Let me explain to you how I learned mathematics. I used math books to define the definition of mathematics, then I used philosophy to understand the concepts of mathematics. After reading and buying hundreds and hundreds of mathematical calculus books, I observed that nature was pure mathematics. I was astonished that upper level mathematics depended heavily on all the principles of the connecting pieces of a puzzle, but if you understand the big picture you will undoubtedly reach the level of mathematics that is magical. Therefore after years and years of learning the Fibonacci sequence, it dawned on me that math is universal, and that the absolute value of truth is a reflection of the universe.
Math is just an invented language where you define rules and find the logical consequences. There's no magic in it, and it isn't some transcended part of the universe.
@MathTopicsByDr.Marrero Thank you. However, I don't think it's about my ideas, as much as an observation of what math is and how it works. If I make the rules of chess, I wouldn't say that the games of chess were written by the universe. If I define the length of a meter, there's nothing special about the average diameter of a star. We make tools that solve problems, and replace them with better tools when we need to.
What a beautiful work of art this video is! I am a physics student at the University of Zurich in Switzerland. I struggled a lot in my first year of the Bachelors, especially with Linear Algebra and Analysis. For me the trick was just to have fun doing math. Math for me is about exploring different ideas and about thinking. I was always an overthinker and now I've managed to direct this into thinking about math and the world in general, questioning things and thinking about why things are the way they are. There is so much more to say, but to summerize, I think the way I learned math is I learned to love it, the rest comes along :D
Thank you so much for your words. They represent a lot for me. I am glad that you like it. I struggled with analysis and linear algebra, too in my years at Havana University. The high school curriculum at that time did not prepare students to such endeavors. Physics is my passion, too. Math gets revealed in physics. Thank you again. Dr. Marrero from Math Topics
Good points... :) The best way to learn not only maths, but any subject for that matter is to learn 'in layers'. Don't try to master one particular subject or topic or aspect at once. First familiarize with the keywords (jargon) in that subject (maths for example). Familiarity alone breeds ease. Try to get the intuitive idea about each concept/topic/keyword. Inter-relate them. Find about other concepts related to it. You first need to see the big picture. Forget the hard and formal definitions. Specially in maths, there is always much simple and intutitive way of interpreting and understanding the concepts (even the so-called abstract concepts). Actually you can easily and intuitively understand maths (even quantum physics). But if you want to be an expert, you must solve hundreds, if not thousands of examples.
For example, I regard a determinant as a single number; yes, it is. However big it might be, still it seems to be a single number eventually. The core of maths is relatively so tiny. However, there are so many properties, techniques, methods, and interpretations of that core that take up thousands of pages.
@@TekCroach I love your insight. As a teacher, the intuitive idea is more effective. When students have a weak math background, procedural mathematics can help, but it sacrifices accurate understanding. Thank you again for taking the time to share.
I would love to cite another example or opinion. I thoroughly and absolutely and most intuitively understand differentiation and integration, but I don't care about so many different methods of solving a given problem. Maybe I could not solve a given sum using 'integrating by substitution' or 'integrating by parts'. But still I know the solution means what. That's the 'layer 1' of learning. Then I can learn about formulas, identities, and properties of calculus. That's 'layer 2'. Then, I can learn advanced concepts or ramifications of calculus like vector calculus, del operator, curl, div, multidimensional application, etc. That's 'layer 3'. And so on...
Excellent Video. If math was ever taught like this , I wish that class would never end. I am going to do some math now and look forward to other such works as your subscriber
Dr. Marrero, you're a good teacher! Keep making such videos. When you teach, I can feel the love and passion you have for the subject. I would be happy to listen to your podcast.
Wow I never could’ve imagined someone explaining mathematics so calmly yet passionate so it’s not monotonous or unapproachable I think even in subjects in which you have know lots of details and facts You can learn it better by have structural thinking instead of road learning
My teaching experience is explaining the mindset needed to use when understanding a concept . It is the window through which to look to see what is relevant I.e. to identify as you put it connections that will enable you to make sense of what you are experiencing. Taking your example of fractions . A key concept is “ What is a whole?” A whole is not as commonly thought a thing not broken up or one complete thing but can be anything considered as the whole . So a half can be considered as a whole,six eggs can be considered as the whole . This is needed as children will often be presented with whole shapes cut into equal parts when introduced to this idea. This sets the idea that only whole shapes or whole numbers can be the starting point . The notion of equivalent fractions i.e. half is two quarters , three sixths etc can be shown as a line of numerators over denominators and connected with multiplication tables where the one times table is the numerator and two times table the denominator . Another important concept is partition . Here basic numbers can be split so five is three plus two , eight is five plus three but also nine minus one and links up with your example of nine as three squared. I call this numbers in disguise. Inverse as you say is another important idea to understand . Maths unfortunately is like the roots of a plant spreading in lots of directions and all connected but because the emphasis is on natural numbers with counting and basic operations people believe that is all it is and say I was never any good at maths because they could not remember multiplication tables. Yet few are helped by the concept of partition so eight times seven can be split up into five lots of seven plus three 😂lots of seven . Five lots of seven can be thought of as half of as ten lots of seven or seventy . Seven tens shared is three and a half tens or thirty five.
