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Polymath Classical
Приєднався 20 чер 2014
Hi, I'm Daniel, a teacher and independent curriculum writer. I teach, make videos, and write resources for teachers, parents, and students pursuing education rooted in goodness, truth, and beauty.
Math textbooks make it hard to take notes
Here's how to get around one of the major drawbacks of using a math textbook. (Sorry for all the audio pops. Bad mic placement. Oops.)
In the classes I offer through Polymath, I avoid textbooks as much as possible for the reasons I list in the video. However, I also teach at Memoria Academy where, like most, we use standard math textbooks. So, while I prefer teaching without textbooks, I'm also interested in sharing effective ways to use them.
Classical Math One guidebook - polymathclassical.com/classical-math-one/
Diophantine Algebra guidebook - polymathclassical.com/curriculum-diophantine-algebra/
Resources, classes, and curricula on my website: polymathclassical.com
I'm also on Odysee!
odysee.com/@pct:2
00:00 Why it's hard to take notes
00:50 Answer this important question
03:58 List key concepts
05:22 Identify & copy memory work
06:40 Final thoughts & book plugs
In the classes I offer through Polymath, I avoid textbooks as much as possible for the reasons I list in the video. However, I also teach at Memoria Academy where, like most, we use standard math textbooks. So, while I prefer teaching without textbooks, I'm also interested in sharing effective ways to use them.
Classical Math One guidebook - polymathclassical.com/classical-math-one/
Diophantine Algebra guidebook - polymathclassical.com/curriculum-diophantine-algebra/
Resources, classes, and curricula on my website: polymathclassical.com
I'm also on Odysee!
odysee.com/@pct:2
00:00 Why it's hard to take notes
00:50 Answer this important question
03:58 List key concepts
05:22 Identify & copy memory work
06:40 Final thoughts & book plugs
Переглядів: 1 197
Відео
Does teaching math classically discourage creativity? and other questions
Переглядів 17411 місяців тому
Special thanks to @KristynSartin for a great question. Classical Math One curriculum- polymathclassical.com/classical-math-one/ Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2 00:00 Introduction 00:49 Question 1a 02:52 Question 1b 10:11 Question 2
Meaning in Math
Переглядів 200Рік тому
A plenary talk I gave on 2 Aug 2023 at The Academy of Classical Christian Studies in Oklahoma City. I recorded the talk on my phone, so I apologize for the bad audio. Time stamps below. See my website for curricula, classes, and resources: polymathclassical.com Memoria Academy: www.memoriaacademy.com/ 00:00 - Introduction 01:38 - Why math seems meaningless 07:39 - Bad assumptions 10:02 - Why ma...
How to think like a mathematician
Переглядів 356Рік тому
Part 2 of my talk: ua-cam.com/video/uK16iTTHI3o/v-deo.html If you liked this video, check out my video "What is classical mathematics?": ua-cam.com/video/bhTvt7bJxf4/v-deo.html Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2
Instantly be a Better Math Teacher by Doing Two Things
Переглядів 223Рік тому
If you liked this video, check out my video "Why You Should Learn Math You'll Never Use": ua-cam.com/video/I-pS2X-ocz4/v-deo.html Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2
How to draw a circle with triangles | Exploring the Pythagorean Theorem
Переглядів 330Рік тому
Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2
How a Latin Translation Trick Can Help You Solve Math Problems | Roger Ascham's The Scholemaster
Переглядів 643Рік тому
Ascham also wrote a book on the art of archery, which is pretty cool. Why math should be taught more like Latin: ua-cam.com/video/bhTvt7bJxf4/v-deo.html Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2 Stock Footage by Mikhail Nilov www.pexels.com/@mikhail-nilov/ Tima Miroshnichenk www.pexels.com/@tima-miroshnichenko/ Yan Krukov www.pe...
2 Notetaking Techniques That Will Forever Change How You Read
Переглядів 6782 роки тому
As a Ph.D. candidate and independent curriculum developer, I do a lot of reading and writing, and these are two fantastic techniques I use daily. If you found this video helpful, please consider subscribing and check out my website at polymathclassical.com. Timestamps 0:00 - Introduction 0:39 - 3 Levels of Focus 1:56 - 2 Types of Notetaking 2:06 - Notes/Reading for understanding 4:36 - Notes/Re...
