# When if ever does SM teach definitions of terms like associative, distributive...

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I know they teach the methodology, but do they ever teach definitions? So if a standardized test were to say "demonstrate the associative rule" they would understand the question...?

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NEM 1. As far as I can recall, this isn't covered in the primary math series.

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• 3 weeks later...

Thanks. I saw my 9 yo sister

(She's in ps) had a quiz with a question like this on it, so it got me thinking. I am wondering if there is a basic math dictionary or site that defines these terms (associative, commutative....), plus words like quotient, divisor, product, etc. I think it would be smart for ds to know these terms cold.

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Would not those terms come up when each individual topic is covered?

IMO, it makes no sense to learn the words separately - it is much easier if they are introduced in the respective context, because then they mean something beyond a memorized definition.

So, I would see no value in lumping them all together and teaching the words at the same point in time.

While schools may do this and may design quizzes and tests about it, mathematically it makes no sense and is not a skill ever needed in real life. Knowing what commutative means becomes meaningful when you actually reverse addition or multiplication order; "distributive" becomes meaningful when distributing factors through terms in parentheses, not before that.

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Thanks. I saw my 9 yo sister

(She's in ps) had a quiz with a question like this on it, so it got me thinking. I am wondering if there is a basic math dictionary or site that defines these terms (associative, commutative....), plus words like quotient, divisor, product, etc. I think it would be smart for ds to know these terms cold.

I tell my son the terms product, factor, etc. as we come upon those topics, even though Singapore has not done so yet. I also think they are good to know. At some level they do need to know the terms.

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I know for sure we've covered sum, difference, product, quotient when we did Singapore 3A (Standards).

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I believe it would be the teacher's responsibility for teaching the terminology. I am currently working my way through the elementary mathematics for teachers book that uses the SM books as it's base and it brings up the terms and how to teach then quite early in the book. (3rd section I believe) It also gives you many different angles and examples of each which helped me really grasp the concepts enough to be more confident in my ability to teach them when the time comes.

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NEM 1. As far as I can recall, this isn't covered in the primary math series.

They learn this in Primary Math, but it isn't given a name until NEM. By that time, it is second nature. There is nothing to stop a teacher from mentioning it. I have with my kids.

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We just started 4A and we covered product and quotient last year for sure. We've already covered factor and multiple for sure this year (Friday). I don't recall whether commutative law was mentioned...we do it al the time and I mention it but I am thinking perhaps the name came up in Miquon last year. Brownie

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Thanks. I saw my 9 yo sister

(She's in ps) had a quiz with a question like this on it, so it got me thinking. I am wondering if there is a basic math dictionary or site that defines these terms (associative, commutative....), plus words like quotient, divisor, product, etc. I think it would be smart for ds to know these terms cold.

That is why I love pairing Singapore with Miquon. We've been learning the laws of mathematics by name (and in ways that are fully comprehensible to young children) since pre-school as in integral part of learning new math concepts.

The axioms of math are spelled out in the Miquon teachers materials, along with ideas for teaching and setting up activities of "discovery" whereby the children "prove" that the laws of math are true using concrete means along with their own minds. After that, they own it!

Understanding these laws and being able to utilize them in problem solving is key to developing mathematical reasoning. Knowing the meaning of words like quotient, divisor or product while useful in giving one a common parlance with other mathematicians are arbitrary names and not so critical to mathematical reasoning. Which is not to say they shouldn't be learned, it is just not as essential as UNDERSTANDING the mathematical laws and being able to use that knowledge in problem solving.

Bill

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