| 1. |
- Sumpter, Lovisa, et al.
(författare)
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Ethics as part of mathematical reasoning in sharing
- 2023
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Ingår i: Prometeica. - : Universidade Federal de Sao Paulo. - 1852-9488. ; :27, s. 649-657
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Tidskriftsartikel (refereegranskat)abstract
- There is a greater need in today's society, to understand and critically discuss how the limited resources of our planet are allocated. Often, mathematical models are used in connection with resource allocation problems, and a common view is that mathematics in itself is neutral. In this article, we challenge this view of mathematics as a neutral practice through an analysis of possible solutions to a sharing task. The tasks come from a research project aiming to study how mathematics can support ethical reasoning and ethical arguments can support different mathematical solutions when sharing a resource. In ethical reasoning, three components are addressed: Information, Coherence, and Engagement. We show that ethical reasoning is part of mathematical reasoning in all the solutions to the task, independent of whether the dividend is treated as indivisible or divisible.
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| 2. |
- Sumpter, Lovisa, et al.
(författare)
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How long will it take to have a 60/40 balance in mathematics in mathematics PhD education in Sweden?
- 2016
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Ingår i: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education. - : International Group for the Psychology of Mathematics Education. - 9781365463457 ; , s. 251-258
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Konferensbidrag (refereegranskat)abstract
- We investigate female participation in PhD education in mathematics. Nine of eleven subject areas for PhD studies in Sweden had reached a 60/40 gender balance in 2010, the exceptions being mathematics and engineering and technology. Using linear regression, we fit a growth model to the increase in the proportion of female PhD students. We show that mathematics has a slower growth rate in female participation than other subjects, and present differences can’t be attributed simply to a lower initial female participation. If current trends continue, it will take approximately another 15 years for mathematics to reach a 60/40 gender balance.
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| 3. |
- Sumpter, Lovisa, 1974-, et al.
(författare)
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La ética como parte del razonamiento matemático en el compartir
- 2023
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Ingår i: Prometeica. - 1852-9488. ; :27, s. 649-657
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Tidskriftsartikel (refereegranskat)abstract
- There is a greater need in today's society, to understand and critically discuss how the limited resources of our planet are allocated. Often, mathematical models are used in connection with resource allocation problems, and a common view is that mathematics in itself is neutral. In this article, we challenge this view of mathematics as a neutral practice through an analysis of possible solutions to a sharing task. The tasks come from a research project aiming to study how mathematics can support ethical reasoning and ethical arguments can support different mathematical solutions when sharing a resource. In ethical reasoning, three components are addressed: Information, Coherence, and Engagement. We show that ethical reasoning is part of mathematical reasoning in all the solutions to the task, independent of whether the dividend is treated as indivisible or divisible.
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| 4. |
- Sumpter, Lovisa, et al.
(författare)
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Modelling gender differences in participation in PhD studies in mathematics
- 2021
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Ingår i: SN Social Sciences. - : Springer Science and Business Media LLC. - 2662-9283. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- In most subject areas, the proportion of women PhD students is around 50%. Mathematics differs despite minimal differences between boys’ and girls’ school achievements. In this paper, we show, drawing on Swedish data from the last 45 years, that low female participation in mathematical PhDs is due to low participative growth rates rather than historical low levels. In comparison, science has twice as strong growth rate, while non-STEM subjects have grown four times faster. The results show that gender differences regarding participation is indeed dynamic, but changes do not occur despite political initiatives such as laws on non-discrimination and encouragement of equal parental leave. Instead, the results imply that in order for maths departments to avoid continuing being gendered institutions, it requires active changes in structures and working environment.
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| 5. |
- Sumpter, Lovisa, et al.
(författare)
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Sharing Four Biscuits Between Three People: An Illustrative Example of How Mathematics is Intertwined with Human Values
- 2024
-
Ingår i: Journal of Humanistic Mathematics. - : Claremont Colleges Library. - 2159-8118. ; 14:1, s. 74-93
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Tidskriftsartikel (refereegranskat)abstract
- Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread no- tion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how math- ematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demon- strate that different solutions—hiding one biscuit, arbitrarily sharing the extra biscuit, randomizing allocation, dividing the extra biscuit into three parts, and successively dividing it into smaller and smaller parts—involve different mathe- matical methods and evoke different human values. We discuss the construction of quantum biscuit splitting devices and the use of machine learning to divide biscuits. We argue that the multitude of different mathematically-correct so- lutions to this problem (each with its own ethical justification) might influence the values held by practicing mathematicians. The example we propose here has been used in teaching to help students understand why mathematics cannot be cleanly separated from human values.