What approach on number sense. I read your post fascinated with your ideas about fractions. Infinitesimal quantities can be understood using your approaches. Students struggle because the rigid concepts of a fraction that you mentioned. Thank you for your smart input. I appreciate your contribution and I will mention it in a coming video.
I would love to have a conversation/podcast with you, Professor. I am a constructivist guide and have endeavored to foster kids and youths into curricular math and advanced mathematics. I am currently working on a young adult novel, which has among its objectives to be suggestive of the love and study of mathematics as both a practical maximization of understanding and manipulation of reality and an exquisite intellectual and spiritual pursuit. I would appreciate your input and ideas about it. Surely we can find common ground and refine our approaches. Good day!
Wow such nice approach learning maths.. I wish i knew earlier.. My problem was, i didn't practise enough and then as we moved to higher classes forgot old formulas.. And concepts... Like exponential function and differentiation formula.
Hello, thank you for sharing your experience with math content. From my teaching perspective, the idea is to find ways and approaches that do not rely too much on memory but on logic and reasoning. We, the teachers, need to find effective dialogue to make our learners great thinkers. Memory is an assistant but not the way our brain works. Thank you again!
@@MathTopicsByDr.Marrero I love this comment on logic and reason. Quick example. I do math now as a hobby and needed to convert degrees to radians. Had forgotten all the equivalencies over the years. But I remembered one fact, that it was based on the circumference formula for a circle 2(pi)R. From that, you can derive them all. So, rather than committing all the equivalencies to memory, remembering one concept and you have them all for life. Your advice = wisdom, Dr. 😏
When I was in the first grade (1976-77), among other things, I was told that 2+3=5, and that 3 +2=5. I reasoned that 2+3=3+2. Eight years later, this was confirmed in an algebra class. I kept it to myself, because I didn't see the connection at six years old. Instead, I used this bit of information all throughout those eight years. It never occurred to me that math was difficult until I got to algebraic word problems; the method for solving them was never explained in a way that made sense to me, and while it didn't get in the way of my love for the subject, it had me questioning my intelligence for decades. To this day, I'm still struggling with calculus, not because it's difficult, but because there's something in my mind that tries to tell me I'm not capable of taking words and transforming them into useful formulas. Therapy remains an option...
Thank you so much for sharing and honesty. Your story is similar to many other learners and in many aspects to mine. There was something that wasn't taught effectively. Thank you again.
@@MathTopicsByDr.MarreroRespetable Dr. Marrero, Grazias for your topic on your UA-cam channel " The ultimate guide to mastering mathematics ". I am close to sity years of age and I strongly agree with you. We can call it a refresher, and shall say that I am delighted that you mentioned that mathematics is a building that has a foundation, A powerful building ,the walls have all the structures of a building, all of them are connected. In a ceremony Ihave heard a super structure, perfect in all it's parts and honorable to the builder. Shall we all call this powerful building a stately and superb edifice. We just have to look at many historical buildings in history, and past civilisations. I agree that we must look for connections. Another way to improve the love of mathematics is to say to ourselves and in classrooms, " We don't need to increase innumeracy and dyscalculia. They are hinderences to mathematical progress". It took me a a long time to master fractions. Not explained clearly, and a parent at home who has antipathy for fractions but expects me to know them. There should not be any issues when a person has learning difficulties. I was never told that factions teach logical thinking. I agree to do mathematics every day. A mathematical environment is worth having. Looking forward watching more of your explanations on UA-cam and practicing mathematics every day. Kind regards, Julian
@@ProfesionalMathRoad Hello, I am using SmartBoard. You can have the basic version for free. However, the full version is paid. Search smartboard. Thank you for watching!
I noticed I cannot explicitly point out what worked well for my development in math. Maybe I think it was a combination of hard work and open mindedness despite not being immediately naturally good. I also noticed my friends who despised mathematics and hated to learn it weren't really committed nor open minded. I cannot/wont blame them but it just may be a factor.
Thank you for sharing essential experiences learning and mastering math. We have common experiences such as the combination of hard work and passion for this subject.
