I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids.
Does independent research prove these approaches increase numeracy?
No, the "making change" comment is an example of how these techniques of thinking about numbers do turn up in real life.
> I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids.
It's a part of a broader strategy to talk about the structure of numbers and the operations on them.
> Does independent research prove these approaches increase numeracy?
Yes. I don't have access to it and can't give you any links, but there has been a lot of research about how to move away from the rote learning of algorithms and move towards understanding what numbers are and how they work. I've seen some of the research as a peripheral part of some of the projects I've been involved with, and it seems that these sorts of exercises really do serve to help students see more about what's really going on.
The problem is the parents pushing back because they don't understand it, and don't believe it can be useful or helpful. For me, it seems obvious that this is a better way to think about things.
I'm not sure I understand what you mean. What universal algorithms are there currently for solving problems and describing the universe? And why are these universal algorithms more important than estimation skill in practice?
Are you suggesting that there's always only one true way to do things in math, and that the quest for the one true way is the only noble pursuit?
FWIW, to me that sentence somewhat reads like a pre-conceived idea about math that could possibly impede your appreciation for valid alternative approaches.
It's worth considering that in computing, the algorithms that have been used for math in processors and standard libraries have been changing dramatically ever since the first transistor. And it's not because the newer algorithms are more universal, it's often because we're simply making different tradeoffs over time. Sometimes it's because better algorithms are being invented, because the algorithms we thought were great turn out to be not universal. Sometimes it's because a new fast approximation formula is discovered that is accurate to the precision of the machine.
There's very little in computing today that is "universal", despite the pedagogical emphasis on this abstract idea. There are, however, lots of algorithms that are canonized. Math constructs that seem universal because everyone knows them and they're popular, and alternatives aren't well known, enough that it becomes hard to imagine the alternatives.
> My kids are entirely missing that in their common core education...
Are you absolutely certain that's true? Common core, as the author pointed out, is still required to teach the old algorithms. Are you sure you're not having an emotional reaction to not quite understanding why some of the new methods are there and/or being unfamiliar with them? Your reaction here is exactly what this entire post was addressing.
From the article, "the Common Core State Standards in the U.S. still requires student fluency with these algorithms"
> Being able to mentally estimate numbers or do simple arithmetic is a good skill
It's not just about the ability to estimate or do simple mental arithmetic. Look at this example from the article: "Describe three ways to see why 35 x 12 is 420". Knowledge of these 'three ways' provides a deeper conceptual understanding of multiplication. I want my students to have a shot at deriving the algorithm for multiplication, not just implementing it.
One of the reasons common core math is so controversial is because it's one of these "shared experience" topics for which everyone has personal experience and considers themselves an expert, yet most don't realize that their own experience is probably quite different from nearly everyone else's. And the reason theirs is different is in large part because their mind works differently and they naturally fell into using skills matched to their own strengths and weaknesses. Take 20 people and pair them off into 10 pairs, and have one person in each pair walk the other through how they calculate 876 - 381 in their head. You will 10 different results[1]. The problem with common core is that it teaches a handful of these approaches rather than letting the student develop their own customized approach.
[1] I have actually done this experiment. Of the 8 pairings, I think we had 7 different algorithms. Only two people did something close enough to be called the same thing.
The implementation and communication about what Common Core is doing needs a little work. The author mentioned this, and I think he's absolutely right. The fact that math-educated parents like you are reacting negatively to Common Core is a symptom of the plan not being very well explained to parents, even though once people see it clearly, they often agree that it looks like a superior way to teach math.
I guess I'll just add a side note that fostering this appreciation for different approaches might actually be getting more directly at the universality you mentioned above. There's a deeper truth behind the meaning of subtracting two numbers than any one algorithm holds, and perhaps the only way to see it is to be familiar with multiple algorithms.
I found it a huge boost to my ability to do computations without paper or other tools when I learned it in elementary school; I think it's valuable, but I'm not certain that the manner in which it is often being taught now is helpful (which, AFAICT, is not so much a matter of the Common Core standards as poor curriculum attempting to implement the standards.)
The traditional algorithms aren’t very intuitive, but they work. Trying to make an algorithm out of the various ways you can break up a problem, ad hoc, seems bananas.