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What do you think about the teaching of maths at different levels of education? How do you think it could be improved not to be so feared?

It is an open place to talk about how everyone thinks math teaching could be improved to be closer to students. Thanks!

  • Mar 18 2011: As a Mathematics teacher I think the best thing we can do as teachers is to share our enthusiasm for Math. Our own enjoyment will spread to the students. I also believe in keeping the explanations simple throughout grade school and high school. Just teach what they need to help them taste success and build confidence. As their mental capacity for logic and numbers improves with age, they will be ready for the higher level Math courses taught in college. I also think it's imperative that the kids NOT use calculators throughout grade school. They need to memorize the multiplication tables right at the beginning.
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    Mar 17 2011: I recently saw a channel on YouTube, that coincidently TED-ED has already featured... It's the channel of this girl Vihart that... I don't want to say teaches... she showcases... math as a subject that actually seems fun. Here's the channel:
    http://www.youtube.com/user/Vihart

    And here's one video that particularly made my jaw drop:
    http://www.youtube.com/watch?v=DK5Z709J2eo

    I hope TED invites her as a speaker one day... She's like the next Salman Khan of sorts... I can imagine myself getting sparked up with her videos and looking the concept in more detail on Khan Academy.

    (and the only reason I say "imagine myself" as opposed to actually doing it is because I have other math classes ahead of me; I plan to explore it later)
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      Mar 17 2011: Thanks for posting these links, Vasil!
      I have seen some of her youtube videos below and I agree that she would make a very interesting TED speaker- great suggestion.
      Can i suggest that you submit Vihart in the TED question which is asking for suggested speakers?
    • Mar 17 2011: Awesome!
      I knew something about her, but not this; It´s good, thanks Vasil!!
      • Mar 20 2011: Hi again Jone,
        It your a teacher and are looking for good ways to teach children math with enthusiasm, engagement, and fun all rolled into one, then you should take a look at the Steiner school method... music is incorporated in the math sessions ! Music actually runs through the whole pedagogical method, right from kinder garden up through the highest classes. Music opens the soul, is naturally rhythmic, and creates an active inner environment for learning. If you don't do anything else the next week, so take a closer look at the educational methods of Rudolf Steiner !!
        • Mar 20 2011: Thank you Daniel!!
          I will search for the Steiner´s method.
          I also love music so it could be interesting...
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      Feb 24 2011: Syd, here you go. If math is the key to the mysteries of the universe, then you just got another real life application for it ;-)
  • Mar 23 2011: At school, as a student of mathematics, I was motivated to learn when the subject was interesting. This let me get started in differential and integral calculus.
    Then I went to University and met such things as Fourier transforms. I had no concept beyond rote learning for many years. Then I met a university lecturer who could describe the concepts, and the historical context of of these things. By discussion, came an appreciation of 'why' as well as 'how' Fourier transforms are used.

    I see similar response from my own children in their learning. When they see why a concept was invented, and what it can do, they become more involved in learning how to do it.
    • Mar 23 2011: I think that it´s true what you say, David.
      Encouraging students and explaining where different math concepts come from is one of the keys of being involved in maths (or in any subject).
      Thank you David.
  • Mar 22 2011: In Montessori schools (attended by the Google founders interestingly), maths is taught using colour. Instead of black pens, coloured pencils are used (eg: red, green, etc as the child prefers).I went to a Steiner school and we learned maths by running the school canteen for a week. We had to work out cost, profit ratios. We had to survey customers to see how much they'd spend and what they'd buy. We had to budget at the supermarket and finally report our 'week end' accounts to the teacher. Fantastic fun. We did fractions when assessing 1/8th of a pizza for example. We costed a pizza and aimed for high profit. Great fun and also taught teamwork, customer focus, business skills and MATHS! This was in the late 1970s and early 80s so there's so much teaching like this but not in the mainstream...why re-invent the wheel, I say?
    • Mar 22 2011: The text about your experience is very interesting and helpful.
      I didn´t know anything about Montessori Schools and It seems good.I think that it would be a very good proposal to work in this different way, It seems to be more relaxed and natural. It gives the space to each student to develop their capacities in a free way.
      Thank you for your comment!!
  • Mar 22 2011: Make it relevant! Hard to understand all those x and y and z etc. calculus looks rather abstract.
    Statistics, make it relevant like Hans Roslign does look how many people have watched his talks.
    Parabolas and quadratic functions look nice but then what? The teachers I had just said they're very useful so learn them!!
  • Mar 17 2011: My opinion has largely been expressed eloquently by other commenters.

