# Which works better for learning 6 * 7 = 42: saying "six sevens are forty-two", or "six times seven equals forty-two"?

When memorizing and recalling the times table, I learned to say "six sevens are forty-two", and always wondered what it would be like to learn to say "six times seven equals forty-two" and whether it would be harder. Likewise, of course, with all the other ones e.g. "seven eights are fifty-six".

• Since this is not an opinion forum, valid answers to this should site published research. Mar 30, 2021 at 0:33
• Is this question asking about the slightly odd/archaic phrasing of "six times seven"? As in seven, but six times. It does have the virtue of being an infix operator so you can read $6 \times 7$ in a natural way.
Mar 30, 2021 at 2:37
• A literal/direct/mechanistic recitation probably involves a lighter cognitive load than a quirkier sentence-translated recitation. So: "one times five equals five", "six times seven equals forty-two", "eleven times twelve equals one-hundred-and-thirty-two"; versus "one copy of five is five", "six sevens are forty-two", "eleven twelves are one-hundred-and-thirty-two". Native English-language speakers may prefer the latter, while non-native English-language speakers may prefer the former. Mar 30, 2021 at 17:40
• @RyanG I never heard 'one copy of five is five'. Interesting. You make a good point about how it would be easier to teach math in English to non-Anglophones using symbol by symbol pronunciation. Had not thought of that. Mar 30, 2021 at 17:48
• I think that "primary mathematics education" would be the academic subject which would study such things. However, my awareness of the field is that it is not conducting studies on such narrow questions. My own personal preference would be to read this as "6 groups of 7 are 42 all together", or some variant of this Mar 30, 2021 at 19:19

Not a proper acceptable answer, just an expansion of my original comment:

A literal/direct/mechanistic recitation probably involves a lighter cognitive load than a quirkier sentence-translated recitation. So:

• one times five equals five
• six times seven equals forty-two
• eleven times twelve equals one-hundred-and-thirty-two;

versus

• one (copy of) five is five
• six (lots of) sevens are forty-two
• eleven twelves are one-hundred-and-thirty-two.

Native English-language speakers may prefer the latter, while non-native English-language speakers may prefer the former.

@DanielRCollins: I would certainly not want to hear something like "twenty fives is one hundred".

Yes, in the sentence-translation (as opposed to mechanistic recitation),

1. the fact that "twenty fives" and "twenty-five" are almost homophonous,
3. the pluralisation,
4. the fact that the noun but not the adverb is pluralised,
5. the option between "is" & "are" ("20 fives is 100" and "20 fives are 100" are differently meaningful),
6. the natural-language ambiguity of in what sense 20 fives is/are/becomes 100,
7. etc.,

all impose cognitive burdens. The process is more akin to a narration than a streamlined recitation, and furthermore detracts from the commutativity of the multiplication operation.

• I think it will be great if learners and educators of primary educations are more aware of what you are distinguishing. Each of them is so important for math education. I have taught Introductory Algebra to college students who had very weak arithmetic skills and could witness negative influences when only one of them was emphasized in primary educations. Apr 1, 2021 at 16:16

I think for first learning, it is easier to think of the former, not the latter. So two twos make a four. After all, what is "times", for someone new to it.

But by the time you are doing the whole multiplication table (and six sevens is pretty high up into it), you've got more familiarity with multiplication and can just start saying "times", which is more efficient (to say or to think about).

• 'can just start saying "times" ' is not clear to me. Could you clarify what you mean? Mar 29, 2021 at 20:19
• Even though this approach may have some advantages, it may also create a barrier that some students cannot jump through and end up giving up learning math, thinking they are not good at "hard" math or being resentful that people are making math harder than it should be. Apr 1, 2021 at 16:13