How to reduce tilting when going over drills?

Tilt originated as a poker term for a state of mental or emotional confusion or frustration in which a player adopts a less than optimal strategy, usually resulting in the player becoming over-aggressive. Tilting is closely associated with another poker term, "steam". - wikipedia

I encounter a similar pattern when I solve 'difficult' math problems in a drill (a practice sheet with a lot of questions ), once I get a few and struggle with a few that I can't solve a question after setting up the basic idea for it/ Can't get up the set up at all, then I got into this tilt mode where I do worse and worse skipping questions through the drill.

So, how do we reduce the amount of 'stress' / 'mental load' that comes when we solve math problems?

One strategy that I adopted early on is going for a few questions instead of a large number, this helped me develop my mathematics abilities a lot , but I feel it is mostly useless when I try to do a large number of problems similar to those we receive in standardized tests.

• If by a drill you mean a test, I have had success with skipping to the end of the test and working backwards if I run into several in the front that are too difficult at first glance. If you are having problems at both ends, it is hard to avoid the conclusion that you did not study well enough... Mar 9, 2021 at 19:38
• Drills mean practice sheets with a lot of questions @Steve Mar 9, 2021 at 20:58

The American comedian Henny Youngman had this joke:

The patient says, "Doctor, it hurts when I do this."

The doctor says, "Then don't do that!”

Unfortunately, some people have the incorrect idea that mathematics is about "solving problems", and lots of them, but it's not. The truth is that math since Euclid is about establishing and understanding basic relationships through carefully-defined concepts, theorems, and proofs.

The exercises are just a way to ascertain whether the student understands the principles instead of cheating their way through the material. If you emphasize a giant mass of exercises to the detriment of the concepts, then you've got the tail wagging the dog. Unfortunately, as societies try to present a facade that more of their citizens understand math, science, and engineering, this kabuki-theater becomes more prevalent, and the robotic (i.e., mechanically computable) exercise lists grow, absurdly, without bound.

Older textbooks from around a century ago had much shorter exercise lists, carefully curated, to highlight the essential discoveries in the presentations. Books now have longer exercise lists mostly to try throw chaff at cheaters, but it gives a bad impression about where the emphasis should be.

If you understand the essential concepts, then you don't need to do endless drill exercises. You will know what's at the heart of them all.

One strategy that I adopted early on is going for a few questions instead of a large number, this helped me develop my mathematics abilities a lot

However, I suspect that they've been given a confusing message by their country's high-stakes and overly-intensive testing regime (again, a response to widespread cheating). Unfortunately there's nothing we as students or instructors can do to solve that. But we can share confidence that if we understand the essential principles, then any standardized-format problems will fall before us. The power of that kind of abstraction is, after all, the whole point of mathematics.

A few things that I find help.

1. Make sure you have some easy drill problems at the start of a homework session. Most books are actually well set up for this approach. Having I, II, and III problems (or A, B, C). The first category are plug and chug. Last category require a little bit of derivation or more detailed word problems. Intermediate are usually multi-step calculations. I find that doing some of the "easy" problems sort of gets you in the zone.

2. Make sure you get through the whole session. Even if you skip some, come back and do all. You'll often find that your subconscious has done some work on the problems while moved on.

3. Go back to the text, if you are just missing a lot. REad the section. Work the example problems. (You should be doing this anyways, before drill!)

4. If you have to peak at answer or hint or if you worked it and got it wrong, you need to REPEAT the whole problem. Actually rework all the cheated or missed problems as a "section" after the end of your drill. Even if you had a "dumb mistake" or say "got it" after checking. You still have to rework it. And in your mind treat it as a "fresh problem". This sounds hokey, but it gets you more into a slight discovery mode. OVerall, at the end of the day, you need to treat this stuff as a bit more like gymnastics routines or music performance. You need to acquire "automaticity" with basic courses like calculus or linear algebra.

5. Avoid music or any distractions (e.g. net). It can be a little arduously monastic. But you will toughen up the willpower muscles over time. Like lifting weights or running cross country. You're not just working on the work, you're working on your CAPACITY for work. "How do you walk around the world?" "One step at a time, but your stride gets better as you walk."

P.S. It's a little hard to advise when so general. Not clear what course, your ability, motivation, etc. Since this is a human behavior problem, not a math problem, there is no precise answer. And a single person might try different approaches. Or different people might have different things that click for them. And...please take this as "fellow sinner" advice. Not as holier than thou.