Geometry Assessments for Secondary Teachers (GAST) represents a collaborative partnership among faculty and staff at the University of Louisville, the University of Kentucky, Florida State University, Alpine Testing Solutions, and Horizon Research, Inc. to develop a knowledge framework and assessments for secondary mathematics teachers' geometry knowledge for teaching. The framework for the assessments will be designed to collect validity evidence for predicting effective geometry teaching and improving student achievement.
Geometry has become an important secondary school subject to prepare students for both postsecondary and work experiences. With the advent of new curricula and technology, the purpose and nature of geometry has changed dramatically in secondary schools across the country. Geometry teachers, to be effective, must have a deep and relevant knowledge of geometry and its applications. The framework of teachers' geometry knowledge for teaching developed by GAST teams of mathematics educators, mathematicians, and classroom teachers will describe the geometry knowledge needed by secondary teachers to teach effectively and improve student achievement. This project will apply models of teacher knowledge developed by researchers at the University of Michigan, Michigan State University, and the University of Georgia to build the framework and subsequent assessments. The assessments will undergo field testing and psychometric analysis to in order to provide predictive evidence of effective geometry teaching and student achievement in geometry.
Past research on secondary teachers' mathematics knowledge have relied on indicators of teacher knowledge like course grades,lists of courses, and teaching experience. GAST will provide measures of teachers' geometry knowledge for teaching that provide predictive evidence of classroom performance and student achievement.The framework and assessments developed in the project could be used by: (1) researchers to explore teachers' geometry knowledge for teaching and its impact on instructional practices and student achievement and to measure relationships among teachers' geometry knowledge, their attitudes and beliefs, their classroom performance, and student achievement; (2) project directors and evaluators of projects, institutes, and other professional development programs and postsecondary course instructors to assess the degree to which secondary teachers possess geometry knowledge for teaching and to determine program impact on this knowledge; and (3) mathematicians, teacher educators, school administrators, and practicing and prospective teachers to provide diagnostic information about teachers' geometry knowledge for teaching.
Knowledge for teaching, for example high school geometry teaching which is the focus of this project, is a specialized knowledge base that includes both knowledge of the geometry content and knowledge of specific strategies and approaches for teaching foundational concepts in the domain of geometry. This means that simply knowing lots of geometry, while necessary, isn't sufficient to guarantee that someone would be an effective geometry teacher. Likewise, knowing lots of strong strategies for teaching in general, while helpful, may or may not apply in the specific case of geometry, and an effective geometry teacher needs to not only have a strong repetoire of pedagogical strategies but know when and how to apply them when teaching specific geometry ideas. Capturing and measuring this specialized knowledge for teaching high school geometry (or any subject) is an important piece of information for developing and delivering courses or professional development for teachers to support their continuing growth in effectiveness with their students. Such measures of geometry knowledge and teaching practices to be an effective teacher of geometry did not yet exist prior to this project. This project, Geometry Assessments for Secondary Teachers (GAST), undertook a careful and systematic process adhering to best test development standards to design and test strong Geometry Assessments for Secondary Teachers. The project was conducted in four phases. In Phase I, we reviewed and synthesized information from a variety of sources to ultimately describe in some detail the appropriate geometry knowledge and teaching practices needed to be an effective geometry teacher (GAST Framework). In Phase II, we used this framework to develop an assessment blueprint that specified what specific assessment items would be targeting and at what depth of thinking, and used this assessment blueprint to develop initial assessment items. In Phase III, two equivalent forms of a preliminary assessment were generated from these items, balancing topic areas, complexity of thinking, and pedagogical strategies across the two forms. We chose to develop two equivalent forms so that these final products could be used in a pretest-posttest format by potential users (e.g. teacher professional development providers, instructors of teacher courses at universities) who wished to have non-identical but comparable measures available. This phase included beta testing of items and refining items as needed. In Phase IV, we undertook a multitude of field testing studies to establish the psychometric characteristics of the assessments and to generate evidence that the assessments were validly measuring the types of knowledge we intended. Additionally, we conducted a study to explore the predictive validity of the assessments in terms of teacher impact on student achievement in geometry. In other words, we explored if teachers who scored higher on GAST tended to be more effective in supporting their students' growth on geometry achievement. Overall results from the assessment development process and field testing indicated acceptable psychometric qualities and form comparability for GAST Form A and GAST Form B. There was evidence that the assessments functioned adequately in measuring teacher knowledge in alignement with the intended blueprint of subdomains that was developed in Phase II. Field testing with different groups of people (practicing geometry teachers, pre-service teachers, college students in mathematics or engineering who were NOT studying to become high school teachers) showed that the practicing teachers outperformed both other groups on the content and the pedagogical elements of the assessment. While results also showed that the college mathematics/engineering students outperformed the pre-service teachers on content, the pre-service teachers outperformed the mathematics college students on pedagogy. Collectively, this is evidence for the existence of specialized knowledge for geometry teaching (strong content AND strong specialized pedagogy) and our assessments were able to capture these distinctions. Finally, field testing did offer evidence suggesting that teachers' scores on the GAST assessments were predictive of student achievement in geometry. In summary, the resultant geometry assessments from this project offer a new tool that has generated evidence of usefulness for capturing and measuring the complex teacher knowledge for teaching geometry. As we continue to seek approaches to support the stronger development of teachers - geometry teachers in the case of this project - to be as effective as possible with their students, having a measurement tool to capture that complex knowledge offers a resource that may prove useful for shaping and refining teacher development courses and projects.