| 1. |
- Sundström (Raman), Manya, 1971-
(författare)
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Coordinating informal and formal aspects of mathematics : student behavior and textbook messages
- 2002
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Ingår i: Journal of Mathematical Behavior. - 0732-3123 .- 1873-8028. ; 21:2, s. 135-150
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Tidskriftsartikel (refereegranskat)abstract
- In this paper I illustrate difficulties students have coordinating informal and formal aspects of mathematics. I also discuss two ways in which precalculus and calculus textbooks treat mathematics that may make this coordination difficult: emphasizing the informal at the expense of the formal and emphasizing the formal at the expense of the informal. By looking at student difficulties in light of textbook treatments, we see evidence that student difficulties are not merely developmental. Students are not given many opportunities to make the kinds of connections which, while difficult, are an essential component of mathematical thinking.
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| 2. |
- Abdulhamid, Lawan, et al.
(författare)
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Primary mathematics teachers’ responses to students’ offers : An ‘elaboration’ framework
- 2018
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 51, s. 80-94
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Tidskriftsartikel (refereegranskat)abstract
- Responding constructively ‘in-the moment’ to student offers is described as a critical, and yet difficult, aspect of skilful and responsive teaching. South African evidence points to limited evaluation of student offers in schools serving poor communities. In this paper, we present and discuss an ‘elaboration’ framework emerging from a grounded analysis of data drawn from video recordings of 18 mathematics lessons prepared and conducted by four in-service primary school teachers in South Africa. This analysis led to a categorization of the situations in which teacher responses to student offers occurred, and the nature and range of these responses. Three response situations are identified within the framework: breakdown, sophistication, and individuation/collectivization, with a range of response (and non-response) categories in each situation. Literature on responsive feedback is drawn in to explore hierarchies and relationships between the emergent categories within situations of elaboration. The elaboration framework provides a tool for lesson observation, and a model for thinking about developments in responsive teaching.
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| 3. |
- Andersson, Christian H., et al.
(författare)
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An examination of pre-service mathematics teachers’ ethical reasoning in big data with considerations of access to data
- 2023
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 70, s. 101029-101029
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Tidskriftsartikel (refereegranskat)abstract
- Implementations of Big Data analysis are reshaping society. The novel ways mathematics operate in society warrants new efforts for mathematics education, both in teaching the new technology and in providing an ethical and critical awareness of its implications. This interview study investigates pre-service teachers' ethical reasoning in data science contexts, focusing on aspects of access to the data that underpin the technology. Findings show that pre-service teachers offer a wide array of ethical arguments related to access to data, that informs their effort to think critically on oppressive situations. However, there is also an indication that their reasoning can be limited by lacking understanding of the related data science methodology, implying that mathematics teacher education should encompass more of this.
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| 4. |
- Bergqvist, Ewa, et al.
(författare)
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The role of linguistic features when reading and solving mathematics tasks in different languages
- 2018
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 51, s. 41-55
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this study is to deepen the understanding of the relation between the language used in mathematics tasks and the difficulty in reading and solving the tasks. We examine issues of language both through linguistic features of tasks (word length, sentence length, task length, and information density) and through different natural languages used to formulate the tasks (English, German, and Swedish). Analyses of 83 PISA mathematics tasks reveal that tasks in German, when compared with English and Swedish, show stronger connections between the examined linguistic features of tasks and difficulty in reading and solving the tasks. We discuss if and how this result can be explained by general differences between the three languages.
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| 5. |
- Bergqvist, Ewa, 1971-
(författare)
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Types of reasoning required in university exams in mathematics
- 2007
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 26:4, s. 348-370
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Tidskriftsartikel (refereegranskat)abstract
- Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students' understanding of the underlying mathematical concepts. It is therefore important to study the types of reasoning students have to perform in order to solve exam tasks and pass exams. The purpose of this study is to examine what types of reasoning students taking introductory calculus courses are required to perform. Tasks from 16 exams produced at four different Swedish universities were analyzed and sorted into task classes. The analysis resulted in several examples of tasks demanding different types of mathematical reasoning. The results also show that about 70% of the tasks were solvable by imitative reasoning and that 15 of the exams could be passed using only imitative reasoning.
