Educational Studies in Mathematics最新文献

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.

Preservice mathematics teachers are sometimes trained in programs so that they have both their own courses and joint courses with mathematics majors from the beginning of their studies. While this is thought to provide them with both deep mathematical knowledge and teaching-specific content right from the start, many of them report disaffection with and disengagement from mathematics during their very first semester. Current approaches often frame this from an individual’s perspective, investigating cognitive and affective individual differences among students. In contrast, we aim to understand this issue from a sociocultural perspective, examining underlying social processes. In this study, we thus explored preservice teachers’ experiences of the mathematics component of their training, using Holland and colleagues’ theory of figured worlds as a theoretical lens. Three group interviews with 14 preservice higher secondary teachers in a common mixed setting in Germany (one course specific to preservice teachers, one general mathematics course together with major students) were analyzed. Our findings displayed that the preservice teachers experienced two dichotomous figured worlds of mathematics and mathematics teaching. Our further analysis of their positioning between these worlds provided new insights to explain their disaffection, disengagement, and consequent learning behavior. We discuss practical implications, focusing on different teaching systems and interventions in teacher education.

The present study examines secondary school students’ geometrical figure apprehension based on Duval’s theoretical framework regarding perceptual, operative, and discursive apprehension. The aim is to explore the cognitive structure of the geometrical figure apprehension dimensions (operative, discursive, and perceptual) in three grades of secondary school students. The tasks in the present study were completed by a sample of 881 students attending public secondary education in Cyprus. Confirmatory factor analysis indicated the stability of the structure of the model concerning secondary school students’ geometrical figure apprehension. However, differences were found in the interrelations among the three main aspects of the model in the examined grades (9, 10, and 11). Moreover, it was observed that students find it easier to solve tasks involving perceptual apprehension compared to discursive apprehension tasks, indicating a possible hierarchical structure of figure apprehension. The present study acts as a pilot study of the constructed instrument. Finally, the results are interpreted in relation to the type of geometrical paradigm in which students work at each hierarchical level.