Världens blickar har under de två senaste decennierna riktas mot östra Asien när lärande och undervisning i matematik står i centrum för diskussioner. En anledning till det ökade intresset är troligtvis att dessa regioner, gång efter annan, placerar sig i topp i olika internationella mätningar som TIMMS och Pisa medan Sverige och många andra OECD-länder hamnar på en mer blygsam placering. Det finns flera tänkbara förklaringar till sådana skillnader. En avgörande faktor för undervisningskvalitet och som ofta lyfts fram är den kinesiska undervisningstraditionen Bianshi Jiaoxue—undervisa utifrån variation av ämnesinnehållet. Denna tradition erbjuder flera intressanta begrepp som kan användas som verktyg för att planera och genomföra undervisning, speciellt med avseende på hur uppgifter kan sammanlänkas för att skapa effektivt och fördjupat lärande i matematik. Vi illustrerar några centrala begrepp inom traditionen genom att lyfta några exempel från en lektion om addition och subtraktion med tal i bråkform genomförd i Shanghai samt från en intervju genomförd med den undervisande läraren. Lektions- och intervjudata kommer från ett av samarbetsprojekt, finansierat av Vetenskapsrådet, mellan forskare från Jönköping University och Hong Kong University. Utgångspunkten relaterat konferensens tema är att en praktisk teori är en viktig komponent för undervisning på vetenskaplig grund. 

Understanding the object of learning is a significant, yet often elusive, part of analysing a lesson through the lens of variation theory of learning. It involves not only specifying the usual learning objectives in terms of content and how to handle it, but also through identification of critical aspects to be discerned. The role of critical aspects in formulating the object of learning in an elaborate and useful way is the focus of this discussion paper. This is explored by comparing two mathematics lessons in China, designed and conducted by two teachers skilfully with bianshi pedagogy. As the content, textbook resources and students’ characteristics are basically the same, the subtle difference in the observed objects of learning becomes apparent. This difference is reflected in two contrasting sets of critical aspects that are structuring the lessons. In Marton (2015), “the object of learning is described primarily in terms of critical aspects and features to be discerned” for a better precision. Our analysis may contribute to a further discussion about how far the critical aspects constitute the meanings behind the content, which is not commonly addressed when a lesson is mainly analysed in terms of patterns of variation in a mechanical manner.

This presentation aims to illustrate how the integration of theory and teaching experiences can support pre-service teachers to generate knowledge for teaching mathematics. The pre-service teachers took part in a 5-week mathematics education course in a teacher education program in Sweden, in which a theory driven lesson study model entitled learning study were established to deepen the teachers’ awareness about the relationship between instruction and student learning. The course design consisted of two intervention cycles in which the pre-service teachers used variation theory as well as their teaching experiences as tools for lesson design and redesign. To enable us to identify if and how theory and experiences drawn from practice were employed and realized, we collected data from the pre-service teachers’ individual written reports at the end of the course. The unit of analysis from the written reports were 64 redesigned mathematical tasks and associated reflections about the reason for redesign. We found five different categories of how tasks were modified: expanding tasks, making tasks more explicit, making tasks less explicit, bringing metaphors and representations to the foreground, and creating new tasks. The findings could contribute to reflections and discussions about course design in teacher education and in what way the integration of theory and practice can be regarded as an important key point for pre-service teachers’ professional and sustainable learning. 

In this study, we examine how 30 pre-service teachers designed and modified mathematical tasks to enhance primary students’ learning. The pre-service teachers took part in a 5-week course in a teacher education program in Sweden in which a theory-based lesson study model entitled learning study were established to deepen the teachers’ awareness about the relationship between instruction and student learning. The learning study course design consisted of two intervention cycles in which the pre- 17 SIG 9 Phenomenography and Variation Theory service used variation theory as a tool for lesson design and re-design. The aim of this study is to explore in what ways the pre-service teachers modify mathematical tasks when employing variation theory during the 5-week mathematics education course in which LS cycles were incorporated. Data were collected at the end of the course and consist of written reports about task refinements based on their reflections about the students’ performance during the lessons. We identified five different ways of task modifications: expanding tasks, making tasks more explicit, making tasks more implicit, bringing metaphors and representations to the foreground, and creating new tasks. These categories might become a complementary tool to variation theory, for reflecting about task design and redesign.

