The Relation of Teaching Quality to the Task Difficulty in Word Problems

Abstract

An important part of any math curriculum is solving word problems. Such problems are particularly difficult for many students. It has been shown that the difficulty of word problems arises from the characteristics of the problems themselves (e.g., arithmetic and linguistic characteristics) and the solver. However, very little is known about how the environmental factor teaching quality (i.e., cognitive activation, supportive climate and classroom management) influences successful solution of word problems. Therefore, in a sample of 387 5th and 6th grade students we measured ability to solve word problems in such a way that we independently manipulated the linguistic (lexical consistency and nominalization) and arithmetic (operation and carry/borrow) complexity. Individual characteristics (intelligence, motivation, mathematical and reading skill, socio-economic status) was also measured. The results showed that both individual capability and environmental factors influenced word problem performance. Intelligence, reading and mathematical skills positively influenced the overall accuracy. In the face of nominalization, the teaching quality scales “cognitive activation” and “supportive climate” were associated with higher solution accuracy of problems with greater reading difficulty. These results provide evidence for the importance of environmental factors, and not only individual factors, on performance on linguistically demanding word problems.

Different complex word problems require different combinations of cognitive skills

“…However, all of the visual representations in these tasks were necessary or helpful for their solution. Previous research indicates that, in contrast, merely decorative illustrations do not affect performance in complex word problems (Lindner, 2020). Similarly, van Lieshout and Xenidou-Dervou (2018) showed that more demanding visual representations in prototype word problems affect solution rates than less demanding illustrations.…”

“…Accordingly, Daroczy et al (2015) call for studies that differentiate at both the task level and the individual level to understand why particular students have difficulties with particular word problems. To our knowledge, the few studies that considered both the individual level and the task level usually focused on one or two specific aspects like verbal skills (Mullis et al, 2013;Pongsakdi et al, 2020;Vilenius-Tuohimaa et al, 2008), student background (Walkington et al, 2017), or environmental factors (Daroczy et al, 2020).…”

“…Considering the student perspective, several individual factors influencing the solution of word problems have been investigated apart from arithmetic skills (Daroczy et al, 2020;Verschaffel et al, 2020), including linguistic skills (Boonen et al, 2013;Boonen et al, 2016;Daroczy et al, 2015;Fuchs et al, 2006Fuchs et al, , 2018Pongsakdi et al, 2020;Swanson et al, 1993;Vilenius-Tuohimaa et al, 2008), spatial skills (Casey et al, 1997;Geary et al, 2000;Hegarty & Kozhevnikov, 1999;Resnick et al, 2020) and reasoning skills (Fuchs et al, 2015(Fuchs et al, , 2020Spencer et al, 2020;Vilenius-Tuohimaa et al, 2008). At the same time, Daroczy et al (2015) point out that few studies compared these factors in a comprehensive design that could reveal unique effects and interactions, and that these studies rarely considered task characteristics at the same time.…”