Single unit counting – An impediment for arithmetic learning

In this paper we direct attention to the single unit counting strategy that is observed to be limiting students’ opportunities to develop their arithmetic skills. We describe what impediments single unit counting may entail when encountering novel subtraction tasks, and how these impediments can be explained. From a sample of 121 interviews of students aged 7-8 we have chosen nine who were using single unit counting as their dominating arithmetic strategy. An analysis based on variation theory reveals that the impediments are related to the students not experiencing numbers as composed units and thereby lack in discerning number relations necessary to handle multi-digit subtraction. Educational implications are discussed grounded in the theoretically driven findings.This work was supported by the Swedish Institute for Educational Research [Grant number 2018-00038]

Kunskapsprodukter för lärarprofessionen – Skolforskningsinstitutets projekt 2016 och 2017

Syftet med denna artikel är att beskriva och diskutera vilka, för lärare, användbara och relevanta kunskapsprodukter som har genererats i 11 forskningsprojekt, finansierade av Skolforskningsinstitutet och beviljade år 2016 och 2017. Forskningsfrågorna är: Vad i resultaten kan ses som kunskapsprodukter och vilken karaktär har dessa? På vilka sätt har lärare medverkat i processen att ta fram dessa kunskapsprodukter? Sammantaget har 55 öppet tillgängliga granskade publikationer analyserats. Sex kvalitativt skilda kategorier av kunskapsprodukter har identifierats: 1) Kunnanden och förmågor, 2) Undervisnings- och lektionsdesign, 3) Didaktiska exempel, 4) Redskap, 5) Processer och metaperspektiv och 6) Generella eller kontextuella förutsättningar. Graden av medverkan från lärares sida har varierat avsevärt; från en aktiv medverkan, där lärare och forskare samarbetar på likvärdiga villkor, till en låg grad, där lärare primärt fungerar som bollplank eller forskningsobjekt. ENGLISH: Knowledge products for the teaching profession – Projects 2016 and 2017 funded by the Swedish Institute for Educational Research   This article examines the knowledge products of relevance to the teaching profession from eleven research projects funded by the Swedish Institute for Educational Research. A total of 55 openly accessible reviewed publications have been analysed. The aim is to describe and discuss which, for teachers, useful and relevant knowledge products that the research projects (granted 2016 and 2017) have yielded. The research questions are: What in the results can be interpreted as knowledge products and what is the characteristic of these? In what ways have teachers participated in the process of producing these knowledge products? Six qualitatively different categories of knowledge products have been identified as descriptions of: 1) Knowings and capabilities, 2) Teaching/lesson design, 3) Didactical examples, 4) Tools, 5) Processes and meta-perspectives, and 6) General or contextual preconditions. The degree of involvement of teachers has varied considerably, ranging from a high degree of active involvement, where teachers and researchers collaborate on equal terms, to a low degree of involvement where teachers primarily act as informants. Keywords: Knowledge products, Swedish Institute for Educational Research, practice-based research, teacher profession, teaching developmen

Teaching and learning addition and subtraction bridging through ten using a structural approach

An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in Swedish Grade 1. A goal was that at the end of Grade 1, students would solve tasks like 15–7= using part-whole relations of numbers. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after and one year after the intervention, to investigate long-term effects and whether students used a structural approach when solving tasks in Grade 2. Results show that students in the intervention group increased their learning outcomes the most and to a larger extent solved tasks in higher number ranges using a structural approach.This work was supported by the Swedish Institute for Educational Research [Grant number 2018-00038]

Theory-informed lesson study as practice based research: identifying what is critical for grade 2 and 3 pupils’ learning of negative numbers

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. O objetivo do artigo é demonstrar como um estudo de aula informado pela teoria pode ser uma forma de investigação baseada em prática onde o conhecimento é gerado dentro do processo das ações dos professores. O estudo de aprendizagem compartilha caraterísticas com o estudo de aula, como o processo iterativo, a abordagem centrada no professor e a atenção à aprendizagem do aluno, mas é guiada por um quadro teórico. A teoria dominante tem sido a teoria da variação. No estudo de aprendizagem, o foco é o objeto de aprendizagem e o que deve ser aprendido para a apropriação do tornar o objeto de aprendizagem. Um estudo de aprendizagem sobre aprendizagem e ensino de números negativos aos jovens alunos (idade 8-9 anos) num contexto sueco é usado como exemplo. A nossa proposta está em ressonância com a sugestão de Morris e Hiebert (2011) de que o estudo de aula é um sistema que pode gerar produtos de ensino que são compartilháveis e abertos para melhoria por outros atores. O ‘produto de ensino’ do estudo de aprendizagem é uma descrição teórica do objeto de aprendizagem, como é constituído e pode ser ensinado. No estudo de aprendizagem relatado, três professores trabalharam em colaboração para identificar os aspetos críticos para perceber a existência de números negativos. Os aspetos críticos emergiram e foram sucessivamente especificados no processo e como resultado de uma análise de dados minuciosa dos sobre a aprendizagem dos alunos e as aulas