The theory-practice divide in teacher education is commonly viewed as there aretwo separate entities – theory and practice. However, in practice-based researchapproaches, theory is commonly integrated with existing practical knowledge withthe aim to deepen teachers’ knowledge about practice or to create new knowledge. In this study, we examine 30 pre-service teachers taking part in a 5-week course in ateacher education program in Sweden, in which an action-research approach termed Learning study was used to deepen the pre-service teachers’ thinking and reasoning about mathematics teaching in order to develop primary student learning. Variation theory was used as a tool to support the pre-service teachers’ reflections on how different ways of structuring the mathematical content are related to student learning outcomes. This research aims to illustrate how the integration of theory and teaching experiences from the 5-week mathematics education course supported pre-service teachers’ generation of knowledge about teaching and learning mathematics. In this study, we regard mathematical tasks created by the pre-service teachers and usedin the lessons as generated knowledge about the practice of teaching. Data were collected during the course and consist of written reports about task refinements inthe pre-service teachers’ lessons. We identified five different ways of re-designing the tasks: expanding tasks, making tasks more explicit, making tasks less explicit,bringing metaphors and representations to the foreground, and creating new tasks.

I den här studien har vi undersökt på vilka sätt 41 grundlärarstudenter, med inriktning mot årskurs 4‒6, designade och förändrade matematikuppgifter för att utveckla kunskap om undervisning och skolelevers lärande av specifika ämnesinnehåll. Under höstterminen 2018 deltog lärarstudenterna i en fem-veckors matematikdidaktikkurs inom ramen för grundlärarprogrammet på Högskolan för lärande och kommunikation, Jönköping University. Kursen är till stor del uppbyggd utifrån learning study‒konceptet (Marton & Pang, 2003), vilket kort kan beskrivas som ett kollegialt, iterativt och intervenerande utvecklingsarbete med inslag av ämnesdidaktiskforskning (Runesson Kempe, 2016). I den aktuella kursen innebar detta bland annat att arbetet utgick från studenternas egna frågor om undervisning och lärande men i samråd med lärare från kursens samverkansskolor. Samverkan med skolor i regionen är en avgörande faktor för kursen eftersom det möjliggör för studenterna att undersöka elevers förståelse av något ämnesinnehåll och utifrån det forma och genomföra undervisning. Vidare var studenterna i kursen indelade i grupper (3‒4 studenter per grupp), i vilka man systematiskt planerade, genomförde och analyserade undervisning i två cykler. I detta arbete användes ämnesdidaktisk forskning och variationsteorin (Marton & Pang, 2003) som redskap för att komma åt vad skoleleverna behöver få syn på för att utveckla kunskap i förhållande till specifika ämnesinnehåll. Studiens data samlades in under kursen och består av lärarstudenternas skriftliga reflektioner om de uppgifter som de designade och prövade i lektionerna och om hur och varför dessa förändrades eller borde förändras. Syftet med studien är att identifiera och beskriva de olika sätt lärarstudenterna förändrade matematikuppgifterna utifrån ett variationsteoretiskt perspektiv. I presentationen visas några sådana exempel.

Purpose

The purpose of this paper is to identify changes in teacher’s pedagogical content knowledge (PCK) as a result of their participation in two learning studies in mathematics.

Design/methodology/approach

A group of four mathematics teachers and the researcher of this paper explored two objects of learning related to division with decimal numbers and the straight-line equation in a learning study (LS) project over the course of one year. The data used consist of eight video-recorded lessons, four written student tests, eight student interviews and 14 recorded team meetings. The analysis was based on the variation theory principle about learning (Marton, 2015) and on ontological assumptions within the phenomenographic approach (Marton, 1981).

Findings

It was found that teachers’ PCK was changed and refined through the LS process in terms of differences in ways of understanding and discussing critical aspects related to each object of learning. In the paper, the terms “presumed critical aspects” and “explored critical aspects” are used to illustrate this difference. Furthermore, the concepts are viewed in relation to three subdomains of PCK: knowledge of content and curriculum (KCC), knowledge of content and students (KCS) and knowledge of content and teaching (KCT).

Originality/value

Bringing out the difference between “presumed critical aspect” and “explored critical aspects” advances the view that critical aspects are dynamic and emergent in practice – in the interaction between teaching and student learning. The research exposes “explored critical aspects” as a specific form of PCK in which KCC, KCS and KCT are intertwined.

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.