The purpose of this study was to explore the ways elementary pre-service teachers responded to hypothetical student misconceptions about area measurement topics, framed in the context of their ...existing understanding and the Mathematical Knowledge for Teaching framework. Data collection consisted of written pre-assessments, followed by semi-structured interviews with 24 pre-service teachers enrolled in a geometry and measurement course. Findings included a frequent misattribution of area understanding to students, tendencies to provide alternate procedural strategies or re-explain concepts, and key differences in pedagogical strategies depending on initial content knowledge or apparent correctness of the student response. While there existed a tendency among some pre-service teachers to encourage procedural approaches, several others were able to leverage their own understanding towards conceptual, student-centered instructional responses. Such responses placed the student at the center of the instructional interaction, paving the way for exploration and mathematical discovery. Recommendations for supporting pre-service teachers in navigating the intersection between content and pedagogical knowledge in area measurement are discussed.
The authors describe the development and validation of 2 forms of the Geometry Assessments for Secondary Teachers (GAST), which were designed to assess teachers' knowledge for teaching geometry. GAST ...assessment scores explained a statistically significant but small amount of the variance of student scores, demonstrating an effect that was greater than the number of years of teaching experience but smaller than the effect of having an advanced degree.
The purpose of this work was to explore how elementary pre-service' teachers (PSTs) responded to a volume task that asked for a coordination of changes in one dimension with changes in volume. We ...carried out both written pre-assessments and follow-up interviews with seventeen PSTs, focused on exploring volume content knowledge. Our findings indicated that the PSTs in the study used primarily the volume formula to respond to the task correctly. In follow-up interviews, PSTs struggled to justify their answers in different ways, however. Recommendations for supporting PSTs in similar teacher education programmes are discussed.
The purpose of this work was to explore how elementary pre-service teachers responded to a novel strategy for justifying the triangle area formula. We conducted interviews with 24 pre-service ...teachers, asking them to evaluate and respond to a hypothetical student strategy for the triangle area. Findings highlighted several interesting struggles our pre-service teacher experienced when assessing the mathematical content of the strategy, as well as differences in pedagogical responses depending on content knowledge. In many cases, pre-service teachers leveraged their understanding towards productive responses, while also grappling with a generalization of the strategy to other contexts. Recommendations for supporting pre-service teachers in navigating the intersection between content and pedagogical knowledge are discussed.
The purpose of this study was to examine middle school students' proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The ...underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through an achievement test from 935 sixth, seventh and eighth grade students. The achievement test included real life problems that required proportional reasoning, and were related to the measurement of length, perimeter, area and volume concepts. In addition, task-based interviews were conducted on 12 of these students to collect more comprehensive data and to support the findings of the achievement test. Findings revealed that although students were mostly successful in giving correct answers, their reasoning lacked a clear argument of the direct and indirect proportional relationships between the variables and that they approached the problems by superficial characteristics of the problems.
