This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…

The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient)…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…

This paper discusses how concepts and procedural skills in problem-solving tasks, as well as affects and emotions, can be subjected to meaningful measurement (MM), based on a multisource model of learning and a constructivist information-processing theory of knowing. MM refers to the quantitative measurement of conceptual and procedural knowledge…

Discusses a performance assessment tool that entails open-ended tasks requiring students not only to provide answers but to show their solution processes. Discusses several areas to address in developing open-ended tasks. Areas include the need to assess important mathematical content and cognitive processes, use of effective prompts, and use of…

This publication describes several different teaching strategies employed to enhance students' understanding of mathematics, such as working in cooperative learning groups, giving presentations based on problems that were solved, and writing about solutions that were found. This innovative approach to teaching mathematics resulted in questioning…

This book contains a set of authentic performance assessments that offer students the opportunity to demonstrate knowledge and multiple science abilities through communication, problem solving, inventiveness, persistence, and curiosity. The specific knowledge and science abilities are drawn from those identified in Benchmarks for Science Literacy…

Students' brains are wired to make them natural, curious learners. The mathematical world around them offers a vast classroom, filled with shapes, spaces, quantities, and experiences to discover and explore, all leading to the construction of understanding. Teachers can use this natural curiosity to tap the inborn neural mechanisms that motivate…