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Virtual reality (VR) research in mathematics education has centred largely on geometry content. This paper contributes by describing VR modules developed for another area that heavily involves three-dimensional objects: multivariable calculus. This paper also contributes by describing an empirical study on students' experiences inside the VR modules through student (conceptual) noticing. One finding was that colourful objects had moderate associated conceptual noticing, but that accompanying animation drastically improved the conceptual noticing. Symbolic and textual elements were conceptually noticed much less. While narration was meant to guide the students' noticing, it often did not produce the conceptual noticing intended, though animation again was a key factor. The conceptual noticing was also found to be connected to the students' emerging understandings of the mathematical ideas discussed in the modules. We end by discussing implications for (a) designing VR modules generally, and for (b) learning specific mathematical content within VR. [ABSTRACT FROM AUTHOR]

The author provides his opinion regarding the paper "Communities in university mathematics" by I. Biza, B. Jaworski, and K. Hemmi. He questions if an adapted community of practice theory (CPT) can create a community of inquiry (COI), if students had the freedom to create an authentic COI with structured teaching methods, and if a community of inquiry theory (CIT) has to include cognitive and constructivist theories.

This paper examines the formation of citizens and their differences in and through the contemporary mathematics education reforms in Turkey. The analysis focuses on how internationally designated mathematical competencies assemble with the nation-specific trajectories and revitalise cultural priorities. Curricular techniques, which aim at improving mathematics teaching and learning, simultaneously order proper and improper modes of action and participation. The orderings include the formation of children as active and responsible for their learning opportunities where they continually make plans and control themselves. The analysis makes visible how seemingly neutral pedagogical tools to teach and learn mathematics assemble with the formation of desired citizens for the globalised world and act upon children who diverge from those globally proposed norms. Cultural-pedagogical translation processes in mathematics education reforms provide a critical confrontation with the differentiation practices of self and Other. [ABSTRACT FROM AUTHOR]

This case-study, drawing on an unanticipated theme arising from a wider study of ability-grouping in primary mathematics, documents some of the consequences of educational triage in the final year of one primary school. The paper discusses how a process of educational triage, as a response to accountability pressures, is justified by teachers on the basis of shared theories about ability and potential. Attainment gains show that some practices associated with the triaging process work for the school, pushing selected pupils to achieve the Government target for the end of primary school. However, other practices appear to coincide with reduced mathematical gains for the lowest attaining pupils and a widening of the attainment gap. This case-study examines the mechanisms behind this, focusing on resource allocation, and assumptions about learners and their potential. The paper suggests a need to create dissonance, challenging shared assumptions, such as fixed-ability, which currently support triage processes. [ABSTRACT FROM AUTHOR]

The Zen concept of beginner's mind describes how one's level of awareness can open one's mind to growth and possibilities, an attitude that would be beneficial for many mathematics students. In this naturalistic case study, two small groups of middle years students engage in the same mathematical task, one group demonstrating the characteristics of beginner's mind and the other not. One group focuses on making sure that all its members can follow the steps of one member's proposed solution. The other group, which displays characteristics of beginner's mind, explores the task thoroughly, and in its openness to ideas it notices mathematically salient details in the task that the first group overlooks completely. This paper suggests that through beginner's mind, students may develop habits of mind that enable them to attend to and think about mathematical possibilities deeply. [ABSTRACT FROM AUTHOR]

We report the results of a study in which we asked 94 mathematicians to evaluate whether five arguments qualified as proofs. We found that mathematicians disagreed as to whether a visual argument and a computer-assisted argument qualified as proofs, but they viewed these proofs as atypical. The mathematicians were also aware that many other mathematicians might not share their judgment and viewed their own judgment as contextual. For typical proofs using standard inferential methods, there was a strong consensus amongst the mathematicians that these proofs were valid. An instructional consequence is that for the standard inferential methods covered in introductory proof courses, we should have the instructional goal that students appreciate why these inferential methods are valid. However, for controversial inferential methods such as visual inferences, students should understand why mathematicians have not reached a consensus on their validity. [ABSTRACT FROM AUTHOR]

The article discusses a research paper written by Elena Nardi, Andreas Ryve, Erika Stadler and Olov Viirman regarding the consideration of university mathematics as a discourse. Topics include the structure of university mathematics lectures, the concept of teaching-by-soliloquy, and shifts in students' perspectives of mathematics education upon entering college.

