Examining Eighth Grade Kuwaiti Students’ Recognition and Interpretation of Reasonable Answers

Abstract

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.

Statistical Thinking at Early Primary School Levels: Curriculum Perspectives in Uae Textbooks

“…Moreover, textbooks have an evident influence on what and how teachers teach in addition to the choice and content of assessment tools. Alajmi and Reys (2010) noted that when a certain topic is not included in the textbook, it is unlikely to be covered in the classroom. Macintyre and Hamilton (2010) asserted that teachers place a high degree of trust in the content covered in the adopted textbook, which leads to an acceptance that the textbook is the curriculum.…”

Estrategias de sentido numérico en estudiantes del Grado en Matemáticas

“…Se han encontrado escasas habilidades asociadas al sentido numérico en profesores de primaria y secundaria tanto en activo como en formación (Tsao, 2004). Alajmi y Reys (2007) estudiaron cómo profesores de secundaria en Kuwait evaluaban lo razonable de una respuesta numérica. Para estos docentes una respuesta es razonable si se realizan los cálculos correctos y la respuesta no se aleja del resultado exacto.…”

“…A pesar de la importancia del sentido numérico en los currículos, los resultados muestran que los estudiantes tienden a usar procedimientos estándares de cálculo en tareas que podrían resolver estableciendo relaciones basadas en su conocimiento numérico (propiedades, relaciones numéricas, estimación, etc.). Estas conclusiones se han extendido a los futuros docentes, quienes muestran poca tendencia a utilizar procedimientos propios del sentido numérico (Alajmi y Reys, 2007;Contreras, Carrillo, Zakaryan, Muñoz-Catalán y Climent, 2012;Gómez, 1995;Tsao, 2004;Veloo, 2010;Yang, Reys, y Reys, 2009).…”