Why You Should Learn Math You'll Never Use
Переглядів 1,2 тис.2 роки тому
This is something like an apology for mathematics; we are often so focused on math's utility that we miss everything else. Resources, classes, and curricula on my website: polymathclassical.com I'm also on Odysee! odysee.com/@pct:2
Was your education inhumane? Let's rethink motivation
Переглядів 2482 роки тому
Resources, classes, and curricula on my website: polymathclassical.com Timestamps 00:00 Why motives matter 01:07 Bad motives are dehumanizing 03:35 Rethinking motivation 04:51 What this means 07:34 Goals of Humane Education 09:43 Conclusion I'm also on Odysee! odysee.com/@pct:2 Thumbnail photo by Lina Kivaka: www.pexels.com/photo/the-radcliffe-camera-building-of-oxford-university-england-5624130/
Why students should write their own textbooks
Переглядів 2,8 тис.2 роки тому
Sorry about the bad lighting. I shot this on a hot day while some storms were brewing, and didn't get enough light through my windows. More resources at polymathclassical.com Summer seminars: polymathclassical.com/summer_seminars/ I'm also on Odysee! odysee.com/@pct:2
6 Ways to Ruin Math
Переглядів 7472 роки тому
I'm sure there are more ways to ruin a subject like math, but here's 6 that I'm particularly wary of. More resources at polymathclassical.com. I'm also on Odysee! odysee.com/@pct:2
How I teach geometry using Euclid
Переглядів 2,7 тис.2 роки тому
Classical Math One: polymathclassical.com/classical-math-one/ Euclid for Parents: polymathclassical.com/summer_seminars/ The geometry software I use: car.rene-grothmann.de Timestamps 00:00 Introduction & Outline 00:50 Structuring Learning 04:55 Week 1 - Introducing Euclid 14:20 Week 2 - Propositions & Constructions 25:10 Context & Narrative I'm also on Odysee! odysee.com/@pct:2
What is classical mathematics?
Переглядів 10 тис.2 роки тому
Teaching math classically involves more than using the Socratic method. I promise that there's a reason why I spend so much time talking about Latin and Literature. See polymathclassical.com for more classical education resources. Timestamps 00:00 Introduction & Definitions 02:40 Historical Overview 13:48 Classical Mathematics 17:55 Conclusions I'm also on Odysee! odysee.com/@pct:2
Instantly subscribed and looking at other videos! I am currently putting our homeschool together and before doing so, i am digging into the "Why's", why we are learning it. Because if I can't find a solid good reason I can't convince my kids to learn it! You sir, hit the nail on the head. I also love how you bring up the idea of Teaching geometry before algebra. I can't wait to listen to more of your videos honestly!
It is not as easy as it is presented. If we read "classics" we cannot touch modern math organically. There is no third option you either choose the modern language or the old one. You cannot mix those without breaking one of them. I am talking about current situation, not the impossibility.
Why is it that these pseudointellectuals who are the farthest thing from being mathematicians love to declare such authoritarian stances on mathematics?
Your point of view Is precious: I work as a Maths teacher in Italian High schools and I have been fighting against this "un-classic" way of teaching: Maths Is sadly and boringly presented as a trickbag of formulae for solving excercises; there Is nor historical/cultural context neither rigorous theoretical foundation; solving "scholastic" excercises is the final end . This way of teaching has been producing very bad results: lhigh-school graduated students, when starting Maths, Physics, Engineering courses, will struggle since the suffer their uncapability of managing the complex theoretical structure of the subject. Unfortunately, such "un-classic" way of teaching in Italy has been infamously exported also to Literature: now students rarely read full Authors' milestone texts...
Boring and rambling introduction ...... I switched off after 5 minutes without knowing what he was trying to explain
It's physically impossible to read Cardano. It's not written in language fit for today's math
Good effort, we must create examples.
You must be my twin -- Blackwing 602s and a slide rule (is that a K&E 4081?)
Epic recovery at 0:53! Great insights👍🏼
Great video, but one question; are those classical treatises still in print?
Mathematics does not work like that, it is impossible to learn calculus by reading the principia
This!
bother giving an argument?
Really wonderful video. Excellent job, thanks!
