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Discourses in school algebra: the textbooks' different views on algebra and the positioning of students
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Educational Sciences, Department of Education.ORCID iD: 0000-0002-6618-2615
2018 (English)In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 23, no 1, p. 47-65Article in journal (Refereed) Published
Abstract [en]

The purpose of this study is to understand the school algebra offered in Swedish mathematic textbooks for grade 8. Using a social semiotic perspective, textbook tasks are analysed with a method inspired by Systemic Functional Linguistics. Five school algebra discourses are identified: symbolic discourse, geometrical discourse, arith-metical discourse, (un)realistic discourse and the scientific discourse. It is argued that these offer different views on the nature of algebra and the positioning of students.

Place, publisher, year, edition, pages
2018. Vol. 23, no 1, p. 47-65
Keywords [en]
textbooks, secondary school curriculum, discourses, algebra, social-semiotics
National Category
Educational Sciences Didactics
Research subject
Curriculum Studies
Identifiers
URN: urn:nbn:se:uu:diva-357353OAI: oai:DiVA.org:uu-357353DiVA, id: diva2:1239082
Available from: 2018-08-15 Created: 2018-08-15 Last updated: 2019-10-30Bibliographically approved
In thesis
1. International large-scale assessments and mathematics textbooks in a curriculum reform process: Changes in lower secondary school algebra in Sweden 1995–2015
Open this publication in new window or tab >>International large-scale assessments and mathematics textbooks in a curriculum reform process: Changes in lower secondary school algebra in Sweden 1995–2015
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Reforming a curriculum entails more than simply launching new steering documents: it includes the development of new materials, evaluation of reform and identification of needs for further action. Drawing from algebra material surrounding the 2011 Swedish curriculum reform, this thesis contributes to understanding the process of curriculum reform concerning mathematics textbooks and international large-scale assessments.

Two analytical frameworks are applied to algebra tasks in six mathematics textbooks from three series, published in 1995–2015, and algebra items from four consecutive TIMSS tests in 2003, 2007, 2011 and 2015. These frameworks are a Systemic Functional Linguistics-framework based on a social-semiotic perspective and a framework adapted from different views on school algebra. They are used in order to understand algebra characteristics in terms of school algebra discourses and algebraic activities. Additionally, the relationship between Swedish students’ results on TIMSS’ algebra-items and algebra characteristics of the test items is explored statistically. The findings are viewed against the test structure over time.

The results show that five school algebra discourses are identified in both materials: the symbolic, arithmetical, geometrical, (un)realistic and scientific discourse. However, in the TIMSS tests, a relational discourse was further identified. The materials comprise the same algebraic activities, although in somewhat different proportions. The major change in textbooks is conservative since it is an increase of the (un)realistic discourse, which concerns features that may have been prevalent in the Swedish syllabus already a hundred years ago. This discourse may also be interpreted as a transformation of a reform idea in the syllabus, on mathematical literacy, into quite superficial everyday connections.

A comparison of the materials show that the algebra characteristic which increases most in textbooks, decreases in TIMSS. Further, students with high achievements on TIMSS perform significantly better on test items with algebra characteristics that decrease in proportion, compared with those which increase in proportion. Relatively seen, the difficulty of the tests for these students thus increases over time. This implies that the validity of interpreting TIMSS results as a knowledge trend is lessened. It is therefore less relevant to use TIMSS results for evaluating and identifying needs for further action. It is suggested that conclusions about student achievements in algebra should not be drawn based on the validity of interpreting and using the aggregate of TIMSS results in mathematics. Also, policy makers should pay more attention to how TIMSS results are used as a base for curricular reform and evaluation.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 151
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Educational Sciences ; 16
Keywords
curriculum reform, algebra, textbooks, international assessment, TIMSS, secondary school, test validity, student achievement.
National Category
Educational Sciences Didactics
Research subject
Curriculum Studies
Identifiers
urn:nbn:se:uu:diva-395267 (URN)978-91-513-0786-2 (ISBN)
Public defence
2019-12-06, sal Bertil Hammer 24:K104, Blåsenhus, von Kraemers allé 1, Uppsala, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2019-11-11 Created: 2019-10-16 Last updated: 2019-11-11

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http://ncm.gu.se/pdf/nomad/23_1_047066_kaplan.pdf

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Palm Kaplan, Kristina

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