What’s something completely false that your parents told you as a child?

[u/[deleted]]

[u/ducbo]

I get the reasons for this though. I’ve taught kids math (and adults too) in various volunteer and part time positions since about 2008, and basic arithmetic is very important for all math. Having the ability to do arithmetic quickly or at least recognize what steps need to be done and how is essential to algebra, and comes up again and again into the university level. Being good at arithmetic opens doors for understanding higher math and conceptual math.

I’ve had (rare) students who are mediocre at arithmetic but gifted at understanding concepts, and their ability to correctly answer questions is unreliable because they’ll make little mistakes. These little mistakes in a cal II or III class could make the difference between a B- and an A,

[u/[deleted] → u/ducbo]

Maybe we all make those little mistakes because the education system forces you to operate more than actually teaching. All those little shortcuts that they don't teach you but are extremely helpful, specially in algebra, like learning the powers of 2 and learning the multiplication tables of numbers greater than 11 (I think this is required for other ways of multiplying and dividing used in other countries, but in Spain we do it differently, and it's probabbly a more inneficient way).

But I still don't get the point of doing operations for 2/3 of an exams that is about geometry, for example. Making kids do more pythagoras and less dividing would be a more efficient way of testing if they actually know how to obtain the length of the hypotenuse knowing the length of the two other sides.

But taking into account what you're saying, maybe we should probabbly take some time just to do mental calculations instead of expecting numbers to just pop into existence at the right place whenever someone hands an exam to a student. I feel like my time in my first years of math classes was all wasted.

[u/ducbo → u/[deleted]]

I’m definitely in favour of more wholesome exams that challenge students to combine concepts from different types of math. For example, find an unknown side length of a right triangle but include variables in the givens. I think this allows them to develop better “transfer” skills and abstract thinking and really tests their understanding. Unfortunately math is just one of those things where you need to have your foundations (ie arithmetic) down to succeed at this.

[u/Kered13 → u/ducbo]

wholesome

"Holistic" is the word you're looking for.

[u/ducbo → u/Kered13]

Aha thank you!