Interrelationship Between the Sciences of Algebra and Geometry
Keywords:
algebra, geometry, analytic geometry, mathematical integration, mathematics education, conceptual analysis, curriculum designAbstract
Historical and theoretical developments have brought the entities of algebra and geometry which originated separate branches of mathematics, closer than ever before. Interconnectedness of the two is, however, well noted yet the deep impact the two have on each other is lightly studied in the field of teaching pedagogy and curriculum design. To bridge that gap, this study utilizes qualitative, conceptual analysis of historical texts, mathematical models and contemporary educational frameworks examining that synergy of algebraic equations and geometric representations. They illustrate the key role analytic and algebraic geometry plays in connecting spatial intuition with the power of symbolic reasoning to solve problems in disciplines including engineering, computer graphics, physics and others. The implications of a unified approach to teaching algebra and geometry are to promote the union of the more analytic way of thinking and the visual way of thinking about geometry. Inferences lead to an argument for further research about algebra–geometry synthesis and the cognitive effects of such synthesis on learning environments.
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