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#### Open Access in DiVA

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Madej, Lars
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Department of Education
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2021 (Swedish)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2021. , p. 101
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Educational Sciences ; 23
##### Keywords [en]

Early algebra, curriculum, mathematics textbooks, primary school mathematics, generalized arithmetic, conceptual knowledge, knowledge levels, mathematics education
##### Keywords [sv]

Tidig algebra, läroplan, läromedel i matematik, matematik i tidiga skolår, generaliserad aritmetik, konceptuell kunskap, kunskapsnivåer, matematikundervisning
##### National Category

Didactics
##### Research subject

Curriculum Studies
##### Identifiers

URN: urn:nbn:se:uu:diva-425573ISBN: 978-91-513-1076-3 (print)OAI: oai:DiVA.org:uu-425573DiVA, id: diva2:1503354
##### Public defence

2021-01-22, Eva Netzelius, Blåsenhus, von Kramers allé 1, Uppsala, 13:15 (Swedish)
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##### Funder

Swedish Research Council, 2015-02043Available from: 2020-12-18 Created: 2020-11-24 Last updated: 2021-01-25
##### List of papers

The overall aim of this thesis is to increase the knowledge of the state of algebraic thinking in the earlier years, so called early algebra, in the Swedish primary school. First, using the Big Ideas of Algebra (Blanton et al., *Journal for Research in Mathematics Education*, *46*(1), 39–87, 2015) as a theoretical framework, the thesis investigates which types of algebraic thinking can be identified in the Swedish mathematics curriculum and in two textbooks series for Grades 1-6. Second, as students’ understanding of the equal sign as a symbol for a relation is an important factor for algebraic success, students’ knowledge of it is studied by using an assessment form based on Matthews et al. (*Journal for Research in Mathematics Education*, *43*(3), 316-350, 2012).

The results of the empirical studies show that Equivalences, Expressions, Equations, and Inequalities (EEEI) were the most prominent Big Idea in the Swedish context. The Big Idea of Generalized Arithmetic (GA) is not represented in the Central content in Grades 1-6 and only slightly represented in the textbooks. Furthermore, there are big differences between the two textbook series, both regarding the total amount of algebraic content and regarding how well each Big Idea is represented in the textbooks. As textbooks are important artefacts in Swedish mathematics classrooms, opportunities to learn early algebra in a classroom might depend on which textbook is used. Concerning students’ understanding of the equal sign, the study shows that they, in general, are able to describe the meaning of the equal sign as relational, but they are less able to use the relational structure of an equality. This implies that “the meaning of the equal sign”, which is part of the algebraic content in the Swedish mathematics curriculum in Grades 1-3, might be learnt as a definition by word rather than by its implications in mathematics. Besides the empirical contributions, the thesis also offers a discussion whether the Big Ideas can be found in mathematics at the university level and in research in abstract algebra and it is argued that algebraic thinking is present in all levels of mathematics, from early algebra in lower primary school to research in mathematics.

1. Dissident maps on the seven-dimensional Euclidean space$(function(){PrimeFaces.cw("OverlayPanel","overlay49917",{id:"formSmash:j_idt594:0:j_idt598",widgetVar:"overlay49917",target:"formSmash:j_idt594:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. On the doubling of quadratic algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay99027",{id:"formSmash:j_idt594:1:j_idt598",widgetVar:"overlay99027",target:"formSmash:j_idt594:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Doubled quadratic division algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay117099",{id:"formSmash:j_idt594:2:j_idt598",widgetVar:"overlay117099",target:"formSmash:j_idt594:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Liftings of dissident maps$(function(){PrimeFaces.cw("OverlayPanel","overlay49919",{id:"formSmash:j_idt594:3:j_idt598",widgetVar:"overlay49919",target:"formSmash:j_idt594:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Teoretiska och praktiska perspektiv på generaliserad aritmetik$(function(){PrimeFaces.cw("OverlayPanel","overlay1298484",{id:"formSmash:j_idt594:4:j_idt598",widgetVar:"overlay1298484",target:"formSmash:j_idt594:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Development of algebraic thinking: opportunities offered by the Swedish curriculum and elementary mathematics textbooks$(function(){PrimeFaces.cw("OverlayPanel","overlay1290139",{id:"formSmash:j_idt594:5:j_idt598",widgetVar:"overlay1290139",target:"formSmash:j_idt594:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. Primary School Students’ Knowledge of the Equal Sign – the Swedish Case$(function(){PrimeFaces.cw("OverlayPanel","overlay1501512",{id:"formSmash:j_idt594:6:j_idt598",widgetVar:"overlay1501512",target:"formSmash:j_idt594:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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