English learners and word problem solving: can changing the representation help?

In this thesis, I investigate various aspects of how English Learners (ELs) perform in mathematical word problems. How do they perform on these word problems compared to their non-English Learner peers? How does this disadvantage affect their response accuracy? To what extent are these word problems prevalent in high- stakes exams? Will integrating more pictorial representations in word problems improve these learners' response accuracy, confidence or cognitive load? Finally, I explored how teachers perceive integrating pictorial representations in word problems to make these problems easier to solve.

In the first study, employing meta-analytic approaches on previous studies researched the English Learners' mathematical word problems achievement revealed that English Learners' response accuracy is worse than non-English Learners when both solve word problems presented in English (d = 0.36). In the second study, I surveyed the prevalence and features of word problems in The General Certificate of Secondary Education (GCSE) maths exams, finding that nearly half of the questions in the Edexcel awarding body's first exam paper were word problems.

Building on these findings, I explored whether changing the representation of word problems by integrating pictorial representations could enhance response accuracy, and confidence or reduce perceived cognitive load. Two distinct populations were tested using two different instruments.

First, Year 10 GCSE students were assessed using ten word-only problems from past GCSE maths exams, alongside alternative word problems with integrated pictures. There was no evidence that changing the problem representation impacted response accuracy, response confidence, or perceived cognitive load. Nevertheless, the language status affected the participants' response accuracy and response confidence that non-English Learners outperformed their English Learner peers.

Second, adults speaking English as an Additional Language and English as a First Language were presented with 12 maths problems in two formats: word-only problems and word problems with integrated pictures. No evidence has emerged that changing the problem representation impacted response accuracy. There was only a

limited effect of the language status on perceived cognitive load. However, changing the representation affected response confidence as all participants showed greater confidence in answering word problems with integrated pictures.

In the final study, I explored the teachers' expectations regarding changing the representation of word problems on English Learners' response accuracy. Comparing these expectations with the actual participants' performance showed a disconnect. While teachers expected that word problems with integrated pictures would be easier to solve for English Learners, the studies conducted on GCSE and adult participants provided limited empirical evidence to support this notion.

English learners often struggle in word problem solving due to the language barrier, but accommodations such as integrating pictures into these word problems may not be the most appropriate approach to improve these learners' achievement.