| 1. |
- Albarracín, Lluís, et al.
(författare)
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Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes
- 2019
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Ingår i: The Mathematics Enthusiast. - Missoula, United States : Montana Council of Teachers of Mathematics. - 1551-3440. ; 16:1
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a qualitative study in which we analyse the video-recordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students’ problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible.
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| 2. |
- Bagger, Anette, 1974-, et al.
(författare)
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The governing of three researchers' technologies of the self
- 2018
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Ingår i: The Mathematics Enthusiast. - : Information Age Publishing. - 1551-3440. ; 15:1-2, s. 278-302
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Tidskriftsartikel (refereegranskat)abstract
- This article sheds light on a number of discursive conditions relating to being researchers in mathematics education and with an interest in diversity. The data derived from a self-reflective trialogue (dialogue of three people) between the three authors, three researchers. Two of Foucault’s governing technologies were adopted: technologies of power and technologies of the self. By exploring regularities between these in our trialogue we construed formations of governing technologies in relation to subjectification and subjectivation. We uncovered five formations: “Tensions between mathematics education (ME) researchers from different traditions through processes of normalization and othering”, “Limiting space between ME researchers within the socio- political through dismissal of knowledge”, “The socio-political tradition of a need for theory connects theory and ME researcher's’ self-cultivation”, “The researchers’ processes of self-cultivation connect theory and compassionate research practices”. and “Research on policy statements as resistance towards technologies of domination in society”.
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| 3. |
- Bergsten, Christer, 1949-, et al.
(författare)
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Secondary school mathematics students exploring the connectedness of mathematics : The case of the parabola and its tangent in a dynamic geometry environment
- 2021
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Ingår i: The Mathematics Enthusiast. - Missoula, MT United States : University of Montana. - 1551-3440. ; 18:1-2, s. 183-209
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Tidskriftsartikel (refereegranskat)abstract
- Drawing on the Semiotic-cultural approach and the Anthropological theory of the didactic, this paper discusses how exploration of historically framed conceptualizations of mathematical objects can establish bridges between different mathematical areas such as calculus and Euclidean geometry. A classroom intervention study in two secondary mathematics classrooms involving dynamic geometry software tools to support the construction of a parabola and its tangent and aiming at the development of representational flexibility between algebraic/ functional and geometrical approaches, illustrates how students may benefit from participation in such explorations.
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| 4. |
- Frejd, Peter, et al.
(författare)
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The spirit of mathematical modeling-a philosophical study on the occasion of 50 years of mathematical modeling education
- 2024
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Ingår i: The Mathematics Enthusiast. - : UNIV MONTANA, DEPT MATHEMATICAL SCIENCES. - 1551-3440. ; 21:1-2, s. 269-300
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Tidskriftsartikel (refereegranskat)abstract
- We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro level, we found aspects such as agency, anticipating, scrutiny and critique as part of SoMM; at the meso level, we found collaborating, consulting and navigating social norms; and at the macro level, interdisciplinarity, relevance and social justice. Through the lens of bildung-based educational philosophies, we see that instruction and assessment traditions have transposed mathematical modeling into teachable practices that drift away from SoMM. We recommend focusing more on fostering mathematical modeling and to assess students through alternative formats (e.g., group projects).
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| 5. |
- Pansell, Anna, 1975-, et al.
(författare)
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Mathematics Teachers’ Teaching Practices in Relation to Textbooks : Exploring Praxeologies
- 2018
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Ingår i: The Mathematics Enthusiast. - : University of Montana, Maureen and Mike Mansfield Library. - 1551-3440. ; 15:3
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we explore affordances of adopting the framework of praxeology by Chevallard in the analysis of mathematics classroom communication in relation to the communication in a textbook. While adopting praxeology, we carried out detailed analysis of communication in both classroom data and textbooks. The construed praxeologies describe the organisation of knowledge expressed for the same type of task in both classroom and textbook. The praxeologies were compared, with specific attention to the teacher’s practice. This analysis illuminates how teachers’ practices, realised in classroom communication, may be compared to other texts describing the same topics, with a focus on procedures, explanations, theoretical aspects, et cetera. Hence, praxeology as a framework enabled an analytical structuring of classroom and textbook communication, and consequently a systematic comparison. In other studies about the use of mathematics textbooks the teaching frequently is categorised as regulated by the textbook, and in this article, we problematize this. The teaching practice was, in fact,closely related to the textbook when comparing exercises and procedures, but when specifically examining the explanations of concepts, it became possible to discern how the teaching practice differed from the textbook.
