Which One Is the “Best”: a Cross-national Comparative Study of Students’ Strategy Evaluation in Equation Solving

Abstract

This cross-national study examined students' evaluation of strategies for solving linear equations, as well as the extent to which their evaluation criteria were related to their use of strategies and/or aligned with experts' views about which strategy is the best. A total of 792 middle school and high school students from Sweden, Finland, and Spain participated in the study. Students were asked to solve twelve equations, provide multiple solving strategies for each equation, and select the best strategy among those they produced for each equation. Our results indicate that students' evaluation of strategies was not strongly related to their initial preferences for using strategies. Instead, many students' criteria were aligned with the flexibility goals, in that a strategy that takes advantages of task context was more highly valued than a standard algorithm. However, cross-national differences in strategy evaluation indicated that Swedish and Finnish students were more aligned with flexibility goals in terms of their strategy evaluation criteria, while Spanish students tended to consider standard algorithms better than other strategies. We also found that high school students showed more flexibility concerns than middle school students. Different emphases in educational practice and prior knowledge might explain these cross-national differences as well as the findings of developmental changes in students' evaluation criteria.

Investigating algorithm-oriented flexibility and structure-informed flexibility in mathematics learning

“…As for Research Question 3, we hypothesize current high school courses may be correlated with the prevalence of Struct-Flex. Previous findings emphasize the effect of prior algebra knowledge on (structure-informed) flexibility (Schneider et al, 2011; Star & Seifert, 2006) and the growth in (structure-informed) flexibility as students age and gain more knowledge in math (Jiang et al, 2022). Based on this, we would expect levels of Struct-Flex to positively associate with students’ age and high school math course level.…”

“…In addition, Jiang et al (2022) also suggest that students’ prior familiarity with a method could affect their strategy choice. They referred to strategy choice models (e.g., Shrager and Siegler, 1998), which state that individuals adapt their strategy choices via recalling both costs and benefits of using a strategy from their previous experiences.…”

“…These advantages may include that the situationally appropriate strategies may take fewer steps to implement, may be faster to execute, may reduce the likelihood of error, and/or could be considered more elegant mathematically. Prior research has indicated that experts often show preferences for situationally appropriate strategies over standard algorithms (Jiang et al, 2022; Star & Newton, 2009). While standard algorithms are more generally applicable and can often be used without taking actions that may be necessary as a result of particular features of a given problem, situationally appropriate strategies are applicable in a more limited range of problems and leverage the linkage between problem-specific structural features and affordances offered by the strategy about these structural features.…”

“…Struct-Flex students would seem to engage more in anticipatory justification, while Algo-Flex students would engage more in algorithmic justification. Similarly, Star et al (2022) and Jiang et al (2022) discuss the case of Spanish middle and high school students, many of whom exhibit knowledge of both standard and situationally appropriate strategies but choose to use and/or express a preference for standard algorithms. In this prior work, these Spanish students were deemed to be lacking in (structure-informed) flexibility, but here we suggest that they instead may be exhibiting Algo-Flex.…”

A complicated relationship: Examining the relationship between flexible strategy use and accuracy

“…Finally, more qualitative research on students' encoding of flexible-eligible problems and how a student decides which strategy to apply is needed to better understand students' rationale for which strategies they employ. For example, secondary school students in Spain tend to prefer standard algorithms and approaches (Jiang et al, 2022).…”