The degree of abstraction in solving addition and subtraction problems

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction.