| 1. |
- Sidenvall, Johan, 1974-, et al.
(författare)
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Mathematical reasoning and beliefs in non-routine task solving
- 2015
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Ingår i: Current State of Research on Mathematical Beliefs XX. - Falun : Högskolan Dalarna. - 9789185941933
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Konferensbidrag (refereegranskat)abstract
- This paper explores low performing upper secondary school students’ mathematical reasoning when solving non-routine tasks in pairs. Their solutions were analysed using a theoretical framework about mathematical reasoning and a model to study beliefs as arguments for choices. The results confirm previous research and three themes of beliefs are used by the student. These themes are safety, expectations, and motivation. The results also show a connection between beliefs and imitative reasoning as a way to solve non-routine tasks.
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| 2. |
- Sumpter, Lovisa, et al.
(författare)
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The Tension Between Division and Fair Share.
- 2024
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Ingår i: <em>Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives.</em>. - Cham : Springer. - 9783031376658 - 9783031376634 - 9783031376627 ; , s. 69-79
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Bokkapitel (refereegranskat)abstract
- This study focuses on sharing, both in equal parts (groups) or unequal parts. Children at age five attending preschool, are faced with two different tasks working in pairs. The analysis focus on the mathematical properties in the reasoning, or when mathematical arguments were replaced with an ethical reasoning. When performing division, different strategies were used, and the norm of fair share was often expressed. It was easier for the children to allocate resources when the dividend was larger than the divisor, and when dealing with a fraction, the cardinality of the number of parts appeared to be a prominent property compared to property ‘equal size’ of the parts. There were also indications of ethical reasoning where the child used different claims to convince their peer. There was a tension between the norm of equal sharing and solutions with unequal parts. One implication is that if wanting to challenge children’s mathematical reasoning in a division task, it could be fruitful to look at fractions instead of repeating tasks where the dividend is larger than the divisor.
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| 3. |
- Jäder, Jonas, et al.
(författare)
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Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving
- 2017
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Ingår i: International Journal of Science and Mathematics Education. - : Springer Science and Business Media LLC. - 1571-0068 .- 1573-1774. ; 15, s. 759-776
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Tidskriftsartikel (refereegranskat)abstract
- Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were found deductively and include expectations, motivational beliefs and security. When it comes to reasoning, a variety of approaches were found. Even though the tasks were designed to demand more than imitation of algorithms, students used this method and failed to solve the task. © 2016 Ministry of Science and Technology, Taiwan
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| 4. |
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| 5. |
- Sumpter, Lovisa, et al.
(författare)
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Preschool children’s collective mathematical reasoning about sharing
- 2022
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Ingår i: A Mathematics Education Perspective on early Mathematics Learning – POEM 2022.
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Konferensbidrag (refereegranskat)abstract
- This study focuses on sharing, both in equal parts (groups) or unequal parts. Children at age five attending preschool, are faced with two different tasks where the mathematical properties in their reasoning, or when mathematical reasoning was replaced with an ethical reasoning is analysed. When performing division, different strategies were used, and the norm of fair share was often expressed. It was easier for the children to allocate resources when the dividend was larger than the divisor, and when dealing with a fraction, the cardinality of the number of parts appeared to be a prominent property compared to property ‘equal size’ of the parts. There were also indications of ethical reasoning where the child used different claims to convince their peer. There was a tension between the norm of equal sharing and the solutions with unequal parts. One implication is that if wanting to challenge children’s mathematical reasoning in a division task, it could be fruitful to look at fractions instead of repeating tasks where the dividend is larger than the divisor.
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| 6. |
- Christiansen, Iben Maj, 1964-, et al.
(författare)
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The crosscurrents of Swedish mathematics teacher education
- 2021
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Ingår i: International perspectives on mathematics teacher education. - Waxhaw, NC, USA : Information Age Publishing. - 9781648026317 - 9781648026294 - 9781648026300 ; , s. 9-48
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Bokkapitel (refereegranskat)abstract
- As with any programs in teacher education, Swedish mathematics teacher education is influenced by changing political winds, developments in Information and Communication Technology (ICT), culture, history, PISA results, research-based program designs, and a fair amount of passion. Content and outcomes are nationally determined and include the requirement of a strong research foundation, but this is often not how practcing techers work, which exerts its own pull on teacher education. The specific implementations of programs take different forms at the universities that offer mathematics teacher education. In order to provide a comprehensive yet meaningful ntroduction to both the current system and current practices, we describe the overall organization of Swedish mathematics teacher education, and then offer short cases of implemented programs. To ensure inclusivity, the various parts are written by mathematics educators from the respective institutions. In this way, both variation across mathematicas teacher education for diffrent grade levels and variation across different institutions working with the same national directives can be distinguished. Issues such as the academization of teacher education are problematized, as are other forces that constitute the crosscurrents in Swedish mathematics teacher education.
