Why are times tables thought to be important?

Question

This question was inspired by a different question on this site which asked by what grade times tables had to be learned. The consensus seemed to be that it is essential that you learn basic times tables for single digit numbers.

I'm asking mainly because I'm in my mid thirties and still don't really feel like I remember my times tables and often spend some amount of time even deciding what 6*4 or 8*4 is, never mind things like 7*8 or 7*6. In many cases I end up either performing some arithmetic trick (6*4=2*12=24, 8*4=10*4-2*4=32) or just add/subtract from a known value (7*6=6*6+6=42, 8*7=8*8-8).

Having said that I hold two Masters in mathematics (one in abstract algebra and one in set theory) from different universities and I have never had any issues with dealing with fractions, algebraic manipulation or similar. My arithmetic tends to be slow, but that seems to rarely be an issue.

To further elaborate on the question and make it more distinct from the possible duplicate. Is there any actual research that causally connects not learning multiplication tables by rote with having problems with further abstract mathematics? Any such research would obviously have to eliminate the possibility that the students that haven't learned multiplication tables by rote are also in general less suited for further mathematical education (that is there isn't some underlying cause of both and instead there is a causal link).

Edit: I'm not sure that the question suggested as duplicate isn't a duplicate but the answers to that question are in my opinion unsubstantiated and incomplete. The only answer substantiated by anything other than "this is what I think/from my experience" just cites a paper which doesn't even answer the question at all. Though that paper cites many papers that might answer the question that seems a bit of a long stretch.

How would you simplify fractions or factor a polynomial when either requires recognizing a greatest common factor? — Amy B, Dec 11 '15 at 14:11
Possible duplicate of What are the arguments for and against learning multiplication table by heart? — Henry Towsner, Dec 11 '15 at 14:20
@amyB It's not like I don't know any multiples of any numbers. But I don't have multiplication tables memorized so much that if you show me say $56$ I automagically factor that in my head to $78$. On the other hand of course if you tell me to factor it it's hardly troubling. Mainly because you can easily see it's a multiple of $4$ since it's $40+16$. So it's $(10+4)4=144$ and I remember that $14=27$. In other words I know how to multiply any two (reasonable say <10^4) numbers you give me but if you ask what's 6*7 The answer is just not in my head I have to do some algebra. — DRF, Dec 11 '15 at 14:26
They are only important because we, as a people, collectively say they are important. They were probably more practically important historically than they are today. I can imagine in a hundred years we have completely abandoned basic mathematics education, and teach computer programming and linear algebra in elementary school. — Steven Gubkin, Dec 11 '15 at 15:56
@dirk Hmm those are arguments why you might need to know them for arithmetic heavy math which you are incapable of outsourcing. I don't see how that has much to do with further abstract math. I wouldn't like to give the idea that I necessarily think learning by rote is bad. I have seen that quantity can turn into quality for things like derivatives for example. I'm just not convinced it's a necessary prerequisite. — DRF, Dec 11 '15 at 16:03
This question has received some renewed interested over the last week, after a TES piece mentioned comments from Stanford's Jo Boaler; see,e.g., the section: Banning times tables. Googling indicates Boaler's position on the matter is neither sudden nor new. (I do not mean to endorse the position; only to mention contemporary news about it.) — Benjamin Dickman, Dec 11 '15 at 17:12
@DRF Haven't you basically answered your own question? Memorizing a table is convenient but isn't that important. Knowing how to do it by hand is important. Being able to manipulate numbers to do things in the most convenient way is best. — Adam, Dec 11 '15 at 17:31
Given your facility with factoring and your ability to figure out facts, I wouldn't put you in a category of students who don't know their times tables. I suggest you edit your question to reflect what you told me in your comment because it changes you from a student who doesn't know their times tables, to a different category. — Amy B, Dec 11 '15 at 19:29
@DRF: "Mainly because you can easily see it's a multiple of 4 since it's 40+16. So it's (10+4)∗4=14∗4 and I remember that 14=2∗7." So you do know and use times tables for this task, just not all of the times tables. Then the debate is just how high should be memorized (5, 10, 12, 16, etc.) — Daniel R. Collins, Dec 11 '15 at 20:58
@DanielR.Collins Hmm I think I haven't correctly phrased the question. My point is not that you shouldn't teach times tables. My point was that I've seen claims that knowing times tables (which I interpret as knowing all of them well) was essential for further mathematical development. I may have misunderstood just how badly students don't know them. I sort of expected that everyone knows the "easy ones" 2x 5x 9x 10x, those are the ones that have always come naturally to me, I also tend to know some other ones namely squares (except possibly 8^2 i have to think). — DRF, Dec 11 '15 at 21:13
@DRF: As a community college teacher, I'd say that the vast majority of students have no idea how to determine divisibility by 3 or 9; many can't tell how to determine divisibility by 5. And I definitely have a noticeable cohort who have no idea how to multiply an integer or decimal by 10, and are amazed when I share it with them. A whole semester asking people to remember perfect squares is usually not enough. People in this cohort nationally have about a 10% college graduation rate. — Daniel R. Collins, Dec 12 '15 at 02:56
This brings to mind a scene in Ionesco's La Leçon (1950) in which the professor warns his graduate student that she will never understand profoundly the principles of arithmetic if she cannot calculate correctly. To prove his point, he asks how will she ever know what 3755998251 times 5163303508 is? She immediately replies with the correct answer. He says she's wrong, check, and amazed asks how does she know it without knowing the principles of arithmetical reasoning. She replies she learned by heart all the possible products of all the numbers. — user1815, Dec 12 '15 at 14:47
@MichaelE2 That sounds like an amazing play. I will have to watch it. — Steven Gubkin, Dec 14 '15 at 16:25

score 2 · Answer 1 · answered Dec 14 '15 at 10:08

I taught gifted students in 4th-6th grades and it was important for them to know their times tables. We simplified fractions, performed long division, identified prime numbers and performed calculations with multi-digit numbers. Students who didn't know the facts practiced on Flashmasters, an excellent electronic flashcard system.

Having said that, my standard for knowing the facts is lower than many of my colleagues. Most of my colleagues insist on the ability to instantly recall facts and their standard is 100 facts in 3 minutes. My standard was a test of all the facts up to 10 by 10 (45 facts in all) in 5 minutes (although most could pass in 3 minutes). Given what you said about using mathematical tricks to find your facts, I believe you would have passed the standard for knowing the facts.

There will always be students who could recall facts in under 2 seconds (as confirmed by the flashmaster), but those who took a little longer whether because they figured them out or they just weren't as fast did fine.

My conclusion it is necessary to know the facts, but there are different levels of knowing them and your level is fine. Many of my colleagues would disagree, but perhaps you are a good example of the fact that my standards work.

Why are times tables thought to be important?

1 Answers1