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  • 51.
    Mårtensson, Pernilla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Hansson, Henrik
    Jönköping University, School of Education and Communication.
    Challenging teachers' ideas about what students need to learn: Teachers' collaborative work in subject didactic groups2018In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 7, no 2, p. 98-110Article in journal (Refereed)
    Abstract [en]

    Purpose

    The purpose of this paper is to contribute to the understanding of the processes that make teachers learn in a collaborative arrangement similar to lesson study (LS) and learning study (LearS). The teachers in this collaboration wanted to enhance teaching and student learning (grades 4-7) about decimal numbers.

    Design/methodology/approach

    The analysis is based on data from five teachers’ collaborative work in an adaptive arrangement of LS and LearS called subject didactic groups. Data consist of eight audio recordings of the teachers’ meetings as well as written and photographic documentation of the meetings. The analysis was carried out through the lens of expansive learning within an activity system (Engeström, 1987). This entailed a focus on contradictions between teachers’ ways of thinking and acting when individually and collaboratively developing their teaching, on the solutions to the conflicts produced by the teachers, and on how these challenged the teachers’ ideas about what the students need to learn.

    Findings

    The authors identified contradictions between formative and summative assessment, exams and stressed students, prevailing norms about teaching and the theoretical tool used for planning and analyzing lessons and student learning, and the local curriculum and time constraints. The solutions to the conflicts were the driving force for developing new and more qualitative knowledge about what the students need to learn.

    Originality/value

    This paper gives explicit examples of contradictions and solutions that can challenge and drive teachers to expand their learning in an adaptive form of LS and LearS suited to daily teaching.

  • 52.
    Pang, M. F.
    et al.
    Faculty of Education, The University of Hong Kong, Hong Kong.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    The Learning study: recent trends and developments2019In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 8, no 3, p. 162-169Article in journal (Refereed)
  • 53.
    Papadopoulos, Ioannis
    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 1573-0816, Vol. 103, no 2, p. 191-207Article 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.

  • 54.
    Papadopoulos, Ioannis
    et al.
    Aristotle University, Thessaloniki, Greece.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    The use of ‘mental’ brackets when calculating arithmetic expressions2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 3 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 451-458Conference paper (Refereed)
  • 55.
    Ramdhany, Viren
    et al.
    University of Johannesburg, South Africa.
    Venkat, Hamsa
    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.
    Christiansen, Iben Maj
    Stockholm University, Sweden.
    Dissonance and continuity in the mathematical education and training experiences of pre-service secondary mathematics teachers2018In: African Journal of Research in Mathematics, Science and Technology Education, ISSN 1811-7295, Vol. 22, no 2, p. 186-195Article in journal (Refereed)
    Abstract [en]

    The education and professional development of pre-service mathematics teachers occur across different contexts. Key contexts of mathematics learning and learning to teach are school, university undergraduate mathematics and mathematics teaching-related learning in teacher education courses. International literature suggests that each of these contexts legitimises different views of mathematics teaching and learning. For pre-service teachers traversing these contexts, moves between sites can be experienced in more continuous or more dissonant ways. The disjunctures associated with dissonant experiences lead to openings for value judgments related to the distinctions that are drawn, opening possibilities for a wider range of pedagogic decisions. In this paper, we explore, through interviews with four pre-service teachers in one post-graduate certificate of education (PGCE) course, perceptions of continuity and dissonance across sites related to mathematics and mathematics education, and teaching and learning. Our findings point largely to experiences of continuity between the high school and undergraduate contexts, with the PGCE course recognised as different from these contexts. 

  • 56.
    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.
    Teachers and researchers in collaboration. A possibility to overcome the research-practice gap?2019In: European Journal of Education, ISSN 0141-8211, E-ISSN 1465-3435, Vol. 54, no 2, p. 250-260Article in journal (Refereed)
    Abstract [en]

    Taking as its point of departure the discussion about the disconnection between research and practice, this article presents learning study as a research approach to overcoming this gap. Learning study has commonalities with design research and lesson study, but is a teacher-researcher collaboration where both have a common object of research. Thus, it is research with teachers, rather than on teachers and focuses on constructing knowledge concerning objects of learning as well as teaching-learning relationships. The focus of the research collaboration is professional problems related to the object of learning that teachers encounter in their everyday practice. The process is guided by a theory of learning and pedagogy?the variation theory. The knowledge product of learning study is a theoretical description of what must be learned in order to develop a specific capability. Examples of knowledge contributions from learning study are given and it is suggested that such knowledge can be considered to be public knowledge that can be shared, used and developed by other teachers in other contexts. Furthermore, it is suggested that there are specific features of learning study that make it a research approach that may strengthen connections between research and practice.

