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
Been many many years since I have done even simple calculus but always had a deep appreciation for the subject, even though I have forgotten it all. Almost 50 now, and I still find myself gazing at a calculus book in a book store and telling myself I should really learn this so I can calculate loads on beams or use it to build something. I might have found the right channel here. Always enjoyed math and enjoyed being around others that have a passion for it.
@@bjen2005 Wow! Your words mean a lot! I appreciate your emotional approach to mathematics and calculus. Calculus is the top of the beautiful building that we call Mathematics. Thank you!
Thanks a lot and i loved the video. Also,please keep making more content like this where Math can be seen like as you did with the x² and x³ ,seeing things from different perspectives and tye connections. Would love to see a podcast more of this.👏
Thank you for your words. They mean a lot for me. I am working on a podcast every Saturday using that approach. Check the last two videos and let me know if you like them. Thank you again!
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...
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 RUclips 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 RUclips and practicing mathematics every day. Kind regards, Julian
Mathematics is not only a useful tool in everyday life and business, but also what drives technology forward and takes us towards better and faster systems. It all starts with a wonderful teacher like yourself sir, who takes the time to explain patiently. Thank you for this video👍
I learn by starting the topic from their little history then the concept and theorems related to that topic and try to think and visualize the concept and then related problems with topic.
@@sumitojha5116 Thank you for taking the time to share your way of learning. In a future video, I will point out your comment. It is a practical approach.
my parents signed me up in an abacus course for mental math that greatly speed up my calculation skills and grasping power, in all subjects. i realised it was like analogy, if we lack discipline and feel lazy waking up for school, we start lacking and even hating school. learning abacus gave me that spirit+discipline that prepared me for math and science
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.
Hi, excellent intro, you described math as relationships and connections wonderfully. Here's a little introduction of me, where I'm at & my total disillusionment with my experience with maths. I'm self studying software, electrical, chemical & electronics engineering because I love these subjects as it's my goal to work as an embedded software engineer prior to starting my own business. I too love math, it's the language of nature, the language that the universe speaks & I have multiple reason to learn, however I got disheartened & frustrated with Karn academy, multiple books, pdf's & countless websites that all do or say the same tired thing. I'm constantly 'remembering' methods instead of learning & understanding why & how they work which they NEVER explain which makes it confusing & unrelatable to reality, but also it's so mechanical, yet math is alive & organic, it shouldn't feel like a robotic process of thought, but rather a creative one. I need to understand the whys and the how's to methods, how else will i develop an art of thinking or learning to approach a new problem or question that has no method. This is why a lot of teachers & authors don't go so far, it's why they can't explain where the origin of the 4 basic operators inception was in relation to reality or what numbers actually are. Have you published any books I can buy? or recommend any that has strong emphasize on method approach & analysis ? the governing laws within each discipline clearly explained? Learning, making mistakes or not being frightened by math isn't my issue, it's finding a good teacher or author that's the hard part! I need to start from the beginning at arithmetic again & build my way up to calculus, so I can read electrical geometric configuration equations, versor operators ect & be able to express my results mathematically through experimentation.
Wow, I read your extensive revision of mathematics learning and I am amazed at the insight into the methods. I agree with you about finding strategies to learn life. I am preparing a video podcast and will share your ideas with the entire audience. Thank you for taking the time to share. I appreciate it.
@@yvonneisaac8822 Thank you for your words. They mean a lot for me. This is the last video of the series: Approaching Continuity: How To Understand A Big Calculus Idea ruclips.net/video/EBrFeuGWd5k/видео.html
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
Thank you for the Socratic treatment of this subject and the humility. I can use this video to convey to my daughters that the path to math is not firmly set but nonetheless a path that they should blaze on their own.
@@i_youtube_ thank you! I will do more. Check the last one. Approaching Continuity: How To Understand A Big Calculus Idea ruclips.net/video/EBrFeuGWd5k/видео.html
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!