I loved your lecture!! Truly! However, I really, really found your piano music distracting! At one point I could not hear what you were saying. :lease remember the volume isn't the same on every computer. Please take the time to edit the background "music" out
Math teachers should step by step to tech the TECHNOLOGY of solving math problems , by other words , to guide brain steps of student thinking to the AHA moments.
Years out of school, I read that lots of math teachers in high school in the USA were actually non math majors but had minors in math, so got pressed into service by the school bureaucracy. Hence the people supposed to teach you the invaluable basics amounted to a cyclops leading the blind. What resulted is people blaming themselves for being bad in math, rather than fixing the system of teaching math. Proof is how school system exiled Hymie Escalante, the teacher who taught AP calculus in poverty stricken east Los Angeles. See movie Stand and Deliver.
@MathTopicsByDr.Marrero what got worse is that during the COVID nonsense, most students now test 1.5 to 2 years behind grade level in all subjects, including math. Not only did that waste years of property tax dollars, it set STEM advances back a similar amount. What the covid tyrants did was world class criminal behavior, yet little is being done about it. Epic waste of human capital.
Can mathematics be learned visually .and how to do people who won field awards or others awards understand mathematics and create nothing to something and how they prove that cannot be proved by nature.
Let me explain to you how I learned mathematics. I used math books to define the definition of mathematics, then I used philosophy to understand the concepts of mathematics. After reading and buying hundreds and hundreds of mathematical calculus books, I observed that nature was pure mathematics. I was astonished that upper level mathematics depended heavily on all the principles of the connecting pieces of a puzzle, but if you understand the big picture you will undoubtedly reach the level of mathematics that is magical. Therefore after years and years of learning the Fibonacci sequence, it dawned on me that math is universal, and that the absolute value of truth is a reflection of the universe.
Hello,
Thank you so much for your valuable comment containing the essential path of a personal passion for this science. I appreciate your insight.
Math is just an invented language where you define rules and find the logical consequences. There's no magic in it, and it isn't some transcended part of the universe.
@ Thank you for sharing your ideas.
@MathTopicsByDr.Marrero Thank you. However, I don't think it's about my ideas, as much as an observation of what math is and how it works. If I make the rules of chess, I wouldn't say that the games of chess were written by the universe. If I define the length of a meter, there's nothing special about the average diameter of a star. We make tools that solve problems, and replace them with better tools when we need to.
Lol
What a beautiful work of art this video is! I am a physics student at the University of Zurich in Switzerland. I struggled a lot in my first year of the Bachelors, especially with Linear Algebra and Analysis. For me the trick was just to have fun doing math. Math for me is about exploring different ideas and about thinking. I was always an overthinker and now I've managed to direct this into thinking about math and the world in general, questioning things and thinking about why things are the way they are. There is so much more to say, but to summerize, I think the way I learned math is I learned to love it, the rest comes along :D
Thank you so much for your words. They represent a lot for me. I am glad that you like it. I struggled with analysis and linear algebra, too in my years at Havana University. The high school curriculum at that time did not prepare students to such endeavors. Physics is my passion, too. Math gets revealed in physics.
Thank you again.
Dr. Marrero from Math Topics
I really respect teacher who love their students !
Thank you!
Thank you very much for such an amazing video.
🙂
Thank you so much for your words. They mean a lot.
Good points... :)
The best way to learn not only maths, but any subject for that matter is to learn 'in layers'. Don't try to master one particular subject or topic or aspect at once. First familiarize with the keywords (jargon) in that subject (maths for example). Familiarity alone breeds ease. Try to get the intuitive idea about each concept/topic/keyword. Inter-relate them. Find about other concepts related to it. You first need to see the big picture. Forget the hard and formal definitions. Specially in maths, there is always much simple and intutitive way of interpreting and understanding the concepts (even the so-called abstract concepts). Actually you can easily and intuitively understand maths (even quantum physics). But if you want to be an expert, you must solve hundreds, if not thousands of examples.
For example, I regard a determinant as a single number; yes, it is. However big it might be, still it seems to be a single number eventually.
The core of maths is relatively so tiny. However, there are so many properties, techniques, methods, and interpretations of that core that take up thousands of pages.
@@TekCroach I love your insight. As a teacher, the intuitive idea is more effective. When students have a weak math background, procedural mathematics can help, but it sacrifices accurate understanding. Thank you again for taking the time to share.
