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My six-year-old daughter enjoys addition but not subtraction. When we walk together, I like to give her some "mental mathematics" questions, such as "What is 13 plus 33" and she enjoys answering them. However, she always asks me to give her addition problems only. So she will refuse to answer the question "What is 21 minus 6".

I have discovered a "trick" that works for her: I will ask the question "What is 21 plus negative 6" and she will give me the answer 15. But still, she will not do 21 minus 6.

Is it normal for her to dislike subtraction while enjoying addition? Is there anything that I can/should do about it other than converting a subtraction problem to an addition problem?

Zuriel
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    I'd say don't worry about what's normal. If she likes to think about negative numbers at 6, she's doing great. (Go down to a more 6-year-old level if you want to get at subtraction, and see if she likes figuring out how far apart the ages of different cretures are: "saqual is 21 centrues old and taqual is 31 centuries old, how far apart are their ages?" BUt only if she's having fun!) – Sue VanHattum Apr 07 '22 at 02:07
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    If she's six years old, don't worry about it. The idea that all children at a certain age ought to be learning some specified thing (One size fits all!!!!) is stupid and dishonest. If she's understanding what you say she's understanding, then she's doing very well. – Michael Hardy Apr 07 '22 at 06:31
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    She must be an algebraist. She realizes the lack of associativity in subtraction makes leisurely discussion of subtractions a dangerously ambiguous practice. Like 6 minus 4 minus 2, is it zero or is it 2 ? In contrast, addition makes for good conversation, unburdened by the need to make some adhoc order of operations rule... – James S. Cook Apr 08 '22 at 05:21
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    @JamesS.Cook I think you meant zero or four. – J.G. Apr 09 '22 at 08:29
  • @SueVanHattum "saqual is 21 centrues old and taqual is 31 centuries old, how far apart are their ages?" - this is a more complicated exercise than 21-6, as these quals can be anywhere from 9 to 11 centuries apart unless you precisely define "old" and "apart". – Rusty Core Apr 10 '22 at 01:39
  • @J.G. Indeed, that is what I should have put there. Curses. Although, I guess the error supports the comment. – James S. Cook Apr 10 '22 at 02:16
  • Have you discussed that 21 minus 6 and 21 plus negative 6 are the same thing? Also has she covered subtraction in class yet? – Amy B Apr 10 '22 at 07:40
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    I’m voting to close this question because this seems like a question about adolescent psychology and not mathematics education – David Steinberg Apr 11 '22 at 20:42
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    As for your “trick” of asking her to add a negative number, have you asked her to explain how she gets the answer and what she is thinking of when she does? – Nick C Apr 11 '22 at 23:00
  • @DavidSteinberg - Note, the daughter is 6. Not 16. Or am I missing a pun? – Malady Apr 12 '22 at 01:26
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    @DavidSteinberg, how is this question not about math education? We have a parent teaching a kid mathematics and wondering if another approach should be adopted because the child refuses to do subtraction. The fact that it's also about child psychology does not mean it's not about math education. (I would argue that most questions about teaching are also about psychology!) – PersonX Apr 12 '22 at 18:43
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    @PersonX I agree that there are psychological aspects to teaching, but at some point the threshold of mathiness is so low, that it doesn't seem to matter any longer. I think this question would be better answered on a message board about *child psychology. – David Steinberg Apr 12 '22 at 22:38
  • I teach young kids and have indeed noticed that Substraction for some reason doesn't come as naturally to quite a few as does addition... – Ashish Shukla Apr 23 '22 at 07:22

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Since the learning proces begins with popping up more and more fingers (numbers) and especially when enhanced by helping and encouraging, it is kind of normal to me at least. Subtracting is a new strain and it does not add much of new abilities; it demands though more work\remembering. It might be an idea to bring this technique up when challenging emotions; then sometimes leveling them is the better way to cope with negative experiences. And there are games in which it makes sense in diminishing possibilities in order to get the upper hand

Kees de Vos
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    Generally speaking, answers here should be more than just gut opinion, and should be backed up by some kind of research or experience. Do you have any sources which support your assertion that "subtracting is a new strain and does not add much of new abilities"? Can you justify the statement that it "demands...more work/remembering"? – Xander Henderson Apr 11 '22 at 21:10
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    This question had no answers for 4 days, so I appreciate the attempt to help out by offering an answer. Thanks, Kees. – Sue VanHattum Apr 12 '22 at 19:47
  • For examining the effect of subtracting, try to do the alphabet backwards (what we haven't learned). Everyone will examine the "strain"and it does not add any new knowledge and why I would call it a strain. – Kees de Vos Apr 13 '22 at 11:48
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It's certainly normal for people's skill at addition to be much stronger than subtraction, and for the preference and comfort level to follow suit.

From a paper by Tom Macintyre and Ruth Forrester, "Teaching Mental Calculation - how successfully are strategies being learnt?", Edinburgh Centre for Mathematical Education (ECME), University of Edinburgh:

Addition tasks are clearly completed in a much more confident manner than the subtraction items, with over 80% of the study group with at most one error on the items. Subtraction items appear to have presented a much bigger challenge to the pupils, with over 50% having 3 or more of those questions wrong.

Daniel Willingham observes one possible reason why that's the case (from "Is It True That Some People Just Can't Do Math?", American Educator, Winter 2009-2010):

Addition and multiplication facts are easier to memorize because they are commutative; that is, 3 + 4 is the same as 4 + 3, and the same is true for 3 x 4 and 4 x 3. That is not the case for subtraction and division. Even well-educated adults from countries with excellent math education will sometimes calculate subtraction and division facts, rather than retrieve them from memory.

Daniel R. Collins
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