We need to create a community that can impact knowledge if possible we can create books on course that cause fear in students and the book(s) should analyse different concept step by step
i like to work in flow like i am painting i am trying figure out the bigger picture of things first and find real life examples in other fields and how they use this topic in bio,chem,physics to bulid a clear understanding .
Cuantas veces cabe 2 dentro de 1 en la fracción 1/2. Esa es otra pregunta que hay que hacerse. Cabe solamente la mitad de 2 que es uno o .5 de 2. Entonces la pregunta es que parte del número que está abajo cabe en el de arriba. Es bien facil uno visualizar esto cuando el número de abajo es más pequeño que el de arriba. Esto es algo que me vino a la mente es posible que mi visualización no sea muy correcta pero quizás sea un buen inicio. Gracias por tu canal y por hacerme pensar. Versión en inglés: How many times number 2 fits into one. That’s another question we can make ourselves. It fits half of number 2 which is one or .5 of 2. Then the question is which part of the number that is under (denominator?) fits into the one over (numerator). It is easy to visualize this when the denominator is less or smaller than the numerator. But is not that easy to visualize it when the denominator is bigger than the numerator. So I think making myself the correct question I can visualize it better. This is something that came to my mind some time ago and I forgot but seen you taking it as and example it came to my mind again. This is some visualization don’t really know if I am correct I take it as brain storming kind of. Any way thank you much for your channel and must important thank you for make me think.🙏👍🇵🇷🇨🇺
Thank you for your suggestion. I am planning that idea. Have you watched the last video about creating a teaching-learning structure that I called Sets of Learning? Check the link below: ruclips.net/video/a6wMqXhAorY/видео.htmlsi=1X0vtQSoL9MYhAbs
Do you think quick mental math is useful for priming your brain for math in general? I know in Singapore and other asian countires kids start with abacus counting, this makes them very good at mental math, but I think it can somewhat hurt the intuitive undarstanding of place value (because abacus has 4+1 beads, not 10). And how all of that would relate to higher level math?
@@JamesSmith-ix5jd Hi James, thank you for sharing. Yes, mental math ability is an engine to master arithmetic that, in broader terms, is number sense. Yesterday, I posted a new video about the importance of number sense in learning the most sophisticated content, such as Calculus. In the American curriculum we need to work more on these approaches. Thank you!
@@MathTopicsByDr.Marrero Sir please mention your gmail id on your channel discription. I have to do with you a very important talk that is not possible here.I am a student of class 11 th❤
Thanks for your reply and your valuable time helping me. Is it possible to share your setup and how you plan and manage producing your videos and what would be your advice if are starting all over once again regarding things to do and to avoid. I am 50 years from Egypt and considering creating math content in Arabic as i am arabic native. Thanks a lot @@MathTopicsByDr.Marrero
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. 😏
@@MathTopicsByDr.MarreroThat’s so interesting to hear, because my teen daughter just got assessed and told she has dyscalculia, and that her main issue is with memory (I think it’s called working memory?) Basically she can learn a topic in maths at school, and all the time they’re working on that topic she’s able to do it. But if she gets given that same topic in a test a few weeks later, after they’re covered other topics in between, she’s then forgotten how to do the topic she learned a week or two earlier!
@ Thank you for sharing. This is an issue in math learning And teaching. This happens across the curriculum. Students forgot almost immediately what they have learned just a few days or weeks ago. Why? One of the problems is the way we teach math. The big ideas in math are not taught effectively. We can talk about this for hours. This is my purpose with this channel. How to teach to create lifelong learning. Thank you!
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.
As a 61 yr old Latino American man this video is literally mirroring my own life experiences. Mathematics was the monster boogey man subject to me ever since the second grade, I had a racist bigoted woman teacher who told me to put my hand down because she refused to answer my questions, plus my own parents weren't well educated either. The best inspirational movies.......Stand And Deliver, Spare Parts, A Million Miles Away, Good Will Hunting, October Sky.