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| 6. |
- Sumpter, Lovisa, et al.
(författare)
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Understanding Segregation : Upper Secondary School Student’s Work with the Schelling Model
- 2019
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Ingår i: Proceedings of the Tenth International Mathematics Education and Society Conference.
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Konferensbidrag (refereegranskat)abstract
- There are few research studies focusing on how humans can better understand segregation using mathematical models. In this paper, we explore how upper secondary school students work with the Schelling model using a computer game that was purposely designed for this study. The students were then allowed to run the model themselves. The results show that it was difficult to anticipate the degree to which segregation is generated within the model. The students mainly gave two types of explanations for the results. The first one was based on human psychology and the other was based on the mathematical principle that underlie the utility function of the model. The results are discussed from a perspective that illustrates the complexity of the subject, rather than as a measure of the teaching intervention.
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| 7. |
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| 8. |
- Sumpter, Lovisa, 1974-, et al.
(författare)
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Upper secondary school students' gendered self-evaluation in mathematics
- 2022
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Ingår i: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). - : European Society for Research in Mathematics Education. ; , s. 1434-1441
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Konferensbidrag (refereegranskat)abstract
- Self-evaluation is considered one of the key concepts when trying to understand motivation, and it is gaining more interest especially when looking at the age span 15-18 years. Previous studies in self- evaluation and mathematics tend to use data from international large scales assessments, arriving with rather ambiguous conclusions, and smaller studies tend to use only one measure without control factors. The aim of this paper was to test the hypothesis that boys are more confident than girls in mathematics, while using Swedish as a control subject. A questionnaire was handed out to 399 upper secondary school students from different regions in Sweden, both vocational programmes and programmes preparing for further studies. Using both non-parametric analysis and linear regression, the results support the hypothesis. The relationship to the idea of confidence gap is discussed.
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| 9. |
- Tsvetkova, Milena, et al.
(författare)
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An experimental study of segregation mechanisms
- 2016
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Ingår i: EPJ DATA SCIENCE. - : Springer Science and Business Media LLC. - 2193-1127. ; 5
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Tidskriftsartikel (refereegranskat)abstract
- Segregation is widespread in all realms of human society. Several influential studies have argued that intolerance is not a prerequisite for a segregated society, and that segregation can arise even when people generally prefer diversity. We investigated this paradox experimentally, by letting groups of high-school students play four different real-time interactive games. Incentives for neighbor similarity produced segregation, but incentives for neighbor dissimilarity and neighborhood diversity prevented it. The participants continued to move while their game scores were below optimal, but their individual moves did not consistently take them to the best alternative position. These small differences between human and simulated agents produced different segregation patterns than previously predicted, thus challenging conclusions about segregation arising from these models.
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| 10. |
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| 11. |
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| 12. |
- 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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| 13. |
- 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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| 14. |
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| 15. |
- Dahlgren Johansson, Anna, et al.
(författare)
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Children’s conceptions about mathematics and mathematics education
- 2010
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Ingår i: Current state of research on mathematical beliefs<em> </em>XVI.
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Konferensbidrag (refereegranskat)abstract
- This paper deals with younger students’ (grade 2 and 5) conceptions about mathematics and mathematics education. The questionnaire consisted of three parts: (1) statements with a Likert-scale; (2) open-end questions where the students could explain further their conceptions; and, (3) a request to draw a picture of yourself doing mathematics. The results from the statements were summarised and the pictures were analysed. Most students in grade 2 had a positive attitude towards mathematics whereas a larger proportion in grade 5 gave negative answers. All students presented mathematics as an individual activity with a focus on the textbook. The elder students narrow the activity down to calculating. A post-questionnaire confirmed the results.
