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In my opinion this is precisely the problem we have with our secondary education. Every few years or so, the schools here in U.S. follow certain educational fads that talk a lot about how all students learn differently and how teachers must create and utilize various teaching styles to fit each student's abilities (imagine that in the classroom of 3040 students!!!), and how knowledge of the subject matter is no longer important, and that students must learn the "concepts" rather than actual subject matter, and on and on.... The reality is that the students must learn the substance before they can apply the “concepts” . They need to memorize the multiplication table because this will make their life MUCH easier down the road. Poor memory is just an excuse for not doing the "boring" memorization. Memory must be developed and improved through sets of simple exercises. For example, a child should read poetry as often as he/she can; this is the best and easiest way to improve one’s memory. This is what we all did in elementary school, by the way; we read poetry A LOT and we had to recite poems on the weekly basis. Also, the multiplication table hung on the wall in my bedroom and I looked at it every time when I went to bed or when I got up. As I recall, no one in my class had problems with memorizing multiplication tables; and there were 20 students in my class in elementary school. Hell, wake me up at night, and I can give you the whole table within five minutes. And I am eternally grateful to my teachers that they made me do that. Memorization is a part of learning process and while it is could be boring, it is absolutely necessary. My students often complain to me that they have poor memories and this makes their learning experience much more difficult that it should’ve been. They tell me that they never were asked to memorize and recite poetry, to remember important historical dates, and yes, they were not required to memorize the multiplication table as well. And I see them failing my and other professor’s classes, getting frustrated and dropping out.

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Why should number sense be sacrificed to improve the memory? Admittedly, a good memory is a useful thing, but amongst the various academic disciplines higher math is the one least likely to be mentioned when ranking those that require a good memory. Every other subject I can think of has more need for recall than math; history, literature, science, art, music, psychology, etc. So why use a young child's first exposure to arithmetic as an opportunity to exercise something that has little relevance to the true subject at hand?
Socrates (see I do use my memory to recall useful information) was concerned that learning to read would lead to laziness in memory. Before the written word, most knowledge had to be memorized (though math was done on fingers or an abacus.) Yet, we don't sacrifice really learning to read in order to improve a child's memory. We encourage them to sound out the words in Hop On Pop and not to simply memorize the entire library. If after they have deciphered The Cat in The Hat for the 6th time we suspect they have memorized it, we deliberately go and get The Cat in The Hat Comes Back, so that their decoding skills will continue to be challenged. This is b/c we see the true value of real reading. Why is the value of mathematical thinking beyond what can easily be memorized so readily discarded? 
. With all due respect, I am not saying here that one has to sacrifice their “number sense” in favor of memorization. All I was saying is that there is nothing wrong with memorizing multiplication table. I am not suggesting that one has to continue memorizing equations and formulas all throughout his school career. Obviously learning mathematics or any other subjects for that matter should not be concentrated on memorization alone. But learning does require certain degree of memorization. As I mentioned before, students often complain to me that they have poor memories and that it hinders their learning process a lot.

~Sandy
mommy to Joey 11, Ian 9, Hayden 7 and Charlie 3
MusicianDad,
I've shared the highlights of your pro finger counting arguments on my Maths Insider blog. Now you're (even more) famous! It was nice sparring with you! 
I agree that lightening speed is not necessarily the main objective (but it’s cool!), especially if accuracy suffers. I’ve seen 10 year olds take 20 seconds to work out 13 + 9 because they’re counting out 13 fingers, then adding another 9. (very uncomfortable!) 
If you have your fingers with you all the time, and use them all the time, there is no incentive to try to memorise and figuring out how to do more than basic arithmetic can be harder than using other visual or memory based techniques. 
This can also be true if you ask a child to visualise counting their fingers or other objects in their head. 
If one has relied on memorization to get through addition and multiplication, then why would they suddenly develop a real number sense, an ability to reason mathematically and the skills to use mental manipulations when it comes time to do more complicated math.
I know plenty of very smart people who did well enough in school in math by memorizing high school math. Instead of ever actually working out a geometric proof they simply read all the ones they thought might be on a test over and over till they memorized them. These people as adult completely lack a math sense. They were the people incapable of taking a mark down on the last piece of fabric on the bolt unless it was a full yard (and that is with a calculator available.) These are the people incapable of finding the upper levels in a parking garage (oh well, at least I can always find good spots up there.) These were the people incapable of applying a simple formula in order to determined what size to make a sheet of paper to be folded into the right size book with a certain number of pages. Never mind something as simple as figuring out what tip to leave at a restaurant. These are all situations that I have run into in my life, with multiple people. 
MusicianDad,
Yes, I'm sorry, I should have contacted you before I used your responses on my blog. No excuses. Thank you for handling the situation with good humour! I'm sure you'd make an excellent blogger! I can see you've contributed extensively here on the mothering.com forums. I can't be the only person who's a fan of your writing style! The blogosphere would welcome you with open arms (Also thanks for the broken link tip  it's fixed now ) One thing this debate has done is highlight the different learning styles and techniques in maths. My oldest 2 kids each have different approaches to maths problem solving and I'm sure my younger 2 will show me another few styles in the future. Future mathematicians come in all flavours! Furthermore, to give your credit, I do agree that as parent and educators, it's more important to foster a love of this much maligned subject. A teacher commented on my blog that although she "aspires to (teach) good number skills" in her students, "There are bigger battles to fight, i.e. doing maths at all." In the end, it's the love of (or at least comfort with) maths that should be our ultimate aim. 

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