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
@@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 see math as a story, its a love story, but also a tragedy, but also a mystery of course, and scifi, and its a long story a very long story and you can't start in the middle
Thank you so much for asking. I can create videos associated with that initial stage of math development. What areas are you interested in? The K-6 is essential to develop the foundation needed for future complexity.
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.
At 52, never regretted not devoting my time to mathematics. The sheer amount of time and energy that they demand, would lead to irreversible social skills atrophy and the opportunity cost would be too high to suffer.
I can solve maths by looking at the examples but without the examples i seeem to struggle and overthink. Sometimes I may solve it but I would have wasted much time, which isn't good for someone writing a CBT test on a timer countdown. I don't seem to concentrate with that timer
Thank you for sharing your experience. This is normal. We have to learn beyond examples and procedures. We need to understand the concepts behind the procedures. This is what I called life time learning. Have you watched my last video about learning sets? This is the link: 1 Powerful Framework To Teach And Learn Math ruclips.net/video/a6wMqXhAorY/видео.html
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
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.
Yo también tuve una formación muy pobre . Me sacan de la ciudad de México y me ponen en middle school sin saber lo que son fracciones decimales y porcentajes. Pensé que esa un estupido y que por eso no entendía las matemáticas . Toda mi vida me he culpado
Gracias por compartir su experieci as. Estas son una de las causas del bajo rendimiento en matemáticas. Y esto es tan importante porque sus efectos puede llevar a los seres humanos a no creer en sí mismos y hacer análisis sobre sus capacidades intelectuales que no son reales. Muchas gracias.
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.
New video from the series: How do I learn Math? How do I teach math? I hope you enjoy it. Approaching Continuity: How To Understand A Big Calculus Idea ruclips.net/video/EBrFeuGWd5k/видео.html
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
One of the most genuine videos I've seen in a long time; a treasure. Thank you.
@@ABCDMT123 thank you so much for your words. They mean a lot for me.
Been many many years since I have done even simple calculus but always had a deep appreciation for the subject, even though I have forgotten it all. Almost 50 now, and I still find myself gazing at a calculus book in a book store and telling myself I should really learn this so I can calculate loads on beams or use it to build something. I might have found the right channel here. Always enjoyed math and enjoyed being around others that have a passion for it.
@@bjen2005 Wow! Your words mean a lot! I appreciate your emotional approach to mathematics and calculus. Calculus is the top of the beautiful building that we call Mathematics. Thank you!
Thanks a lot and i loved the video.
Also,please keep making more content like this where Math can be seen like as you did with the x² and x³ ,seeing things from different perspectives and tye connections.
Would love to see a podcast more of this.👏
Thank you for your words. They mean a lot for me. I am working on a podcast every Saturday using that approach. Check the last two videos and let me know if you like them. Thank you again!
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...
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 RUclips 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 RUclips and practicing mathematics every day. Kind regards, Julian
Mathematics is not only a useful tool in everyday life and business, but also what drives technology forward and takes us towards better and faster systems.
It all starts with a wonderful teacher like yourself sir, who takes the time to explain patiently. Thank you for this video👍
Thank you for your words. They mean a lot for me.
Hermoso video profesor. Abrazo desde Uruguay.
Muchas gracias! Encantado que le haya gustado
I really respect teacher who love their students !
Thank you!
I learn by starting the topic from their little history then the concept and theorems related to that topic and try to think and visualize the concept and then related problems with topic.
@@sumitojha5116 Thank you for taking the time to share your way of learning. In a future video, I will point out your comment. It is a practical approach.
my parents signed me up in an abacus course for mental math that greatly speed up my calculation skills and grasping power, in all subjects. i realised it was like analogy, if we lack discipline and feel lazy waking up for school, we start lacking and even hating school. learning abacus gave me that spirit+discipline that prepared me for math and science
Discipline is the word to reach the top. Thank you for sharing your story.
I like that idea. Moving education forward
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.
