Developing algebraic reasoning of first graders

In the first years of schooling in mathematics, pupils at first learn arithmetic, followed by a transition to algebra. This does not mean, however, that teachers in the first years of schooling cannot include in the education tasks encouraging development of algebraic reasoning. The inclusion of tasks promoting algebraic reasoning has positive effects on learning and pupils’ better understanding of mathematical content. In the master's thesis we defined reasoning and types of reasoning. We presented arithmetic and algebraic reasoning and examples of algebraic reasoning development in mathematics lessons. We examined the topics and objectives in the curriculum from 1st to 5th grade that enable algebraic reasoning development. We presented examples of converting problems from arithmetic to algebraic. Since problem solving encourages algebraic reasoning development, we also touched on the area of problem-based learning. In algebraic reasoning, the ability to formulate rules and generalizations is important, so we also presented the types of generalizations in mathematics, inductive and deductive reasoning. The purpose of the research was to determine whether first-graders have already developed algebraic reasoning and, if so, to what extent they show it. We were interested in the extent to which we can improve algebraic reasoning in first-graders, with a teaching program with an emphasis on tasks for algebraic reasoning development. We were also interested in whether there are gender differences in checking the initial and final state in algebraic reasoning development. The research showed that the first-graders, before starting the teaching program, with an emphasis on tasks for algebraic reasoning development, did not show it in the majority, i.e. their problem-solving procedures did not contain elements of algebraic reasoning. We found out that the first-graders showed algebraic reasoning at the end of the teaching program. We can summarize, that algebraic reasoning of the first graders can be improved with a teaching program. The results of the research also showed, that there is no difference between the gender in checking the initial and final state in algebraic reasoning development