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By tracking a group of young students over the course of a year, the authors show “that children learn to associate individual problems with the correct answers. Repeated problem solving during the early stages of arithmetic skill development also contributes to memory re-encoding and consolidation, thus resulting in enhanced hippocampal activity and ability to recall basic arithmetic facts… The maturation of problem-solving skills is characterized by a gradual decrease in the use of inefficient procedures such as counting and an increase in the use of memory-based strategies.”
"As a scientific justification of rote learning, the study seems likely to further polarize the controversy over math teaching styles, in which arithmetical fundamentalists are squared off against the popular and progressive forces of “discovery-based” learning, in which students are encouraged to find their own ways to the right answer." (
read the whole thing)
Via Instapundit
12 comments:
Absolutely correct! Memorization of the basic tables is paramount, and these silly attempts at changing what has worked since the invention of math does nothing less than mal-educate children into believing that they cannot "do math."
I have one of my least favorite instructors this semester. She's a nice lady. A flaming leftist, but a really nice lady. And she does this "lets think this through and discover it" thing and it makes me absolutely nuts. We're in upper level courses in our specialty. We aren't there if we don't think about the information. But we wasted one whole class period reinventing a method of categorizing different sedimentary rocks. Five minutes! It would have taken five minutes to state... these sorts are biogenic, those are chemical precipitates or evaporites and those are made of cemented particles and we call them siliciclastics. Half of those five minites would be defining siliciclastics...
With math with little kids... they can spend weeks "discovering" addition, and not have any "math facts" memorized at the end of it, or they could spend those weeks memorizing math facts and actually *using* them.
It's sort of like... thanks but no thanks Phonecians, thanks but no thanks Babylonians, thanks but no thanks Greeks... we'll just start over and do it our way.
They treat gender the same way.
lol Paddy, not bad.
That equation takes me back 50 years - funny how once those things are drilled into a person one glance, even after years of not using them, one says "solving quadratic equations".
Which further reminds me that a customer has asked me to mill a table top in the form of a parabola. I can do that, just can't guarantee where the focus will be. Details, details...
I recognize that on the chalkboard.
Quadratic formula.
x= -b ± √ b2(sq) 4ac / 4a(sq)
It fills in a square. Important for calculating parabolas.
Shortcuts for completing the square
They figure radio waves, ocean waves, the arc of a ball that is thrown, the break even points for business propositions. They can assist in choosing the right car rental where anticipated miles traveled and time rented are variables. They solve distance VS. currents VS time problems. They solve electrical resistance problems. The shape of satellite dishes, and the shape of lenses, the arc of a canon ball or rocket shot. They can calculate the amount of fencing needed to enclose a field, and the times required for various vehicles traveling at differing speeds. They solve how much work varying machinery can produce over time. They can solve for workers schedules. They can resolve the shape of an airplane wing. The equation can be used to calculate the distance and angle of firing for a sniper's bullet to precisely intersect the head of his distant target, and many other such marvelous things.
One day right before hosting a party I was finishing my algebra for business homework and became quite bored. So I changed all homework's symbols to Egyptian hieroglyphics that I made up just to see if it would work, a hand for a 5, a foot for 2, a snake for 3, an ibis for equals, a tree for "times" and so on.
Then wrote the problems in my make believe hieroglyphs.
Then solved them in my make believe hieroglyphs.
Then checked them using regular numbers and symbols and they came out right!
Duh.
Why wouldn't they? It's all just symbols anyway innit.
But my pages were beautiful and artistic and I was well chuffed with my fancy deed. Bing bong. Guests arriving. I showed my art math to the first guest to arrive who responded, "Barf. I'm reminded all over again why I despised math so badly."
Repetitio mater studiorum est
"these sorts are biogenic, those are chemical precipitates or evaporites and those are made of cemented particles and we call them siliciclastics."
God, I love it when Synova talks dirt.
At this point I *live* dirt. :)
Two field trips in three days to view Permian sandstone and Pennsylvanian limestone and I have a sunburn to show.
I should put some pictures up. Maybe on my blog. I put a bunch on facebook.
I put pictures of rocks on my blog... the formating sucks and I've gone on about the technical stuff because I have to remember it so I figure the more times I repeat, the better.
Keep your eyes on your own damn paper, Chip A!
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