I am not so sure this approach would work very well in public schools, only in private schools with highly selective admissions criteria and highly trained and educated teachers. So 99 percent of American children will not and cannot receive it. They are simply not ready or able to begin with. Not to mention the consensus against "Eurocentric" learning based on the work of "Dead White European Males" because of the radically different demographics of the country. Nowadays the overwhelming trend is toward "multiculturalism", "diversity," "equity", and "decolonization" of the curriculum. Even many expensive private schools are going in this direction. And to top it off, the classroom of today is dominated by kids who have their minds (and eyes) focussed on what is on their cellphones, or literally have buds in their ears, or head phones over their ears, listening to their favorite music. I suppose the speaker has never witnessed or heard of this happening in schools, but it does. And, btw, there are still beatings taking place in schools. It is just the teachers and staff members who are receving the beatings. All of this is to say that the speaker has the best of intentions, quite noble actually, but he does not seem grounded in, well, what is happening on the ground. But more power to him, resisting the forces of social and cultural dissolution and chaos. I wish him well.
im not a fan of this approach, learn maths rigorously yeah, but historically? we're better at maths now than we were like noone should learn Galois theory as Galois wrote it. The modern treatments are far superior in generality and application to actual maths
Those are some big words for him. I really doubt his knowledge of mathematics transcends beyond high school calculus.
No maths, move on. This is a waste of time
Utter poppycock. Does this guy know any math? Has he ever taught anything? Aside from badgering people who do and who have? One great thing about "math" is that it becomes progressively clearer what it's actually about. That's why it makes literally no sense to go back looking for some lost essence.
657 subscribers. That is as it should be.
Ooh, that's a burn. Total KO. Rapier-like. Gotcha. 645 more than you I notice. Although it's not really a fair comparison, since you haven't made any videos and tried to find an audience for them.
You mistake, @@Ozymandi_as , the second comment I made, as the only one. The statement to which you reply followed the discussion of specific shortcomings which I consider to be egregious. "It is just false to maintain that, since we speak English, what happened in 16th-century England has had the decisive effect on U.S. education. It is false because our educational system is primarily modeled on 19th-century German education. From Kinder-garten through the research university, our educational system of the period following the Civil War (the one in the United states, not the one in England) was shaped by educational authorities who consciously modeled, with variations, what the Germans were doing. " Next, the entire claim that classical education was reformed by focussing on Latin in 16th-century England is ridiculous. ALL European education was based on Latin, going back to the Roman Empire. " The Bible was in Latin. Church schools were the only schools. " Man, this whole video stinks. " When the Italian Renaissance revivified Platonism, intellectuals across Europe engaged more seriously in mathematics, since Plato taught that the divine was approached by means of mathematics -- a doctrine articulated eloquently by Galileo. Nothing to do with English educational reform. " Finally, the most ridiculous aspect of this hopeless, clueless video is the failure to understand that mathematics is involved in SOLVING PROBLEMS. If you can solve a set of challenging problems well, you're a trained mathematician. Sigh."
It is just false to maintain that, since we speak English, what happened in 16th-century England has had the decisive effect on U.S. education. It is false because our educational system is primarily modeled on 19th-century German education. From Kinder-garten through the research university, our educational system of the period following the Civil War (the one in the United states, not the one in England) was shaped by educational authorities who consciously modeled, with variations, what the Germans were doing. Next, the entire claim that classical education was reformed by focussing on Latin in 16th-century England is ridiculous. ALL European education was based on Latin, going back to the Roman Empire. The Bible was in Latin. Church schools were the only schools. Man, this whole video stinks. When the Italian Renaissance revivified Platonism, intellectuals across Europe engaged more seriously in mathematics, since Plato taught that the divine was approached by means of mathematics -- a doctrine articulated eloquently by Galileo. Nothing to do with English educational reform. Finally, the most ridiculous aspect of this hopeless, clueless video is the failure to understand that mathematics is involved in SOLVING PROBLEMS. If you can solve a set of challenging problems well, you're a trained mathematician. Sigh.
Mathematics as a field underwent a revolution in the late 19th century, and the material from before around 1880 is completely trivial compared to what came later. While it is important to read the historical material as you suggest, it is very important to do so only after learning 20th century methods, because they are so much more powerful than the earlier methods. For example, Euclid's approach to the Pythagorean theorem is relatively dated, although it needs to be learned. It is important to learn the modern formulations of the theorem first, and then examine the classics. This is difficult to do. Also, your emphasis on the classical literature is not good, it is a type of traditionalism, which undercuts progress.
Disagree. Learning history accelerates insight into the current.
@@ace6285 In the case of mathematics, it's the opposite.
@@ace6285 The original comment is spot on.
Please do a quick TLDR of what the video is going to be about. You may not realize this, but there are a billion videos on youtube and not a lot of time, so if you do get suggested by the algorithm, please don't expect people to stick around for a detailed treatment of things you are passionate about. I mean 14 minuts to get to what classical maths is, in a video that is titled "What is classical mathematics" ...
