How to succeed as a math student // A conversation with Kyle Broder // Part I

[@ishansharma6890]

Kyle was not only my math tutor but also coach/mentor when in year 11/12. Amazing, inspiring and genuine person. Great to see this Kyle.

[@wwbbcg01]

Thank you for the emphasis on the importance of "procedural fluency"! Many conversations about math education lately have been about how we "waste time" teaching computation, when the reality is it is just as important as conceptual understanding. Often times that repetition is what sparks the conceptual understanding much later.

[@KyleBroder]

It was a pleasure meeting you Trefor, I hope that this is one of many more conversations to come!

[@DrTrefor]

Likewise!!

[@playitback-os7mh]

In my opinion, if you try something and it works instantaneously, you probably already had the skill to do it. Thus, you develop merely a bit. However, if you struggle for a long time until you finally find the answer, this is a huge achievment and development. Thus, if you do not fail at all you will not develop much.

[@DrTrefor]

I really like this point. We associate struggle with failing and negative emotions so much, but really it is the source for so much growth.

[@johncrwarner]

I have found that the impetus that works best for me in learning learning in general is where there is a story a narrative that connects it to other things and being told that story and learning that story even though it turns out not to be the whole story was what motivated learning and then the self checking (doing the exercises and practice drills were for a purpose) As a mathematics teacher in the equivalent of a high school (it was a school for 13 - 18 year olds in Britain) I would hear from students "I am no good at mathematics" at 13 years old. The school used a problem-solving approach so trigonometry involved making a primitive plumb line and angle measure starting with a tree outside and measuring angles and working out using scale diagrams noticing that different scales worked then realising that the ratios of the sides had interesting properties. My students often enjoyed their classes and more importantly were able to give things a go building formalism as we went.

[@I0MSammy]

I absolutely loved that statement about learning row reductions to build character! Yes, in some circumstances there may be an easier solution but we should try to exercise the mind in all ways just like the body. The greatest athletes do not focus on how much they can lift in the gym, but how they exert control over their muscles (concentric/eccentric), just like we should be trying to do with our minds. It is like we are developing a "mathematical mobility" and it's only in this manner that we can learn to understand mathematics at a deeper level.

[@fbkintanar]

6:00 "what you want to cultivate is an understanding of the mountain itself". I think this is true at multiple scales: learning a subject or field, learning a subfield or research program, learning a group of definitions (and their equivalent formulations / alternative vocabulary, immediate consequences, big theorems and how to navigate to them), really learning and internalizing a particular proof to an important theorem. I struggle with how to do this systematically, and Kyle's suggestions about using Anki flashcards is intriguing. Like you want to master a proof because it might show up in your comprehensives. One particular proof of it is a pathway, a choice of landmarks and lemmas that guide your way to the end in sight. You might start by remembering that pathway and landmarks, but eventually you want to know the mountainside well enough that you can make your way to the goal by a different pathway of your own devising, which is dress rehearsal for applying the theorem or its lemmas or proof techniques to related problems or even in a completely different (sub)field. I'm trying to imagine what flashcards might be useful to make digesting and internalizing this material over weeks and years more systematic. Start with the lemmas, and remember how they were used? Then throw away old cards and replace them with your own discoveries about alternative lemmas and pathways? Give just enough details of a solved problem, so that you still have to think to reconstruct the full solution. Then work on nearby unsolved problems, and figure out what the differences are.

[@sleve_mcdichael]

I really like that mountain analogy! Very inspiring (as someone who often goes wandering down a 'wrong' path).

[@axisepsilon514]

For some reason, this reminds me of P vs NP. It's easy to verify whether u understood what u are learning right now but it's always hard to learn new concepts as in it will take some time to actually understand what you are learning. We live in a society where we are always pressured to get through more contents and learn more in such short period of time. However, it is more important to actually take some time and explore and gain new insight/intuition. Also I'm taking linear algebra and I 100 percent agree. Computation is very very important. I wasn't able to understand what null rank were until I actually worked through the computation which also helped me understand how to prove different theorems. By computing, I was actually able to gain the intuition behind those core concepts.

[@ronitdutta5499]

Love your profile pic

[@GoatzAreEpic]

What an amazing video! I loved to see how important mental models are for truly understanding some areas

[@EADgbeist]

"Procedural fluency"... I'm stealin' that. Thanks guys this was/is an excellent conversation.

[@DrTrefor]

Ha I stole this from someone else to pass it on:D

[@adolfocarrillo248]

Bright future for Good math workers, that's for sure, the future is on the math workers!!!

[@SAAARC]

i appreciate this talk

[@karennelson7461]

Such a rich conversation! I would love to see you write a book expounding on some of these ideas.

[@jefferybenzos5879]

Thanks for the new channel recommendation!

[@DrTrefor]

Hope you enjoy, he does some awesome stuff:)

[@kylemunsami6039]

This is so informative! Big thumbs up to both of you. It's extremely inspiring to many during these crazy times.

[@DrTrefor]

Thank you, glad it was interesting:)

[@smartbox6592]

Succeeding and having A grades in Maths are very subjective. Categorically some people have Maths ability as early as 6 years old, while others at 16 years old or late comer. This group can pass their Maths exam even they sleep in class, while others still failed even 100% listening in class. We cannot deny the fact that Maths seems like paranormal for some people due to the perception of their parents or siblings or relatives. It's time for the educationist to develop learning Maths as happy as possible since kindergarten.

[@silversky216]

Kyle looks like Grant Sanderson(3 blue 1 brown) with a little beard.

[@Ash-bc8vw]

en.wikipedia.org/wiki/William_Thurston Will Thurston more information on him on this wiki link