Hi, excellent intro, you described math as relationships and connections wonderfully. Here's a little introduction of me, where I'm at & my total disillusionment with my experience with maths. I'm self studying software, electrical, chemical & electronics engineering because I love these subjects as it's my goal to work as an embedded software engineer prior to starting my own business.
I too love math, it's the language of nature, the language that the universe speaks & I have multiple reason to learn, however I got disheartened & frustrated with Karn academy, multiple books, pdf's & countless websites that all do or say the same tired thing. I'm constantly 'remembering' methods instead of learning & understanding why & how they work which they NEVER explain which makes it confusing & unrelatable to reality, but also it's so mechanical, yet math is alive & organic, it shouldn't feel like a robotic process of thought, but rather a creative one.
I need to understand the whys and the how's to methods, how else will i develop an art of thinking or learning to approach a new problem or question that has no method. This is why a lot of teachers & authors don't go so far, it's why they can't explain where the origin of the 4 basic operators inception was in relation to reality or what numbers actually are. Have you published any books I can buy? or recommend any that has strong emphasize on method approach & analysis ? the governing laws within each discipline clearly explained? Learning, making mistakes or not being frightened by math isn't my issue, it's finding a good teacher or author that's the hard part!
I need to start from the beginning at arithmetic again & build my way up to calculus, so I can read electrical geometric configuration equations, versor operators ect & be able to express my results mathematically through experimentation.
Wow, I read your extensive revision of mathematics learning and I am amazed at the insight into the methods. I agree with you about finding strategies to learn life. I am preparing a video podcast and will share your ideas with the entire audience. Thank you for taking the time to share. I appreciate it.
Beautiful absolutely beautiful.
Mathematics must be taught outside the box.
Your idea of connectivity is is paramount.
Thank you.
@@yvonneisaac8822 Thank you for your words. They mean a lot for me. This is the last video of the series: Approaching Continuity: How To Understand A Big Calculus Idea
ruclips.net/video/EBrFeuGWd5k/видео.html
❤ from Pondicherry India
Thank you very much for such an amazing video.
🙂
Thank you so much for your words. They mean a lot.
Thank you for making this soulful video.
@@miscibi Very welcome!
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
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.
Thank you for the Socratic treatment of this subject and the humility. I can use this video to convey to my daughters that the path to math is not firmly set but nonetheless a path that they should blaze on their own.
Thank you for your words. Yes, I agree with your statement about the personal commitment to learn it. Thank you again!
Great teaching sir i like the idea of what else
Glad to hear that. Thank you!
Thank you. It's a great video and we need more.
@@i_youtube_ thank you! I will do more. Check the last one. Approaching Continuity: How To Understand A Big Calculus Idea
ruclips.net/video/EBrFeuGWd5k/видео.html
Marrero, you got my sub. Thanks for taking time out to do this.
@@MrTheelicitor thank you so much and I appreciate your support!
What a useful video!!! This channel was a great discovery. Saludos desde España de un futuro profesor de matemáticas!!
@@isaackleiner7881 Gracias, espero que te guste. Tambien puedes colaborar con topicos que te gustarian. Saludos. Thank you! Glad that you like it.
Math is a powerful tool to solve complex and real problems of life 😮
I agree with you. Thank you for sharing!
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!
Sir, i love your way to teach math, it is superb!!
@@sunilmehra4u Thank you so much for your words. Glad you like it!
We need to create a community that can impact knowledge if possible we can create books on course that cause fear in students and the book(s) should analyse different concept step by step
Yes, we need to create a learning community that provides new insights. Thank you for sharing!
i like to work in flow like i am painting i am trying figure out the bigger picture of things first and find real life examples in other fields and how they use this topic in bio,chem,physics to bulid a clear understanding .
The big picture is essential to discover what makes sense. The application is the final reason that responds to the why. Thank you for sharing
Yes, inverse operations is to do and undo. You slipped and said undo cubed with square root. All else was very well stated. Thanks for sharing!
