Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

Combinatorial enumeration has a variety of important applications, but there is much evidence indicating that students struggle with solving counting problems. The roots of such difficulty, as well as ways to mitigate such difficulty, have not yet been thoroughly studied. In this paper, one particular aspect of students' counting activity is…

This study explores two number composition and decomposition activities from a numeracy perspective. Both activities have the same mathematical structure but each employs different tools and contexts. Twenty kindergarten children engaged individually with these activities. Verbal utterances as well as actions of the child and interviewer were…

This paper reports on one part of a large study which attempted to identify the linguistic and hierarchical characteristics of van Hiele theory amongst grade 10 learners. The sample consisted of a total of 359 participants from five purposively selected schools from Mthatha District in the Eastern Cape Province of South Africa. The performance of…

This case study contributes to efforts to characterize teaching that is responsive to children's mathematical thinking. We conceptualize "responsive teaching" as a type of teaching in which teachers' instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children's…

It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…

This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in…

Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

Participants in this study were asked to report what strategies were most often used in their attempts to foster their students' problem solving abilities. Participants included 70 second through fifth-grade elementary teachers from 42 schools in a large state of the south central region in the U.S. Data analyses of the interviews revealed that…

Six middle school students identified as having a specific learning disability or at risk for mathematical difficulties were taught how to solve multi-step equations by using the self-regulated strategy development (SRSD) model of instruction. A multiple-probe-across-pairs design was used to evaluate instructional effects. Instruction was provided…

High school mathematics students often complete homework and study for unit tests without support to consider how these actions could contribute to their mathematical learning. Learning to learn mathematics invites students to bring into view how they learn mathematics. The constructivist grounded theory study reported in this presentation…

Self-regulated learning is an elaborate metacognitive process consisting of an individual's awareness of the thought process, flexibility in one's approach to problem solving, and motivation to persist through obstacles until a goal has been met. Strategies and instructional practices used to develop mathematically proficient thinkers also develop…

In this paper, we share our experience of searching for ways in which to access learner dispositions and the evolution of an instrument that we have used as both a written and an interview instrument. We argue for the importance of understanding young learner mathematical learning dispositions in order to inform ways in which to support learning.…