Students' spirits brutally crushed by regressive pedagogic techniques
When I tutored fourth-grade kids in a bombed-out section of Houston some decades back, I was surprised to find that they'd been confidently reassured by teachers and family that they need never memorize the multiplication table. Given a problem like 6x7, they would laboriously add 6 and 6, get 12, add 6 again, and so on. They would get there eventually, of course, and it's nice that they understood the connection between addition and multiplication, but we'd reach the end of the hour before they had time to grind through more than a couple of problems. They weren't ever going to advance any further, without some shortcuts that involved memorization. But no one really expected them to progress. The main focus was social promotion, keeping the age groups together. The teachers knew barely more than the kids did, though they all seemed awfully nice and well-meaning. They welcomed the volunteer efforts of my colleagues and me without any visible trace of suspicion or resentment, and generally maintained order among their young students.
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This summer I made a certain boy write out his times tables, in scientific notation, many times. Now that school is back in session, he suddenly is finding mathematics much easier. Because he has memorized the multiples of 9, say, factoring is easier. The more advanced calculations are coming more freely, because mental resources are available for them -- the simpler problems are known issues, which don't require much thought.
"The teachers knew barely more than the kids did, though they all seemed awfully nice and well-meaning."
This was, sadly, my experience with the Education majors at my college. It was sometimes quite frightening that these students were going to be called upon to teach concepts to children when they barely knew how to do things themselves. And I'm talking about very basic and simple things.
And it's not like the PhDs were any better. The Dean of the department had asked her secretary to open an attachment that her own anti-virus software would not let her open, and she suspected (mind you, she wasn't sure) that this was where the virus outbreak in her department's computers came from. /facepalm
I had a history grad class with a dear older lady getting an MA in education (she was a teacher's aid or an administrator. I don't recall what). She could barely read the books we used in class (R.R. Palmer's "12 Who Ruled," for example) and could not write a coherent paragraph. But was doing very well in the Masters of Ed program.
LittleRed1
1) As others have already pointed out, a problem in teaching elementary school math is that many elementary school teachers are not very competent at math. If THEY don't know their multiplication tables, how can they teach their students?
2) The Ed School revulsion at "kill and drill" – learning multiplication tables- is related to many in Ed Schools preferring Whole Language to Phonics to learning reading. Learning reading by the Phonics method involves learning/memorizing basic word/sound combinations, a.k.a. phonemes. What Whole Language advocates forget is that their method , e.g., where a reader deciphers “ltrs” to mean “letters” – also involves memorization, and even MORE memorization than Phonics. After all, phonics involves learning the basic 40+ phonemes, whereas there are THOUSANDS of words to memorize.
Adults conclude that while they as adults do not like memorization drills, that children do not like them either. They also assume that because adults do not need memorization drills- because they already know the material- that children, who have a much smaller knowledge base than adults, do not need memorization drills, either.
It is not difficult to find examples of children LIKING repetition, i.e., memorization. Consider the 4-5 year old child who wants to have the SAME story read every night. The adult goes batty reading the same story, but the child wants it. And when the adult changes the story a bit, out of boredom, the child immediately informs the adult that the adult is NOT reading the story correctly. Because children have a much smaller knowledge base than adults, they need more repetition/reinforcement of what they know.
As a substitute teacher, I have led first graders doing spoken phonics drills. They appeared to enjoy it. They are directed to speak during these drills – all of us like to talk/speak.
Part of the whole language/phonics conundrum is that as adults, we read by the whole language method. If we see words with letters taken out, we can figure out what the word means- which supports whole language. But for beginning readers, memorizing/LEARNING the basic building blocks of sound letter combinations/ phonemes comes before learning whole words.
Organic Chemistry involves learning hundreds of chemical reactions. Some students say memorize. Professors say learn.
3) I once substituted in a 5th grade class of “problem children” whose teacher used memorization: in this case, student recital of poems. An additional benefit was that it improved classroom behavior. Students wanted to be listened to while they were reciting their poems. The quid pro quo was that students needed to listen when other students were reciting their poems.
4)I was exposed to the New Math in 9th grade. I very much liked New Math- in my case Illinois Math- for its emphasis on proofs. Before Illinois Math, while I did well in math, I never enjoyed it. Now I enjoyed it.
Applying what I learned in New/Illinois Math about commutative, associative, and distributive principles of basic arithmetic enabled me to become very good at estimating answers. Since 19X 6l= (20-1)X61, 61X20 is a good estimate of the answer. Etc. This was an example of Discovery Math- which I came up with on my own. But I could have never become a good estimator without the previous old school drilling on the multiplication tables. My having memorized the multiplication tables helped me in making independent discoveries during my Illinois Math/New Math years.
Ed School types who love the Discovery method of learning forget that it is a lot more efficient to tell students: here is how you do it, with the caveat that different students may find a different way. [The irony here is that in many elementary math classes today, students are forced to use the particular method the teacher pushes, and have grades reduced if they use a method different from the teacher. Not exactly Discovery, is it?] Discovery works better with a higher knowledge base. For example: constructing proofs, a method by which students discover basic truths about math, works much better with 9th or 10th graders than with 4th graders. Nor does constructing proofs work with all 9th and 10th graders. It works best with the most capable.
I had a professor in college who had met Max Beberman, the founder of Illinois Math, the New Math program I was exposed to in high school. Max Beberman told my professor that he had never intended that learning multiplication tables be slighted. Unfortunately, that is precisely what occurred. My guess is that New Math, in the hands of teachers who were not competent at math in the first place, a description which applies to many elementary school teachers, became a disaster.
The New Math/Illinois Math was better designed for future scientists and engineers, not future citizens. Max Beberman developed Illinois Math teaching at the University of Illinois lab school, a school populated with faculty brats, a population which is not average.
You raise many good points, but the one that strikes me especially is the one about children liking repetition. Even as a teenager, I can remember that my favorite thing to do was to watch one of a few specially-favorite movies over and over. Now, I find it very difficult to watch a movie twice most times.
Now, I find it very difficult to watch a movie twice most times.
That has more to do with Hollywood's money coming from sexual slavery, abortion, and cultural demolition than anything else.
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