How are arithmetic skills in the four operations related for boys and girls

Which solving strategy is better for arithmetic tasks, the school-taught algorithmic approach or the number-based strategies, is an ongoing discussion especially in relation to students with learning difficulties in mathematics. In a Danish context, focus in the curriculum has been on teaching number-based strategies since 2001. A prerequisite for using number-based strategies is an adequately developed number sense. Thus, Linsen et al. (2015) found that although numerical magnitude processing skills was linked to both mental and algorithmic computation methods the relationship was stronger for mental computation. Studies of students’ solving strategy have shown that school-taught algorithms were often their first choice (Reys & Chang, 1998) even if test items were designed to evoke number-based strategies (Torbeyns & Verschaffel, 2016). The aim of this study was to investigate Danish low-achieving students’ arithmetic ability. The specific research questions were (1) whether the proportion of correct answers differed between boys and girls in general, (2) the extent to which the ability to solve a more advanced arithmetic problem correctly (e.g. division) differed with the ability to solve a less advanced problem (e.g. subtraction), and (3) finally, whether this link between ability to solve problems correctly between arithmetic operations interacted with gender. Data consist of 531 Danish eight grade students’ (boys 306) correct and wrong answers to arithmetic problems in a computerized diagnostic test. The students participated in an intervention for low achieving or less motivated students to prepare them for further education. The test was administered before the intervention. For this analysis, we have selected one whole-number problem from each arithmetic operation (87+15; 806-456; 83*15; 4032:8) based on the criteria: fewest correct answers, most not answered and most wrong answers, in that order. All problems involve carrying and are more complicated to solve algorithmically than by the use of number-based strategies. In all problem types except addition, boys had more correct answers than girls. The probability of solving an advanced problem correctly was significantly depending on the ability to solve less advanced problems, but did not interact with gender. Hence, while the division problem was solved correctly by 47% (95% CI: 41-54%) of the students who had solved the multiplication problem correctly, only 18% (14-22%) of the students who had failed solving the multiplication problem correctly were able to solve the division problem. Likewise, the division problem was solved correctly by 35% (31-41%) of the students who had solved the subtraction problem correctly and only 21% (15-28%) of the students who had failed solving the subtraction problem correctly was able to solve the division problem. The results supports the notion that difficulties in basic arithmetic operations are linked to the ability to manage more advanced arithmetic operations.