Search results for: Mathematical concepts

The present article reports on the results of three different investigations into pre-service teachers’ understanding of the mathematical concepts of area and perimeter. The results indicated that many pre-service teachers across the cohorts had a procedural understanding of area and perimeter, displayed similar misconceptions to their student counterparts, and were limited in their ability to demonstrate examples of the mathematics knowledge required to teach these topics.

This study describes changes in secondary mathematics teachers’ mathematical knowledge for teaching function through their engagement in a mathematics methods course teaching experiment. The participants in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the connections they could make between function representations, and to consider the role of definition in mathematics and the K-12 classroom. The course focused on function which supports work in the classroom; by focusing on one topic, teachers experience the sequencing of tasks and topics in ways that build a conceptual understanding, much in the way that they might design a curricular sequence in their own classroom.Furthermore, the course activities provided teachers with opportunities to refine and elaborate those initial understandings.

In this article, the author describes the development of a series of tasks designed to investigate and measure teachers’ mathematical knowledge for teaching geometry and measurement. The author presents three design features for rich, open-response items that assess mathematical knowledge for teaching. The set of six two-dimensional geometry and measurement tasks embody these design features and illustrate the ways in which the tasks are grounded in the context of teaching, capture nuanced teacher performance, and measure common and specialized content knowledge. The examples of teacher performance on these tasks illustrate the ways in which the tasks can differentiate teacher performance.

The goal of this study is two-fold: 1) to examine the role content knowledge plays in prospective teachers’ (PSTs) ability to recognize children’s conceptual understanding of mathematics, and, 2) to examine examined PSTs' ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. The results of this study suggest that content knowledge is necessary but insufficient in supporting PSTs’ ability to recognize evidence of children’s conceptual understanding of mathematics.