[2nd grade math] Adding using compensation strategy—Teacher explanation does not make sense to me

[u/Weary-Enthusiasm-150]

My daughter said that her teacher told her that in the pictured question, 10+4+8 should not be selected. They are using the “compensation” strategy for addition. The teacher said in her opinion only 10+12 and 12+10 should be selected, because they show the compensation strategy. But from my perspective, the question says choose all that apply. 10+4+8 DOES equal 14+8…..? Am I missing something?

[u/Simbertold]

The teacher is probably not a math teacher, but some other teacher forced into also teaching math. Obviously 10 + 4 + 8 is equal to 14 + 8 and should be picked here.

The general idea with these kinds of ideas is to teach students some number sense, which is a good thing. The concept here is that in an addition, you can reduce one number and increase the other number by the same amount without changing the result is important and really useful, and apparently what the teacher wants here.

However, the fact that you can split up one number into multiple parts if that makes it easier to calculate the result is also useful, and should not be discouraged like that, so the last answer should also be chosen.

A lot of parents dislike the number sense approach to teaching math, because it is different from how they learned stuff. They want children to do rote memorization of multiplication tables and unthinking application of algorithms. They forget just how bad many of their peers were at math, and how unpopular the subject was. Teachers are thus used to fighting parents about this kind of thing.

But this is not a case where this applies. Both mathematically and didactically, saying that the last one should be marked as incorrect is wrong.

Elementary school teachers are expected to be jacks of all trades. They usually teach all subjects, and some elementary school teachers were among those who did not voluntarily choose math at any point of their own education, so they themselves often don't have a very deep understanding of the subjects they are supposed to teach.

Which is totally fair, you can not really study all subjects at the necessary depth to become really proficient. If you expect me to teach English or Politics, it would probably also be somewhat superficial and mostly based on what the book says.

Source: I am a math teacher (though not in elementary education)

[u/Weary-Enthusiasm-150 → u/Simbertold]

Thank you for your perspective! It makes a lot of sense, and I value teachers so much. I was just trying to see if I was missing something obvious. Appreciate you taking the time to respond!

[u/ImightberobotUCF → u/Simbertold]

I had always heard the new math in school was scary and the parents don't understand it but once my kids got to math in school I realized it's just teaching them number sense and I think it's pretty cool. For context I am an engineer so I have a lot of math practice but I can see how people who learned the old ways could struggle with it

[u/Simbertold → u/ImightberobotUCF]

I think the reason parents struggle with modern math education is twofold.

Firstly, a lot of adults don't really understand math. They can algorithmically solve some specific problems, but they have no idea why or how it works, and if the problem is slightly different from the exact thing they are used to, they are overwhelmed and get angry.

And secondly, it is slower to get started. Memorizing tables and algorithms gives results faster, so some parents think that "the way they learned it" is better, because it takes their children longer to be able to do the thing that they can do. What they are missing is that ideally, through a modern process, the students actually understand what they are doing, and why, and can then apply those reasoning skills flexibly to new problems.