The purpose of this study was to investigate the affordances and constraints of a technological tool to foster pre-service teachers' (PSTs) noticing skills including attending to, interpreting, and responding to students' mathematical work. Participants were 99 junior or senior PSTs in a mathematics pedagogy course at a large university. Using…

This study is an examination of 79 elementary prospective teachers' (PSTs') capacity for recognizing the core ideas involved in modeling fraction addition problems and their difficulties in solving and presenting the process of fraction addition using area, length, and set models. PSTs completed a written task in which they represented the process…

This study is an investigation of the possible relationship between clinical interview skills and teacher noticing. In a multiple case study, video-recordings of pre-service teachers' (PSTs') mathematical clinical interviews and their written critiques of a mathematics lesson were examined using qualitative content analysis. Findings suggest that…

Despite the importance of teachers' conceptions of and competency in problem solving, limited attention is given to this area in the current literature. We examined 96 preservice elementary teachers' problem-solving conceptions and performances by having them define and create metaphors for problem solving and then investigated the relationships…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

The purpose of the study was to investigate how Lesson Study influences pre-service teachers' learning to professionally notice students' mathematical thinking. The initial and last video-recorded discussions were analysed using a qualitative method. Findings suggest that Lesson Study can be useful means to improve pre-service teachers' noticing…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…

A task-based written survey was administered to 69 pre-service teachers (PSTs) at a large Midwestern University in the USA to examine their recognition of examples/non-examples of [one-fourth] presented in various forms of the area model, their perceived mathematical key points in identifying examples/non-examples, and their instructional…

To shed light on the value of the area model as a tool to elicit pre-service teachers' (PSTs') understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an "atypical" way. We administered a written…

In this study we investigated pre-service teachers' (PSTs) proportional reasoning and how they interpret their calculations in proportional tasks. We administered a written questionnaire to 199 PSTs and used an inductive content analysis approach for data analysis. We found that one item, in which PSTs were asked to interpret the meaning of the…

This study is an investigation of elementary preservice teachers' (PSTs') exploration of model breaking points in fractions. Eighty-three PSTs at two universities in the Midwestern and Southwestern regions of the USA were asked to explore the area model of fraction addition through a series of tasks and explain their reasoning in determining its…

This study investigated 111 pre-service teachers' (PSTs') flexibility with referent units in solving a fraction division problem using a length model. Participants' written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest…

We investigated how pre-service teachers (PSTs) interpret their calculations in proportional tasks. A written questionnaire was administrated to 199 PSTs and an inductive content analysis approach used for data analysis. We found that one item that asked PSTs to interpret the meaning of their results had unusually low success; open coding on the…

This study investigates patterns exhibited by pre-service teachers (PSTs) while practicing feedback in response to students' solutions on a procedure-based mathematics assessment. First, we developed an analytical framework for understanding mathematics PSTs' written feedback. Second, we looked into how a learning module on a multimedia platform…

Despite the importance of teachers' conception of effective problem-solving instruction, limited attention is given to this area in the current literature. In this study we examined 96 preservice teachers' (PSTs) views on effective problem-solving instruction and how their conceptions are related and reflected in their views on problem solving and…