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| 7. |
- Eriksson, Helena, et al.
(författare)
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Algebraic and fractional thinking in collective mathematical reasoning
- 2021
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Ingår i: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 108:3, s. 473-491
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Tidskriftsartikel (refereegranskat)abstract
- This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the El´konin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic thinking. Further analysis showed that these arguments were characterised by interplay between fractional and algebraic thinking except in the conclusion stage. In the conclusion and the evaluative arguments, these two types of thinking appeared to be intertwined. Another result is the discovery of a new type of argument, identifying arguments, which deals with the first step in task solving. Here, the different types of arguments, including the identifying arguments, were not initiated only by the teachers but also by the students. This in a multilingual classroom with a large proportion of students newly arrived. Compared to earlier research, this study offers a more detailed analysis of algebraic and fractional thinking including possible patterns within the collective mathematical reasoning. An implication of this is that algebraic and fractional thinking appear to be more intertwined than previous suggested.
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| 8. |
- Fahlström, Magnus, 1971-, et al.
(författare)
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A model for the role of the physical environment in mathematics education
- 2018
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Ingår i: Nordisk matematikkdidaktikk. - 1104-2176. ; 23:1, s. 29-46
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop an analytical tool for the role of the physical environment in mathematics education. We do this by extending the didactical triangle with the physical environment as a fourth actor and test it in a review of literature concerning the physical environment and mathematics education. We find that one role played by the physical environment, in relation to mathematical content, is to portray the content in focus, such as geometry and scale. When focusing on teachers, students, and the interaction between them, the role of the physical environment appears to be a precondition, either positive (enabling) or negative (hindering). Many of the findings are valid for education in general as well, such as the importance of building status.
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| 9. |
- Frid, Staffan, et al.
(författare)
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Who is best in mathematics? Grade nine students’ attitudes about boys, girls and mathematics
- 2020
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Ingår i: Interim Proceedings of the 44<sup>th</sup> Conference of the International Group for the Psychology of Mathematics Education. - Khon Kaen, Thailand : PME. ; , s. 152-161
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Konferensbidrag (refereegranskat)abstract
- Sweden has a reputation for its equality work, but at the same time mathematics is still considered a male domain. We studied grade nine students’ attitudes about who could be considered best in mathematics, both from an individual perspective and how they perceived different groups in society would answer. A questionnaire was used and the analysis showed that girls more often think that this is not a matter connected to biological sex, whereas boys more often state that boys and girls are equally good. Two groups are stereotyped as thinking that boys are better in mathematics both by girls and boys: boys in grade nine and boys in general. This is not reflected in their self-evaluation. Overall, the students showed an awareness of the concept of gender, including some intracultural dimensions of the concept.
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| 10. |
- Hedefalk, Maria, 1971-, et al.
(författare)
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Five year Olds in between Sharing and Division
- 2022
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Ingår i: Philosophy of Mathematics Education Journal. - 1465-2978. ; 39
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Tidskriftsartikel (refereegranskat)abstract
- Sharing and division are two concepts that have overlapping properties, and both are connected to the interpretation of fairness. In the present study, we study preschool children’s work with a case where eight biscuits were shared between soft toys. The focus is onthe different arguments that the children express. The results show that children use both ethical arguments and mathematical arguments in their solutions. Some of the arguments can be categorised as ‘Fair sharing related to number of pieces only’ or ‘Fair sharing employing ad hoc attempts at equal size’. The arguments that were coded as sharing not associated with mathematical sense of fairness were either classified as ethical reasoning or play. In the discussion, we raise the need of the combination of ethical reasoning and mathematical arguments if we want to create situations for children to develop critical thinking.
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