This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

Our study investigates preservice teachers' perceptions of real-world problems; their beliefs about teaching real-world contexts, especially ones sociopolitical in nature; and their ability to pose meaningful real-world problems. In this paper we present cases of three preservice teachers who participated in interviews that probed their thinking…

This paper outlines a framework to explain the early development of place-value understanding based on an analysis of data from 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. The children were assessed individually on number knowledge tasks (recalled facts, subitizing, counting, place-value understanding) and…

Considering the role of mathematics-focused professional development programs in improving teachers' content knowledge and quality of teaching, we provided teachers opportunities for dealing with mathematics problems and positioning themselves as students in a large-scale long-term professional development (PD) project. In this proposal, we aimed…

The positive correlation between spatial ability and mathematical ability has been well-documented, but not well-understood. Examining student work in spatial situations that require numerical operations provides us with insight into this elusive connection. Drawing on student work with angle, length, volume, and area, we examine the ways in which…

Based on the findings of a larger study on middle school students' problem solving behaviors, we identified three sub-components for understanding the iteration of unit area in this paper: the mechanism of iteration, an identical unit, and the specificity of the identical unit. A three-stage progression on the acquisition of these components is…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

This study aims to design learning situations and tasks that promote and assess the capacity of primary school children to transfer mathematical knowledge to new contexts. We discuss previous studies investigating mathematical transfer, and particularly the strengths and limitations of tasks used to assess transfer in these studies. We describe…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

In Yucatec Maya middle schools in the Yucatán, math scores are low and drop out rates are high. Although addressing larger social and economic causes may ameliorate these issues, improving math instruction may be a more immediate, feasible approach. This ethnographic, mixed-methods study explores community approaches to problem-solving relevant to…

Ethnographic research is an emerging research technique in the field of education. Ethnographic research was a procedure usually used in anthropology but now it is getting popular in educational field. This kind of research relies on qualitative data, its perspective is holistic and its procedures of data analysis involve contextualization. Data…

This report presents dual analyses of an undergraduate student, Cassie, whose work provides nice contrasts between Grounded Theory (GT) analysis and Knowledge Analysis (KA). The analyses highlight particular methodological differences, such as grain size of findings, positioning of novices and more general implications about expert-novice studies.…

The study reported on in this paper is an interview study conducted with 20 7th and 8th grade students whose purpose was to understand the generalizations they could make about non-linear meanings of multiplication (NLMM) and non-linear growth (NLG) in the context of solving combinatorics problems. The paper identifies productive challenges for…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

The study reported in this paper is part of a larger study on the roles of examples in learning to prove. We focus here on manifestations of students' productive use of examples for proving in the course of exploring conjectures and proving or disproving them. In this context, we define productive use of examples for proving as students'…