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- 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. |
- 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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| 3. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Upper secondary students’ task reasoning
- 2008
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Informa UK Limited. - 0020-739X .- 1464-5211. ; 39:1
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Tidskriftsartikel (refereegranskat)abstract
- Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.
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| 9. |
- 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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| 10. |
- Sumpter, Lovisa, 1974-, et al.
(författare)
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The tension between division and fair share
- 2024
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Ingår i: Teaching mathematics as to be meaningful - foregrounding play and children’s perspectives. - Cham : Springer. - 9783031376658 - 9783031376634 - 9783031376627 ; , s. 69-79, 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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