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| 16. |
- 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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| 17. |
- Eriksson, Helena, 1965-
(författare)
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Att utveckla algebraiskt tänkande genom lärandeverksamhet : En undervisningsutvecklande studie i flerspråkiga klasser i grundskolans tidigaste årskurser
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this thesis is to develop and explore teaching possible to promote algebraic thinking together with young, multilingual students six to twelve years old. One underlying assumption for the aim is that algebraic thinking can be developed by students participating in learning activities that are characterized by collective mathematical reasoning on relations between quantities of positive whole and rational numbers. Two overall research questions support this work: (1) What in students work indicate algebraic thinking identified in learning activities and as experiences of algebraic thinking? (2) How can learning models manifest in learning activity, in what ways do learning models change and enhance, and which characteristics of learning actions are enabled? Data was produced by interviews and from research lessons with students in lower grades in a multilingual Swedish school. The research lessons were focused on learning activity as suggested by Davydov (1990, 2008/1986), aimed at developing theoretical thinking – here algebraic thinking. They were staged in two research projects conducted as networks of learning studies. In these learning studies, the group of teachers iteratively designed and revised learning activities whereby the students could identify mathematical knowledge and collectively solve mathematical problems. The findings in the articles signal that learning models were developed as rudimentary, preliminary, prototypical and finally symbolic. Rudimentary models were grounded in algebraic thinking when the students analysed problem situations and identified the problem. Preliminary and prototypical models were developed by initiating and formalising actions understood as algebraic thinking. Different tools were initiated by the students and the teachers. These tools were formalised by the students. The students used algebraic symbols and line-segments to think together when comparing different quantities (Article 2). They carried out operations using unknown quantities when reflecting on additive and multiplicative relationships (Article 3). The students also used algebraic symbols to reflect on subtraction as non-commutative (Article 3). The different tools they used interacted on different levels of generalisation (Article 1). Algebraic thinking grounded the students reflections but interacted with, for example, fractional thinking in their arguments during the development of their learning models (Article 4). The different ways of thinking interacted in arguments when developing the rudimentary, the preliminary and the prototypical models. However, in the conclusion of their collective reasoning and in the development of the symbolic learning models, these different ways of thinking were intertwined in the same arguments (Article 4).As a conclusion, the four articles signal that learning models including algebraic symbols developed in a learning activity can be used by newly-arrived immigrant students to reflect on structures of numbers.
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| 18. |
- Eriksson, Helena, et al.
(författare)
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Fair sharing and division – mathematical reasoning regarding integers and fractions in preschool and preschool class
- 2024
-
Ingår i: Proceedings of Cerme 13. - : Alfréd Rényi Institute of Mathematics, Budapest, Hungary and ERME. - 9789637031045 ; , s. 2096-2103
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Konferensbidrag (refereegranskat)abstract
- This paper identifies and discusses children’s mathematical reasoning in preschool and preschool class when they work with a fair sharing case. The case came from a selection of cases designed to promote collective mathematical as well as ethical reasoning. Data comes from six children’s work when sharing four paper biscuits between three soft toys, first when the children were five years old and then, a year later, when they were six years old. The results show that their reasoning, both when they were five and six, used mathematical and ethical arguments. In preschool class, the students were able to use each other’s arguments in collective reasoning to identify, predict, and verify their reasoning. The students began to measure the fraction parts of a remainder but could not evaluate the conclusion with respect to what is aspects for division; equal numbers and equal size. The results also signal that teacher’s input, of posing evaluating questions, appears to stimulate the reasoning.
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| 19. |
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| 20. |
- 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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| 21. |
- 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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| 22. |
- 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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| 23. |
- Hedefalk, Maria, 1971-, et al.
(författare)
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Matematiska och etiska resonemang i förskolan : didaktisk modellering som intervention
- 2024
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Ingår i: Forskning om undervisning och lärande. - : Lärarstiftelsen. - 2000-9674 .- 2001-6131. ; 12:2, s. 68-84
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Tidskriftsartikel (refereegranskat)abstract
- The article examines didactic choices in teaching where mathematics and sustainable development meet. The purpose of the teaching was to encourage preschool children to reason collectively about distribution problems. It was the children's reasoning about possible solutions that was in focus, not a correct answer. The preschool teacher's role was to create opportunities for agency: enable childrens own contributions to knowledge, pit different conflicting perspectives on sustainable solutions against each other and discuss the solutions. Based on the didactic modeling method, researchers and preschool teachers discussed the teaching based on different expertise. Documentation created during these meetings was analysed, in order to investigate if the didactic what and how questions could help the preschool teachers create agency in teaching. The result shows how reflection on the didactic issues created opportunities for agency in relation to organization of time and environment, of pairing children for collective work and language development work.
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| 24. |
- Hedefalk, Maria, et al.
