PROPORTION IN SWEDISH UPPER
SECONDARY SCHOOL TEXTBOOK TASKS
Anna Lundberg
Kirsti Hemmi
Linköping University, Department of Mathematics
Proportional reasoning, understanding of ratio, proportion and
proportionality are prerequisites for success in higher studies in
mathematics and science but also for many practical applications.
Research shows that these topics are difficult even for many adults (e.g.
Keranto, 2004). We have noticed that Swedish upper secondary school
students still have problems, for example when they change units of
velocity. They very often use the trial and error strategy. Most of the
studies conducted in the field shed light on the teaching and learning of
these notions in primary and lower secondary grades but we have very
little knowledge about what happens during the upper secondary school
(Lamon, 2007). The purpose of this paper is to investigate what
possibilities Swedish upper secondary school textbook tasks offer
students to develop their understanding of proportion and
proportionality during the first course in mathematics and how the
qualities in the tasks match with the proportion tasks in the national
examinations. The first course is interesting to investigate as it is the
base for all the further studies for both the theoretical and the practical
programs. Textbooks are important artefacts in the teaching of
mathematics. Research also shows that mathematics textbooks have a
dominating role in the teaching of mathematics in Sweden as teachers
usually choose examples and tasks from the textbook (e.g. Johansson,
2006). That is why it is important to study what kind of exercises and
possibilities to insights about proportion and proportionality the
textbooks offer to the students. In order to analyse the tasks we will
develop a classification tool by using the relevant theories from earlier
research on proportion and proportionality as well as ideas from various
textbook studies. For example, there are three central types of
proportion problems identified in many research papers (e.g. Cramer &
Post, 1993): numerical comparison, missing value and qualitative
prediction & comparison. We are going to test these kinds of
classifications when analysing the data but we will also look at other
qualities in the tasks like cognitive demand, structure and context. Our
study does not attend to investigate the general quality of mathematics
textbooks but is limited to the way that proportion and proportionality
are treated in the textbook tasks. By comparing the textbook tasks with
the national examination tasks we will investigate if the textbook tasks
have the potential of developing the qualities in students’ reasoning
demanded in the national examinations. This study is an introduction to
a wider study on this topic that includes an analysis of the Swedish
students’ solutions of the national examination tasks involving
proportional reasoning and proportionality.
References
Cramer, K. A., & Post, T. R. (1993). Connecting research to teaching:
Proportional reasoning. Mathematics Teacher, 86(5), 404-407.
Johansson, M. (2006). Teaching mathematics with textbooks : A classroom and
curricular perspective. Doctoral thesis. Luleå: Luleå University of
Technology.
Keranto, T. (2004). On the Mathematical and Pedagogical Content Knowledge
of Prospective Teachers: the Case of the Division of Fractions and
Proportional Reasoning. In A.Laine, J. Lavonen, & V. Meisalo (Eds.),
Proc. 21st Annual symposium of the Finnish Association of Mathematics
and Science Education Research. (pp. 178-200). University of Helsinki.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a
theoretical framework for research. In F. K. Lester (Eds.), Second
handbook of research on mathematics teaching and learning. (Vol. 1, pp.
629-667). Charlotte, NC: Information Age Publishing.
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