Educational Studies in Mathematics最新文献

Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students’ visual attention to the teacher’s gestural cues during collaborative problem solving remains a largely unexplored field in mathematics education research. This mixed-method case study investigated relations between students’ visual attention, teacher gestures, and students’ collaborative problem-solving process on a geometry task. The data were collected with video cameras and mobile gaze trackers on four students simultaneously in two Finnish 9th-grade mathematics lessons with the same teacher. The findings show that the students attended to their own papers most of the time during the teacher's gestures, but differences in student attention between the gesture types emerged. The qualitative analysis showed that the teacher’s tracing, pointing, and representational gestures helped in directing student attention to targets relevant to the situational learning process. We conclude that teacher gestures can both convey mathematical contents and direct student attention, which intermediates mathematical thinking in problem solving.

This study argues that the works of philosopher Jürgen Habermas can provide useful directions for mathematics education research on statistical literacy. Recent studies on the critical demands posed by statistical information in media highlight the importance of the communicative component of statistical literacy, which involves students’ ability to react to statistical information. By adapting Habermas’ construct of communicative rationality into a framework for statistical literacy, a novel analytical tool is presented that can provide theoretical insights as well as in-depth empirical insights into students’ communication about statistical information. Central to the framework are the four validity claims of comprehensibility, truth, truthfulness, and rightness which interlocutors need to address to engage in statistical communication. The empirical usefulness of the framework is shown by presenting the results of a study that examined Grade 5 students’ responses to fictional arguments about the decline of Arctic sea ice. The Habermas-based framework not only reveals that complex evaluations of statistical arguments can take place even in Grade 5 but also shows that students’ evaluations vary greatly. Empirical results include a content-specific differentiation of validity claims through inductively identified sub-categories as well as a description of differences in the students’ uses of validity claims.

Recent studies have highlighted the importance of ordinality skills in early numerical development. Here, we investigate individual differences in ordering sets of items and suggest that children might also differ in their tendency to spontaneously recognize and use numerical order in everyday situations. This study investigated the individual differences in 3- to 4-year-old children’s tendency to spontaneously focus on numerical order (SFONO), and their association with early numerical skills. One hundred fifty children were presented with three SFONO tasks designed as play-like activities, where numerical order was one aspect that could be focused on. In addition, the children were administered tasks addressing spontaneous focusing on numerosity (SFON), numerical ordering, cardinality recognition, and number sequence production. Our results showed that children had substantial individual differences in all measures, including SFONO tendency. Children’s SFONO tendency was associated with their early numerical skills. To further investigate the association between SFONO tendency and numerical ordering skills, a hierarchical regression was conducted for a group of children who could successfully order sets from one to three at a minimum and were regarded as likely having the requisite skills to spontaneously focus on numerical order. The findings reveal that SFONO tendency had a unique contribution to children’s numerical ordering skills, even after controlling for age, cardinality recognition, and number sequence production. The results suggest that SFONO tendency potentially plays a relevant role in children’s numerical development.

Definitions play an integral role in mathematics and mathematics classes. Yet, expectations for definitions and how they are intended to operate, i.e., mathematical norms for definitions, can remain hidden from students and conflict with other discursive norms, explaining differences in mathematicians’ and students’ understandings of the nature of definitions. We examined how six inquiry-oriented Introduction to Proof instructors supported their students in revising their definition drafts to adhere to mathematical norms. We identified four procedures that effectively supported students’ drafts in adhering to various mathematical norms, particularly to those that worked to increase clarity. We discuss how the instructors’ teaching practices provided different opportunities for students to engage with mathematical norms for definitions, general mathematical norms, and mathematical content.

Grasping mathematical objects as related to processes is often considered critical for mathematics understanding. Yet, the ontology of mathematical objects remains under debate. In this paper, we theoretically oppose internalist approaches that claim mental entities as the endpoints of process–object transitions and externalist approaches that stress mathematical artifacts—such as physical manipulatives and formulas—as constituting mathematical objects. We search for a view on process–object duality that overcomes the dualism of mind and body. One such approach is commognition that describes mathematical objects as discursive entities. This paper expands the nature of mathematical objects beyond discourse and highlights the role of learners’ interaction with the environment by adopting ecological onto-epistemology. We develop a functional dynamic systems perspective on process–object duality in mathematics learning emphasizing embodied actions and the re-invention of artifacts’ affordances. As a main result, we reconsider process–object duality as a reification of repetitive actions into a cultural artifact that consists of two steps: (1) forming a new sensory-motor coordination that brings new perception to the fore and (2) crystallizing a new artifact in a mathematical environment that captures this new perception. An empirical example from research on embodied action-based design for trigonometry illustrates our theoretical ideas.

