Journal of Mathematical Behavior最新文献

Our study focuses on the interplay of two secondary school mathematics teachers’ emotions and decision-making in pivotal teaching moments. We highlight the interaction between teacher emotions and in-the-moment decision-making, and resources that coordinate this interplay, suggesting a theoretical and methodological way of addressing it. Our analyzed data comes from three teachers’ lessons and four semi-structured interviews. When analyzing pivotal moments where the teacher handles students’ errors, it appeared that teacher emotions and resources are interrelated elements of the decision-making. Findings show that: (1) teachers’ emotions, while handling students’ errors, are mostly negative, but differ in their kind and source; (2) the formation of teacher emotions and actions often seems to draw on the same resources (social-spatial, anticipatory-temporal, moral-ideological dimensions, and teacher’s responsibility about mathematics; (3)teachers’ actions, while handling students’ errors, differ in relation to the resources and the emotions that coordinate their formation.

Understanding algebraic properties is a key component of building mathematical thinking across grades K-8, yet less is known about the development of students' use of mathematical properties within their strategies. This article presents results from four conversations with 24 5th-grade students over a school year, that focus on examining the development of students grouping within strategies for multiplication and division problems. Findings add to previous research on student strategies within multiplication and division by detailing some of the nuances in students' use of grouping. Additionally, a focus on student strategies reveals students' progression in more explicit use of grouping underlies the development of more planful use of the distributive and associative properties of multiplication.

Logical structures count as critical learning content for learning to prove. They are often not sufficiently explicated, and students struggle to use and articulate them in their proofs. In this design research study, we adopt a scaffolding approach to engage high school students in using and articulating logical structures. The qualitative analysis of the design experiments reveals the potentials and limitations of graphical scaffolds, showing how graphical scaffolds must and can be complemented by linguistic scaffolds to enable students to select and combine arguments in a deductive chain and write a proof text. Implications for language-responsive proof teaching and learning are discussed.

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.