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Thursday, July 5, 2018

Traditional Math Teaching vs. Effective Math Teaching

I hate to be so blunt, but the title explains it all and how I feel about traditional math teaching.  What's the difference?  To me, the key difference would be in the foundation of each philosophy.  It is there that we part ways.

Traditional teaching, in a nutshell, believes that all knowledge can be ordered sequentially and split up into topics.  Then, in order to get that knowledge from teacher to student, the teacher simply tells the student what the concept or skill is and demands exorbitant amounts of practice.  Proceed to the next concept.  Supposedly at the end of this exercise, the student is now competent.  One problem is that the student is simply doing mindless tasks over and over again.

It's not that telling students things cannot produce understanding.  It can.  But in order for that to happen, the student has to have fired neural circuits that relate to that information before it is given to them.  Even then, I believe that they need as reasonable effort as possible before they are given conceptual information.  I'm not talking about conventional knowledge.  Yes, just tell them that.  How would they ever figure that out.  What I am talking about is conceptual breakthroughs that took mathematicians decades, centuries, or millennia to discover.  So proceed with what is reasonable.

Effective math teaching requires students to do the work of discovery and conceptual construction.  The learning environment will be carefully constructed so that students feel that they did all of the work.  When students feel like they did all of the work of discovery, mindsets change.  Confidence grows.  Little do they know the teacher spent ridiculous amounts of time designing the learning setting for that occur.

Those familiar and comfortable with traditional teaching will ironically say that the teacher isn't teaching.  It takes time for students, parents, and administrators to shift their paradigm to see that the status quo is all for show.  When students begin to excel with effective math teaching methods, they will resent stepping foot into another traditional classroom.

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