Publications

This study uses structural equation modeling to investigate the relationships between pre-service teachers’ (PSTs’) course-taking history, beliefs about mathematics, beliefs about students’ mathematical ability, and opinions about (1) how student errors should be addressed when they occur and (2) how much emphasis should be given to various forms of assessment. The results indicate that some types of courses are strongly associated with beliefs about the nature of mathematics. Specifically, PSTs who have taken more mathematics courses are more likely to see mathematics as a set of rules. PSTs’ views about mathematics strongly predict their beliefs about who can do high-level mathematics, how they think student errors should be addressed, and which forms of assessment they think are most appropriate. Implications for teacher preparation programs are discussed.

The early development of spatial reasoning skills has been linked to future success in mathematics (Wai, Lubinski, & Benbow, 2009), but research to date has mainly focused on the development of these skills within classroom settings rather than at home. The home environment is often the first place students are exposed to, and develop, early mathematics skills, including spatial reasoning (Blevins-Knabe, 2016; Hart, Ganley, & Purpura, 2016). The purpose of the current study is to develop a survey instrument to better understand Kindergarten through Grade 2 students’ opportunities to learn spatial reasoning skills at home. Using an argument-based approach to validation (Kane, 2013), we collected multiple sources of validity evidence, including expert review of item wording and content and pilot data from 201 parent respondents. This manuscript outlines the interpretation/use argument that guides our validation study and presents evidence collected to evaluate the scoring inferences for using the survey to measure students’ opportunities to learn spatial reasoning skills at home.

Classroom assessment research in the United States has shifted away from the examination of teacher-made tests, but such tests are still widely used and have an enormous impact on students’ educational experiences. Given the major shifts in educational policy in the United States, including the widespread adoption of the Common Core State Standards, I argue that researchers should examine the tests and quizzes that teachers create and administer in order to determine whether those policies have had the intended impact on teachers’ assessment practices. Furthermore, these inves­tigations should be grounded in discipline-specific conventions for developing and demonstrating knowledge. I then propose a research-based framework for analysing mathematics exams that focuses on alignment with learning goals, cognitive complex­ity, variety of task formats, attentiveness to culture and language, and clarity of expectation. This framework is meant to be used formatively, helping researchers, administrators, and teachers iden­tify strengths and areas for growth.

High-school mathematics teachers tend to use computational, constructed response questions in their classroom tests. However, the rapid shift to distance learning resulting from the COVID-19 pandemic created technological obstacles to using these items.  This study investigated teachers’ reasons for using particular items and how they adapted their assessment practices during distance learning.  Teachers reported using computational items because they provided insight into students’ thinking, helped with determining point allocations, and prevented academic dishonesty.  During distance learning, most sample teachers maintained their use of these items by collecting students’ written work via uploaded photographs or a “whiteboard” feature in a paid assessment system. Despite continued use of computational questions, few teachers reported using shown work to determine student understanding or to assign partial credit.  Instead, they relied heavily on auto-grading and reported collecting student work mostly to deter cheating.  Implications of these findings and future directions for research are discussed.

There is renewed interest around including performance assessments in state and local assessment systems to spur positive changes in classroom instruction and student learning. Previous research has identified the external conditions that mediate the role of assessment in changing instructional practices. We extend that work by focusing on the internal classroom conditions that support improvements in student learning. We identified six key instructional practices from three teacher quality frameworks that may result from policy changes that include complex, performance-based assessments. For each practice, we explored the bidirectional relationships among the instructional core of students, teachers, and content. We argue that altering these relationships requires teachers and students to have both the disposition and the capacity to change, and we identify the assumptions that need to hold in order for those changes to occur in response to the inclusion of performance assessments in state and/or local assessment systems.

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