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High School Geometry: For Some, Why Is This More Challenging Than Algebra 1?

Several of my current Geometry students have commented on this very distinction.  This has prompted me to offer a few possible reasons.
 
First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal two-column proof variety) that involve stepwise, deductive reasoning.  For many, this is their first exposure to this type of thought process, basically absent in Algebra 1.
 
Second, a large part of Geometry involves 2-d and 3-d visualization abilities and the differences in appearance between shapes even when they are not positioned upright.  Still further, for a number of students, distinguishing the characteristic properties amongst the different shapes becomes a new challenge.
 
Third, in many cases Geometry entails the ability to form conjectures about observed properties of shapes, lines, line segments and angles even before the facts have been clearly established and stated.  This level of abstract thinking is rarely encountered in Algebra 1.
 
Implications based upon the aforementioned are significant.  For those following a Science/Technology/Engineering/Math (STEM) course track and headed into Precalculus, Calculus, General Chemistry and Organic Chemistry, the ability to visualize shapes and chemical structures in 2-d and 3-d space is extremely important.
 
In order to better prepare students for dealing with Geometry's rigors, many educators have believed that certain math instructional practices even going back to the elementary school level will have to be improved within the classroom.  In the meantime, all students can still take steps to increase their current mental capacities and reasoning abilities by following a brain-enhancing diet (such as my "Maximum Mental Health Diet" recommendations offered when requested at any tutoring session).  Among other things, this includes daily consumption of long-chain Omega-3 essential fatty acids through fish or supplements and an abundance of colorful, antioxidant-rich plant foods.

Comments

Thanks for the insight.  I am currently tutoring a student who has similar visualization issues.  
 
It has always seemed that 3D visualization is either something you can do or you can't.  I always could, thankfully.  However, this seems to present a challenge when trying to teach someone else how to do it.  Are there any resources you could point me to?  
 
Again, thank you so very much for your article.
Jennifer, thanks very much for your comment.
 
There must be math kits available for constructing a variety of 2-d and 3-d shapes and similar to the molecular model kits that prove invaluable for helping Organic Chemistry students visualize a variety of structures in space and, therefore, significantly aiding in clarifying many concepts.
 
Dr. Bruce

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