| 1. |
- Aretorn, Lena, 1966-
(författare)
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Mathematics in the Swedish Upper Secondary School Electricity Program : A study of teacher knowledge
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical knowledge is often a prerequisite for students at Swedish upper secondary vocational programs to be able to study vocational courses, for example electricity courses in the Electricity Program. Electricity Program students study mathematics in their electricity courses as well as in their mathematics course. The mathematics in those two settings has a different character. A goal of this thesis is to investigate what constitutes that character. In this study three mathematics and five electricity teachers have been interviewed about how they would explain three mathematical electricity tasks to students on the Electricity Program. Teacher knowledge in both electricity and mathematics has been used in the analyses and has been compared between the different teacher groups. In addition to providing an overview analysis of all the teachers’ explanations, detailed analyses have been carried out, comparing pairs of teachers’ explanations. The teachers’ choices of explanations and their use of specific and general mathematical knowledge have been studied. Mathematics contains a wide range of subject areas but also a wide range of representations and methods that highlight different aspects of mathematics. This study shows that different teachers emphasize different aspects of mathematics in their explanations of the same tasks, even though intended to the same students, both in the their choices of explanation and in their use of mathematics. The electricity teachers drew upon their practical electrical knowledge when they connected their explanations of mathematics to vocational work. The electrical knowledge they used not only grounded the tasks in a, for them, well-known real-world environment. The electrical knowledge actually helped them to solve the tasks, albeit in a more concrete/specific way than the mathematics teachers. The electricity teachers drew upon more specific mathematical knowledge in their explanations of the interview tasks, whereas the mathematics teachers drew upon more general mathematical knowledge in their explanations. The different explanations of mathematics from the two kinds of teachers are markedly different, depending on whether they have a more practical/vocational or a more general/algebraic approach. The solutions to the interview tasks turned out to be the same but the character of the solutions paths are substantially different. This raises questions regarding the students’ abilities to reconcile the different approaches.
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| 2. |
- Birky, Geoffrey, et al.
(författare)
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One problem, nine student-produced proofs
- 2011
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Ingår i: The College Mathematics Journal. - : Informa UK Limited. - 0746-8342 .- 1931-1346. ; 42:5, s. 355-360
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Tidskriftsartikel (refereegranskat)abstract
- The context of this paper is a project aimed at meeting the challenges of teaching an introduction-to-proof course at our own institutions. These courses are typically taken by second year students intending to major in mathematics or computer science and are taught in sections of 15 to 24 students. These students benefit from being given the freedom to explore different methods of proof without the presumption that they will use a certain method. This is the story of how what could have been a routine, closed problem became an open one.
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| 3. |
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| 4. |
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| 5. |
- Raman, Manya
(författare)
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High achievement in mathematics education in India : A report from Mumbai
- 2010
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Ingår i: Journal of Mathematics Education at Teachers College. - New York, N.Y, USA : Teachers College Columbia University. - 2156-1397 .- 2156-1400. ; 1:2, s. 46-51
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Tidskriftsartikel (refereegranskat)abstract
- This paper reports a study aimed at characterizing the conditions that lead to high achievement in mathematics in India. The study involved eight schools in the greater Mumbai region. The main result of the study is that the notion of high achievement itself is problematic, as reflected in the reports about mathematics achievement within and outside India as well as the complexities of a school system which, despite democratic ideals, has difficulty serving the needs of all students. This study provides snapshots of three mathematics classes that embody some of these complexities to provide a balanced account of conditions that either support or detract from the goal of high achievement in India.
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| 6. |
- Raman Sundström, Manya, 1971-, et al.
(författare)
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Beauty as fit : A metaphor in mathematics?
- 2013
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Ingår i: Research in Mathematics Education. - : Informa UK Limited. - 1479-4802 .- 1754-0178. ; 15:2, s. 199-200
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Tidskriftsartikel (refereegranskat)abstract
- Beauty, which plays a central role in the practice of mathematics, is almost absent in discussions of school mathematics. This is problematic, because students will decide whether or not to continue their studies inmathematics without having an accurate picture of what the subject is about. In order to have a discussion about how to introduce beauty into the school mathematicscurriculum, we need to have a clear idea about what beauty means. That is the aim ofthis study, with a focus on characterising beauty in mathematical proof.