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| 6. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Mathematical reasoning in teachers' presentations
- 2012
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 31:2, s. 252-269
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on available algorithms, often without arguments that justify the reasoning, which may lead to rote learning. The students are given some opportunities to see aspects of creative reasoning, such as reflection and arguments that are anchored in the mathematical properties of the task components, but in relatively modest ways.
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| 7. |
- Björklund, Camilla, 1977, et al.
(författare)
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Strategies informed by various ways of experiencing number relations in subtraction tasks
- 2022
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 67
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to develop greater understanding of how the way students experience a task is related to which, and how, number relations are discerned. We study how 42 Grade 1 students solved a word problem in a number range that was new to them: 32–25 = __. The variation theory of learning has informed our analysis, opening for thorough analyses of what constitutes differences in the students’ acts in solving the arithmetic word problem and how they experience the task. Observations of their strategies and ways of reasoning revealed that how the students discern the semantic structure and number relations relates to their ways of encountering the task and consequently their success in solving it. The study offers a complementary approach to understanding arithmetic skills that contribute knowledge as to why some students develop powerful ways of solving arithmetic tasks while others get stuck in cumbersome strategies.
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| 8. |
- Boesen, Jesper, 1971, et al.
(författare)
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Developing mathematical competence: From the intended to the enacted curriculum
- 2013
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 33:1, s. 72-87
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Tidskriftsartikel (refereegranskat)abstract
- This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with nearly 200 teachers. Contrasting to most studies of this size, qualitative analyses were conducted. The results show that teachers are positive to the message, but the combination of using national curriculum documents and national tests to convey the reform message has not been sufficient for teachers to identify the meaning of the message. Thus, the teachers have not acquired the functional knowledge of the competence message required to modify their teaching in alignment with the reform. The results indicate that for complex reform messages, such as the competency message, to have intended impact on classroom practice, special attention needs to be put on the clarity of the message. To have high-stakes tests, for example, does not alone seem to be sufficient. © 2013 Elsevier Inc.
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| 9. |
- Elofsson, Jessica, 1970-, et al.
(författare)
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Playing number board games supports 5-year-old children's early mathematical development
- 2016
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Ingår i: Journal of Mathematical Behavior. - Oxford : Elsevier. - 0732-3123 .- 1873-8028. ; 43, s. 134-147
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Tidskriftsartikel (refereegranskat)abstract
- The study examined effects of playing number games (linear number board game, circular number board game, and nonlinear numerical activities) on the development of number knowledge and early arithmetic. A passive control group was also included in the design. 114 5-year-old preschool children participated. Four tasks (number line estimation, counting, naming Arabic numbers, and arithmetic calculation) were used as dependent measures. Children assigned to an intervention participated in six 10-min sessions during a period of three weeks. Children playing the linear number board game improved their performance on the number line estimation task, while children playing the other games did not. Furthermore, children playing the linear number board game showed a substantial enhancement of their calculation performance. The positive effects of playing linear number board games support the representational mapping hypothesis. The finding concerning calculation provides support to the assumption that a linear representation is important for early arithmetical learning.
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| 10. |
- Eriksson, Göta
(författare)
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Arithmetical thinking in children attending special schools for the intellectually disabled
- 2008
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 27:1, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- This article focuses on spontaneous and progressive knowledge building in “the arithmetic of the child.” The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical interviews. Theoretical models elucidate behavior patterns and the corresponding mental structures underlying them. The individual interviews of the pupils were video recorded. The results show that the activated behavior patterns, which are responses to well-adapted contexts presented by the researcher, are compatible with findings in Swedish compulsory schools. Six of the pupils’ mental structures in the study are numerical. A substantial implication for specialeducation is the harmonization of the content in teaching with the children’s own ways of operating, which implies a triadic teaching process.
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