Showing papers in "The Journal of Mathematical Behavior in 2011"

TL;DR: In a ten-week teaching experiment, two students, neither of whom had previously seen the conventional ǫ-δ definition of limit, reinvented a formal definition, capturing the intended meaning of the conventional definition.

TL;DR: In this article, the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus were presented, and a framework emerged that includes four overarching end goals for understanding the first year calculus.

TL;DR: This article implemented one-on-one fractions instruction to eight preservice teachers, which was centered on problem solving and on progressively formalizing the participants' intuitive knowledge of fractions, and found that the intervention showed improvement on one measure of conceptual knowledge but not on a transfer task, which required the teachers to generate word problems for number sentences involving fractions.

TL;DR: In this article, the notion of a personal example space is introduced, defined as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task.

TL;DR: Artigue et al. as discussed by the authors report on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations.

TL;DR: The authors explored misconceptions of the number line which are revealed when pre-service primary teachers locate negative decimals on a number line and found that these misconceptions explain a large percentage of wrong answers.

TL;DR: The authors examined the roles and purposes of proof mentioned by university research faculty when reflecting on their own teaching and teaching at their institutions and found that learning how to prove theorems is the most prominent role of proof in upper division undergraduate mathematics courses and that this training is considered preparation for graduate mathematics studies.

TL;DR: In this article, the authors investigated the functional thinking ways in the early grades, particularly those of elementary school fifth grade students through linear function tables and found that the students were able to discover the correspondence relationship and generalize this relationship.

TL;DR: The authors conducted semi-structured interviews with in-service fifth grade teachers to examine teachers' reactions to arguments that.999 ǫ = 1 and found that teachers continue to develop repeated decimal understandings and misunderstandings throughout their careers, and that the curriculum, everyday experience and perceptions of student learning combine to form or reinforce these understandings.

TL;DR: In this paper, a teaching experiment designed to integrate algebra and proof in the high school curriculum is presented, where students are asked to generate algebraic proofs involving multiple variables, based on conjectures they themselves generated.

TL;DR: This article investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID, and found that students treated the specific given example as a generic example and were able to reach a generalization in a process of systematic change and comparison.

TL;DR: In this paper, the authors discuss how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems compared to other students who are proficient in numeracy and are skilled readers.

TL;DR: In this paper, a redesign of a teacher development programme was proposed to help teachers realize Polya's original vision of Look Back in the classroom. But, although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare.

TL;DR: The authors argue that the way words are used in natural language can influence how the same words are understood by students in formal educational contexts, and that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics.

TL;DR: This article investigated the use of pedagogical representations by Chinese and U.S. teachers to solve mathematical problems in the Learner's Perspective Study and found that multiple representations were constructed simultaneously to develop the connection of relevant concepts in the US. classrooms while selective representations are constructed to develop relevant concepts and strategies of using representations to solve problems by Chinese teachers.

TL;DR: This article analyzed interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem and found that increasing their meta-level awareness of the features of their mental constructions may help students overcome common difficulties with the infinite.

TL;DR: In this paper, the authors used authentic research projects and related curriculum materials when teaching elementary statistics in secondary and undergraduate settings, and measured content knowledge, perceived usefulness of statistics, and statistics self-efficacy.

TL;DR: In this paper, the authors look at 21 fifth grade students as they discuss a linear graph in the Cartesian plane, where the problem presented to students depicted a graph showing distance as a function of elapsed time for a person walking at a constant rate of 5 miles/h.

TL;DR: In this article, a series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students' conceptualizations of distribution over the course of 8 weeks of instruction.

TL;DR: In this article, the authors explore processes of flexibility and coordination among acts of visualization and analysis in students' attempt to reach a general formula for a three-dimensional pattern generative model.

TL;DR: In this paper, the authors explore how work that learners do with models can help them to transform, not simply their understanding of key concepts, but also how they come to view themselves as thinkers and learners, as collaborators in a social process that their work and thinking help to constitute.

TL;DR: The authors describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students' conceptual levels, and one class room teacher is assigned to each student at the start of the year.