Do mathematics textbooks contribute to the poor performance of Norwegian pupils

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.

Summary of the thesis by Tom Rune Kongelf:

Do mathematics textbooks contribute to the poor performance of Norwegian pupils?

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

New curriculum (LK20) and digital learning

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.

The techniques suit the best pupils

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.

Algebra textbooks don’t follow the national curriculum

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).

The textbooks don’t facilitate

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.