' performance about 60% of the time. Overprediction was more common than underprediction. The authors anticipate data generated with the TAPSS instrument will be used to determine the effects of the teacher professional-development program on teacher judgment accuracy and the extent to which this type of knowledge is associated with student learning. The TAPSS instrument and the sample described here represent several advancements in the field of measuring teacher judgment accuracy, including the iterative development of a new instrument available to researchers and program evaluators. The authors expect that teacher judgment accuracy will ultimately yield important insight into the elusive link between teacher knowledge and student learning.

This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades K, 1, and 2 student abilities. The test was administered to 4,486 participating grade K, 1, and 2 students in 67 schools located in 10 public school districts in Florida during fall 2015. Focused on counting, word problems, and computation, the student assessment was designed to serve as a baseline measure of student achievement for use as a covariate in a randomized controlled trial evaluating the impact of a teacher professional development program called Cognitively Guided Instruction (CGI) on student learning.

This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades K, 1, and 2 student abilities. The test was administered to 4,535 participating grade K, 1, and 2 students in 66 schools located in 9 public school districts in Florida during spring 2016. Focused on number, operations, and equality, the student assessment was designed to serve as a baseline measure of student achievement in a randomized controlled trial evaluating the impact of a teacher professional development program called Cognitively Guided Instruction (CGI) on student learning.

This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades 1 and 2 student abilities. The test was administered to 2,373 participating grade 1 and 2 students in 22 schools located in 2 public school districts in Florida during fall 2013. Focused on counting, word problems, and computation, the student assessment was designed to serve as a baseline measure of student achievement in a randomized controlled trial evaluating the impact of a teacher professional development program called Cognitively Guided Instruction (CGI) on student learning.