The best math classes I have attended had prepared note sheets. These were Calculus II and III. Each class would have multiple exercises where we would work out the problems and fill in the sheets. The problems were very relevant to the tests and quizzes. The notes were also graded. That was just one way to get students to engage more with the material and have some structured examples that they could study before tests.
That sounds like a good idea as well. Were these note sheets presenting problems analogous to the examples presented in class? Or were they identical to the examples given by the professor?
Alternatives: shoving the content into flashcards or into patchwork of hypertext documents (like private Wiki), instead of assemblying a textbook out of it.
Those are good alternatives. I like the flashcard idea better than the wiki idea; I steer students away from digital solutions whenever possible for various reasons. The main downside of the flashcards is that it becomes difficult to treat them hierarchically without introducing cataloging methods or something like a Zettelkasten system. If a student is already experienced with such methods, however, index cards would be a pretty cool alternative.
Hi why avoiding digital solutions? I use my tabled Samsung Ultra for reading/annotating the textbook and for doing all the exercises. All my notes and worksheets are clean and not messy, such as when I used the paper. I can erase erros and use simple coloring schemes and highlighting. Also all material is nicely organized in folder and/or labelled. The screen is huge so that I can put the textbook and the notes on each half of it. Writing with the digital pen is such a pleasure. I still use paper occasionally, if I have not the tablet with me or if I don't plan to keep the stuff I'm writing.
Hello, what’s your plan for the channel? Hoping more videos! This is the best mathematics channel on TH-cam as it focuses more on building the world of math for yourself in order to develop deep and thorough understanding. Thank you!
Thank you! I do have plans to continue making videos. I've got two more videos planned out; I just need to find time to record them. I teach full-time during the year and am writing a Ph.D. dissertation, so finding time to make videos can be a bit of a challenge--but I definitely plan to stick around. Thanks for your comment!
That's a good question. Doing problems is an excellent way to learn the skill aspect of math, but math is not merely a computational skill. There is also quite a bit of theoretical understanding one must have, and the best way to achieve that is through a combination of problem solving and note-taking. The point of the note-taking is to enable you to make connections between ideas and better retain the information you've studied--which in turn will enable you to make better connections. To put it another way, problem solving is a way of looking at the individual trees in the forest, but the reflection inherent in note-taking provides you with a broader perspective, ideally to see large sections of the forest.
The best math classes I have attended had prepared note sheets. These were Calculus II and III. Each class would have multiple exercises where we would work out the problems and fill in the sheets. The problems were very relevant to the tests and quizzes. The notes were also graded. That was just one way to get students to engage more with the material and have some structured examples that they could study before tests.
That sounds like a good idea as well. Were these note sheets presenting problems analogous to the examples presented in class? Or were they identical to the examples given by the professor?
Alternatives: shoving the content into flashcards or into patchwork of hypertext documents (like private Wiki), instead of assemblying a textbook out of it.
Those are good alternatives. I like the flashcard idea better than the wiki idea; I steer students away from digital solutions whenever possible for various reasons. The main downside of the flashcards is that it becomes difficult to treat them hierarchically without introducing cataloging methods or something like a Zettelkasten system. If a student is already experienced with such methods, however, index cards would be a pretty cool alternative.
Hi why avoiding digital solutions? I use my tabled Samsung Ultra for reading/annotating the textbook and for doing all the exercises. All my notes and worksheets are clean and not messy, such as when I used the paper. I can erase erros and use simple coloring schemes and highlighting. Also all material is nicely organized in folder and/or labelled.
The screen is huge so that I can put the textbook and the notes on each half of it. Writing with the digital pen is such a pleasure. I still use paper occasionally, if I have not the tablet with me or if I don't plan to keep the stuff I'm writing.
Hello, what’s your plan for the channel? Hoping more videos! This is the best mathematics channel on TH-cam as it focuses more on building the world of math for yourself in order to develop deep and thorough understanding. Thank you!
Thank you! I do have plans to continue making videos. I've got two more videos planned out; I just need to find time to record them. I teach full-time during the year and am writing a Ph.D. dissertation, so finding time to make videos can be a bit of a challenge--but I definitely plan to stick around. Thanks for your comment!
@@polymathclassical all the best 👍
Actually, this is brilliant.
Thank you! Glad you found it interesting!
The school doesn't given you manuals instructors editions
Why would you take notes? You do problems.
That's a good question. Doing problems is an excellent way to learn the skill aspect of math, but math is not merely a computational skill. There is also quite a bit of theoretical understanding one must have, and the best way to achieve that is through a combination of problem solving and note-taking. The point of the note-taking is to enable you to make connections between ideas and better retain the information you've studied--which in turn will enable you to make better connections. To put it another way, problem solving is a way of looking at the individual trees in the forest, but the reflection inherent in note-taking provides you with a broader perspective, ideally to see large sections of the forest.