(författare)
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Matematiska och etiska resonemang i förskolan – didaktisk modellering som intervention : [Mathematical and ethical reasoning in preschool – didactic modeling as an intervention]
- 2024
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Ingår i: Forskning om undervisning och lärande. - 2000-9674 .- 2001-6131. ; 12:2, s. 68-84
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Tidskriftsartikel (refereegranskat)abstract
- I artikeln undersöks didaktiska val i undervisning där matematik och hållbar utveckling möts. Undervisningens syfte var att uppmuntra förskolebarn att kollektivt resonera kring fördelningsproblem. Det var barnens resonemang om möjliga lösningar som låg i fokus, inte ett rätt svar. Förskollärarens roll var att skapa möjligheter för agens: att barnen kunde göra egna bidrag i kunskapandet, där barnen kunde ställa olika konflikterande perspektiv om hållbara lösningar mot varandra och diskutera lösningarna. Utifrån metoden didaktisk modellering förde forskare och förskolläre diskussioner om undervisningen utifrån olika expertis. Dokumentationen som skapades under dessa möten analyserades, för att pröva om en didaktisk modell som hanterar de didaktisk vad- och hur-frågorna kunde hjälpa förskollärarna att skapa agens i undervisningen. Resultatet visar hur reflektion kring de didaktiska frågorna kan skapa möjligheter för agens i undervisningen. Didaktiska lösningar handlade om organisation av tid och miljö, om svårigheter att para ihop barn för kollektivt arbete samt språkutvecklande arbete.
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| 25. |
- Hedefalk, Maria, et al.
(författare)
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Studying Preschool Children’s Reasoning Through Epistemological Move Analysis
- 2017
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Ingår i: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education. - Singapore. - 9789811137426 ; , s. 1-8
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a theoretical tool for analysing mathematical reasoning using Epistemological Move Analysis (EMA) in combination with a framework focusing on arguments and the foundation of these. We also suggest the addition of evaluative arguments when talking about different types of arguments besides predictive and verifying arguments. The tool was applied on data of preschool children’s mathematical reasoning. The results indicate that different types of epistemological moves are connected to the different types of or the lack of arguments, and will fill (or not fill) gaps that occurs in the reasoning.
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| 26. |
- 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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| 27. |
- Landtblom, Karin, 1959-
(författare)
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Mean, median, and mode in school years 4–6 : A study about aspects of statistical literacy
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis explores different aspects of statistical literacy such as mathematical knowledge, context knowledge, use of words, and conceptions. The focus is on measures of central tendency: mean, median, and mode, and school years 4–6 (ages 10–13). The thesis contains of five papers and the phenomenon is studied in different contexts. In the first three papers, data is generated through a questionnaire answered by prospective teachers, teachers, and students in grade 6. In papers 4–5, second hand data is generated through textbook analysis where all tasks about the measures in seven different textbook series were analysed.Papers 1–3 showed that all respondent groups, primarily express procedural knowledge. They sometimes mix up the definitions of mean and median. Mean appears to be the most familiar measure and different contexts appropriate for mean are suggested. Median and mode appear to be less familiar, especially median which according to the students only exists in a school context. All respondent groups show several ways to express the mean using different colloquial connotations. Median and mode on the other hand do not bring any connotations, leading to difficulties to express explanations. For mode, some students used a homonym that gives a wrong meaning to the concept. This implies that the support for understanding mean, based on colloquial words, is not available for median or mode. The results from paper 4 show a high proportion of procedural tasks dealing with above all quantitative values for mode. Only one textbook definition of mode exemplified with qualitative values. In paper 5, tasks were examined out of mathematical properties related to input object, transformation, and output object. Here, tasks about both mean, median, and mode were examined. The results show that the distribution of the tasks was skew, meaning that students have different opportunities to learn various mathematical properties of the three concepts, something that was even more complex given that in many tasks, the mathematical properties in focus were implicit. Overall, statistical literacy according to the results generated in the five different studies, appear to be pre-dominantly about numbers and procedures. Very little attention seems to be on contextual knowledge, something that is crucial in statistical literacy.
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| 28. |
- Landtblom, Karin, 1959-, et al.
(författare)
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Teachers and prospective teachers’ conceptions about averages
- 2021
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Ingår i: Journal of Adult Learning, Knowledge and Innovation. - : Akademiai Kiado Zrt.. - 2631-1348. ; 4:1, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we explore prospective teachers and teachers’ conceptions about averages. The results show that when talking about which of the averages that is easiest and hardest to explain, respectively, the two groups differ in their responses. When teachers’ motivations most often are based on pedagogical explanations, the prospective teachers indicate conceptions based on personal experiences, often linked to procedures. When studying the conceptions about which of the averages that is most and least useful, the results indicate that there is no difference between the two groups. Mean is considered most useful, similar to what has been reported in previous studies, and mode is considered least useful by both groups. Few of the respondents recognize the mathematical properties of averages, particularly that “usefulness” is linked to which data that is in focus. The implications of the results are discussed.