Graphical abstract

Gestures are one of the ways in which mathematical cognition is embodied and have been elevated as a potentially important semiotic device in the teaching of mathematics. As such, a better understanding of gestures used during mathematics instruction (including frequency of use, types of gestures, how they are used, and the possible relationship between gestures and student performance) would inform mathematics education. We aim to understand teachers’ gestures in the context of early algebra, particularly in the teaching of the equal sign. Our findings suggest that the equal sign is a relatively rich environment for gestures, which are used in a variety of ways. Participating teachers used gestures frequently to support their teaching about the equal sign. Furthermore, the use of gestures varied depending on the particular conception of the equal sign the instruction aimed to promote. Finally, teacher gesture use in this context is correlated with students’ high performance on an early algebra assessment.

While numerous studies have investigated teachers’ professional learning through their interaction with resources, the question of how teachers’ knowledge evolves at different stages of the instructional process remains underexplored. To address this gap, this article builds on the documentational approach to didactics (DAD) and the theory of instrumental orchestration to investigate teachers’ professional learning in terms of document development through their interaction with resources in and out of class. To this end, the paper proposes a theoretical and methodological model to analyze the evolution of a document, focusing on the joint evolution of utilization schemes and professional situations. This model provides analytical tools to track the development of teachers’ professional knowledge. The theoretical and methodological model was applied to a case study involving a Tunisian primary school teacher who used the technological resource GeoGebra for the first time to introduce the properties of parallelograms to 6th grade students (aged 11–12). Findings suggest the relevance and operationality of the proposed model, through a short-term analysis of documentational genesis, to track the evolution of the teacher’s professional knowledge related to the use of GeoGebra in class. This model can be considered as a theoretical and methodological contribution, deepening the understanding of teachers’ professional learning when using technological resources and providing insights into the dynamic nature of teachers’ professional knowledge development.

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children’s fluency, as well as the strategies used to create equal groups, was analyzed. Findings indicated that for large numbers, fluency was greater for an even number of objects than for an odd number of objects. In general, most children reached only one solution. For all four tasks, most children created only two equal groups of caps, even though they could have created three groups or more. A significant association was found between tasks and a preferred strategy. While children employed between one and two strategies when working on a single task, when considering all four tasks, they generally employed between two and three strategies.

Students’ proficiency in the language of instruction is essential for their mathematical learning. Accordingly, language-responsive instruction, which includes adapting teaching material to students’ language needs, is thought to promote mathematical learning, particularly for students with lower levels of proficiency in the language of instruction. However, empirical evidence for the effectiveness of this type of instruction in heterogeneous classrooms is scarce, and potential differential effects for learners with different learning prerequisites still need to be studied. The present study examines whether language-responsive instructional materials can promote students’ learning of fractions. We conducted a quasi-experimental intervention study with a pre- and posttest in Grade 7 (N = 211). The students were assigned to one of three instructional conditions: fraction instruction with or without additional language support or to a control group. The results showed that both intervention groups had higher learning gains than the control group. However, students with lower proficiency in the language of instruction benefited more from fraction instruction with additional language support than without it. The opposite was true for students with higher proficiency in the language of instruction. Moreover, learning gains depended on students’ levels of mathematics anxiety. Our study contributes to a more detailed understanding of the effectiveness of language-responsive instruction in heterogeneous classrooms.

In this theoretical article, we argue that the imminent collapse of earth systems that sustain life forms calls for mathematics education as a field to reflect on and re-evaluate its priorities and thus practices. We consider both what ecological collapse means for mathematics education and whether mathematics education might offer meaningful gestures in response. We explore how the relationship between the social and the ecological is conceptualised in mathematics education (and other relevant) research and what this implies for mathematics education. We read, in this scholarship, a growing focus on the ecological and conceptualisations of socio-ecological relations between existing entities that are dialectical, or mutually dependent. More rarely, are they seen as entangled and monist, and it is in this thought that we locate our contribution of multi-layered gestures of mathematics education. We describe these, in terms of three broad practices: listening for socio-ecological entanglement; attending to the scales of socio-ecological entanglements; and living entanglement as mathematics educators. We exemplify these gestures through examples of curriculum innovation. This article, a socio-ecological gesture in itself, is written in the spirit of opening a conversation into which we invite others.