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Sub-studies 2 and 3 give a clear indication that textbooks do not facilitate for teachers and pupils to follow the national curriculum when they try to associate meanings with letters representing variables through generalisations from number theory.

**Tom Rune Kongelf **

PhD Candidate and Assistant Professor

**Tom Rune Kongelf **at the Faculty of Engineering and Science has submitted his thesis entitled *"Mathematical content and mathematical methods in textbooks used in the lower secondary school in Norway. Goldmines or pitfalls for developing mathematical competence in problem solving and algebra?"* (*«Matematisk innhold og matematiske metoder i lærebøker brukt på ungdomstrinnet i Norge. Gullgruve eller fallgruve for utvikling av matematisk kompetanse i problemløsning og algebra?»)* Friday 6 September 2019.

His research is of great current interest since the Norwegian Directorate for Education and Training will publish a new national curriculum in the autumn of 2019 which will be due for teaching for the school year 2020-2021, according to the consultative document from March this year.

In his thesis Kongelv shows that the mathematics textbooks in use today are not optimal aids for helping students understand mathematics, partly because the textbooks don’t meet the curriculum requirements, partly because they are written in a way that complicates learning for pupils who don’t belong to the group of high achievers.

Tom Rune Kongelf has been enrolled in the PhD-programme in Engineering and Science, Specialisation in Mathematics Education. He is the twenty-fourth candidate to graduate with this specialisation.

The PhD-research has been funded by Sogn og Fjordane University College (Høgskulen i Sogn og Fjordane) (now Høgskulen på Vestlandet - Western Norway University of Applied Sciences). Additionally NoGSME (Nordic Graduate School in Mathematicd Education) and Network for Research on Mathematics Textbooks has contributed.

In his thesis Tom Rune Kongelf studies how mathematics textbooks at secondary school level deal with problem solving and algebra.

The study is in the context of national education policy, and findings are discussed in light of curricula and poor performance on international tests like PISA and TIMSS.

The focus on textbooks, problem-solving and algebra is very pertinent considering the renewal of school subjects (LK20) and the introduction of digital learning resources in schools.

Findings from the study have played an important role in the recently released guidance document on digital learning resources from the Norwegian Directorate for Education and Training.

Kongelf addresses people in teacher education, publishing and education policy in particular.

In his first sub-study Kongelf examines nine problem solving techniques in a total of 740 examples from six different textbooks for Year 10. He finds that the textbook examples are full of problem solving techniques, yet the techniques are not emphasised. This indicates that it is up to the mathematics teacher whether Norwegian pupils get the chance to learn these well-known techniques.

Kongelf also finds that solutions to traditional and simple math problems involve problem solving strategies which have often been associated with more difficult problems and which suit the best students.

Kongelf claims that problem solving techniques is something all Norwegian pupils, independent of age and level, must get the opportunity to learn more about in the future than what current textbooks provide.

In his second sub-study Kongelf examines six different textbooks and analyses the text and examples in the introductory chapters to algebra.

He finds that the concept of variables is not clearly explained, and that the introduction is markedly focused on manipulation procedures.

Kongelf concludes that the textbooks do not introduce algebra in accordance with the national curriculum (LK06).

In his third sub-study he examines 2,547 maths problems from the algebra introduction chapters in five textbooks.

Kongelf finds that seen together, the books contain many different types of math problems, but algebraic manipulation is clearly the most dominant activity. The manipulation is mainly evaluating algebraic expressions and inserting values for variables in algebraic expressions.

Sub-studies 2 and 3 give a clear indication that textbooks do not facilitate for teachers and pupils to follow the national curriculum when they try to associate meanings with letters representing variables through generalisations from number theory.

**The Candidate**: **Tom Rune Kongelf **(1974 Sogndal)** **are employed as an Assistant Professor at the Western Norway University of Applied Sciences, Department of Language, Literature, Mathematics and Interpreting,Campus Sogndal.

Academic background: General teacher education, Sogndal (1998), 4. year in Mathematics at Agder University College (Høgskolen i Agder - HiA) (1999), Masters degree (second degree level - hovedfag) in Mathematics Teaching (HiA 2001). Worked on several high-level national projects in mathematics teaching.

The trial lecture and the public defence will take place at Gabriel Scotts Auditorium – B1-001, Campus Kristiansand Friday 6 September 2019.

Head of the Department of Mathematical Sciences **Ingvald Erfjord **will chair the disputation.

*Trial lecture at 10:30 a.m.*

*Public defense at 12:30 p.m.*

**Given topic for trial lecture**: *"New research on pupils learning of algebra and how this will influece new textbooks and their use in the teaching of mathematics"* (*"Nyere forskning på elevers læring av algebra og hvordan dette vil påvirke utformingen av lærebøker og deres bruk i matematikkundervisningen")*

**Thesis Title**: *"Mathematical content and mathematical methods in textbooks used in the lower secondary school in Norway. Goldmines or pitfalls for developing mathematical competence in problem solving and algebra?" (*"*Matematisk innhold og matematiske metoder i lærebøker brukt på ungdomstrinnet i Norge. Gullgruve eller fallgruve for utvikling av matematisk kompetanse i problemløsning og algebra")*

Search for the thesis in AURA - Agder University Research Archive, a digital archive of scientific papers, theses and dissertations from the academic staff and students at the University of Agder. The thesis will also be available at the University Library, and some copies will also be available for loan at the auditorium where the disputation takes place.

First opponent: Professor Raymond Bjuland, University of Stavanger, Norway

Annenopponent: Professor Andreas Ryve, Mälardalen University, Sweden

Associate Professor Unni Wathne, University of Agder, is appointed as the administrator for the assessment commitee.

**Supervisor were** Professor Emerita Barbro Grevholm, University of Agder