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| 29. |
- Landtblom, Karin, 1959-, et al.
(författare)
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Which measure is most useful? Grade 6 students’ expressed statistical literacy
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- There is a growing body of research stressing statistical literacy, both for students to develop as an ability but also the need for studies investigating conceptions about various concepts in statistics. This is particular interesting in statistics, since concepts are tightly connected to their contexts. Students aged 12–13 answered a questionnaire about mean, median, and mode. They were asked about which measures that was easiest or hardest to explain combined with questions about usefulness, and if they could provide a definition to the different concepts. Their responses were coded against a set of categories taken from framework about statistical literacy covering knowledge elements and dispositional elements. The analysis used mixed methods, and the results indicate that students’ responses were primarily based on mathematical knowledge and use of words. When discussing what measure that was easiest or hardest to explain, a variety of conceptions were expressed, whereas the explanations about which measure that was most or least useful, were mainly related to context knowledge. Implications for teaching and research design are discussed.
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| 30. |
- Markkanen, Peter, 1964-, et al.
(författare)
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Building a joint problem-solving space: how collaboration in collective mathematical reasoning can develop
- 2024
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This study investigates how collaborative, collective mathematical reasoning emerges when students jointly solve problems regarding fair sharing. Three 6-year-old children worked collaboratively in a group with a problem related to fair sharing, and their teacher was present. The data, captured in video recordings, was analysed using two frameworks: collective mathematical reasoning, and the theory of joint problem space. The results show that different things, such as physical artefacts aimed at sharing resources, challenges related to the task, and the students’ conceptions of mathematics, affect the students’ possibilities to engage in collaborative collective mathematical reasoning.
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| 31. |
- Nyman, Martin, et al.
(författare)
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The issue of ‘proudliness’ : Primary students’ motivation towards mathematics
- 2019
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Ingår i: LUMAT. - 2323-7112. ; 7:2, s. 80-96
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed.
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| 32. |
- Nyman, Martin, 1968-
(författare)
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What do students’ feel about mathematics? : Compulsory school students’ emotions and motivation towards mathematics
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted.This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music.The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.
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| 33. |
- Pettersson, Annika, 1966-
(författare)
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Grafisk och algebraisk representation : Gymnasieelevers förståelse av linjära funktioner
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns upper secondary students’ understanding of algebraic and graphic representation of linear functions. Components of the students’ concept images, so-called ‘concept elements’, were studied as a way to capture their understanding. Four aspects affect the graphical view of a linear function, namely the parameter k, the parameter m, the scale of the coordinate axes and the domain of the function. Concerning the scale of the coordinate axis, there is a need to distinguish between two kinds of slope. When the scale of x-axis is changed, the k-value of the function, the so-called analytic slope, is constant but the visual slope changes. The tasks were designed so that three aspects were held constant in each task and one was varied. The study is qualitative and consists of two sub- studies. In the first, six students worked with two tasks involving the parameters k and m in the dynamic software GeoGebra. In the second, eight students were interviewed about a task concerning functions with different domains. Both studies also involved a task concerning the aspect of slope in a non-homogeneous coordinate system (a system with different scales on the axes). The results indicate three main findings: Firstly, students displayed difficulties in distinguishing between analytic and visual slope. Secondly, the word ‘start value’ can lead to conceptual problems when there is no visible intercept between the graphical representation of the function and the y-axis. Thirdly, the students displayed almost no concept elements in relation to the domain of a function.
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| 34. |
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| 35. |
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| 36. |
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| 37. |
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| 38. |
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| 39. |
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| 40. |
- Sidenvall, Johan, 1974-, et al.
