Summary
Contents
Subject index
The Sage Handbook of Research on Classroom Assessment provides scholars, professors, graduate students, and other researchers and policy makers in the organizations, agencies, testing companies, and school districts with a comprehensive source of research on all aspects of K-12 classroom assessment. The handbook emphasizes theory, conceptual frameworks, and all varieties of research (quantitative, qualitative, mixed methods) to provide an in-depth understanding of the knowledge base in each area of classroom assessment and how to conduct inquiry in the area. It presents classroom assessment research to convey, in depth, the state of knowledge and understanding that is represented by the research, with particular emphasis on how classroom assessment practices affect student achievement and teacher behavior. Editor James H. McMillan and five Associate Editors bring the best thinking and analysis from leading classroom assessment researchers on the nature of the research, making significant contributions to this prominent and hotly debated topic in education.
Classroom Assessment in Mathematics
Classroom Assessment in Mathematics
Classroom assessment (CA) in mathematics has evolved considerably over the past 20 years, from summative assessments like daily quizzes, chapter tests, unit tests, and end-of-course assessments primarily used to assign student grades to formative assessments (or assessments for learning), which include teacher questioning and feedback during lessons, student writing assignments, and individual or group projects. Changes in mathematics CAs have been stimulated by changes in national mathematics standards—the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991), the Assessment Standards for School Mathematics (1995), the Principles and Standards for School Mathematics (2000), and more recently, the Council of Chief State School Officers (CCSSO) Common Core State Standards in Mathematics (2010). These documents not only describe important mathematics content for Grades K–12, but they also identify important mathematical processes like problem solving, reasoning, and inquiry that all students should develop.
As a result of widespread acceptance of these national documents, the goals of mathematics teaching have become broader and deeper with regard to student learning. Therefore, CAs must be varied and flexible in order to capture students’ levels of learning and thinking and provide teachers with important feedback about different levels of learning. Therefore, teachers now must incorporate a wider range of assessments, like portfolios, projects, and extended-response items, to assess students’ higher-level learning.
In this chapter, we examine the research on CA in mathematics by analyzing research findings with regard to teachers’ implementation of effective CA practices in mathematics and their effects on student learning and attitudes. We have organized our review of the research on CA in mathematics into three categories: (1) formative assessment practices in mathematics, (2) summative assessment practices in mathematics, and (3) the impact of external mathematics assessments on CA and instruction. We end the chapter with a discussion of topics for further research.
Formative Assessment Practices in Mathematics
As noted in the formative assessment section of this handbook, research has shown that formative assessment can lead to improved student achievement. Formative assessment is multifaceted and complex. Leahy, Lyon, Thompson, and Wiliam (2005) characterized this complexity as teachers paying attention to “everything students do—such as conversing in groups, completing seatwork, answering and asking questions, working on projects, handing in homework assignments, even sitting silently and looking confused …” (p. 19). In order to effectively use formative assessment to improve student achievement, teachers must pay attention to all of this information from students and use it to inform their practices. Hence, classroom practice is where we begin our review of the research on formative assessment in mathematics. We then share insights from the literature about challenges involved in implementing formative assessment in the mathematics classroom and professional development.
Classroom Practice
Several researchers have described formative assessment practices in mathematics classrooms. Generally speaking, even though the task is daunting, teachers are attempting to implement formative assessment into their practice in various ways. Specifically, the research on formative assessment classroom practices falls into four categories: (1) integrated practices, (2) isolated practices, (3) student work analysis, and (4) technology.
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