Educational theories are hard to articulate, and most parents who home educate do not precisely care. Their goals are more practical. I want Junior to be able to read, write, and do math at a level that will get him into college. PERIOD.
Allow me to dig just two inches deeper, and let’s pick a topic, Math, and talk about concept teaching or example teaching in conjunction with math — a prime topic for example vs. concept teaching.
Most students get through public school education by learning a concept in math, say how to solve a quadratic equation
a x^2 + b x + c =0
the solution is x = (-b +- Sqrt(b^2 – 4 a c))/2a.
Most students learned that in 8th grade (likely you did too), and most students know how to use it in patterned situations with lots of examples of applications for how to use the quadratic equation, but most students have no clue what the solutions mean, what the equation i s really good for (physically in real time and space or mathematically). They have simply learned an equation, and they have followed umpteen examples with a certain pattern, and when they see a problem that looks like one of the examples they went through, they can imitate what they remember from their examples and actually do the problem more or less correctly.
HOWEVER, if the problem they are faced with is somewhat unlike the examples they have gone through in class, they do not have a clue how to solve the problem because conceptually, they have no understanding.
This is public education’s big down fall. When students have to think outside the box, because they were never taught conceptually but only via examples, they cannot extrapolate from their understanding of the bigger picture and figure out how to solve a problem.
Teaching with examples is weak teaching, which produces students who cannot think very deeply. It is the malaise of our primary and secondary education, and it is largely a product, in my opinion, of 1. the fact that our classes are too big and so we do not have time to engage with students individually to really teach to where they need instruction and 2. a product of an educational system that makes use of standardized testing to evaluate performance.
There is no fixing of those problems in a blog, but what I will discuss in the next blog is how to center your teaching (you the coop teacher, home educator, or teacher at a school) around student learning needs…. around where the student conceptually does not understand the problem, rather than teaching by giving students examples which he or she needs to imitate.
Let me close with this for today. We discuss analysis and imitation in Classical Writing as a means of learning to writing well… imitating great writers. CLEARLY we believe in imitation, so why am I ‘knocking’ examples. Isn’t looking at an example and doing what it did, a form of imitation?
Yes, it is. When we study an example we are engaging in principles of imitation, and that is one important learning strategy, but note this — the word imitation in our books is always preceded by ANALYSIS.
We analyze first, we find out ‘conceptually’, what the passage consists of in words, sentences, and paragraphs. We analyze at the word, sentences, and paragraph level for content, organization, and style. We want to know the HOW and the WHY of the author’s choice to write the passage the way he did.
Analysis precedes imitation…. imitation without analysis is not only poor writing, it is rote and pointless writing. Analysis learning is conceptual learning, and it must precede imitation, or the imitation is not worth engaging in.
I will discuss conceptual learning more in the next blog.