NEW APPROACH TO MATHEMATICS TEACHING BASED ON THE CULTURAL ONTOLOGY

Curricular tradition often distills teaching to convey only the "correct" knowledge for a specific domain at a particular level, time, and place, as seen in commonly used textbooks.The development of knowledge, if mentioned at all, typically outlines steps leading to specific knowledge while avoiding debate with alternatives.For instance, in teaching geometry, figures like Euclid, Pythagoras, and Thales are highlighted, whereas Lobachevsky, Bolyai, and Riemann are often omitted, despite their significant contributions.By excluding these figures, we deprive students of a deeper understanding of the discipline they are learning.A linear, distilled curriculum presents correct knowledge as an undisputed path to learning.However, this approach is flawed regarding meaningful learning.The disciplinary policy frequently contrasts the tradition of scientific progress (e.g., Matthews, 2015) and contradicts essential learning conditions (e.g., Marton, 2015).In this study, eight third-year undergraduates-future junior high mathematics teachers-were asked to define mathematical contexts shared by mathematics and physics (e.g., derivatives), contexts relevant only to one discipline (e.g., irrationality in mathematics), and content lacking consensus across different mathematical theories (e.g., parallel lines).They then learned about various historical definitions of the concept of angles and how these definitions influence current mathematics curricula and textbooks at all school levels.The DC-Structure (Tseitlin & Galili, 2005) defines the term "ontology" in both philosophical and computational senses (Zhitomirsky-Geffet, 2016) and provides examples of cultural ontologies in Euclidean and Non-Euclidean Geometries (CCK -Content Knowledge).Undergraduates were asked to add the basic concepts, axioms, and results of Non-Euclidean Geometry to the existing structure, distinguishing it from Euclidean Geometry.After this learning experience, they redefined the mathematical contexts they initially defined.The results demonstrated varied complexity.Some students found it challenging to recognize differences within the mathematical content, while others acknowledged the importance of such recognition for future mathematics teachers.They appreciated the experience for fostering meaningful learning of disciplinary knowledge and its impact on teaching practices.Some undergraduates reported that the experience helped them recognize connections between their courses and shifted their views and perceptions of the knowledge they acquired.The research was conducted based on constructive-qualitative methodology (Shkedi, 2011).