Tables: "Knowing" is not enough.
Moderators: Bob Hazen, Theodore, elliemaejune
Tables: "Knowing" is not enough.
When kids "learn" their tables, they, of course, must crawl before they walk.
But how many are ever challenged to proceed to running?
Point to a child's sibling. Ask "What is his/her name?" The child will look puzzled, but answer.
Now ask "What is 5x7?" Again, I hope, the child will (eventually) answer.
Now say....
"Yes... it is 35. But you couldn't answer that... yet... the way you answered the first question. WITH PRACTICE you can get to the point where you can answer that fast. But it takes a little time to get out of several bad habits... e.g. repeating the question (out loud or in mind) and prefacing the answer with a time buying/ wasting "um".
Hope you will give your learners a chance to see how skilful they can become.
Tom
But how many are ever challenged to proceed to running?
Point to a child's sibling. Ask "What is his/her name?" The child will look puzzled, but answer.
Now ask "What is 5x7?" Again, I hope, the child will (eventually) answer.
Now say....
"Yes... it is 35. But you couldn't answer that... yet... the way you answered the first question. WITH PRACTICE you can get to the point where you can answer that fast. But it takes a little time to get out of several bad habits... e.g. repeating the question (out loud or in mind) and prefacing the answer with a time buying/ wasting "um".
Hope you will give your learners a chance to see how skilful they can become.
Tom
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my son loves the fact that by the middle of 3rd grade he could rattle off any multiplication problem
Many children would take great delight in having the skill, being able to do this "party trick".
But for many, it takes an adult they care about showing an interest. It takes teachers no turning something which CAN be fun unto something that is hated before it has progressed to the point where it can be enjoyed.
For some reason, "doing flash cards" with a computer is easier for many kids than doing them with a human. Maybe it is the computer's lack of emotional response to wrong answers? My Windows freeware and shareware mostly lacks "sugar" to help the "pill"... but with a little encouragement from adults, kids can use it to make progress.
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...also known as...
http://tinyurl.com/SheepdogOffers
 David Brown
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David Brown wrote:I think with tables it's important that they know why 5 X 7 is 35 not just that it is 35.
Agreed. I get so frustrated when I see people "take sides" on how to teach math facts (memorization vs. comprehension). Both are essential.
David Kocur
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dkocur wrote:Agreed. I get so frustrated when I see people "take sides" on how to teach math facts (memorization vs. comprehension). Both are essential.
I agree...If they only memorize the facts it will be harder for them to do harder problems in the future; if they only comprehend them they will have the same problem in a different way.
"Lay down true principles and adhere to them inflexibly. Do not be frightened into their surrender."
~Thomas Jefferson
~Thomas Jefferson
Well, yes, if you have some experience looking at problems that way. Knowledge of how to do 98 x 5 and 2 x 5 in your head doesn't necessarily extend to realizing it's the same as (98 + 2) x 5.
David  knowing why basic math works is important, but multiplication is easy to demonstrate using manipulatives, and once it's been demonstrated once, that's all you need to know. You don't need to keep thinking about the "why". Memorization is arguably more important because it takes up the bulk of the time in basic math, and provides the big speed advantages in more advanced material. In Calculus, you are bombarded with formulas, most of which aren't explained until Calculus II. Physics has formulas that aren't explained until you take Calculus 1. The important thing is arriving at the correct answer with 100% accuracy and a high degree of speed  the "why" only matters if you don't remember the formula and have to derive it on your own.
David  knowing why basic math works is important, but multiplication is easy to demonstrate using manipulatives, and once it's been demonstrated once, that's all you need to know. You don't need to keep thinking about the "why". Memorization is arguably more important because it takes up the bulk of the time in basic math, and provides the big speed advantages in more advanced material. In Calculus, you are bombarded with formulas, most of which aren't explained until Calculus II. Physics has formulas that aren't explained until you take Calculus 1. The important thing is arriving at the correct answer with 100% accuracy and a high degree of speed  the "why" only matters if you don't remember the formula and have to derive it on your own.
Theodore, I disagree with you about whether or not a student should know what 98*5+2*5 is equal to. EVERY algebra student should know that 98x+2x =100x. All the above problem did was say what x is. Yes!, every (and I mean every) student should know the answer immediately. You have to have some standards in the classroom. I ALWAYS tell my students 'if it always works for letters it must always work for numbers, if it doesn't work for all numbers it doesn't work for all letters'.

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Yes! I fully agree with you that Every Algebra student and also other student who good in Math subject must know the answer of 98*5+2*5. I think i give answer of this question which 500. Some student are very good in Math and they see the question and quickly give answer, not take time to write. It's my personal experience.
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