Word Problems, Item Difficulty and Low Performers

Word problems are amongst the most difficult problems students encounter1. We investigated students’ ability to recognize the symbolic problem matching the arithmetic situation of the word problem and whether this was influenced by item difficulty in semantic structure (easy vs. difficult) and students’ mathematics achievement level (teacher ratings: 1-5). A total of 1081 3rd to 6th grade students (86 classes, 31 schools) answered a paper-and-pencil test including 64 multiple-choice items (single-digit and multi-digit numbers: 14 addition, 13 division, 14 multiplication and 23 subtraction) with four answer options (one correct). Example: “Paul eats 6 carrots. Noah eats 2 less than Paul. How many carrots does Noah eat?” Options: 2+6; 2-6; 6-2; 4-2. We modelled the four operations separately with item as observation unit, correct answer (1/0) as a binary response variable and student-ID as random effect. Fixed effects were grade, mathematics achievement (high achievers [HAs] vs. low achievers [LAs], item difficulty and their interaction. For addition problems LAs performed worse on ‘difficult’ items compared to HAs, suggesting that difference in ability between LA and HA to choose correct symbolic problem partly relates to the difficulty of the problem. In other arithmetic operations it relates to the operation itself. Thus, teaching word problems should not only focus on solving the problem but also the understanding that multiple types of situations can be expressed by the same symbolic problem.