Abstract
Numerous researches conducted in recent decades have reported on the difficulties experienced by students learning geometry. The main reason for these difficulties is the gap between the level of instruction and the students’ ability to understand and learn. In other words, the students have a low level of geometrical thinking, while the teachers are attempting to instill knowledge that is at a higher level of thinking than the current level of their students. On this background, we present in this article an ethnomathematical approach combined with Van Hiele’s theory of levels of thinking, with the aim of improving the instruction of geometry by making it effective, interesting, and more successful for students. For this purpose, the article will present Van Hiele’s theory and the various levels of thinking, followed by the characteristics of the stages of thinking and stages of instruction. Other perspectives on learning geometry will be presented in the fifth section, followed by an attempt to explain students’ difficulties in geometry through cognitive load theory and students’ attitudes toward this subject, the ethnomathematical approach and its effect on the instruction of geometry will be presented, finally the effect of integrating cultural values on learning mathematics.
Highlights
Formal geometry is perceived as the most complex field of instruction among the various mathematics subjects taught in high school
We present in this article an ethnomathematical approach combined with Van Hiele’s theory of levels of thinking, with the aim of improving the instruction of geometry by making it effective, interesting, and more successful for students
Other perspectives on learning geometry will be presented in the fifth section, followed by an attempt to explain students’ difficulties in geometry through cognitive load theory and students’ attitudes toward this subject, the ethnomathematical approach and its effect on the instruction of geometry will be presented, the effect of integrating cultural values on learning mathematics
Summary
Formal geometry is perceived as the most complex field of instruction among the various mathematics subjects taught in high school. Students define a square according to its appearance as “a quadrangular whose sides are equal to each other and whose angles are right”, rather than knowing the formal definition: “A square is a parallelogram with one right angle and a pair of adjacent, equal sides” a definition that emphasizes the connection between the square and the parallelogram, in particular, and between the square and the family of parallelograms, in general In such studies, researchers found that students have difficulties in identifying and constructing geometrical shapes, regardless of whether they learned formal or informal geometry. The researchers examined how simple geometry concepts are understood among three groups: 8th-grade students, 10th-grade students, and teachers in elementary school They found similar definitions of geometrical shapes among all three groups, leading to the conclusion that certain elements in understanding and misunderstanding concepts and the development of geometrical understanding operate among individuals, regardless if they are students or teachers. We will present the importance of combining Van Hiele’s theory with the ethnomathematical approach in the instruction of geometry, which assists in organizing and constructing an individualized curriculum for each student according to his or her level, making learning easier and more fun, interesting, and successful for the students as evidenced by a research we conducted and that included the development and implementation of an ethnomathematical curriculum among two groups of Bedouin students in Israel
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