We all talk about making schools better.  The problem is that most of that talk does not seem to be translating into results.  So, let me start out saying that I am not an expert in education.  And, my knowledge of education is primarily based upon my own schooling (which went on and on and on…), my teaching, and my involvement with my children’s schools (both public and private, at all levels).  But, as a sentient being, I understand the differences that teachers can make and there are different ways to teach- and they have profound differences.

So, I will recount one experience – at the graduate school level- that has stuck with me for 4 decades now.  Because it dealt with a simple concept and shattered our expectations.  It made me- and I’m guessing my 11 other fellow students in that class- better able to understand patterns, analyze results, and understand that truisms must be subject to scrutiny.  Perfect knowledge for us about to begin careers in research and design.

My professor put this picture on the board.  He asked us to explain the behavior.

One person gave this answer.

Another gave that answer.

My professor stopped us- short.  And, said that given this information, we know nothing.  Two points don’t tell us anything.  And, you know, we “knew” that.

The equation that describes a straight line is y = mx + b.  It’s clear you need three points- minimum.  But, if you are studying new phenomena, three points really tell you nothing.  Because there can be noise (random errors) in the data, because the monitoring equipment can have a flaw, because the people in the test may not be valid subjects, etc.

But, there are more profound points to be learned.  Drs. Philip Kellman of UCLA and Christine Massey of the University of Pennsylvania have been studying learning and advising schools and teachers for more than a decade.   Last year, they authored a paper, Integrating Conceptual Foundations in Mathematics through the Application of Principles of Perceptual Learning, which explains some of their research. (Another, earlier, paper is found here.)  They believe that our brain’s capability to recognize patterns should be employed to teach complex skills.  And, have achieved quantified improvement in teaching students with these concepts.  (I think, long before this concept became accepted knowledge, that my schooling involved such learning, as well.)

One school using this technique is the New Roads School in Santa Monica.  You know, that rich city overlooking the water outside of LA.  But don’t be fooled by its locale.  No, this school interviews its potential students, choosing from those applicants in a 100 mile radius or so, using foundation money to be able to let all children get schooling here.  The minority majority school population employs these principles as part of its educational approach.

Which brings us back to the equation for a straight line.  Instead of drawing graphs, providing the equation, and explaining that m is the slope of the line and b is the point where the line crosses the y axis (i.e., where the value of x is zero), they do something different.  Kind of like what my MIT professor did.  Teachers put up graphs and ask the students which verbal or written description provides the same information.  After the discussion, the students truly understand the concepts behind the straight line equation.

You see, the point is NOT to know the equation for the straight line, but to understand the principles behind it.  Once those patterns are identified, we implicitly recall the equation- and can use it for so many different applications.  Admittedly, this process has the students often guessing at the proper results.  And, as they progress, they begin mastering the concept, soon arriving at the proper results every time- in record time.  Kind of like the way children today learn and master video games.  Comprehension is garnered without memorization.  And, if I am any example, one memorizes the facts- in spite of the learning method.

Many folks resist this teaching concept, putting forth the argument that pattern recognition gets in the way of higher conceptual learning.  But, that’s wrong.   Any place where structures, rules, patterns must be learned can gain benefit from this approach.  Not only math, but chemistry, music, and grammar (among others), are all viable targets for this teaching method.

I can recall an argument I had with one of my undergraduate professors (admittedly one of many, many arguments with this individual).  He was berating me for diving into solving the assigned problems immediately.  Without spending time determining what were the salient features of the problem.  Instead, I would rush right in and use what I considered to be logical approaches to solve the problem.  He was angry because I often had to restart my analysis from another approach three or four times, before I reached a solution.  I asked him if I turned in the wrong answer.  He said that was not the point- I had wasted time with the wrong approaches before I solved the problem.  I countered that I turned in my answer in a shorter period than any other person in the class- and I knew when the answer was right and wrong.  So, why was my method wrong?  To say we agreed to disagree was and is a vast understatement.

We know that discipline, flexibility, and self-control are characteristics that render folks “good learners”.  These are all buzz-words that demonstrate that learners rely on the brain’s executive functions- attention and working memory of our cognitive systems- that provide organized and focused thought.  It’s time to recognize the advances in our knowledge of the brain, its interactions, and our learning can lead to profound improvements in the education of our children.