Educational Studies in Mathematics最新文献

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students’ conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools contribute to forming these conceptions, guided by an emerging theory that describes this process. A workshop for high school students was organized, involving 36 participants working in pairs across four sessions, each with access to a computer. These sessions involved problem-solving activities, with the teacher introducing key concepts in the initial three sessions. The analysis, employing grounded theory, aimed to characterize the nature of students’ conceptions of sampling distribution as evident in their responses. The findings reveal a transition from empirical to informal conceptions of sampling distribution among students, facilitated by computational mediation. This transition is marked by an abstraction process that includes mathematization, processing, uncertainty/randomness, and conditional reasoning. The study underscores the role of digital simulations in teaching statistical concepts, facilitating students’ conceptual shift critical for grasping statistical inference.

Research has highlighted the important role that the senses play in mathematics thinking and learning, particularly in the area of visualisation, but also in relation to physical movement. Recent scholarship suggests that sensory experiences are not limited to the five cardinal senses but involve a range of other specific senses as well as combinations of senses. The aim of this article is to explore how this expanded understanding of the senses matters to mathematics education research. We frame our argument in terms of aestheticizing mathematics education research, focusing not only on mathematics knowing, but also on implications for investigating the mathematical sensorium; for the latter, we propose the use of re-enactments as powerful research methods. To empirically elaborate on this argument, we illustrate the use of this method to investigate how senses matter in developing multiplicative thinking around/with multitouch technology.

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.