Journal of Mathematical Behavior最新文献

More college mathematics classrooms are adopting active learning practices like groupwork. These practices typically foreground vocal communication and interpersonal interactions, both of which are mediated by language. Given that undergraduate classrooms in the U.S. are also becoming more racially and linguistically diverse, this study focuses on multilingual students of color, whose learning experiences have often been overlooked. Specifically, this study aims to learn more about the relationship between groupwork and equity in classrooms with linguistic diversity. Using positioning theory, this study analyzes the learning narratives of 26 multilingual students of color about their experiences working with peers in groups. Findings demonstrate that while multilingual students described enacting a range of different positional identities during groupwork, they were more likely to report being positioned by others in deficit ways. Results highlight how the positional identities perceived to be available to students were often constrained by normative classroom Discourses about language, participation, and mathematics.

It is important to understand teachers’ views about problem-posing (PP) tasks and the prompts that are used in such tasks to engage students in posing problems. In this study, we explored 15 middle school mathematics teachers’ views about PP prompts. We found that the teachers’ views were motivated by their curricular reasoning around engaging and challenging their students and addressed five main prompt characteristics: openness, promoting critical thinking, providing scaffolding, more or less intimidating, and allowing for differentiation. The teachers’ reasoning suggested they attended to how PP can create opportunities for sensemaking, deepen students’ learning of mathematics, and foster students’ identities as creative doers of mathematics. However, they did not address connecting students’ life experiences to mathematics, another key goal of teaching mathematics through PP. The findings have implications for curriculum developers and researchers regarding the design of PP tasks and the implementation of such tasks in the classroom, and they suggest several directions for future research.

Using a mixed methods approach, we report results from the evaluation and validation stages of a fully online Measure of Graph Selection and Reasoning for Dynamic Situations, implemented with undergraduate college algebra students across three U.S universities. The measure contains six items; each includes a video animation of a dynamic situation (e.g., a fishbowl filling with water), a declaration of understanding, four Cartesian graphs from which to select, and a text box for explanation. In the evaluation stage, we demonstrate usability and content validity, drawing on individual cognitive interviews (n = 31 students). In the validation stage (n = 673 students), we use Rasch modeling to evidence reliability and internal structure, establishing a continuum of item difficulty and confirming the viability of a partial credit scoring approach for graph selection. Rasch results provide statistical support that the theorized graph reasoning framework (Iconic, Motion, Variation, Covariation) from Johnson et al. (2020) forms a hierarchical scale.

This research presents a study on the problems posed by pre-service primary school teachers by focusing on the problem-posing tasks situation as the research variable. The investigation was carried out with 205 students of a bachelor’s degree in Primary Education Teacher in Spain. They were asked to pose problems with fractions based on two given initial situations: numerical and contextualized. For each problem, we analyze its plausibility, the meanings of fractions, the mathematical structure, and the reasonability of the context. Results indicate that mostly posed problems use part-whole or operator meaning of fractions, as well as the additive or multiplicative structure. There are no differences between the plausibility and reasonability of the problems based on the initial situation, although it has shown better results when the given situation is contextualized. In addition, in contextualized situations, teachers show greater ability in formulating problems with a wide variety of structures and meanings of fractions.

Few studies have considered the relationship between what families recognize as mathematical and their mathematical identities despite attention to forms of informal mathematical learning. The trends in what goes unrecognized as mathematical for families reflect larger societal expectations about who and what can count as mathematics, rendering mathematical practices at home invisible. Limited views of mathematics as centered in school and tied to algorithms lead many rich and informal practices to go unrecognized by families, contributing to negative images of their mathematical selves. This study looks at the practices and activities mothers engage in with their young children that involve mathematics, specifically focusing on how they frame mathematics and their activity within it.

This study examined the relation of mathematical learning and problem-solving to influences close to the child (proximal) and social structures more removed (distal). A socio-ecological lens enables examination of multi-level influences within the religious practice of tithing (giving 10% of one’s earnings to the church). Distal influences (e.g., tax law) and proximal influences (e.g., norms for payment, parental practices) are investigated to explain the emergence of mathematical problems during the practice of tithing. Exploration of children’s success and strategy use as a function of problem context found differential success and strategy use when children solved problems of tithing, as compared to a mathematically similar school context. This research demonstrates how proximal and distal factors can illuminate the contours of everyday mathematical performance.

Our study explores boundaries and boundary crossing between communities of mathematics teaching (MT) and visual art teaching (AT). We focus on teacher collaboration, draw on communities of practice and examine the existing boundaries and the way collaborating members handle them. We present data from 17 group meetings of secondary school art and mathematics teachers who try to develop ways of linking ΜΤ and ΑΤ. Results indicate the emerging boundaries by means of discontinuities regarding mathematical practices and tools used in MT and AT, and the disciplines’ teaching and curriculums. Via analysis of the central boundary – the analytical or visual ways of thinking – we present members’ boundary handling that indicates the development and developmental process of integrated practice. The study incorporates boundary crossing processes and learning mechanisms in which the two separate ways of thinking are gradually transformed into an integrated one and reveals possible ways of integration in teaching and learning.

Analogical reasoning is an important mathematical process for undergraduate students. However, it is unclear how students understand analogies that are presented to them, and more importantly, how students understand and create their own analogies. In this paper, we present a case study of four students as they reason analogically about several structures in abstract algebra. In particular, we expand on the notion of structure sense to include a wider range of structures in advanced mathematics and attend to each students’ analogical structure sense associated with each structure. Findings suggest that although students may possess a strong structure sense for group-theoretic structures, it is not necessarily the case that they possess a comparatively strong analogical sense of structure for ring-theoretic structures. In addition, those students with weaker senses of structure for group-theoretic structures are still able express productive reasoning about ring-theoretic analogies. Implications for future research and instructional practice are discussed.

This study contributes to understanding the influence of different problem posing tasks on the performance of in-service teachers in posing important and worthwhile mathematical problems. The problem posing tasks pertain to the part-whole concept of fraction which presents ongoing challenges for teachers and students. The study sample was comprised of 40 in-service primary school teachers who completed an electronic problem posing test. The problem posing tasks included different problem situations and prompts that addressed: (a) four types of problem posing processes (editing, selecting, comprehending, and translating), and (b) four levels of complexity (uni-structural, multi-structural, relational, extended abstract). The results suggested that in-service teachers’ performance is mainly influenced by the process involved in a problem posing task, being higher in problem situations that are more closed structured compared to more open structured. The level of complexity was not found to influence in-service teachers’ performance.