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  • 1.
    Boesen, Jesper
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Lithner, Johan
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    Palm, Torulf
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    The relation between types of assessment tasks and the mathematical reasoning students use2010In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 75, no 1, p. 89-105Article in journal (Refereed)
    Abstract [en]

    The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.

  • 2.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication. University of Witwatersrand, Johannesburg, South Africa.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Coding teaching for simultaneity and connections: Examining teachers’ part-whole additive relations instruction2016In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 93, no 3, p. 293-313Article in journal (Refereed)
    Abstract [en]

    In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations instruction were developed. Teachers’ use of multiple representations within an example, attention to part-whole relations within examples, and relations between multiple examples were identified, with teachers’ linking actions in speech or gestures pointing to connections between these. In this article, the coding framework is detailed and exemplified in the context of a structural approach to part-whole teaching in six South African grade 3 lessons. The coding framework enabled us to see fine-grained differences in teachers’ handling of part-whole relations related to simultaneity of, and connections between, representations and examples as well as within examples. We went on to explore the associations between the simultaneity and connections seen through the coding framework in sections of teaching and students’ responses on worksheets following each teaching section.

  • 3.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Wei Sönnerhed, Wang
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Hernell, Bernt
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations?2016In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 92, no 1, p. 91-105Article in journal (Refereed)
    Abstract [en]

    The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied, focusing specifically on expressions of the type a ± (b × c) with brackets emphasizing the multiplication compared to expressions of the type a ± b × c without such brackets. Data were collected from pen and paper tests, before and after brief (about 7 min) instructions, of 169 Swedish students in year 6 and 7 (aged 12 to 13). The data do not seem to support the use of brackets to detach the middle number (b) from the first operation (±) in a ± b × c type of expressions.

  • 4.
    Kullberg, Angelika
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Björklund, Camilla
    Department of Education, Communication and Learning, University of Gothenburg, Gothenburg, Sweden.
    Brkovic, Irma
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816Article in journal (Refereed)
    Abstract [en]

    In this paper, we report how 5-year-olds’ arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children’s ways of experiencing numbers’ part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report is based on an analysis of assessments with 103 children (intervention group n = 65 and control group n = 38) before and after the intervention and a follow-up assessment 1 year after the intervention. Our findings show that the learning outcomes of the intervention group were significantly higher compared to those of the control group after the intervention and that differences between the groups remained even 1 year after the intervention. In particular, the results show that children participating in the intervention group learned to recognize and use part-part-whole relations in novel arithmetic tasks.

  • 5.
    Papadopoulos, I.
    et al.
    School of Primary Education, Aristotle University of Thessaloniki, Thessaloniki, Greece.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Exploring the way rational expressions trigger the use of “mental” brackets by primary school students2020In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816Article in journal (Refereed)
    Abstract [en]

    When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way students evaluate this expression. It also seems that a connection exists between this way of evaluation and an understanding of structure. Both issues are examined in this paper. A number of arithmetical expressions in a rational form were given to primary school students from Greece and Sweden. The collected findings strengthen our hypothesis that this rational form of the arithmetical expressions was of critical importance for the students’ decision on how to evaluate these expressions. They temporarily put aside their knowledge about the rules for the order of operations. Instead, the way they evaluated the expressions indicates an implicit use of what we call in this paper “mental” brackets. It is very likely that the use of these “mental” brackets is closely connected with students’ structure sense.

  • 6.
    Venkat, Hamsa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mediating primary mathematics: theory, concepts, and a framework for studying practice2018In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 97, no 1, p. 71-92Article in journal (Refereed)
    Abstract [en]

    In this paper, we present and discuss a framework for considering the quality of primary teachers’ mediating of primary mathematics within instruction. The “mediating primary mathematics” framework is located in a sociocultural view of instruction as mediational, with mathematical goals focused on structure and generality. It focuses on tasks and example spaces, artifacts, inscriptions, and talk as the key mediators of instruction. Across these mediating strands, we note trajectories from error and a lack of coherence, via coherence localized in particular examples or example spaces, towards building a more generalized coherence beyond the specific example space being worked with. Considering primary mathematics teaching in this way foregrounds the nature of the mathematics that is made available to learn, and we explore the affordances of attending to both coherence and structure/generality. Differences in ways of using the framework when either considering the quality of instruction or working to develop the quality of instruction are taken up in our discussion. 

1 - 6 of 6
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