Different possibilities to learn from the same task

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator less than 1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task was used in the lessons, the way it was enacted provided different possibilities to learn

Diferentes posibilidades para aprender con una misma tarea

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator less than 1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task was used in the lessons, the way it was enacted provided different possibilities to learn.En este artículo nos centramos en la variación del diseño y la implementación de una tarea específica durante tres sesiones de clase de matemáticas en octavo grado en un estudio de aprendizaje (Marton y Tsui, 2004; Runesson, 2008). El tema de las clases fue la división con un divisor entre 0 y 1. Los profesores querían que sus estudiantes entendieran que, cuando se divide por un divisor menor que 1, el cociente es mayor que el numerador. Cuatro profesores colaboraron, en un proceso cíclico, en la planificación, análisis y revisión de las tres sesiones de clase. El estudio muestra que la implementación de la tarea cambió entre las sesiones. A pesar de utilizarse la misma tarea en las sesiones, la manera en que se implementó proporcionó diferentes posibilidades para aprender.This research was funded by a grant from the Swedish National Research Council

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]

Focusing on the object of learning and what is critical for learning: A case study of teachers’ inquiry into teaching and learning mathematics

During the last decade, Lesson Study, a Japanese professional development model involving a community of learners, has been spreading to countries around the world. Lesson Study is a systematic process of inquiry into classroom practices where teachers collaborate in planning, implementing, observing and revising lessons. The approach used in the study reported in this paper involves a version of Lesson Study, namely Learning Study. Whereas the underpinning theory in Lesson Study is often implicit, Learning Study has an explicit theory that can help teachers to pedagogically theorise about their practice, students’ learning and the object of learning. Through one Swedish Learning Study in mathematics, I demonstrate what teachers can learn by exploring what is critical for their students’ learning and how teaching can be improved to enhance learning

Pedagogical and learning theories and the improvement and development of lesson and learning studies

Purpose It has been suggested that, if pedagogical and learning theories are integrated into lesson and learning study, a systematic construction of pedagogical knowledge is possible (Elliott, 2012). In this Special Issue, it is reported how theory and theoretical concepts can add value to lesson and learning study. The purpose of this paper is to introduce the Special Issue and explore the above concepts. Design/methodology/approach This paper presents the Special Issue papers thematically and the main issues are discussed. Findings Together the papers suggest that pedagogical theories and theorizing practice may contribute to the improvement of teachers’ practical knowledge and knowledge about teachers’ professional tasks and objects. Furthermore, some theories and theoretical concepts hitherto under-exploited in lesson and learning study are presented and discussed from the point of view how these might improve the quality of the studies. Originality/value As a total, this collection of papers bring out issues about the role of pedagogical and learning theories and how these could inform lesson and learning study