Many Paths to an Endpoint

When I was in university, I had a professor for a geometry course that all math teachers were required to take.  I found it interesting at the time that he was a professor that students seems to really like or really dislike, in terms of teaching style.  At the time, I chalked it up to his habit of bringing in ideas and skills from related courses, and the lack of good mathematical understanding by some students, which, I thought, should allow them to integrate the different areas of mathematics. 







This professor's teaching philosophy revolved around building intuition.  He gave us projects to give us chances to use the big ideas he presented in class and guided us when we needed help.  When I went into teaching, I brought that idea of 'building mathematical intuition' with me.  I loved teaching grades 8 and 9, where we had time to explore the ideas of integers, fractions, and decimals with pictures and manipulatives.  In my first set of grade 8 classes, I had put into motion a plan to build a strong understanding of these concepts through the use of algebra -- before my classes got ripped away from me so that I could teach grade 12, but that's another story.  I loved teaching calculus, which is also very visual. 

I came across an article differentiating right-brain and left-brain mathematics at "The Right Side of Normal."  It got me thinking.  Ever since I've started observing my children's mathematical development, I've been assuming that the sequences I've seen are pretty representative, though not necessarily at the same speed as the norm. 

"For the right-brained child, the learning pattern is opposite but just as viable. In the early years, the right-brained learner needs to explore global concepts that can be visualized, such as negative/positive numbers, variables, math patterns, equality, and so forth (mathematics) so he can build the understanding necessary to be ready to learn algebra later. At that time, right-brained learners use their foundation with math concepts to begin understanding the reason to learn math facts, such as addition/subtraction, multiplication/division, and so forth (arithmetic)."

That sounds familiar. Are we just a family of right-brained learners?

"Okay, so let’s talk about what the foundational strengths of a right-brained math learner would be: either visual-related or kinesthetic-related."

Wait.  Don't most children enjoy touching and manipulating things?  But from what I recall, most children are not right-brain dominant. 

For many years, my job (as a tutor) was to help students succeed in the current (at the time) school system.  We did a lot of large concept work and also skill-building.  Granted my work was with kids aged 12 and up, so they were already at the integration stage.  The reason many of them had trouble was that they tried to apply methods without sufficient understanding.  Were they right-brained learners who needed the "big ideas" to go on, or were they left-brained learners who now had enough "arithmetic" that their brains were ready for the "big ideas"?  The problem was the same.  There was not enough support for the development of mathematical understanding.  Would a shift in school-wide pedagogy change this, or is it that we still need better mathematically educated and confident elementary school teachers?

Looking back, I realize now that I had very little understanding for learners who were strongly left-brained.   I wonder how it would look for a classroom to simultaneously support both sequences of learning.  I am still convinced that both "arithmetic" and "mathematics" must be supported within a child, even in the early years.  Finally, I am excited and curious to watch as my right-brained learners go through the elementary years.