Primary school students’ arithmetic knowledge levels activated when solving additive problems: an analysis from mathematical connections

Abstract

This research explored the level of arithmetic knowledge of primary school students in solving additive verbal arithmetic problems based on mathematical connections. Theoretically, the study was based on the classifications of problems according to their semantic structure, levels of arithmetic knowledge and, mathematical connections. The participants were two Colombian primary school students (4th and 5th). For data collection, twenty additive problems were designed and formulated that were applied in the form of a questionnaire, then a semi-structured interview was developed to find out what the experience of each student was like in solving the problems. The results showed the mathematical connections (different representations, part-whole, implication, reversibility, procedural...) established by the students to solve problems and the levels of arithmetic knowledge achieved. In this sense, the students reached level 4 of directional relationships because they solved problems with equalization and comparison structures that are the most complex to solve. Also, they achieved level 3 because they solved combination problems with the unknown in a part of the whole and comparison problems. The students achieved level 2 because they solved change, increase, and decrease problems with the unknown in the modification quantity and they obtained level 1 because they solved change problems with the unknown in the final quantity and combination with the unknown in the whole. However, even though the students reached level 4, one of them had difficulty solving the equalization problems 3 and 4 because he did not establish the procedural connection and the other student did not solve the equalization problem 5 because he did not establish connections of different representations.

Semantic structures; Additive problem; Arithmetic knowledge; Mathematical connections; Primary education