I would love to cite another example or opinion. I thoroughly and absolutely and most intuitively understand differentiation and integration, but I don't care about so many different methods of solving a given problem. Maybe I could not solve a given sum using 'integrating by substitution' or 'integrating by parts'. But still I know the solution means what. That's the 'layer 1' of learning. Then I can learn about formulas, identities, and properties of calculus. That's 'layer 2'. Then, I can learn advanced concepts or ramifications of calculus like vector calculus, del operator, curl, div, multidimensional application, etc. That's 'layer 3'. And so on...
Excellent Video. If math was ever taught like this , I wish that class would never end. I am going to do some math now and look forward to other such works as your subscriber
@@abhiroopkumar1064 Thank you so much for your words. I appreciate your encouragement.
Dr. Marrero, you're a good teacher! Keep making such videos. When you teach, I can feel the love and passion you have for the subject. I would be happy to listen to your podcast.
Thank you so much for your words. I appreciate it a lot. I am thinking to start a weekly podcast.
@MathTopicsByDr.Marrero do it! I will support you!
@@MathTopicsByDr.Marrero Let me be your first guest. 🙂
@@NewCalculus of course! I am planning. I will keep you posted. Thank you!
Wow I never could’ve imagined someone explaining mathematics so calmly yet passionate so it’s not monotonous or unapproachable
I think even in subjects in which you have know lots of details and facts
You can learn it better by have structural thinking instead of road learning
@@knw-seeker6836 Thank you for your encouragement! I appreciate it a lot.
a great video i am from Pakistan and i want from your channel to have the pattern for mathematics from start to finish not any random concept
My teaching experience is explaining the mindset needed to use when understanding a concept . It is the window through which to look to see what is relevant I.e. to identify as you put it connections that will enable you to make sense of what you are experiencing. Taking your example of fractions . A key concept is “ What is a whole?” A whole is not as commonly thought a thing not broken up or one complete thing but can be anything considered as the whole . So a half can be considered as a whole,six eggs can be considered as the whole . This is needed as children will often be presented with whole shapes cut into equal parts when introduced to this idea. This sets the idea that only whole shapes or whole numbers can be the starting point . The notion of equivalent fractions i.e. half is two quarters , three sixths etc can be shown as a line of numerators over denominators and connected with multiplication tables where the one times table is the numerator and two times table the denominator . Another important concept is partition . Here basic numbers can be split so five is three plus two , eight is five plus three but also nine minus one and links up with your example of nine as three squared. I call this numbers in disguise. Inverse as you say is another important idea to understand . Maths unfortunately is like the roots of a plant spreading in lots of directions and all connected but because the emphasis is on natural numbers with counting and basic operations people believe that is all it is and say I was never any good at maths because they could not remember multiplication tables. Yet few are helped by the concept of partition so eight times seven can be split up into five lots of seven plus three 😂lots of seven . Five lots of seven can be thought of as half of as ten lots of seven or seventy . Seven tens shared is three and a half tens or thirty five.
What approach on number sense. I read your post fascinated with your ideas about fractions. Infinitesimal quantities can be understood using your approaches. Students struggle because the rigid concepts of a fraction that you mentioned. Thank you for your smart input. I appreciate your contribution and I will mention it in a coming video.
sir i very thankful from india
Thank you!!!
Sir, i love your way to teach math, it is superb!!
@@sunilmehra4u Thank you so much for your words. Glad you like it!
I would love to have a conversation/podcast with you, Professor. I am a constructivist guide and have endeavored to foster kids and youths into curricular math and advanced mathematics. I am currently working on a young adult novel, which has among its objectives to be suggestive of the love and study of mathematics as both a practical maximization of understanding and manipulation of reality and an exquisite intellectual and spiritual pursuit. I would appreciate your input and ideas about it. Surely we can find common ground and refine our approaches. Good day!
Wow such nice approach learning maths.. I wish i knew earlier.. My problem was, i didn't practise enough and then as we moved to higher classes forgot old formulas.. And concepts... Like exponential function and differentiation formula.
Hello, thank you for sharing your experience with math content. From my teaching perspective, the idea is to find ways and approaches that do not rely too much on memory but on logic and reasoning. We, the teachers, need to find effective dialogue to make our learners great thinkers. Memory is an assistant but not the way our brain works. Thank you again!
@@MathTopicsByDr.Marrero I love this comment on logic and reason. Quick example. I do math now as a hobby and needed to convert degrees to radians. Had forgotten all the equivalencies over the years. But I remembered one fact, that it was based on the circumference formula for a circle 2(pi)R. From that, you can derive them all. So, rather than committing all the equivalencies to memory, remembering one concept and you have them all for life.
Your advice = wisdom, Dr. 😏
Great teaching sir i like the idea of what else
Glad to hear that. Thank you!
