Students have little opportunity to work with mathematical problems

NEWS
Students at upper secondary school are offered limited opportunities to work with problem solving. In order to deepen the understanding of problem solving, Jonas Jäder has studied some of the components that are valuable for students' problem solving. He defends his dissertation on January 10 at Umeå University.

Text: Ingrid Söderbergh

Students studying mathematics.

ImageAnna-Lena Lindskog

A large part of the tutoring (or teaching) in mathematics, not least in Sweden, is used for students to work on mathematical tasks. For example, these assignments are taken from a textbook, and have a major impact on the opportunities for students’ learning. Previous research has shown that routine-type tasks, which can be solved by using a familiar method, are not enough to support students in their learning of mathematics. The students then risk focusing too much on rote learning.

In contrast to routine tasks, mathematical problems require a student to construct all or part of the solution method.

In his dissertation, Jonas Jäder shows that the proportion of mathematical problems among tasks in textbooks is low. Among the tasks that begin each new chapter, and which are often regarded as the simplest, the proportion is as low as four percent. These results are relatively similar in textbooks from twelve different countries, on five continents and with widespread results in international knowledge surveys.

The results indicate that the design of the textbook is not the decisive factor for student achievement, but that there is a development potential in the design of textbooks with regard to the proportion of mathematical problems. Furthermore, since it has been found that students in the Swedish upper secondary school to a large extent work with the initial tasks, there is also a potential to develop the selection of tasks to increase the proportion of mathematical problems in teaching. In addition to learning opportunities, this could also affect students' beliefs about mathematics. One view of mathematics that students have is that it consists of tasks that can be solved in the most secure way for the student, namely by using an already familiar method.

With a goal to deepening the understanding of the challenges that mathematical problems offer and that create different learning opportunities, Jonas Jäder has developed an analytical framework. By using the framework, it is possible to studythe problem-solving process; both the constructionof new methods and the understanding of the mathematical concepts involved as valuable.

“A more nuanced picture of what it means to work with mathematical problem solving can be a support in the design, selection and use of mathematical tasks in teaching”, says Jonas Jäder.

Jonas Jäder lives in Hudiksvall, and has worked as a teacher for 18 years, primarily in upper secondary school but also in primary school. For the past 4-5 years he has worked with teacher training at Dalarna University.

On Friday 10 January, Jonas Jäder at the Department of Department of Science and Mathematics at Umeå University, defends his thesis entitled: A task to teach – On mathematical tasks as a resource for learning. Swedish title: Med uppgift att lära – Om matematikuppgifter som en resurs för lärande. The dissertation takes place at 13:00 in room N360, Naturvetarhuset at Umeå University. Faculty opponent is Frode Rönning, Professor at the Department of mathematics, Norwegian University of Science and Technology