THE ANALYSIS OF COGNITIVE DEMAND AND MATHEMATICAL COMPETENCIES: A CASE STUDY OF THE PYTHAGOREAN THEOREM

Abstract

無中文摘要

The purpose of this study was to analyze and compare different perspectives of the way the Pythagorean theorem questions appeared in three mathematics textbooks. Tudo é Matemática (Brazilian textbook), Nani (Taiwanese book), and New Syllabus Mathematics (Singaporean textbook) regarding number of exercises and worked examples, cognitive demand and mathematical competencies. This research used content analysis as research methods and exams based on the PISA exam were applied to students from Brazil and Taiwan to check their difference in performance and mathematical reasoning.

The analysis of the number of exercises and worked examples showed that both Taiwanese and Singaporean textbooks have a superior amount of exercises and worked examples compared with the Brazilian one which makes Taiwanese and Singaporean textbooks advantageous over the Brazilian book.

From the perspectives of cognitive demand, results showed that Taiwanese and Singaporean textbooks are more different from each other because Taiwanese textbook opts to focus more on lower-level demand, while Singaporean textbook has a strong focus on higher-level demand questions.

Regarding mathematical competencies results also showed that the Taiwanese textbook is more different than Singaporean textbook. Overall Singaporean textbook is more different from the other two textbooks because many of its questions use level 2 and 3, while the other two textbooks are more used to test students in between levels 0 and 1.

Finally, the exam showed that students from Taiwan have higher performance in a PISA-based exam than Brazilian students. Through a qualitative research, the results also revealed that the cultural aspects of students from each country also influenced the way students answered to the questions.