Can public knowledge be created through practitioner research? : Learning studies and variation theory as mechanisms and strategiesbbehind knoeledge production in practitioners´research

In this paper, we address the question if teachers’ collaborative research can produce practice- based knowledge relevant beyond the borders of the local school context. It has been argued that teachers’ collaboration in professional learning communities (PLC) are aiming at practical innovations and change foremost in teacher learning, and thereby do not strive to create public practical knowledge beyond the borders of the local school. The purpose of this paper is to discuss a particular type practitioner research in schools, a type of theory-based lesson study, that have shown to have potential of creating knowledge products that enhance student learning that also are sharable between teachers

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 learning

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

Kunskapsprodukter för lärarprofessionen : skolforskningsinstitutets projekt 2016 och 2017

Syftet med denna artikel är att beskriva och diskutera vilka, för lärare, användbara ochrelevanta kunskapsprodukter som har genererats i 11 forskningsprojekt, finansieradeav Skolforskningsinstitutet och beviljade år 2016 och 2017. Forskningsfrågorna är: Vad iresultaten kan ses som kunskapsprodukter och vilken karaktär har dessa? På vilka sätt harlärare medverkat i processen att ta fram dessa kunskapsprodukter? Sammantaget har 55öppet tillgängliga granskade publikationer analyserats. Sex kvalitativt skilda kategorierav kunskapsprodukter har identifierats: 1) Kunnanden och förmågor, 2) Undervisnings- ochlektionsdesign, 3) Didaktiska exempel, 4) Redskap, 5) Processer och metaperspektiv och 6)Generella eller kontextuella förutsättningar. Graden av medverkan från lärares sida har varieratavsevärt; från en aktiv medverkan, där lärare och forskare samarbetar på likvärdigavillkor, till en låg grad, där lärare primärt fungerar som bollplank eller forskningsobjekt.This article examines the knowledge products of relevance to the teaching professionfrom eleven research projects funded by the Swedish Institute for Educational Research.A total of 55 openly accessible reviewed publications have been analysed. The aim is todescribe and discuss which, for teachers, useful and relevant knowledge products thatthe research projects (granted 2016 and 2017) have yielded. The research questions are:What in the results can be interpreted as knowledge products and what is the characteristicof these? In what ways have teachers participated in the process of producingthese knowledge products? Six qualitatively different categories of knowledge productshave been identified as descriptions of: 1) Knowings and capabilities, 2) Teaching/lessondesign, 3) Didactical examples, 4) Tools, 5) Processes and meta-perspectives, and 6)General or contextual preconditions. The degree of involvement of teachers has variedconsiderably, ranging from a high degree of active involvement, where teachers andresearchers collaborate on equal terms, to a low degree of involvement where teachersprimarily act as informants

Beyond the borders of the local : How “instructional products” from learning study can be shared and enhance student learning

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.

Kunskapsprodukter för lärarprofessionen : skolforskningsinstitutets projekt 2016 och 2017

Syftet med denna artikel är att beskriva och diskutera vilka, för lärare, användbara ochrelevanta kunskapsprodukter som har genererats i 11 forskningsprojekt, finansieradeav Skolforskningsinstitutet och beviljade år 2016 och 2017. Forskningsfrågorna är: Vad iresultaten kan ses som kunskapsprodukter och vilken karaktär har dessa? På vilka sätt harlärare medverkat i processen att ta fram dessa kunskapsprodukter? Sammantaget har 55öppet tillgängliga granskade publikationer analyserats. Sex kvalitativt skilda kategorierav kunskapsprodukter har identifierats: 1) Kunnanden och förmågor, 2) Undervisnings- ochlektionsdesign, 3) Didaktiska exempel, 4) Redskap, 5) Processer och metaperspektiv och 6)Generella eller kontextuella förutsättningar. Graden av medverkan från lärares sida har varieratavsevärt; från en aktiv medverkan, där lärare och forskare samarbetar på likvärdigavillkor, till en låg grad, där lärare primärt fungerar som bollplank eller forskningsobjekt.This article examines the knowledge products of relevance to the teaching professionfrom eleven research projects funded by the Swedish Institute for Educational Research.A total of 55 openly accessible reviewed publications have been analysed. The aim is todescribe and discuss which, for teachers, useful and relevant knowledge products thatthe research projects (granted 2016 and 2017) have yielded. The research questions are:What in the results can be interpreted as knowledge products and what is the characteristicof these? In what ways have teachers participated in the process of producingthese knowledge products? Six qualitatively different categories of knowledge productshave been identified as descriptions of: 1) Knowings and capabilities, 2) Teaching/lessondesign, 3) Didactical examples, 4) Tools, 5) Processes and meta-perspectives, and 6)General or contextual preconditions. The degree of involvement of teachers has variedconsiderably, ranging from a high degree of active involvement, where teachers andresearchers collaborate on equal terms, to a low degree of involvement where teachersprimarily act as informants