This master’s thesis examines the academic performance and strategies for solving ratio problems among 9th-grade elementary school students. Proportional thinking is one of the fundamental mathematical concepts that students begin to develop in elementary school when learning about relationships between quantities. In the 9th grade, students build on this knowledge through the formal study of ratios, where they are introduced to the concept and notation of a ratio, as well as formal strategies for solving ratio problems. Experience with tasks that promote proportional thinking provides an important foundation for later understanding of functions, fractions, and measurement.
The theoretical part presents the key concepts related to proportional thinking, while its development is described through Piaget’s theory of cognitive developmental stages. Particular attention is given to the concepts of ratio and proportion, different types of ratios and types of ratio problems, as well as the strategies students apply when solving such problems. The relationships between ratios and other mathematical topics are also considered, along with the position of proportional thinking within the Slovenian elementary school mathematics curriculum.
The empirical part combines quantitative and qualitative research approaches and includes a pre-test and post-test, a textbook analysis, and an analysis of selected lessons. The aim of the study was to examine students’ performance in solving ratio problems in relation to the type of ratio, the type of ratio problem, and the strategy applied in the solution process before and after the formal instruction on ratios. Furthermore, the study investigated differences between higher- and lower-achieving students in terms of their performance and the strategies they used.
Previous studies indicate that one of the main challenges students encounter in developing proportional thinking is the transition from additive to multiplicative thinking. When solving problems, students often rely on formal procedures in a routine manner without adequately understanding the multiplicative relationships between quantities. Differences in performance are also evident across different types of ratios and ratio problems. Findings indicate higher performance with rates and on missing-value problems, whereas students tend to experience greater difficulty with scalar ratios and numerical comparison problems.
The results confirm that the formal teaching of ratios alone does not necessarily lead to greater academic performance in solving ratio problems. To successfully develop proportional thinking, it is important that, in addition to formal procedures, students encounter different types of ratios and types of ratio problems. The findings contribute to a better understanding of students’ academic performance and strategies for solving ratio problems and provide a basis for the further development of teaching practices in this area.
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