I was hoping to find a personal way of reviewing my self in geometry... But this was how we were taught geometry... So, goodbye... I'm not even hoping to be a teacher... Education is not for me... I am for math. I am for engineering. Not education... Because I finished a bachelor's degree in engineering, not education.
😂😂😂
@@rucellegarciano4105I promise you, no one cares.
Dude, you sound like a psychologist!(it's not a compliment!)
I love this! Looking back, it wasn’t until I got to grad school that I started learning math in a way similar to this classical approach you mentioned. I wonder how much more deeply I could understand things had I started learning this way sooner.
The only aspect I'll disagree with is that notion that it's completely independent. Good video regardless!
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.
Sounds too much like an ignorant child pretending to know something. Disliking and moving on.
Fabulous video!! So happy I found your channel!
These are pretty good tips. Thanks!
in particular, trig functions are key to understanding physics. they are beautiful doors to the beauty of physics.
Well said Daniel. To carry on with the idea of engagement I also use my notes to agree or disagree with the author, why an approach is brilliant or silly, and general free flowing thoughts on the topic. It somewhat ties back with your video on writing your own textbook but I'm just modifying the given text/lesson with my reactions to it. (+1 for the Blackwing Box.)
Thank you! Also, glad that you appreciate my taste in pencils. They're expensive, but as they're "tools of the trade", they're easy to justify.
I was educated at a Jesuit School. I had five years of Latin and three years of ancient Greek. I also have a doctorate in Mathematics with a 30 year academic and industrial career in my field. While I enjoyed learning classical languages, they had NOTHING to do with learning math. You’re teaching the history of mathematics- not mathematics. Mathematics evolves in part by simplifying and generalizing older theorems and proofs. Forcing students to read the works of Greek mathematicians handicaps their progress in mathematics because the original proofs no longer provide the best explanations. In fact it hobbled the development of the most significant mathematician of the twentieth century, Alan Turing. Evangelicals lost all credibility in mathematics when Van Til published his epistemology.
Thanks for your comment. While I understand your points, I respectfully disagree that students are handicapped by being exposed to historical math texts. I don't advocate teaching solely historic Greek mathematics and never have. What I'm attempting to do is re-humanize high school mathematics at a time when textbooks are soulless and ultra-pragmatic, completely failing to address the wonder, complexity, creativity, and beauty of mathematics in favor of bare computational competency. What I'm working toward is a way of teaching high school mathematics in a way that simultaneously 1) produces greater competency (by emphasizing the interconnectness of mathematical ideas, which standard high school textbooks do badly), and 2) gives students a glimpse into the beauty and creativity of mathematics by exposing them to its historic development (including pointing out how old prejudices get in the way of progress--e.g. your example or Viete's algebra being crippled by the law of homogeneity). In any case, you might disagree with my methods, which is fine, but those are my goals, and I think historical texts are key in achieving them. There is no discipline that does not benefit from studying its own history. Thanks again for your thoughtful input! I appreciate the feedback.
Agree with what you say in its entirety - "Memory is a byproduct of thought" - i.e. if you do not think about it, you will not remember it. I used to encourage students to do work at home by explaining how this helps to make memories more permanent. The more pathways that exist to a memory, the stronger the reinforcement, so by associating the learning with different environments / people / emotional states /etc. more pathways to the memory are formed. The biggest issue most young people face when trying to learn, I think, comes from poor teaching in High School, this is caused by multiple factors but one thing that always helps is the understanding that we can only build strongly on the things we already know (our schema) so 1) we must identify students' existing schemata and 2) Ask when planning for every lesson you teach "What is the one core concept every pupil must add to / have in their schema to succeed in the learning outcome of the lesson". Linking key concepts to pupils' underlaying schema is a very powerful tool, as a well developed schema allows pupils to work things out for themselves more easily and completely. Teaching is not the imparting of knowledge, it is guiding pupils to learn whilst being a facilitator, dispeller of misconceptions, motivator, solid point in reality (always the same, ready to repair relationships, reacting the same way to every event, every time) and to impart a love of learning. Keep up the great work, the world needs more people like yourself, helping the next generation to succeed and grow.
Great points! Thanks for your comment. I'll admit that I disagree that teaching isn't the imparting of knowledge. There must necessarily be *some* content that is passed from teacher to student; you can't teach students to "think for themselves" in a vacuum. But--and I think this is your point--we do our students a disservice when teaching becomes *merely* an imparting of knowledge. It's a balancing act, like nearly everything else in life, and it's all too easy to err by extremes.