(författare)
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Mathematical reasoning and beliefs in non-routine task solving
- 2014
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Ingår i: Current State of Research on Mathematical Beliefs XX.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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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| 41. |
- 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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| 42. |
- Sollerman, Samuel, 1973-
(författare)
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Kan man räkna med PISA och TIMSS? : Relevansen hos internationella storskaliga mätningar i matematik i en nationell kontext
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The overall purpose of the thesis is to contribute to the knowledge of relevance of international large-scale assessments (ILSAs) in mathematics, when these are to be used and interpreted in a national context. If a nation is to engage in ILSAs, draw conclusions from them and act on them, one should be aware of what they are measuring and how well it fits in with the national mathematics education and the mathematics they are trying to teach their students.The relevance is linked to the validity of the ILSA, which means that the assessment should measure the right things and do that in such a way that the results are as informative and useful as possible. In this thesis, the Swedish context is used as an example of a national context, against which the ILSAs PISA and TIMSS are contrasted.One way to study validation is to use an argumentation-based validation method, Assessment Utilization Argument. In this model, an argument consists of making claims on the basis of data and warrants. The claim is an interpretation of assessment results and the assertion of a claim carries with it the duty to support the claim and, if challenged, to defend it. Warrants are created and functions as propositions to justify the inferences from the data that lead to the claim.The ILSAs have been contrasted with the Swedish context through studies in three areas; content of the assessments, implementation of the assessments and results from the assessments. Based on these areas, the frameworks and tests from ILSAs were analyzed and compared with policy document and national tests from the Swedish context. Warrants were created based on these three areas.The analysis of the warrants showed that the ILSAs had a high level of conformity with the Swedish context and the ILSAs coincide in such a way that the results from these are relevant for studying the development of performance in a Swedish context. The analysis also showed that certain content and abilities in the Swedish context were not covered by the ILSAs. The Swedish students do not have the opportunity to show all those skills that the Swedish mathematical context covers and there were also indications that they do not make full efforts to show their skills. In order to create a more complete picture of Swedish students' mathematical skills, the assessment of students’ skills in mathematics should be complemented with other assessments.The results are discussed in relation to the development of national policy documents, including the risk if a nation decides to adapt their policy document to the ILSAs. In the case of Sweden there are indications that policy document develops in the same direction and closer to the frameworks of ILSAs. It becomes important to thoroughly examine the relationship between the ILSAs and a national context so that one can be aware of how, if and it what way the large-scale assessment impact a national context.This thesis contributes to a holistic approach based on a national context, with an overall method and covers the areas content, implementation and results of the ILSAs. It shows that opportunities and limitations can be found in all of these three areas. When the results of ILSAs are to be used in a national context, it is important to thoroughly examine what is meant to be assessed and what is really being assessed in these studies and to compare it with the purposes and content of the national context, so that suitable and valid conclusions could be drawn.
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| 43. |
- Ståhlberg, Peter, et al.
(författare)
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Talutrymme och genus
- 2016
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Ingår i: Nämnaren. - 0348-2723. ; :4, s. 34-36
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Tidskriftsartikel (populärvet., debatt m.m.)
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| 44. |
- Sumpter, Lovisa, 1974-
(författare)
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A reason to believe : beliefs as an influence on students task solving
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Upper secondary students’ task solving reasoning was analysed, with a focus on what grounds they had for different strategy choices and conclusions. Beliefs were identified and connected with the reasoning that took place. The results indicate that beliefs have an impact on the central decisions made during task solving. Three themes stand out: safety, expectation and motivation.
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| 45. |
- Sumpter, Lovisa
(författare)
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"...and they lived happily ever after"
- 2015
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Ingår i: Current State of Research on Mathematical Beliefs XX. - Falun : Högskolan Dalarna. - 9789185941933 ; , s. 47-50
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 46. |
- Sumpter, Lovisa, 1974-, et al.
(författare)
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Are we playing chinese whispers? Issues in questionnaire development
- 2017
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Ingår i: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education. - 9789811137426
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Konferensbidrag (refereegranskat)abstract
- In this paper, using gender as the topic in focus, we argue that transferring items and surveys from one cultural context to another might be highly problematic. For instance, in the Nordic context, gender issues are addressed in teacher education that reflects how equity is viewed on a societal and political level. Consequently, research on teacher students’ gendered beliefs should acknowledge and take into consideration their knowledge of gender equity during item development. Rather than being translated and adapted, items should be re-constructed and embedded in the context in which they are to be used in order to achieve a valid, reliable instrument. In addition, how gender equity is expressed develops over time, which differs in different cultural contexts. Consequently, time is also a factor to consider.
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| 47. |
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| 48. |
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| 49. |
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| 50. |
- Sumpter, Lovisa
(författare)
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Beliefs as an influence on mathematical reasoning
- 2004
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Ingår i: Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. ; , s. 357-
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Konferensbidrag (refereegranskat)
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