Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of the books, the structure of the lessons, and the nature of the mathematical problems presented. Findings showed USA and Kuwaiti mathematics textbooks are larger than Japanese textbooks; this larger size is consistent with a great deal of repetition. The Japanese texts do not address fractions until the third grade; they use linear models and connect fractions with measurement. In the USA and Kuwait, fractions are introduced in the first grade. The Harcourt text uses concrete material to help students learn fraction procedures. For the Kuwaiti series, the lessons depend on using some pictorial representation of the area model to illustrate fraction ideas. All these textbooks focus on standard algorithms as the main computational methods.

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This study describes mathematics teachers' views on the significance of reasonable answers and how they address this concept in their classrooms. Data were gathered from thirteen eighth-grade Kuwaiti mathematics teachers in two middle schools. All teachers in Kuwait use the national textbook and follow the accompanying instructional plans provided by the Ministry of Education. The results revealed that the overwhelming majority of Kuwaiti teachers reported that an answer needed to be exact to be reasonable. Only three teachers reported discussing reasonable answers and their discussions were in response to student mistakes. None of the teachers addressed the concept proactively, considering reasonableness when planning their lessons or preparing activities or exercises. They defended their lack of attention to this concept by noting that the notion of reasonableness is not included in the Kuwaiti national curriculum.

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This research documents Kuwaiti eighth grade students' performance in recognizing reasonable answers and the strategies they used to determine reasonableness. The results from over 200 eighth grade students show they were generally unable to recognize reasonable answers. Students' performance was consistently low across all three number domains (whole numbers, fractions, and decimals). There was no significant difference in students' performance on items that focused on the practicality of the answers or on items that focused on the relationships of numbers and the effect of operations, or on both. Interview data revealed that 35% of the students' strategies were derived from two criteria for judging answers for reasonableness: the relationships of numbers and the effect of operations, and the practicality of the answers. They used strategies such as estimation, numerical benchmarks, real-world benchmarks, and applied their understanding of the meaning of operations. However, over 60% of the students' strategies were procedurally driven. That is, they relied on algorithmic techniques such as carrying out paper-and-pencil procedures. Additionally, some of the students' strategies reflected misunderstandings of how and when to apply certain procedures. Given these findings, mathematics education in Kuwait should shift the emphasis from paper-and-pencil procedures and provide systematic attention to the development of number sense and computational estimation so Kuwaiti students will be more adept at recognizing reasonable answers.