Hi Daniel. How you doing?
This is so amazing!
Thank you! Be sure to watch the second part, if you haven't already. It's where I make my main points.
Skip to 13:48 to get the point in the video. He want to expose students to great articles in the history of math. (Similar to the way that we read the great authors when we study litterature)
It is very difficult to read the classics of mathematics without a foundation in modern textbook mathematics. Although it is important to read the classics, it must always be done after you learn the modern methods, because it cuts down the time to read the classics by a factor of 10, sometimes a factor of 100.
Thank you for this video! God Bless.
You are so welcome!
I actually think that the emphasis on logic and proofs is very important to transport the beauty of mathematics. I like the attitude of mathematics that you actually need to prove something before you believe it and I think it's important to prove that to students. It does probably help many to tell stories about mathematicians who found those insights, but I personally don't need that. Rather than how other people got to insights, I care about how I can get to those insights. I also don't need to hear stories of Columbus to be curious about America, I need to learn about its impact on our lives and our impact on America. Learning is a lot about personal relevance, and mathematics have a lot more personal relevance than just beauty that is not transported sufficiently.
I care more about ''visuals', Can you picture it and explain it simply? Can you develop an intuition of it that a child can understand and use it as a metaphor to help explain your ordinary world? Sure.. Study Euclid, but it's more important to develop intuitions about say Logarithms and Calculus can describe and predict your own development and experiences. How Trigonometry can explain cyclic behavior. Chaos Theory predict future recourse. Can Mathematics enhance one's reading of Literature and Movies?
The woke people already hate math: it’s racist.
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?
Almost (but not quite) an American Monty Python!
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.
Actually, this is brilliant.
Thank you! Glad you found it interesting!
What a great video!
Thank you! I'm glad you enjoyed it!
England?? What about Italy? I get it's about education and not 'research', but none of the English people you mentioned at 3:36 was a great mathematician.
Precisely. I'm not discussing mathematicians here, but rather the theorists who gave us classical education. Later in the video, I situate mathematics within the classical framework. Thanks for your comment!
Say something please! You’ve gone on and on and haven’t said anything.
If the theoretical backdrop isn't helpful to you, feel free to skip to the conclusion (starts around 18:00).
Very insightful video! One big question I have coming out the other side pertains to your first point about moving too quickly through material. I definitely agree that we shouldn't be leaving students who still have confusions behind by proceeding to new content too hastily, however I wonder about the opposite problem: What is to be done for the exceptional student who may feel bored having to go through all the repetition necessary to ensure everyone is on the same page? The reason I'm curious about this is I suspect the exceptional student could become disengaged with the subject in much the same way as the struggling student, but for opposite reasons. Instead of feeling like they're left behind they may feel like they're never truly moving forward (perhaps to put it another way they may feel like they're being held back from "getting to the good bits", whatever that may mean to them). I find it difficult to reconcile the needs of these two hypothetical students (struggling and exceptional), let alone accommodating the whole spectrum of needs we may find in between. I'd love to get your thoughts on this since you seem to have dedicated a great deal to thinking about these kinds of issues. P.S. A bit of background about myself: I am not a teacher, I am currently an undergraduate physics student. I don't know if I'll go into teaching after, but I certainly think about education quite frequently. This is why I've made plenty of use of the speculative "may" above since I haven't personally found myself in quite this scenario yet. The only experience I have in teaching mathematics so far is in the extremely informal setting of helping my peers where I can when they get lost. There's definitely a sense of gratification I get in the moment where clarity manifests itself in their expression, it helps me feel like I really do know what I'm talking about. Who knows, maybe this sense of gratification I get will inevitably push me to pursue teaching sometime down the line!
This is a great question. Unfortunately, there's no easy answer for how to balance the pace to account for both struggling and exceptional students. Practically speaking, if the environment allows for it, perhaps one good thing to do would be to give the exceptional students opportunities to present/teach key aspects of the lesson to the class. This would have to be done carefully to avoid creating an obvious cultural split between "good" and "bad" students in the classroom. However, keeping gifted students engaged by allowing them to share their insights is usually beneficial to all. Thanks for your comment!
I was always using the gym analogy too. It’s great to see someone more experienced and qualified thinking in the same lens. Thanks for the amazing video.
Thanks for the comment! I'm so glad you enjoyed it.
You are genius 😊😊
Thanks! I'm so glad you enjoyed the video.
The school doesn't given you manuals instructors editions
Errant was here