Evidence is building that High intensity interval training, e.g. Tabata sprints, is more effective at physical conditioning than low intensity endurance techniques. In terms of weightlifting, “low-rep, high-weight” workouts seem to be better than “high rep, low-weight” workouts.*
I wonder if something analogous is true for mental training. E.g., will you improve mathematical ability faster by grinding through a bunch of relatively easy problems, or by spending a shorter amount of time mentally exhausting yourself on problems that push your limits? Anyone know of any solid evidence?
My experience seems to reflect the latter being more effective. I spent a lot of time my last year or two of undergrad grinding through a bunch of relatively easy calculus problems in order to finish up my degrees in a reasonable amount of time. In my second year of grad school, I took a measure theoretic probability & statistics sequence that was the opposite—a small number of problems, but each one was a struggle. It was rare that I could finish more than 25% of the problems the first time I attempted them. Unsurprisingly, I felt like I improved much more in mathematical ability after taking that sequence than I improved after my undergrad calculus grind. The effect seems stronger than this though—I felt like the measure theory sequence improved my ability to do difficult yet standard calculus problems more than the calculus grind ever did even though I wasn’t actually doing those types of problems during the measure theory sequence. The effect was probably mediated through improving my general mathematical/logical reasoning abilities. Now these are just my impressions—untrustworthy for the whole gamut of reasons—plus even if we take them at face value there’s a ton of confounders. Nonetheless, it’s Bayesian evidence. Anyone else have a similar experience?
* I’m not an expert here and could very easily be wrong. If you have evidence one way or the other to share, please allow me (and others) to update.
I remember an unconference now from the July minicamp on deliberate practice now. IIRC the speaker suggested something similar to beoShaffer’s comment.
I forgot to mention that I was basing my info on a keynote speaker that I suspect may have done the minicamp unconference. Was the speaker a female psychology professor who made numerous movie references.
From what I understand deliberate practice would generally favor the small number of hard problems, especially for building overall mathematical competence/your ability to tackle hard problems. However, doing the easy problems in a challenging way, like trying to do them as fast as possible while still maintaining a high standard of accuracy, would also lead to improvement, particularly for you ability to do that specific type of problem quickly and accurately.
I wonder if something analogous is true for mental training. E.g., will you improve mathematical ability faster by grinding through a bunch of relatively easy problems, or by spending a shorter amount of time mentally exhausting yourself on problems that push your limits? Anyone know of any solid evidence?
What’s the basis behind HIIT? If I remember correctly, it’s that the high intensity activity kicks your metabolism up a notch, continuing to burn calories / seem active for a significant period after the training is officially complete. Is there a similar mechanism for learning and memory?
There’s solid evidence that spaced repetition- like in the Saxon method- is demonstrably better than doing something once and moving on with little review. In general, it seems like practice is a very important part of mathematics ability.
There are also time-based effects for learning things before going to sleep- but I’m not sure how practical using those would be.
Evidence is building that High intensity interval training, e.g. Tabata sprints, is more effective at physical conditioning than low intensity endurance techniques.
“physical conditioning” is a very general term. For instance: Is evidence building that Tabata sprints are more effective for preparing for a 100k ultra-marathon?
Of course competitive runners do some sort of interval training, and—if information on The Internet (reddit) is to be believed—runners do not train the full distance. And if basic health and looks is your goal, running is probably not the most time-efficient (of even effective) way for doing it. But this “endurance is all wrong” meme is overshooting it a bit...
Evidence is building that High intensity interval training, e.g. Tabata sprints, is more effective at physical conditioning than low intensity endurance techniques. In terms of weightlifting, “low-rep, high-weight” workouts seem to be better than “high rep, low-weight” workouts.*
I wonder if something analogous is true for mental training. E.g., will you improve mathematical ability faster by grinding through a bunch of relatively easy problems, or by spending a shorter amount of time mentally exhausting yourself on problems that push your limits? Anyone know of any solid evidence?
My experience seems to reflect the latter being more effective. I spent a lot of time my last year or two of undergrad grinding through a bunch of relatively easy calculus problems in order to finish up my degrees in a reasonable amount of time. In my second year of grad school, I took a measure theoretic probability & statistics sequence that was the opposite—a small number of problems, but each one was a struggle. It was rare that I could finish more than 25% of the problems the first time I attempted them. Unsurprisingly, I felt like I improved much more in mathematical ability after taking that sequence than I improved after my undergrad calculus grind. The effect seems stronger than this though—I felt like the measure theory sequence improved my ability to do difficult yet standard calculus problems more than the calculus grind ever did even though I wasn’t actually doing those types of problems during the measure theory sequence. The effect was probably mediated through improving my general mathematical/logical reasoning abilities. Now these are just my impressions—untrustworthy for the whole gamut of reasons—plus even if we take them at face value there’s a ton of confounders. Nonetheless, it’s Bayesian evidence. Anyone else have a similar experience?
* I’m not an expert here and could very easily be wrong. If you have evidence one way or the other to share, please allow me (and others) to update.
How about ‘deliberate practice’? I’m fairly sure that it implies that you’re working on a problem that challenges you and pushes your limits.
I remember an unconference now from the July minicamp on deliberate practice now. IIRC the speaker suggested something similar to beoShaffer’s comment.
I forgot to mention that I was basing my info on a keynote speaker that I suspect may have done the minicamp unconference. Was the speaker a female psychology professor who made numerous movie references.
Nope, it was a male. I think it was Mark E, known around LW as Mark E
(I don’t recall how to say/spell his last name, I just remember it being somewhat complicated and that it’s also part of his LW name)
Nevermind then.
From what I understand deliberate practice would generally favor the small number of hard problems, especially for building overall mathematical competence/your ability to tackle hard problems. However, doing the easy problems in a challenging way, like trying to do them as fast as possible while still maintaining a high standard of accuracy, would also lead to improvement, particularly for you ability to do that specific type of problem quickly and accurately.
What’s the basis behind HIIT? If I remember correctly, it’s that the high intensity activity kicks your metabolism up a notch, continuing to burn calories / seem active for a significant period after the training is officially complete. Is there a similar mechanism for learning and memory?
There’s solid evidence that spaced repetition- like in the Saxon method- is demonstrably better than doing something once and moving on with little review. In general, it seems like practice is a very important part of mathematics ability.
There are also time-based effects for learning things before going to sleep- but I’m not sure how practical using those would be.
Off-Topic Nit-Picking:
“physical conditioning” is a very general term. For instance: Is evidence building that Tabata sprints are more effective for preparing for a 100k ultra-marathon?
Of course competitive runners do some sort of interval training, and—if information on The Internet (reddit) is to be believed—runners do not train the full distance. And if basic health and looks is your goal, running is probably not the most time-efficient (of even effective) way for doing it. But this “endurance is all wrong” meme is overshooting it a bit...