Creativity is often characterised by three components: fluency, flexibility, and originality. Specifically, in the mathematics classroom, in order to promote these aspects of creativity, educators recommend engaging students with multiple-solution tasks and open-ended tasks. In the past, various methods were used to measure fluency, flexibility and originality. This study raises questions and dilemmas regarding these methods and measures, and illustrates the complexity of these issues with data collected from fifth-grade students engaging with three such tasks. Some of the questions raised are related to differences between multiple-solution tasks and open-ended tasks, and between creative process and creative outcomes. In addition, the gap between the potential embedded within a task and its actual results is discussed. [ABSTRACT FROM AUTHOR]

In this paper we analyse drawings made by students from the U.S. and Finland when asked to draw their mathematics class. This activity was given to students from 8 classes (n= 131, 9–10 years old) in Finland and 5 classes (n= 94, 8–9 years old) in the U.S. Two separate analyses were conducted: an a priori coding of all drawings and an in-depth analysis of 3 drawings from each country. The coding of drawings focused on students' conceptions about communication and teaching in mathematics. The in-depth analyses captured additional aspects of the class. The results show that the U.S. students have greater self-confidence with respect to knowing/learning mathematics than their Finnish counterparts. In addition, U.S. comments during class were more related to the lesson (teaching), and their teachers gave more feedback. However, little meaningful differences in the overall communication patterns in the Finnish and U.S. classrooms were found. [ABSTRACT FROM PUBLISHER]

This research project investigated the reasons why senior secondary school students elect not to enrol in a higher mathematics course. All Year 11 and Year 12 mathematics students within Western Australian schools (aged 17–18 years) were invited to participate in a single, anonymous, online survey comprised predominantly of qualitative items. In line with a symbolic interactionist theoretical perspective, participant responses (n = 1351) were analysed to determine the meaning students conferred upon decisions to enrol in mathematics courses. In particular, responses indicated that students are dissatisfied with mathematics, there are other more viable courses of study to undertake, and that the Australian Tertiary Admissions Ranking (ATAR) score can be maximised by taking a lower mathematics course. Additional testimony suggests that there are few incentives offered to students undertaking a higher mathematics course, and that such courses are not needed for university entrance nor in later life. In light of these findings, a discussion synthesises student-led suggestions with current literature which could lead to higher future enrolments in secondary mathematics courses. [ABSTRACT FROM AUTHOR]

This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems. [ABSTRACT FROM AUTHOR]

We investigated two factors that predict students' achievement and behaviour in undergraduate mathematics: gender and personality. We found that gender predicted students' achievement and behaviour when considered in isolation, but ceased to be predictive when personality profiles were taken into account. Furthermore, personality accounted for significantly more variance in undergraduates' achievement and behaviour than did gender, but the converse was not the case. We therefore argue that personality provides the more productive lens through which to understand the behaviour of undergraduate mathematics students. We relate this finding to recent research emphasising gender differences in mathematics education, and suggest that researchers wishing to promote equity in participation at and beyond the undergraduate level should consider shifting their focus to individual differences in personality. [ABSTRACT FROM AUTHOR]

A consistent message emerges from research on undergraduate students' perceptions of assessment which describes traditional assessment as detrimental to learning. However this literature has not included students in the pure sciences. Mathematics education literature advocates the introduction of innovative assessment at university. In this literature however students' voices tend to be unheard. We investigate mathematics students' perceptions of assessment at one high-ranking UK University. We find that, in contrast to the message from the general literature, students perceive traditional assessment as the best discriminator of ability. We suggest that the drive towards the introduction of innovative assessment in mathematics should be considered in the light of students' perceptions and that further research is needed to investigate the origins of those perceptions as well as how those perceptions may be influenced by the subject of study. [ABSTRACT FROM PUBLISHER]

The article focuses on the action research study regarding the teacher-student dialogue on one-to-one interactions in a post-16 mathematics classroom in England. The study addresses some research questions such as the form and function of utterances, the correlation of the utterances to the scaffolding strategies, and the aspects of said strategies that gave value to the students. Results show that telling does not affect in effective teacher-student dialogue. Moreover, the study also demonstrate the techniques on how to change individual teaching styles.