I have been reading the recent discussions concerning "algebra vs geometry" with great interest. However, contained within these discussions, I have sensed some other conflicts: - high school math education vs college math education - isolated math courses vs an integrated math curriculum - subject-based curriculum vs an integrated school curriculum Each of these controversies is an issue in itself, but using them as an overview of the concerns of ÃÂ³isolation vs integrationÃÂ² in education, we can attempt to focus on the primary issue of algebra vs geometry.
By looking at algebra and geometry as separate fields of study, do we create the same situation as considering math and science as distinct disciplines? The division that we imply within these two intertwined areas of mathematics tends to reinforce the artificial barrier that has existed between algebra and geometry for many years. A typical high school mathematics student studies Algebra I, Geometry, and then Algebra II. They realize that some topics are "algebra-focused" while others are "geometry-focused". This "shifting" encourages them to identify with one subject vs the other and to formulate opinions such as ÃÂ³I like geometry better than algebraÃÂ² or ÃÂ³I like algebra better than geometryÃÂ². What does this type of isolation do for the study of mathematics?
Rather than wresting with questions such as: - How many years of geometry should we teach? - Should geometry be a full year course? - etc. should we be looking at issues such as: - Is this isolation beneficial or harmful, both mathematically and attitudinal - Should a high school student ÃÂ³put asideÃÂ² their algebra skills in order to study geometry? - Is this isolation being caused by the names of the courses themselves (geometry, algebra)? - Should algebra and geometry be ÃÂ³blendedÃÂ² into more of a continuum of study?
As a high school teacher, I listen to students compare algebra to geometry. Many like one better than the other. Although we may not see this distinction in the subjects, if they do, then itÃÂ¹s real!
Do you feel that there is a need for: - an integration of algebra and geometry into a single continuum? - maintaining the study of algebra and geometry as separate courses?