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| 6. |
- Peng, Aihui, 1977-, et al.
(författare)
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Values in Effective Mathematics Lessons in Sweden : what do they tell us?
- 2012
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Ingår i: The Mathematics Enthusiast. - : University of Montana, Maureen and Mike Mansfield Library. - 1551-3440. ; 9:3, s. 409-430
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Tidskriftsartikel (refereegranskat)abstract
- This study aims to examine values in effective mathematics lessons in Sweden from the perspectives of students in different groups and their teachers. By using methods with lesson observations, student focus group interviews and teacher interviews, it shows that instructional explanation and classroom atmosphere with quietness are shared-values of students and their teachers. The findings propose some crucial issues which related to how mathematics teaching could be adjusted to different students’ learning conditions and whether it needs more instructional explanation in mathematics teaching in Sweden.
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| 7. |
- Szabo, Attila, fil.dr. 1965-, et al.
(författare)
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Displaying gifted students’ mathematical reasoning during problem solving : Challenges and possibilities
- 2024
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Ingår i: The Mathematics Enthusiast. - 1551-3440. ; 21:1-2, s. 179-202
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Tidskriftsartikel (refereegranskat)abstract
- When solving problems, mathematically gifted individuals tend to internalize intuitive ideas and approaches, and to shorten their reasoning. Consequently, for teachers it is difficult to observe gifted students’ mathematical reasoning in the context of problem solving. In this paper we investigate nine gifted Swedish 9th grade students’ mathematical reasoning during problem solving in small groups at vertical whiteboards. The data consists of 5 filmed group-activities, that were analysed according to a framework of collaborative problem-solving (Roschelle & Teasley, 1995). The analysis shows that every group solved proposed problems successfully within different socially negotiated Joint Problem Spaces (JPS) and, importantly, that students were able to verbalize and display their mathematical reasoning. Additionally, it is indicated that using vertical whiteboards facilitated considerably the exhibition of students’ mathematical reasoning.
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| 8. |
- Szabo, Attila, et al.
(författare)
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Examining the interaction of mathematical abilities and mathematical memory : A study of problem-solving activity of high-achieving Swedish upper secondary students
- 2017
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Ingår i: The Mathematics Enthusiast. - : University of Montana, Maureen and Mike Mansfield Library. - 1551-3440. ; 14:1-3, s. 141-159
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we investigate the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii (1976). Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students' selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them. Furthermore, the ability to generalise, a key component of Krutetskii's framework, was absent throughout students' attempts. These findings indicate a lack of flexibility likely to be a consequence of their experiences as learners of mathematics.
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| 9. |
- Österholm, Magnus, 1976-
(författare)
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The role of theory when studying epistemological characterizations of mathematics lecture(r)s
- 2012
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Ingår i: The Mathematics Enthusiast. - : Information Age Publishing. - 1551-3440. ; 9:3, s. 431-464
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Tidskriftsartikel (refereegranskat)abstract
- The study presented in this paper is a contribution to the scientific discussion about the role and use of theory in mathematics education research. In particular, focus is here on the use of and comparison between different types of theories and frameworks, which is discussed primarily through the example of an empirical study examining what types of messages about mathematics are conveyed in lectures. The main purpose of this paper is to examine how different types of theories and frameworks can affect different parts of the research process.
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| 10. |
- Bergman Ärlebäck, Jonas
(författare)
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On the use of realistic Fermi problems for introducingmathematical modelling in school
- 2009
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Ingår i: The Mathematics Enthusiast. - : Montana Council of Teachers of Mathematics & Information Age Publishing. - 1551-3440. ; 6:3, s. 331-364
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Tidskriftsartikel (refereegranskat)abstract
- In this paper an analytical tool referred to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme is used to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extra-mathematical knowledge used by the students during the problem solving session.
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