Assessing and Advancing Non-Euclidean Geometries in Middle School Mathematics Education: A Case for Curriculum Inclusion

Abstract: This study offers a comprehensive investigation of 14-15-year-old students’ comprehension of non-Euclidean geometries, with a specific focus on the assessment of their understanding through a 15-itemed test. The primary objective of this research is to assess the current state of students’ knowledge and proficiency in non-Euclidean geometries and to provide insights into the potential inclusion of these concepts in the mathematics curriculum. Drawing inspiration from previous research, this study adapted questions from ministry exam papers to create a rigorous assessment tool. The data collection process involved administering the 15-itemed test to a sample of middle school students within the target age group. The test aimed to evaluate their grasp of non-Euclidean geometries, a topic that has traditionally received limited attention in the mathematics curriculum. The results of the test reveal a notable gap in students’ understanding of non-Euclidean geometries. A majority of the participants demonstrated limited proficiency in this area, highlighting the need for enhanced educational strategies to address this deficiency. The findings strongly suggest that the incorporation of non-Euclidean geometries into the standard math curriculum is needed. Such inclusion has the potential to broaden students’ mathematical horizons, foster critical thinking skills, and stimulate their curiosity in the realm of non-Euclidean geometries. In conclusion, this research underscores the pressing need to rethink the middle school mathematics curriculum for 14-15-year-old students by incorporating non- Euclidean geometries. By doing so, we can better equip students with a more holistic mathematical education and promote the development of essential analytical skills. This study contributes to the broader discourse on mathematics education and suggests a potential pathway for enhancing mathematical learning outcomes among middle school students.Keywords: analytical dexterity, curriculum inclusion, educational implications, mathematics education, middle school students, non-Euclidean geometries, test assessment