r/HomeworkHelp • u/Weary-Enthusiasm-150 Primary School Student • 7d ago
Primary School Math—Pending OP Reply [2nd grade math] Adding using compensation strategy—Teacher explanation does not make sense to me
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?
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u/Simbertold 7d ago edited 7d ago
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)
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u/Weary-Enthusiasm-150 7d ago
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!
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u/ImightberobotUCF 6d ago
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
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u/Simbertold 6d ago
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.
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u/_Cyanidic_ 7d ago
I kind of hate how schools always try to force students to adopt methods of doing arithmetic rather them teaching them the basics and then showing them the tricks; allowing them to decide for themselves what they want to use.
From googling it seems compensation strategy essentially means taking a bit from one of the addends and prematurely adding it to the other addend to make it easier to compute the full sum. In this case reducing 14 to 12 so you can increase 8 to 10 would follow this doctrine and to a lesser extent decreasing 14 to 10 and increasing 8 to 12. Breaking the equation down like with 10 + 4 + 8 is not technically incorrect but doesn't use the compensation strategy. I think the confusion comes from the fact the question isnt worded to only use compensation, considering thats all the teacher is looking for.
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u/Intrepid_Bobcat_2931 7d ago
I'll throw in my hate for choosing obscure buzzwords to be fancy and elevated.
"Compensation strategy" - sounds like a teacher that wanted to be an MBA
How about: "Going by round number strategy", or just "Round number approach"
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u/Weary-Enthusiasm-150 7d ago
Thanks for your response!! I get the strategy I just think the teacher is interpreting the question differently than me, I guess.
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u/Weary-Enthusiasm-150 5d ago
Update: teacher confirmed for me that she misinterpreted the question. Thanks everyone for the input!
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u/TristanTheRobloxian3 7d ago
its splitting up the numbers into "easier" numbers to work with. having a 10 in there si way easier than a 14 or a 10 + 4 + 8 for example.
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u/PlanetAcorn 7d ago edited 7d ago
I have not heard of this being named the compensation strategy, nor have I ever seen teachers attempt to teach "strategy" to 2nd graders before. Always have assumed that people figured this out some times later in life.
I assume the compensation strategy goes like this:
15 + 16
-> I remove 5 from the right side to make the left side whole to the tens place
20 + 11
-> then add these two which it easier because you only have to evaluate the tens place
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If thats the case, theres no way for 10 + 4 + 8 to be simplified without evaluating some addition before 10 + 12.
But then also, I think the teacher is way out of his/her league to be teaching this "compensation strategy" at all, just teach it normally with the standard carry and let the kids figure it out themselves. It also doesn't seem like the workbook is meant for this either.
Edit: My bad I looked the compensation strat up and it appears to be the other way. Where you add a number that pushes a number to the tens place and subtract it at the end.
15+16 -> 20+16 -> 36 - 5 -> 31
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u/angrypuggle 7d ago
I think the question is badly set. If the teacher wants kids to use the compensation method only they should not put an answer that is mathematically correct but uses a different method and would be marked wrong.
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u/wedontliveonce 6d ago
Why would using "compensation strategy" not apply when adding 3 numbers?
10 + 4 + 8 = 10 + 2 + 10 = 22
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u/MMmek 5d ago
1.I dont see any "compensation" in the problem. Probmplem said ALL THAT APPLY.
2. By definition
The compensation strategy is a mental math technique used to simplify addition by adjusting one number to a "friendly" number (such as a multiple of 10 or 100), and then adjusting the final sum in the opposite direction
Ejecting 4 from 10, then later 4 emits 2 to 8, you get 2 tens and 2.
It's compensation straight away. Teacher should get reeducated.
Why compensation had to be limited to 2 terms ?
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u/Opposite-Lettuce2074 5d ago
What is the compensation strategy. Why are we ignoring correct answers to abide by arbitrary rules that achieve the same thing that the simple math proves? If it’s equal, it’s equal, no matter the strategy.
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u/Ericskey 7d ago
I would have to look up what compensation strategy is. I imagine it is based on a preference to adding 10, so the last choice is on the way to the first two choices and can be looked at as providing an intermediate step
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u/CalculadoraAlicia-ap 5h ago
You are right: the question says "choose all that apply," so anything equal to 22 counts.
14 + 8 = 22.
Compensation is just moving the same amount from one number to the other, so the total does not change, to make a round 10:
-
Move 2 from 14 to 8: 14 - 2 = 12 and 8 + 2 = 10, so 12 + 10 = 22.
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Move 4 from 14 to 8: 14 - 4 = 10 and 8 + 4 = 12, so 10 + 12 = 22.
10 + 4 + 8 also equals 22, because it is just 14 split apart: 10 + 4 = 14, then 14 + 8 = 22. Or group the other way: 4 + 8 = 12, so 10 + 12 = 22. So it is the same idea in two steps, and it should be selected too. The one that does not work is 12 + 6 = 18.
A kid-friendly way to say it: if I take some away from one number, I have to give the same amount to the other number, or the total changes.
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u/falcon3268 7d ago
This is a 2nd grade math? They should just be learning basic math nothing complex until later one
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