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| 7. |
- Raman Sundström, Manya, 1971-
(författare)
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Beauty as Fit : An Empirical Study of Mathematical Proofs
- 2012
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Ingår i: Proceedings of the British Society for Research into Learning Mathematics. ; , s. 156-160
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Konferensbidrag (refereegranskat)abstract
- Beauty has been discussed since ancient times, but discussions of beautywithin mathematics education are relatively limited. This lack ofdiscussion is surprising given the importance of beauty within the practiceof mathematics. This study explores one particular metaphor of beauty,that of beauty as fit, as a way to distinguish between proofs that areconsidered beautiful and those that are not. Several examples areexamined, supported by empirical data of mathematicians andmathematics educators who judged and ranked different proofs in aseminar on mathematical beauty.
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| 8. |
- Raman-Sundström, Manya, 1971-
(författare)
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Beauty in Mathematics Textbooks
- 2011
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper poses two questions:Should mathematics textbooks try to convey the beauty of mathematics?If so, how?These questions are difficult, and subjective, and will not be settled in this paper, but the purpose in raising them is to discuss if we agree that the answer to (1) is yes, then how can we make progress on question (2).
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| 9. |
- Raman Sundström, Manya, 1971-
(författare)
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Elements : a love song
- 2011
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Ingår i: The Mathematical Intelligencer. - : Springer Science+Business Media B.V.. - 1866-7414.
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Annan publikation (populärvet., debatt m.m.)
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| 10. |
- Raman Sundström, Manya, 1971-
(författare)
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Excavation
- 2012
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Annan publikation (populärvet., debatt m.m.)
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| 11. |
- Raman-Sundström, Manya, et al.
(författare)
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MATHEMATICAL BEAUTY
- 2012
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Ingår i: PROCEEDINGS OF THE 36TH CONFERENCE OF THE INTERNATIONAL GROUP FOR PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL. 1. - Prag : INT GRP PSYCHOL MATH EDUC, CHARLES UNIV PRAGUE, FAC EDUC. ; , s. 155-155
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Konferensbidrag (refereegranskat)
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| 12. |
- Raman Sundström, Manya, 1971-, et al.
(författare)
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Two beautiful proofs of Pick's theorem
- 2011
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Ingår i: Proceedings of Seventh Congress of European Research in Mathematics Education. - : University of Rzeszow Publishing House. - 9788373386839 ; , s. 224-232
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Konferensbidrag (refereegranskat)abstract
- We present two different proofs of Pick’s theorem and analyse in what ways might be perceived as beautiful by working mathematicians. In particular, we discuss two concepts, generality and specificity, that appear to contribute to beauty in different ways. We also discuss possible implications on insight into the nature of beauty in mathematics, and how the teaching of mathematics could be impacted, especially in countries in which discussions of beauty and aesthetics are notably absent from curricular documents.
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| 13. |
- Wistedt, Inger, 1943-, et al.
(författare)
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Quality and Equity from a Swedish perspective
- 2010
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Ingår i: <em>Mapping Equity and Quality in Mathematics Education</em>. - New York & Heidelberg : Springer. - 9789048198023 ; , s. 341-350
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 14. |
- Wistedt, Inger, et al.
(författare)
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Quality and equity in mathematics education : a Swedish perspective
- 2010. - 1
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Ingår i: Mapping equity and quality in mathematics education. - Dordrecht : Springer Netherlands. - 9789048198023 - 9789048198030 ; , s. 341-350
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Discussions about quality and equity in education around the world often focus on the disadvantaged, the students for whatever reason do not have the resources to make the most of public education, or to get an education at all. In Sweden, where there is a fairly even economic playing field, the discussion -- which is not always made public -- addresses another type of inequity, namely that bright and talented students are not given sufficient education, particularly in math and science, to help them reach their potential. We describe some of the historical and cultural background for this inequity, and offer a modest, but not unbiased, account of what we claim is a false dilemma involved in promoting excellence in a democratic society.
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