| There are some cases where one is teaching something that does not
require the student to have special prior knowledge (besides vocabulary),
and that prior knowledge does not really help. For example, teaching
a passage for memorization and recitation, such as a nursery rhyme to a
small child. One might need to explain it or answer questions, such
as what a "tuffet" is or what "curds and whey" are but one can basically
just recite the nursery rhyme a few times to a child and the child will
learn it in no time.
But many, perhaps even most things, one teaches, are more easily learned if the student has some sort of previous understanding that helps make sense of the new material. This can be something relatively simple. When I was in first grade, my father would have me read to him out of The Weekly Reader we received on Fridays. One night, I got to the word "doughnut" and could not recognize or pronounce it. He had me sound it out by asking what "D-O" spelled. I said "do" (as in due). Then he asked about "nut", and I said that word (as in walnut or peanut). He told me to put the two words together. "Do nut." "What does that sound like?" I said "Do not." But that didn't fit the context. Then he said "No, it is like a bagel." "What is like a bagel?" Then I was totally confused because I had never heard the word "doughnut", nor had I ever seen or eaten one before. My father found it hard to believe; but I never had had doughnuts at home or anywhere else I had been where someone handed me one and said "Here's a doughnut." or "Here, have a doughnut." or "Those doughnuts in the bakery case look delicious." But generally it is more involved. Much of arithmetic, for example, is somewhat cumulative, and it is easier to learn certain concepts or ways to calculate answers if you already have understanding of some previous concepts or calculations. Converting decimals to fractions, for example, requires that students can read decimals and state them in fraction form, such as .03 as being 3 one hundredths, which then makes it easy to write it as 3/100. To then get the simplest fraction something like ".5" represents, students need to be able to turn 5/10 into one half in some way, say by dividing both numerator and denominator by the same number -- in this case, 5. If they cannot do that, or do not understand why multiplying or dividing numerators and denominators by the same number results in no change of the value of the fraction, you have to explain and demonstrate that in some way. Or they have to see that 5/10 can mean "5 out of 10" and perhaps see that as half, because they have worked with quantities of five and ten, as in changing a $10 bill for two $5 bills. This is all about the teachers' understanding the logic, or a logical learning/teaching progression, of the material and the concepts involved. Included in understanding what I call the "logic" of teaching the material, is knowing the order of what one would likely have to learn (or what would be helpful, even if not necessary, to know) in order to learn the next step. For example, typically to teach students to divide, you would teach them to multiply first because it is very difficult to divide in your head without knowing multiplication "tables" or what I guess today they call "multiplication facts". But you do not need to teach multiplication tables to show how division works -- you can do that by having kids divide things among themselves, or ask kids how they would divide, say, a bunch of M&M's among themselves evenly. (Typically they would let everyone take, or be given, one, and then everyone gets another, etc. until they are all gone -- like dealing out a deck of cards.) Then at some point you can show them there is another way to do it, by knowing how to do "division" in their heads or on paper. You then will have primed them to want to learn about multiplication so they can do division without having to divide up thousands or millions of things one or two at a time. Too often, teaching is not conceptually understood in the above way,
and that often causes teachers to be ineffective with students, even though
they are doing what they are trained to do or what research supposedly
shows to be "best practice." One has to keep in mind the point of
teaching, and therefore of any teaching practice or method, I think, in
order to do it well, because generally just giving students more information
that really does not mean anything to them (information they cannot absorb
or assimilate) does not help them learn what you want them to know.
The point is to lead or take students from the knowledge and skills they
have to the greater or higher levels of knowledge and skill that you want
them to have -- and to do it in a way that......
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