Abstract:

Lithuanian mathematical education programs for primary school indicate that students should be able to apply knowledge of the bonds of numbers when solving problems in the area of mathematical activity of numbers and calculations, when the condition of the task asks to choose a rational method of calculation. In the specific case, students have to understand the distributive law of multiplication (a + b) x c = a x c + b x c and use it in calculations, but there is no requirement to name that law.

This article presents a study conducted in a 4th grade primary school. Forty-six students of two 4th grades participated in the study. The aim of the study was to determine whether students were able to rely on knowledge of the bonds of numbers when solving the problem of applying the distributive law of multiplication. The students were presented with two numerical expressions representing the distributive law of multiplication, where the members of the compounding action in parentheses and their products with the same number differed, but the final results were the same. An explanation was requested as to why the final sum of the different products was the same.

The results of the study showed that when comparing two phenomena, representing the distributive law of multiplication, the majority of the student group did not notice that the sums of the numbers in the parentheses were the same, which led to the same final results. These students - they made up three quarters of the interviewees - have at best only reached the beginning level of mathematical reasoning. A small part of the survey sample uses the knowledge of the number bonds and is able to answer the formulated question of the researchers, but lacks the ability to create detailed explanations. Only less than a quarter of the interviewees have reached the developing and consolidating levels of mathematical reasoning.

Keywords:

Mathematical reasoning, number bonds, algebraic problem, distributive law of multiplication, primary school.