Wooow. This is amazing 🔥
Thank you!
Fantastic!!!
Thank you!
When I was in the first grade (1976-77), among other things, I was told that 2+3=5, and that 3 +2=5. I reasoned that 2+3=3+2. Eight years later, this was confirmed in an algebra class. I kept it to myself, because I didn't see the connection at six years old. Instead, I used this bit of information all throughout those eight years. It never occurred to me that math was difficult until I got to algebraic word problems; the method for solving them was never explained in a way that made sense to me, and while it didn't get in the way of my love for the subject, it had me questioning my intelligence for decades. To this day, I'm still struggling with calculus, not because it's difficult, but because there's something in my mind that tries to tell me I'm not capable of taking words and transforming them into useful formulas. Therapy remains an option...
Thank you so much for sharing and honesty. Your story is similar to many other learners and in many aspects to mine. There was something that wasn't taught effectively. Thank you again.
The big picture of calculus is well explained by Gilbert Strang in MIT podcasts on You Tube.
Reading and practicing will definitely help in overcoming your strugle.
@@MathTopicsByDr.MarreroRespetable Dr. Marrero, Grazias for your topic on your UA-cam channel " The ultimate guide to mastering mathematics ". I am close to sity years of age and I strongly agree with you. We can call it a refresher, and shall say that I am delighted that you mentioned that mathematics is a building that has a foundation, A powerful building ,the walls have all the structures of a building, all of them are connected. In a ceremony Ihave heard a super structure, perfect in all it's parts and honorable to the builder. Shall we all call this powerful building a stately and superb edifice. We just have to look at many historical buildings in history, and past civilisations. I agree that we must look for connections. Another way to improve the love of mathematics is to say to ourselves and in classrooms, " We don't need to increase innumeracy and dyscalculia. They are hinderences to mathematical progress". It took me a a long time to master fractions. Not explained clearly, and a parent at home who has antipathy for fractions but expects me to know them. There should not be any issues when a person has learning difficulties. I was never told that factions teach logical thinking. I agree to do mathematics every day. A mathematical environment is worth having. Looking forward watching more of your explanations on UA-cam and practicing mathematics every day. Kind regards, Julian
Thank you, just wondering which application you are using in the video 😊
@@ProfesionalMathRoad Hello, I am using SmartBoard. You can have the basic version for free. However, the full version is paid. Search smartboard. Thank you for watching!
I noticed I cannot explicitly point out what worked well for my development in math. Maybe I think it was a combination of hard work and open mindedness despite not being immediately naturally good. I also noticed my friends who despised mathematics and hated to learn it weren't really committed nor open minded. I cannot/wont blame them but it just may be a factor.
Thank you for sharing essential experiences learning and mastering math. We have common experiences such as the combination of hard work and passion for this subject.
Attitude is everything. If you don’t enjoy what you’re doing you need to be doing something else.
@@a.s.vanhoose1545 I agree with your statement. Thank you for taking the time to share.
Great video sir. Subscribed!
Thanks for the sub! Glad that you like it!
Good video!
Glad you enjoyed it
I loved your lecture!! Truly! However, I really, really found your piano music distracting! At one point I could not hear what you were saying. :lease remember the volume isn't the same on every computer. Please take the time to edit the background "music" out
Thanks for the tip!
Name of this wonderful piano piece ?
Mathematics. Thank you for commenting.
I would love to join you too
You are in. Thank you!
Math teachers should step by step to tech the TECHNOLOGY of solving math problems , by other words , to guide brain steps of student thinking
to the AHA moments.
Absolutely Right !!!
Years out of school, I read that lots of math teachers in high school in the USA were actually non math majors but had minors in math, so got pressed into service by the school bureaucracy. Hence the people supposed to teach you the invaluable basics amounted to a cyclops leading the blind. What resulted is people blaming themselves for being bad in math, rather than fixing the system of teaching math. Proof is how school system exiled Hymie Escalante, the teacher who taught AP calculus in poverty stricken east Los Angeles. See movie Stand and Deliver.
Thank you for sharing your ideas.
@MathTopicsByDr.Marrero what got worse is that during the COVID nonsense, most students now test 1.5 to 2 years behind grade level in all subjects, including math. Not only did that waste years of property tax dollars, it set STEM advances back a similar amount. What the covid tyrants did was world class criminal behavior, yet little is being done about it. Epic waste of human capital.
Can mathematics be learned visually .and how to do people who won field awards or others awards understand mathematics and create nothing to something and how they prove that cannot be proved by nature.
Hi Sir
I would join Sir
Thank you!
WE+C=29WM(SCCP16+88)=