Bah... I can tell you why the first algorithm/example works because of the commutative and associative properties of math. Learning "why" a solution works, doesn't require learning some arcane algorithm.
If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.
You are not a six year old child learning arithmatic. You have missed the point.
> The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
Mental methods are taught so that children do understand numbers, which gives them a better grounding for future learning.
We're saying the same thing. I understand that children need to understand the underlying concepts. I'm saying there are already well established methods for teaching those.
Waving a hand and saying the "old way" is simply an algorithm and a poor method because it glosses over the details is like saying teaching someone how to use a calculator will make them forget how math works.
That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
>That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
That was a point I made elsewhere on this thread. When helping my second-grader with her homework, it sometimes seems that they are just changing what the student is required to memorize (and also increasing the volume), without necessarily imparting additional understanding.
That problem relies on what they call the "Add it Up" method, and it is specifically a technique with which I've helped my daughter. I observed that kids can completely learn the method and ace a test without understanding the concepts behind it.
There is also pretty good evidence that the old methods did not promote understanding.
> That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
You do not understand what it is trying to teach. It is teaching children that taking one number from another can be done using columns, but it can also be done in your head by breaking big numbers down into small numbers and counting up.
Understanding math concepts might be trivial for us but math-untrained minds such as grade schoolers and probably their parents, it could be an almost impossible high-bar to reach.
That's a pretty horrible attitude to take to learning.
It's like asking why ever read a book, with a level of english past the level of a memo asking if you have completed a task. This article also seems to suggest that people don't understand how to preform basic mental arithmetic.
In the states there also seems to be this insane way of thinking that you should learn an algorithm to do things in a particular way, if you can do it one way you should understand it and all the other methods should just fall into place.
There's an infinite number of things you could be learning, wouldn't it be better to concentrate your efforts on the things that are valuable to you individually? I'm not of the belief that you need to learn things at specific ages and I also believe that you learn much faster when you have an application in mind for a particular skill. That in mind I think students should be encouraged to explore the things that are of interest to them. (hey I took double maths for A-level and enjoyed every minute of it)
(hey I took double maths for A-level and enjoyed every minute of it)
yes I completely agree about specialization. but A) this is about people learning addition and B) some people are totally clueless about what is useful to them. there really is a lot of good that comes out of studying general stuff that stands to the a lot of people
If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.