    The full text will be freely available from 2021-05-28 00:05
  • 57.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Kullberg, Angelika
    University of Gothenburg, Sweden.
    Learning to Teach with Variation: Experiences from Learning Study in Sweden2017In: Teaching and Learning Mathematics through Variation: Confucian Heritage Meets Western Theories / [ed] Rongjin Huang and Yeping Li, Sense Publishers, 2017, p. 355-374Chapter in book (Other academic)
  • 58.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. University of Witwatersrand, Johannesburg, South Africa.
    Lövström, A.
    Jönköping University, School of Education and Communication.
    Hellquist, Björn
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Beyond the borders of the local: How “instructional products” from learning study can be shared and enhance student learning2018In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 7, no 2, p. 111-123Article in journal (Refereed)
    Abstract [en]

    Purpose: The purpose of this paper is to present how experiences gained from a theory-informed lesson study – learning study (LrS) – in regard to a specific learning goal can be shared and used by other teachers in new contexts.

    Design/methodology/approach: A group of teachers worked together in a cyclic, iterative process of planning, evaluating and revising teaching. The aim was to provide possibilities for grade 2 and 3 students to become familiar with negative numbers. The teacher group came to the conclusion that the students needed to be able to differentiate some aspects of negative numbers. The conjecture was put to the test in a follow-up study (FS) with five new teachers and eight classes. One lesson was taught based on the empirical findings in the LrS.

    Findings: The results suggest that teachers’ collaborative work has possibilities to produce knowledge about critical aspects of learning that can be communicated and adopted in new contexts. The teachers in the FS were able to make sense of the results from LrS and incorporate the critical aspects in their teaching in a way that enhanced students’ learning.

    Originality/value: It is demonstrated that teacher collaboration in LrS can create knowledge that goes beyond the border of the local context. 

  • 59.
    Runesson Kempe, Ulla
    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.
    Lövström, Anna
    Mörbylånga municipality, Mörbylånga, Sweden.
    Theory-informed lesson study as practice based research: identifying what is critical for grade 2 and 3 pupils’ learning of negative numbers2017In: Quadrante, ISSN 0872-3915, Vol. XXVI, no 2, p. 19-42Article in journal (Refereed)
    Abstract [en]

    The aim of the paper is to demonstrate how a theory-informed lesson study can be a form of practice-based research where knowledge is generated within the process of teachers’ actions. Learning study shares features with lesson study, such as the iterative design, the teacher driven approach and with attention to student learning, but is guided by a theoretical framework. The dominant theory has been variation theory. In learning study, the focus is the object of learning and what must be learned to make the object of learning one’s own. A learning study about learning and teaching negative numbers to young pupils (age 8-9) in a Swedish context is used as an example. Our proposal is in resonance with Morris’ and Hiebert’s (2011) suggestion; that lesson study is a system that can generate instructional products that are sharable and open for improvement by other actors. The ‘instructional product’ from learning study is a theoretical description of the object of learning, how it is constituted and can be taught. In the learning study reported, three teachers worked in collaboration to identify the critical aspects for realizing the existence of negative numbers. The critical aspects emerged and were successively specified in the process and as a result of a thorough analysis of data on pupils’ learning and the lessons. 

  • 60.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lövström, Anna
    Hellqvist, Björn
    Making distinctions – critical for the learning of the 'existence' of negative numbers? Exploring how 'instructional products' from a theory informed Lesson study can be shared and enhance student learning2017Conference paper (Refereed)
    Abstract [en]

    In this paper, we present how experiences gained from a theory informed Lesson study in regards to a specific learning goal can be shared and used by other teachers in new contexts. A group of teachers worked together in a cyclic, iterative process of planning, evaluating and revising teaching. The aim was to provide possibilities for grade 2 and 3 students to become familiar with negative numbers, thus to extend the number range from N to Z. Based on theoretical tenets about learning and empirical findings in the study the teacher group draw the conclusion that the pupils needed to be able to differentiate some aspects of negative numbers. The conjecture was put to the test in a follow-up study with five new teachers and eight classes. One lesson was taught based on the empirical finding in the Lesson study. When learning gains from pre- to post-test in these classes were compared to those in the Lesson study, similarities were found. It is suggested that accumulate evidence about ‘what must be learned’ across different classroom settings can be gained through a theory informed and goal oriented Lesson study.

  • 61.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Variationsteori som redskap för att analysera lärande och designa undervisning2017In: Undervisningsutvecklande forskning: exemplet learning study / [ed] Ingrid Carlgren, Malmö: Gleerups Utbildning AB, 2017, p. 45-60Chapter in book (Other academic)
  • 62.
    Sidenvik, Emil
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Historiska talsystem och taluppfattning: En studie om hur det egyptiska talsystemet kan användas till att stärka elevers taluppfattning2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna studie undersöks vad som är kritiskt för elever när ett historiskt talsystem ska användas i undervisningen. Syftet med studien är att identifiera kritiska aspekter som elever behöver urskilja för att kunna utveckla sin taluppfattning genom undervisning där det egyptiska talsystemet används. Syftet besvaras med hjälp av två forskningsfrågor; Vilka aspekter är kritiska? Vilka variationsmönster kan synliggöra de kritiska aspekterna?

