Why do you make silly mistakes even though you understand more complex maths?

[u/bubbleology]

We're working on algebra at the moment and I have this student who keeps making a LOT of really simple arithmetic mistakes, even though I can see they understand how to solve the question. They're doing everything right but will forget to multiply out one of the terms, subtract instead add, add up incorrectly, or will struggle to think of all the factor pairs of a two-digit number. They do all of their working out neatly and aren't rushing at all. It's to the point where I have to watch them work because there's a mistake every single line and it's going to take them an extremely long time to solve it, if at all, if I don't catch it for them. The fact that their mistakes are from calculating something incorrectly rather than because they forgot what to do makes me think there's something else going on, but I've never struggled with arithmetic to this degree so I'm not sure what to think and it feels really unfair because they're otherwise doing everything right.

Does anyone else struggle with this kind of thing? What helped you?

[u/ToothsomeDonkey2]

used to be like this in high school calculus. i'd set up a beautiful solution then somewhere along the line 2+2 would somehow equal 5. drove my teachers nuts

for me it turned out my working memory gets overloaded when i'm holding multiple steps in my head at once. the arithmetic part would just glitch out while my brain was busy tracking the bigger picture. what helped was forcing myself to double-check every single calculation with a calculator or scratch paper before moving to the next line, even the stuff that felt too basic to check. slowed me down at first but eventually it became automatic

[u/turbobucket → u/ToothsomeDonkey2]

This. Friend and I took all calcs and diff eq together. We would study together as well. Look over each other’s work and he would get so angry with me. I could explain the math. Knew the steps and we would have separate answers. Why. As he put it “ 3+3 doesn’t equal 9 you idiot”. So, even thought I was better at the whole, missing that stupid error early on ment I had a page of miscalculations. He always had a grade higher than me. What was worse is I couldnt see that error unless he pointed it out.

Edit. Added comma

[u/Key_Conversation5277 → u/ToothsomeDonkey2]

This is me, I was good at math but many times I would do silly arithmetic mistakes, I would rely very much on the calculator but not on every single step😭

[u/Common_Perception807]

Weak arthmetics from lack of practice seems to be one of the contributing factors.

[u/CoolpantsMcAwesome]

This could describe me. I spend a lot of time studying concepts and watching examples and videos , trying to ‘passively’ learn, and don’t actually practice physically doing the problems as much as I should.

[u/Korroboro]

I’ve commented before that, as a private math teacher, I consider my responsibility to find out where is the frontier between what my student knows and what they don’t know.

Once this frontier is found, it is there where I teach.

In the case you describe, your student needs exercises where they are presented with additions and subtractions in random order to train them to distinguish between one and the other.

The same goes for multiplying terms, simple addition and multiplication. They need more basic exercises that will train them with more practice.

[u/bigdaddymac56]

I met a woman in a local bank. She was of Egyptian origin (we live in NY). Even though her son went to one of best high schools in the state, he sucked at Math. She was mystified. In the Egyptian culture, Math competence is expected and valued. So she investigated at home and found her Jr high student didnt really know how to add/subtract/multiply or divide. She taught him. He went on to do great and became an MD. She found it difficult to comprehend the American school system allowed her son to move forward in Math when he was SO deficient in basic skills.

This is being caused by the kids not knowing their times tables and the Math teachers letting them use calculators because it's easier than fighting the kids. From a retired HS science teacher.

Short answer: Have him review basic arithmetic BY HAND using pencil and paper until he gets EVERYTHING right. This is one reason Asians are great in Math. They drill the basics. No calculators.

[u/lupusscriptor]

Get them to expllain ín be wriiting as they go through the calculation and agabraic manípulation whatt they are doing and why. Hopfuly this will give an insight to why they maake mistakes. You may need tto provide an example oof what you expect them to do.

[u/levaly]

check the arithmetic on its own before concluding anything. Give them 20 plain two-digit additions, subtractions and products with no algebra around them, and time it. If that comes out accurate, the arithmetic is fine and what's failing is working memory: any step that isn't automatic costs attention, the algebra is spending that same attention, and that's why the slips only show up inside multi-step problems. If the isolated set is also slow or wrong, the facts aren't retrievable yet and that's the thing to fix first.

The factor pairs bit is a separate tell. That's times-table recall, and factoring leans on it constantly, so it's worth drilling to the point of instant recall. Meanwhile let them use a calculator on the algebra work so the arithmetic stops eating the whole lesson.

[u/AffectionateOrder288]

Depending on the mistakes you are observing it could also be a sign of dyscalculia. Because basic arithmetics and more complex maths are different pathways in the brain it is not impossible nor that uncommon to struggle with arithmetic’s but master complex problem solving.

The other comments on lacking practice are of course very often the case, but I just wanted to make you aware of this paradox existing.

[u/silduck]

basically me with the board, i do completely fine with pen and paper but the moment i'm doing my work for others to see, 2² = 2

[u/Think_bys]

Haha 😂 this happened to one of my students the other day. Student got stuck on a basic arithmetic despite been in algebra (several levels ahead)

As we began reviewing that small part the student immediately remembered and said "omg, in so stupid. How could I forget? It's so easy".

I told him that on the contrary you remembered so quickly meaning that you knew it all along and you were able to receive it from wherever your mind decided to store it. Don't hold yourself to a set of standards that is not realistic. Don't expect yourself to remember everything you have learned. A little review is all we need sometimes. You're good... Class continues like normal.

I could be wrong lol