Analysis of the content complexity of mathematics in the fifth grade of elementary school

Teachers strive to teach well, which requires power, energy, and influence on people, especially on students. Power comes from the school position itself, but the teacher must be able to teach dynamically and be dedicated to the subject matter to reach the goal (Paterson, 2005).They must take into account many didactic elements in the learning process itself, i.e., motivation, various methods that help students to acquire knowledge more efficiently, constantly monitor students’ progress, encourage them to think, check their misconceptions, etc. (Žakelj, 2003). The teacher’s first step in a teaching process is to determine the desired achievements or students’ results as well as a clear definition of knowledge, skills, and processes for students’ development. The basis for teaching are always the learning objectives in the curricula and different taxonomies. Taxonomies direct teachers’ attention to different aspects of knowledge, skills, abilities and processes (Rutar Ilc, 2003). Students encounter various learning contents in all areas on a daily basis. Teachers present to students some completely new topics as well as upgrade their previous knowledge in others. In this master’s thesis, we focus mainly on more demanding mathematical learning content in the 5th grade of primary school. In the theoretical part, we first presented in more detail knowledge, learning, and lessons, theories of learning and teaching (we were mainly interested in behaviorist, cognitive, and constructivist approaches). We studied the role of these and the role of representations in the formation of mathematical concepts, as well as the importance of the teacher’s professional development for quality teaching of mathematics.In the empirical part, with the help of our own online survey questionnaire, we researched the teachers’ opinions on more demanding learning content in mathematics in the 5th grade. We were also interested in their views on different teaching approaches (primarily behaviorist cognitive, and constructivist), which can be used in teaching more complex mathematical content and differ in terms of students’ role and activity in the learning process.The results of the research showed that teachers chose written division with a two-digit number as the most demanding learning content both for teaching and students’ understanding. It is followed by the learning contents parts of the whole, perimeter and area, and the conversion of units of measurement. Teachers who teach for a shorter time (from 1 to 18 years) highlighted as demanding the following learning contents: geometric shapes and solids, volume measurement, written multiplication, exponentiation, equations, and inequalities. On the other hand, teachers who teach for a longer time (from 19 to 40 years) highlighted as demanding the learning contents of the cube and square prism net and the proportionality. Teachers have decided on the mentioned learning topics to be difficult mostly because of the difficulty of the procedure and the complexity of the interpretation. Some teachers also deal with the issue of choosing the most appropriate representation for certain learning content. Based on the results received in our survey, we also noticed a difference between teachers’ opinions about the change in their way of teaching since they have been teaching. Teachers with more experience (19 to 40 years of teaching) believe that their way of teaching has partially or fully changed over the years. While, teachers with less experience (1 to 18 years of teaching) think the exact opposite or are undecided on this issue. With the obtained results, we also found that teachers usually approach the learning content division with a two-digit natural number in a way that is closest to behaviorist approaches. In contrast to the learning content measuring the area, where teachers mostly identify with the constructivist approach. Based on the findings of the research, we can conclude that the choice of teaching approach is to a large extent conditioned with the nature of content itself, and not so much with the teacher's attitude towards learning content.