    Studien baseras på variationsteorin och metoden learning study. Studien har utförts i två klasser i årkurs fyra. Studien består av ett för- och eftertest, samt en lektion som hållits i båda klasserna. Resultatet visar på att det fanns fyra kritiska aspekter för denna elevgrupp. Lektionen innehöll tre olika variationsmönster som resultatet påvisar ha belyst de kritiska aspekterna, eftersom eleverna presterat bättre i samtliga delar som testats. I vissa delar har andelen elever som svarat rätt ökat från 13% till över 50%. I studien dras slutsatsen att användning av historiska talsystem är ett effektivt sätt att utveckla elevers taluppfattning samt att de variationsmönster som använts i denna studie har lyckats belysa de aspekter som var kritiska för eleverna så att de har kunnat urskilja dem.

  • 63.
    Ullergård Pappas, Sofia
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Gustafsson, Joanna
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Talsortsräkning – en strategi för huvudräkning och för att förstå tal.2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Enligt TIMSS–studien 2015 presterar elever inom matematikämnet sämre i kategorintaluppfattning och aritmetik än i de övriga kategorierna. Med det som utgångspunkt är syftet med vår litteraturstudie att beskriva hur huvudräkningsstrategin talsortsräkning behandlas inom matematikdidaktisk forskning. Frågeställningarna ”vilka fördelar/nackdelar har strategin talsortsräkning?”, ”när väljer elever talsortsräkning?” och ”vad bör en lärare tänka på när undervisning om strategin planeras och genomförs?”utformades utifrån syftet. För att vidare besvara frågeställningar har vi analyserat ett flertal publikationer. Det analyserade materialet omfattar 9 vetenskapliga tidskriftsartiklar och 2 konferensbidrag. Samtliga publikationer är studier som utförts inom matematikdidaktik och berör huvudräkning. Forskning visar att talsortsräkning kan vara användbar i ett flertal situationer. Det kan vara en god ide att låta elever påbörja undervisning om huvudräkning med strategin talsortsräkning. Strategin används främst av elever med lägre taluppfattning och vid enkla uppgifter och har visat sig mer effektiv att använda vid additionsuppgifter jämfört mot subtraktionsuppgifter. Resultatet visar på ett antal olika nackdelar gällande talsortsräkning. Vid beräkning av subtraktionsuppgifter kan det exempelvis bli nödvändigt att behöva byta räknesätt samt att det finns en risk för att negativa tal kan uppstå. Det har visat sig att en lärares roll och förhållningssätt vid undervisningssammanhang har en stor betydelse för elevers syn och användning av strategier.

  • 64.
    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. 

  • 65.
    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.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Shifts in early number learning in South Africa2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 3, Research reports (L-Z) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 422-429Conference paper (Refereed)
    Abstract [en]

    In this paper, we report on outcomes from the Structuring Number Starters intervention project focused on early grades’ number learning in South Africa. Using tests drawn from the Maths Recovery programme, a cross-attainment sample of Grade 2 students in six schools took part in oral interview assessments early in 2011, 2014 and 2018, with professional development activities for their teachers occurring across this period. Student outcomes point to increasing proportions, over time, of students able to use more sophisticated counting strategies, and to work with number structure for more efficient calculation.

  • 66.
    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 Witwalersrand, Johannesburg, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwalersrand, Johannesburg, South Africa.
    Watson, Anne
    Department of Education, University of Oxford, Oxford, United Kingdom.
    Mason, John
    Architecture of mathematical structure2019In: For the Learning of Mathematics, ISSN 0228-0671, Vol. 39, no 1, p. 13-17Article in journal (Refereed)
    Abstract [en]

    In this paper, we provide an elaboration of the notion of mathematical structure – a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and connects these terms. The terminology is then applied to teaching and learning phenomena related to multiplicative reasoning, illustrating how the demarcation of terms can offer a more precise language of description of learning about structure. We present ‘formatting activity’ as a key pedagogic action for accomplishing a focus on structure in teaching.

  • 67.
    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.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Improving multiplicative reasoning in a context of low performance2019In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 1, p. 95-108Article in journal (Refereed)
    Abstract [en]

    In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12–13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention consisting of four lessons, designed with attunement to classroom culture and levels of learning, was implemented. Outcomes based on pre- and post-testing pointed to substantial gains in both schools, leading to interest in understanding the nature and extent of changes in models and calculation approaches in high performance and high gain item clusters. Increases in appropriate setting up of symbolic models of multiplicative situations and in more efficient calculation are discussed. 

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