Відео

@16:32 - this is pretty cool - I'm reliving 8th grade all over again in Junior College. Years later , I want to really understand math.

nice vid

I suspect the idea of the Trivium would apply to each maths area or concept, not the entire field of mathematics in one go. The idea being to make sure the basics are understood and known before you build more complicated concepts. Classical tradition taught Euclid, who did exactly that, for geometry building understanding up from the obvious through using reasoning/ logic to get a firm grasp of the more complicated concepts/ principles. In any case, medieval students usually learnt to read and count at " petty" school, before going to grammer school, where the main aim was to get them fluent at Latin, so they could understand lectures in any European University, where the main subjects were theology, law and medicine. Latin was needed even if not goung to Uni., in order to conduct conversations, such as business ones, with people who did not speak English. Algebra was still emerging and in fact didn't exist for most of the time of classical education. Calculus did not exist till 1600's. Grammer school students may have learnt some logic or rhetoric, for wise thinking, coherent communication, and debates, but studies in other areas, such as Euclidean maths ( Geometry being part of the Quadrivium) was usually not taught till University.

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

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

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.

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.

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.

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.

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.)

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.

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.

Hi Daniel. How you doing?

This is so amazing!

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)

Thank you for this video! God Bless.

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.

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.

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.

Actually, this is brilliant.

What a great video!

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.

Say something please! You’ve gone on and on and haven’t said anything.

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!

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.