This master thesis deals with students' performance in solving equations and their understanding of the equation solving process. Equations are one of the first algebra topics to appear in mathematics lessons. It is the basis for further learning, so we tested students' knowledge at the end of Year 5 of primary school education.
In the theoretical part, firstly, the guidelines for learning and the stages of the child's development are presented. This is followed by the basic concepts related to solving equations that pupils learn in primary school and an overview of ways of solving equations that are suitable for teaching at classroom level. Solving with reasoning, with a diagram and with a table are presented. In addition, two models that attempt to illustrate the abstract process of solving an equation (the balance model and the number axis) are described in more detail and their effectiveness is evaluated. Finally, a review of previous research findings in the area of equation solving and algebraic thinking is presented, showing the difficulties students have in understanding symbolic notation, equality and equation solving on the one hand, and the success of younger students in solving algebraic problems with appropriate guidance on the other hand.
In the empirical part, we tested how primary school students in grade 5 think during the equation solving process. Their performance and reasoning process was tested by means of an interview while solving a knowledge test. Our aim was to find out how students understand the equation and what difficulties they encounter in the process of solving linear equations. The study was based on a cavalier non-experimental method of pedagogical research with a combination of qualitative and quantitative research approaches. The participants were 10 pupils in grade 5 of primary school. The students were given a closed-ended knowledge test, and at the same time, questions were asked through a semi-structured interview to gain insight into the students' understanding of equations and equation-solving procedures at the end of grade 5 of primary education.
We found that students understand conservation of equality and are able to find the unknown quantity, and that the way the unknown quantity is written and the position of the equal sign in the equation affect their success in solving equations. Pupils still think of the equal sign as an operation symbol that points in the direction of the solution, but they understand that in some cases it represents the equality of two units. The results of the study show that pupils are successful in converting mathematical text into algebraic notation, but have difficulties in formulating text according to algebraic notation. We expect that, based on the results of the study, teachers will be able to take a more holistic approach to teaching equations in the future, spending more time in the first period of education to reinforce the concepts and to make the experience of equality notations as varied as possible.
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