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Algebraic reasoning in upper secondary school
Stockholm University, Faculty of Humanities, Department of Humanities and Social Sciences Education.
Stockholm University, Faculty of Humanities, Department of Humanities and Social Sciences Education.ORCID iD: 0000-0002-6684-2353
2019 (English)Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

The participants (n = 85) in this study were 16-17 years old and in their first year of upper secondary school in Sweden. In total, three lessons were recorded and transcribed, all with the same teacher. The first two lessons were conducted in a class of the Social Science Programme, i.e. a university-preparatory programme, and the third lesson in a class of the Building and Construction Programme, i.e. a vocational programme. The difference between the classes could be understood from their grade averages from compulsory school, 265 and 278 for the former two classes and 200 for the latter, where 340 is the highest possible score. The classes were chosen for different reasons, such as if there would be any differences according to former grades or choice of education. The intention was to use the same learning tasks in all classes, but small changes were made according to the analyses made after each lesson.

Learning Study has been used in several studies, initially to test the Variation Theory, and is therefore also the most commonly used theory. It originates in the iterative process used in Lesson Study, and the methodology for Learning Study could be described by this iterative process:

  1. Find an object of learning
  2. Make a pre-test
  3. Design the lesson
  4. Implement the lesson
  5. Make a post-test
  6. Analyse the lesson
  7. Revise the lesson
  8. Return to 4

Other theories have been used in former Learning Studies, e.g. Learning Activity (LA). This study also uses LA as a theoretical framework and the research questions are:

  • What kind of tasks and discussions in the classroom could lead to the development of algebraic reasoning?
  • What learning actions, i.e. algebraic reasoning, could be shown orally, bodily or symbolically?
  • What qualities in the reasoning could be seen? 

In order to analyse the lessons, the LA framework was used. Aspects to examine and questions to ask were, for example:

  • What is the learning task, and what is it possible for the student to understand of the task?
  • What is intended with the lesson, and what are the students trying to do?
  • What is known/unknown for the students?

An important part of LA is reflection, e.g. considering goals, motives, means of action by oneself and others, etc. Important questions were thus:

  • How are solutions handled (both by the teacher and by classmates)
  • How are solutions evaluated in class?
  • What kind of reflections are made?

The preliminary results from the study show that the mathematical tool could be helpful, if used, in developing algebraic reasoning. Its usefulness could depend either, or both, on the way in which the tool was introduced and the way in which the learning tasks were presented and handled in class. Analyses in relation to the LA framework also raised questions about the motive of the tasks, e.g. reducing variables. The importance of this in a mathematical sense is clear, but the task did not enable the students to see this.

Place, publisher, year, edition, pages
2019.
Keywords [en]
Algebra, Learning Study, Learning Activity
National Category
Didactics
Research subject
Didactics
Identifiers
URN: urn:nbn:se:su:diva-172884OAI: oai:DiVA.org:su-172884DiVA, id: diva2:1350530
Conference
World Association of Lesson Studies (WALS) International Conference, Amsterdam, Netherlands, 3–6 September, 2019
Projects
Developing algebraic reasoning capability
Funder
Swedish Institute for Educational Research, 2016/151Available from: 2019-09-11 Created: 2019-09-11 Last updated: 2019-09-23Bibliographically approved

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CiteExportLink to record
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