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Thread: Factoring in the "modern math" curriculum

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    Factoring in the "modern math" curriculum

    Okay, I took a Unisom last night and woke up pondering the following. (I take it when I have trouble sleeping but I've also found it induces a bit of extra free-association.)

    In the current education system in the US, when teaching the concept of multiplication, we have the following argument: n x m is defined as n groups of m. So, for example, 3 x 4 = three groups of four which is, according to the curriculum, not the same as 4 x 3 = four groups of three. I am not happy with this teaching method, which supposedly helps the student "later on" in their Math education. (Where I cannot say.)

    But I woke up thinking about just how they are going to teach factoring? Clearly 12 = 3 x 4 and 4 x 3. But supposedly the two expressions are not the same. And how can they also relate that 12 = 2 x 6? And, God forbid, factoring a number into it's prime factors.

    Does anyone know how they teach this?

    -Dan
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    Re: Factoring in the "modern math" curriculum

    Quote Originally Posted by topsquark View Post
    Okay, I took a Unisom last night and woke up pondering the following. (I take it when I have trouble sleeping but I've also found it induces a bit of extra free-association.)

    In the current education system in the US, when teaching the concept of multiplication, we have the following argument: n x m is defined as n groups of m. So, for example, 3 x 4 = three groups of four which is, according to the curriculum, not the same as 4 x 3 = four groups of three. I am not happy with this teaching method, which supposedly helps the student "later on" in their Math education. (Where I cannot say.)

    But I woke up thinking about just how they are going to teach factoring? Clearly 12 = 3 x 4 and 4 x 3. But supposedly the two expressions are not the same. And how can they also relate that 12 = 2 x 6? And, God forbid, factoring a number into it's prime factors.

    Does anyone know how they teach this?

    -Dan
    Modern math curriculum is designed with software development in mind. Graphics design frequently involves linear algebra, and matrix multiplication is non-commutative.

    I only know the overarching goals of modern mathematics education from a couple of articles I read on the subject, but I have no idea about the specifics of how it is taught. I would assume that once factoring is established, they can say, "Numbers are nice, but not everything you try to multiply will work this way." Then, they can start factoring, with the explicit understanding that they cannot just factor in any math system they come across.
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    Forum Admin topsquark's Avatar
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    Re: Factoring in the "modern math" curriculum

    Quote Originally Posted by SlipEternal View Post
    Modern math curriculum is designed with software development in mind. Graphics design frequently involves linear algebra, and matrix multiplication is non-commutative.

    I only know the overarching goals of modern mathematics education from a couple of articles I read on the subject, but I have no idea about the specifics of how it is taught. I would assume that once factoring is established, they can say, "Numbers are nice, but not everything you try to multiply will work this way." Then, they can start factoring, with the explicit understanding that they cannot just factor in any math system they come across.
    Yes, but the grades they teach the multiplication thing is somewhere in the middle school range... grades 3 - 6. Factoring would be in there somewhere. As I recall we were doing prime factorization in 7th grade when I went through. So they would be teaching factoring in the "usual" whole number system, maybe in 5th or 6th grade, before they would get to examples in more advanced systems, such as "clock math."

    -Dan
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