Decreasing use of counting & increasing use of direct retrieval & derived facts through years 1–4, girls using counting substantially more and the other two strategies substantially less than boys

Sex differences in mental strategies for single-digit addition in the first years of school. Pernille B. Sunde, Peter Sunde & Judy Sayers. Educational Psychology, An International Journal of Experimental Educational Psychology. Volume 40, 2020 - Issue 1, Pages 82-102. https://doi.org/10.1080/01443410.2019.1622652

Abstract: Strategy use in single-digit addition is an indicator of young children’s numeracy comprehension. We investigated Danish primary students’ use of strategies in single-digit addition with interview-based assessment of how they solved 36 specific single-digit addition problems, categorised as either ‘error’, ‘counting’, ‘direct retrieval’ or ‘derived facts’. The proportional use of each strategy was analysed as multi-level functions of school age and sex. In a first study (260 interviews, 147 students) we found decreasing use of counting and increasing use of direct retrieval and derived facts through years 1–4, girls using counting substantially more and the other two strategies substantially less than boys, equal to more than 2 years’ development. Similar results appeared in a subsequent study (155 interviews, 83 students), suggesting that the pattern is pervasive in Danish primary schools. Finally, we ask whether sex differences in strategy use is generally under-reported since many studies do not explicitly address them.

Keywords: Sex differences, single-digit addition, strategies, years 1–4, mathematics

Implications
The marked sex-difference in development of strategy may have implications for research as well as teaching practice. Regarding research of variation and development of strategy use, our results suggest that sex may be a significant component of variation that should not only be tested for (or neutralised by balanced study designs), but incorporated in the statistical analyses instead of appearing as apparent statistical background noise. Sex differences in strategy use (or any other behaviour or skill) may also be of interest in its own right in order to identify differences between boys and girls in a given age or cultural context. For teaching practice, knowledge of the existence of substantial variation in different students’ development of strategy use, much of which connecting to the individual’s sex may also be of importance. For instance, students who overly rely on counting in single-digit problem solving (of which girls are overrepresented) may need explicit teaching and encouragement to memorise number facts and patterns in number bonds. Thus, if instruction in the early years of school focus on counting strategies and procedural knowledge in the teaching of arithmetic this would disadvantage the girls as they are more prone to construct narrow knowledge and rely on the taught algorithms (Hornburg et al., 2017). Furthermore, Laski et al. (2013) points out that girls’ persistent counting provide them with fewer opportunities to practice derived fact strategies and retrieval and that might lead to girls’ poorer accuracy in these strategies. Considering the findings of this study, it would be relevant to investigate the effects of different aspects of instructional practices on sex specific development of strategies in arithmetic in the early years. For example, boys are known to be more willing to take risks in a competitive environment and it could be that teaching promoting a competitive learning environment may be more beneficial for boys, whereas girls might experience a reinforcement of the feedback loop (Bailey et al., 2012).

Conclusion and perspectives
We have shown the existence of considerable specific sex differences in one of the foundational aspects of teaching number in the early years arithmetic, in the very first years of formal Danish schooling. Considering the lack of research on the learning and development of number and arithmetic in the early years of school in Denmark, as well as early sex differences, we find that it is important that these findings are reported. The reasons behind these sex differences, equalling 2–3 year’s, remain to be explicated. No matter the reasons behind these sex differences, their sheer magnitude in this as well as in at least one previous study (Bailey et al., 2012) may suggest that sex differences and their underlying causes deserves more attention than appear to be standard in most studies of arithmetic in early years of school. Although a systematic review of the extent to which the presence and magnitude of sex differences in arithmetic research is beyond the scope of this paper, it seems that sex differences are sometimes not quantified in research papers, which means that sex differences in arithmetic patterns possibly could be underreported. The occurrence of differences in arithmetic patterns between boys and girls may be considered politically sensitive and vulnerable to partisan misinterpretations, but this does not change the fact that they sometimes exist and should be investigated, quantified and explained as any other predictor variable in education research. Knowledge on how individual differences and sociocultural factors interact to produce the resulting sex differences might thus prove useful to inform targeted teaching and educational practice that ‘decrease’ rather than unintentionally enhance sex differences no matter what have caused them.