Response to "Why you should learn geometry"

In Walter Whiteley’s article titled “Why you should learn geometry” he refers to an article published by David Eggenschwiler titled “Why you should learn algebra”.  Eggenschwiler’s article argues that high school algebra “teaches the mind how to think”.  He states that “what you learn to think about it not as important as how you learn to think” and that learning algebra lets you think more abstractly and creatively, which then can be applied to other areas such as music and critical writing.  While I would say that Whiteley agrees with Eggenschwiler’s ideas, he also wants to broaden the ideas to include geometry.  Whiteley makes a strong point that if people continue to view algebra as the central mathematical knowledge and geometry and associated visual reasoning as marginal, then we will exclude people with “enormous potential to contribute to science, engineering and mathematics”.

While I agree with the ideas behind both Eggenschwiler and Whiteley, I believe that the learning of mathematics should not be limited to just algebra and/or geometry but should also include things such as the arts and history.  To relate to Whiteley’s ideas – if we do not include many different entry points into the learning of mathematics (algebraically, visually, musically, creatively, historically, etc.), we will end up excluding people who can bring new ideas and insights to the fields of mathematics and mathematics education.

To answer Whiteley’s question about if I feel as if I know enough geometry to bring it in when it is relevant in the math I am teaching, my answer would be yes and no.  Do I always know the correct way to explain things in terms of proofs or terminology? No, I do not.  But do I know how to explain things using shapes or geometrical ideas?  Yes, I would say I do.  An example of when I use geometry or visual representations the most is if I am solving word problems.

My input on the recent trends to reduce or remove geometry from many math programs is that I think that geometry is something that is very important to use in the classroom for the same reasons Whiteley stated in his article.  I think geometry allows students who are visual learners a way to access the concepts they are learning.  However, I think requiring students to know so many different postulates and theorems might be a bit much.  It is like with anything in education – if teachers are required to do x amount of things with geometry, the purpose behind incorporating geometry is often lost.  This is because teachers are told exactly what to do even if it is not the most natural or best approach.  It is similar to an article I read on the use of manipulatives.  The ideas behind using manipulatives are great, but often times teachers feel as if they have to use manipulatives when it may not be the best approach for them in particular, and therefore the intended benefits of using manipulatives are lost.