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…

This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

Teacher telling continues to be poorly understood within inquiry. In this paper I extend prior efforts to reimagine telling within contemporary pedagogical thought. Using a case study, I investigated a well-regarded teacher's use of mathematical telling while supporting groups and individuals working on tasks. The teacher used seven unique types…

This paper represents research that exists at the crossroad of scholarly practice and scholarly inquiry. We share the design, enactment and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST) which engaged 18 prospective teachers in two sessions of one on one problem posing with 3rd…

In this paper we frame our observations in enactivism, specifically problem posing, to propose the notion of problem drift as a method to analyze the curriculum generating actions of small group learning systems in relation to teacher interventions intended to trigger specific content goals. Teacher attentiveness to problem drift is suggested to…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher…

Math Teachers' Circles (MTCs) bring math teachers and university mathematicians together to engage in collaborative mathematical activity. Currently there are over 110 MTCs across 40 states. A key claim is that MTCs are "communities of practice." However, to date there has been no research to substantiate this claim. In this paper, we…

Conventions play an important communicative role in mathematics. Likely due to the complex relationship between conventions and school mathematics, few education researchers have questioned or investigated the consequences of instruction and curricula that primarily, if not unquestionably, maintain conventions. Drawing on Piagetian notions of…

The aim of this paper is to build up an argument about the importance of a mathematical analysis of young children's activity in relevant for the age educational tasks. Most of current approaches (psychological, social, and pedagogical) are limited to the study of the development of children's thinking, paying less attention to the involved…

The classroom implementation of open-ended mathematics tasks, such as Model-Eliciting Activities (MEAs), can be challenging for teachers. This case study research considers a teacher, Adam, implementing a lesson intended to be an MEA on graphical antiderivative. We describe the lack of alignment of the written, intended and enacted curricula that…

This study on the mental solving of systems of linear equations is part of a larger research program, aimed to gain a better understanding of the potential of mental mathematics activities with topics/objects other than numbers. Through outlining the study details and the activities engaged with, the paper reports on the variety of strategies…

This research highlights a university-school division collaboration to pilot a professional development framework for integrating STEM in K-8 mathematics classrooms. The university researchers worked with mathematics coaches to construct a realistic and reasonable vision of STEM integration built upon the design principles of model-eliciting…

This cross-case analysis of three distinct letter writing activities between prospective teachers (PTs) and K-12 learners provides insights into PTs' levels of feedback according to Hattie and Timperley's (2007) framework. PTs' written feedback from letter writing activities conducted in teacher preparation programs were analyzed using this…

Research about teacher noticing of students' mathematical thinking has been an important and ongoing strand of research and practice in mathematics education. Our work extends this agenda by working collaboratively with teachers to learn together how to notice students' mathematical strengths. The lens on strengths runs counter to the prevalent…