Cuantas veces cabe 2 dentro de 1 en la fracción 1/2. Esa es otra pregunta que hay que hacerse. Cabe solamente la mitad de 2 que es uno o .5 de 2. Entonces la pregunta es que parte del número que está abajo cabe en el de arriba. Es bien facil uno visualizar esto cuando el número de abajo es más pequeño que el de arriba. Esto es algo que me vino a la mente es posible que mi visualización no sea muy correcta pero quizás sea un buen inicio. Gracias por tu canal y por hacerme pensar.
Versión en inglés: How many times number 2 fits into one. That’s another question we can make ourselves. It fits half of number 2 which is one or .5 of 2. Then the question is which part of the number that is under (denominator?) fits into the one over (numerator). It is easy to visualize this when the denominator is less or smaller than the numerator. But is not that easy to visualize it when the denominator is bigger than the numerator. So I think making myself the correct question I can visualize it better. This is something that came to my mind some time ago and I forgot but seen you taking it as and example it came to my mind again. This is some visualization don’t really know if I am correct I take it as brain storming kind of. Any way thank you much for your channel and must important thank you for make me think.🙏👍🇵🇷🇨🇺
Wooow. This is amazing 🔥
Thank you!
We really need a course from beginners to advance ❤🎉
Thank you for your suggestion. I am planning that idea. Have you watched the last video about creating a teaching-learning structure that I called Sets of Learning? Check the link below:
ruclips.net/video/a6wMqXhAorY/видео.htmlsi=1X0vtQSoL9MYhAbs
Do you think quick mental math is useful for priming your brain for math in general?
I know in Singapore and other asian countires kids start with abacus counting, this makes them very good at mental math, but I think it can somewhat hurt the intuitive undarstanding of place value (because abacus has 4+1 beads, not 10).
And how all of that would relate to higher level math?
@@JamesSmith-ix5jd Hi James, thank you for sharing. Yes, mental math ability is an engine to master arithmetic that, in broader terms, is number sense. Yesterday, I posted a new video about the importance of number sense in learning the most sophisticated content, such as Calculus. In the American curriculum we need to work more on these approaches. Thank you!
I'm proud of you that you are teaching Mathematics. It is very interesting subject.The way you are teaching ,it's excellent
@@mohindersinghchahal Thank you so much for your words. They mean a lot for me.
I love mathematics and if you want to perfect in mathematics you should have practice and practice practice more❤
I agree with you. It is a lot of practice. My concern is the lifetime learning. How can we achieve it? Thank you for sharing!
@@MathTopicsByDr.Marrero Sir please mention your gmail id on your channel discription. I have to do with you a very important talk that is not possible here.I am a student of class 11 th❤
@@MathTopicsByDr.Marrerosir please mention your g m@i| In your channel discription. A very important talk.
@@MathTopicsByDr.Marrero"Sir, it would be great if you could include a way to contact you in your channel description."
@ I will update it. Thanks.
What is the software you are using as a whiteboard and recording? Thanks for everything.
Thank you! I use SmartBoard. They have a free and a paid version. I use the paid version.
Thanks for your reply and your valuable time helping me. Is it possible to share your setup and how you plan and manage producing your videos and what would be your advice if are starting all over once again regarding things to do and to avoid. I am 50 years from Egypt and considering creating math content in Arabic as i am arabic native. Thanks a lot @@MathTopicsByDr.Marrero
Good video!
Glad you enjoyed it
Great video sir. Subscribed!
Thanks for the sub! Glad that you like it!
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. 😏
@@MathTopicsByDr.MarreroThat’s so interesting to hear, because my teen daughter just got assessed and told she has dyscalculia, and that her main issue is with memory (I think it’s called working memory?)
Basically she can learn a topic in maths at school, and all the time they’re working on that topic she’s able to do it. But if she gets given that same topic in a test a few weeks later, after they’re covered other topics in between, she’s then forgotten how to do the topic she learned a week or two earlier!
