Is addition a shortcut for counting, or is that wrong, too?
What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
131–140 of 425 posts
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#132I've been teaching my 5 year old multiplication and division for the last couple of weeks. I'm at a loss how you would teach it without explaining that it is repeated addition. For example, the other day I asked her how many fingers and toes the three kids at the table had, and she came up with "20 fingers and toes each times 3 kids means there are 60 fingers and toes." I think the units are intuitive in most cases a…
You can teach (some intuition for) multiplication without numbers by multiplying lengths to get areas. Then show e.g. how the number of seats in a theater is the number of seats in a row * the number of rows. Let the school teacher press the algorithms on him, teach him your hacker's sense of wonder.
> Then show e.g. how the number of seats in a theater is the number of seats in a row * the number of rows.
How do you do that without adding up the number of seats in the rows or columns (ie repeated addition)?
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#133I don't understand. The author is mixing up physics (dimensional analysis) and maths, and trying to give the multiplicand a special role (I didn't even know there was a distinction between the two terms - to me they are both factors). This might be true in the physical world, but in the world of numbers, I think the distinction is irrelevant. Furthermore, being able to compute/define multiplication through repeated a…
Not defending the article, but how would you compute: \pi*\pi using repeated addition?
3.14159 + 3.14159 + 3.14159 + (3.14159*0.14159)
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#134Earlier quoted context omitted.
I have a PhD in physics and more maths qualifications than I can shake a stick at; to me, multiplication is repeated addition. I’m not sure what the teacher is trying to do here, but I do think the outcome of what they’re trying to do is far more complicated than the simple “multiplication is repeated addition”. I also happen to have an 8-year-old going through third grade right now, and when we were talking through…
I think the useful distinction is that, when you teach multiplication as a mechanical computation (arithmetic) it's useful to talk about it as repeated addition. As you get to negative numbers, rational/irrational numbers, complex numbers, matrices, etc. it becomes more useful to think about multiplication in more abstract ways, among which repeated addition is still often a useful way to look at it. I also think it'…
Your last two paragraphs are, I believe, the crux of my own argument. Sure, matrices aren’t even commutative, and complex numbers have their own quirks because of i^2 == -1, but these concepts build on the earlier axioms the kid has learnt. Our entire education system is built on “lies-to-children”, and as you progress they point out that what you comfortably believed was a gross simplification. This is no different.
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#135Earlier quoted context omitted.
That's not the norm?
No, it's not. It depends a bit on your teachers but also on which "level" of math you're in (in the US). Lower level but still algebra/geometry classes tend to teach facts, not derivations from foundational concepts. Those are the classes aimed at non-Honors and maybe non-College Prep students (2 of the 3 typical "tracks" students end up in the US, names may vary by state and decade).
The way Geometry is taught in the US is awful. Instead of learning that you can use shapes to do useful calculations like square roots, you slog through postulates and theorums without any sense of why you have to do them. Rarely is what is learnt in geometry ever used in later high school courses, save for trigonometry. I hope it is different in other countries.
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#136I don't understand. The author is mixing up physics (dimensional analysis) and maths, and trying to give the multiplicand a special role (I didn't even know there was a distinction between the two terms - to me they are both factors). This might be true in the physical world, but in the world of numbers, I think the distinction is irrelevant. Furthermore, being able to compute/define multiplication through repeated a…
I have a PhD in physics and more maths qualifications than I can shake a stick at; to me, multiplication is repeated addition. I’m not sure what the teacher is trying to do here, but I do think the outcome of what they’re trying to do is far more complicated than the simple “multiplication is repeated addition”. I also happen to have an 8-year-old going through third grade right now, and when we were talking through…
I have got almost exactly the same situation: PhD, physics, forgotten more math than most folks ever learn, etc., and with an 8 year old learning the same level of mathematics as you describe.
I think the only difference might be I used "iterated" rather than "repeated" when helping him. Anyone who is just learning multiplication likely lacks the depth of experience necessary to make use of the "correct" jargon and abstract concepts as a starting point. "Repeated addition" is a useful aid in learning the operation to build that experience.
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#137tl;dr: "Nothing"
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#138Earlier quoted context omitted.
That's not the norm?
Oh god, no. Not at all, especially in the US.
I can tell you how great my math education was. I don't even recall the quadratic formula or completing the square is. I'm almost certain they were part of the curriculum at some point.
I recall in later math course, notably calculus, the teacher assumed we we're familiar with some concept because we we're supposedly taught it the prior year, yet not a single student in the class could recall it having been taught before.
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#139Earlier quoted context omitted.
pi + pi + pi + (.141592... of pi) ~= 9.8696 You need the concept of a ratio, so arguably I'm using multiplication to define multiplication, but you're sort of cheating by asking about a fractional number.
However, pi is already a ratio…
Right, that's why it's cheating. He's asking about a number set that requires the concept of ratios, and ratios are multiplication.
Re: What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
#140Earlier quoted context omitted.
pi + pi + pi + (.141592... of pi) ~= 9.8696 You need the concept of a ratio, so arguably I'm using multiplication to define multiplication, but you're sort of cheating by asking about a fractional number.
Pi is definitely not a fractional number... I don't think it's cheating at all, multiplication on the naturals is repeated addition, that's not the case for the reals.
This is an interesting statement.
While it's true, it obscures the fact that pi is defined as a fraction: Circumference/Diameter.
That this fraction cannot be represented as a numeric fraction is one of the great insights of early mathematics.