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Comment by apwell23 | Hacker News Reader

OP described a specific type of practice to get good test grades using 'Anki cards' . Standardized tests test for grinding and dedication not expertise or 'getting good'.

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It depends entirely on the cards and what's done when a card is missed. If the cards are straight definitions then probably not the best way to "get good at math". But if the cards (you can do this with plugins) are things like generated problems using specific mathematical techniques (solve a system of linear equations, for instance) and after failing a card you can go back and study the material, then it's effective. You can also throw textbook problems into cards if you don't want to use a generator, but that's a lot more effort than most people are willing to put in. You don't even need to put in the solutions if you're willing to keep the book around. It does mean cards take longer than a few seconds, but it still has the effect of taking advantage of spaced repetition to develop mastery of a technique.

Thinking about how to learn is fascinating. A few short things that helped me:

Essentially we need to get fundamentals first.

Then apply the knowledge and get challenged (feedback loop) -> build a project, play in front of others, speak the language.

Improve - not by force, but by understanding (remembering something and understanding something are two different things).

Synthesise - learn about a topic in a different manner or try to find similar concepts in completely different context /

Use mentors to amplify the knowledge and get feedback quicker.

Immerse yourself in practicality (work in a field, live in a country etc.)

This is a great summary. Thank you!

I had great success using Anki cards during my undergrad to fully internalize important definitions (i.e. trig identities, etc.) for utilization within practice problems.

Sometimes, you just know a thing or don't, and for me, spaced repetition cards helped a ton with the static things you just have to memorize (or derive). Knowing definitions is important—you're absolutely right that it's just one piece of the puzzle though.

There is no (multiple choice) standardized testing in the Finnish school system and I cannot imagine passing the math tests based on rote learning. I have to assume she took the test somewhere else.

EDIT: The exams at the end of high school can be considered standardized tests, but they are taken at your own school, graded by your own teacher and only verified by the national test organisation. They are not multiple-choice tests.

> I cannot imagine passing the math tests based on rote learning.

why not. Its not exactly rote learning like a parrot. You just learn tricks and patterns in problems. Tests usually have a limited amount of patterns.

These are not tests generated from patterns. You may be asked e.g. to solve an applied problem you've never heard of or to sketch a proof to a given (simple) lemma you've never proved before.

OTOH, you are not supposed to solve every problem in the exam, so perhaps you can get the best grade even if you skip all the problems where there's no pattern to apply. In that case, that's a loop hole which the exam creators should plug.

> solve an applied problem you've never heard of or to sketch a proof to a given (simple) lemma you've never proved before

Can you link me to finnish high school question that is asking for 'sketch a proof to a given (simple) lemma you've never proved before '

I agree that this cannot be rote learnt .

I hear these problem types are not as common as they used to be, but here's some recent examples in this direction.

Fall 2023: "Prove that 2^12345678910 - 1 is divisible by 1023."

Spring 2022: "Using induction, show that the sum of the numbers on the line n of Pascal's triangle equals 2^n."

Here's the full exam from fall 2023: https://yle.fi/plus/abitreenit/2023/syksy/matematiikka_pitka...

I cannot seem to access that link outside finland.

That is indeed a tough proof to solve sight unseen. Any reason you say that students are seeing that question for the first time in the test. Seems like a famous questions, even chatgpt got the proof correctly .

I think the pressing question here is what the Anki cards contained w.r.t. these problems :-)

The high school curriculum and the text books are not focused on proofs or famous questions. Further, the goal of the exam is to find out your position in the normal distribution of your peers' math skills. You are not supposed to be able to beat everyone else by rote learning (so if you can do it, it's quite a hack!).

I don't think ChatGPT is a good comparison, because it has obviously memorized much more than a human could, and a test to poke its strengths and weaknesses would look different.

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