@ Thank you for sharing. This is an issue in math learning And teaching. This happens across the curriculum. Students forgot almost immediately what they have learned just a few days or weeks ago. Why? One of the problems is the way we teach math. The big ideas in math are not taught effectively. We can talk about this for hours. This is my purpose with this channel. How to teach to create lifelong learning. Thank you!
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.
As a 61 yr old Latino American man this video is literally mirroring my own life experiences.
Mathematics was the monster boogey man subject to me ever since the second grade, I had a racist bigoted woman teacher who told me to put my hand down because she refused to answer my questions, plus my own parents weren't well educated either. The best inspirational movies.......Stand And Deliver, Spare Parts, A Million Miles Away, Good Will Hunting, October Sky.
sir i very thankful from india
Thank you!!!
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!
Fantastic!!!
Thank you!
Everything is algebra and Learning it is a art how to mod stuff around and deriving trig naturally. That's the issue being naturally at it
Thank you for commenting. I agree with “modifying stuff around”
Amazing work Sir. What a powerful presentation. How can we keep in touch with you kindly
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.
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 see math as a story, its a love story, but also a tragedy, but also a mystery of course, and scifi, and its a long story a very long story and you can't start in the middle
Thank you for sharing!
I tell my son that maths is magic. Where I try to show him different ways to solve some operations
@@katunguben2132 it is magic ✨ you are correct. Thank you for sharing!
Name of this wonderful piano piece ?
Mathematics. Thank you for commenting.
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.
🔥🔥🔥💯🥂🥂
plz can you show us how to teach math to our children's of primary school
Thank you so much for asking. I can create videos associated with that initial stage of math development. What areas are you interested in? The K-6 is essential to develop the foundation needed for future complexity.
video doesnt start until 4:30 btw
☠️
I would love to join you too
You are in. Thank you!
3 to the power of 2 is another way of saying 3 time 3 also
Yes
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 !!!
Pythagoras concept of his theory can be taught to Pre stages
we legiminitly learn study math by memorizing without inderstanding
You are correct. The is the cause of math failure across the curriculum.
At 52, never regretted not devoting my time to mathematics.
The sheer amount of time and energy that they demand, would lead to irreversible social skills atrophy and the opportunity cost would be too high to suffer.
Thank you for sharing.
I can solve maths by looking at the examples but without the examples i seeem to struggle and overthink. Sometimes I may solve it but I would have wasted much time, which isn't good for someone writing a CBT test on a timer countdown. I don't seem to concentrate with that timer
Thank you for sharing your experience. This is normal. We have to learn beyond examples and procedures. We need to understand the concepts behind the procedures. This is what I called life time learning. Have you watched my last video about learning sets? This is the link:
1 Powerful Framework To Teach And Learn Math
ruclips.net/video/a6wMqXhAorY/видео.html
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!
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.
Yo también tuve una formación muy pobre . Me sacan de la ciudad de México y me ponen en middle school sin saber lo que son fracciones decimales y porcentajes.
Pensé que esa un estupido y que por eso no entendía las matemáticas . Toda mi vida me he culpado
Gracias por compartir su experieci as. Estas son una de las causas del bajo rendimiento en matemáticas. Y esto es tan importante porque sus efectos puede llevar a los seres humanos a no creer en sí mismos y hacer análisis sobre sus capacidades intelectuales que no son reales. Muchas gracias.
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!
New video from the series: How do I learn Math? How do I teach math? I hope you enjoy it.
Approaching Continuity: How To Understand A Big Calculus Idea
ruclips.net/video/EBrFeuGWd5k/видео.html
My maths is too weak 😢
@@iftikharazim7880 Thank you for your comment. Do not worry; I was weak in math, too. This is the primary purpose of this channel.
My math Besick Verey weeck I don’t understands 😊
Thank you for sharing. Math learning is a lengthy process. But if you put your time and effort will payoff.
Türkçe altyazı ekle be adam :)
As a friendly advice: skip first 5 minutes.
Thank you for sharing