    I might add a note on my own math experience that goes towards the issue of relevancy. I saw a "trickle down" effect of mathematics- you take what graduate students might learn, water it down, and teach it to undergraduates. Take what undergraduate math majors might learn, water it down, and give it to high school students, etc. It leads to some nonsense - I learned ideas in 7th grade algebra that didn't have any relevance until studying abstract algebra. Classes in high school were sometimes a mix of random topics. I wonder if we could decide what practical and abstract mathematical skills we would want public school graduates to have and develop self-contained courses to empower them with these skills.

    Public education in America seems to serve the purpose of preparing some and weeding out others for university. I have a difficult time reconciling this model with the ability to teach math in a useful, enjoyable way.
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    Mar 16 2011: I think the biggest problem why math may be so difficult for and individual to understand has a lot to do with the way it's taught. The main reason why individuals may have trouble with conceptualizing math is like Ross said, they have nothing to relate to. These numbers can have no meaning to a student. When teaching math we should stress the relevance it has to real life and more real life applications should be emphasized in class rooms. The brain learns through how things relate to eachother and individuals can retain more information if there is something they can relate to when they are being taught something particular in math.
  • Mar 16 2011: I'm glad that this topic is being discussed. As someone who has been extremely passionate about mathematics, done a significant amount of tutoring, and taken a large amount of mathematics, I've definitely developed an opinion on this subject. I have two main qualms with the current state of mathematics.

    One of the largest problems I see with math today is that on first glance the overwhelming majority of it seems useless to most students. Math is taught in a very strange way and I think that turns off a lot of students. The strange manner in which math is taught is that it is largely separated from its useful applications. Math by itself means nothing, it only has value when it is applied to the incredible number of fields that it can advance, be it physics, chemistry, confirming originality of art or literature, improving the economy, or countless other areas. It is, in my opinion, not worthwhile to have students simply do calculation after calculation, completely out of context of its application.

    My second problem with mathematics is that it is geared toward calculus and not statistics. Calculus is an extremely powerful tool for students who need it in the future, but for the rest it is something that will quickly be forgotten. Statistics on the other hand is something that is extremely useful for all students. Statistics can teach us how to analyze a situation and make the best decision. Statistics can show students the probability of a payoff, or their chance of success in a certain area. It seems that the last 2-3 years of most high school curricula are focused on teaching students calculus, rather than statistics which I feel has better appeal and application.

    So in conclusion my vision for mathematics is passionate teachers who educate students on relevant material in a manner that students can actually relate to.
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      Mar 16 2011: I really hate stats (or at least the way it has been taught to me), although I adore math in general.

      I am an idealistic math kind of person. I believe that mathematics is not only beautiful and an art, but also crucial as part of the human development. I'm thinking about Pythagoras, Pascal and others.

      I truly believe we need to stop seeing mathematics as a necessary evil and work towards seeing it more like an art. Like a game... because it is. And of course the usefulness can come into place. Calculus is just so much more interesting ;)
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      Mar 17 2011: To say that math by itself means nothing and math only has value in application, you might as well say that art means nothing.

      Also, it would be hard to gear math toward stats instead of calculus, since many areas of stats are built on calculus. I teach a college stats class for students majoring in fields that use stats far more than calculus, i.e. journalism and sociology. There is no way to have the students reach a true understanding of the normal distribution without going deep into calculus. The alternative is to give the students a z-table and say, "Just take it on faith that this works." That is a fundamentally flawed approach to education, regardless of the subject being taught.
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      Mar 17 2011: YES to statisitics!

      * The way to learn to think in probabilities
      * One of the best tools for scientific research
      * It can reduce a lot of numbers to a very small amount of understandable and meaningful numbers
      * It is the key to understanding and programming AI
      * You can learn to beat people in poker
      * It shows a lot of cognitive biases you have as a human
      * TED loves statisticians! (or that is what I like to believe)
      * It can be thought in a very visual and intuitive level.

      (ok, maybe i'm of topic,...)
  • Mar 16 2011: What do you think about Khanacademy? I think that it´s amazing and a very good tool to experiment with students.
    There are several people working on different math programs (like Wolfram alpha) to try another way to teach maths.
    They are opening new directions in math education.

    http://www.ted.com/talks/lang/eng/conrad_wolfram_teaching_kids_real_math_with_computers.html

    http://www.ted.com/talks/salman_khan_let_s_use_video_to_reinvent_education.html
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      Mar 16 2011: Do you teach math Jone? Have you used Khan Academy in your classroom? If so, I'd really like to hear about your experience.
      • Mar 17 2011: I haven´t used Khan Academy with my students, but I want to do it. I need time to organize my work I think how tutoring students.
        I will tell you when I try it.
        Thanks for your interest Tim!
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    Mar 7 2011: Hi Jone,
    I have started a concept called the Dope Science Movement. It is geared toward increasing mathematics and science proficiency via music. Since people seem to respond to music very strongly, and several entities and organizations have successfully used song to increase concept retention, I wanted to try to use music as an avenue for creative expression of academic subject matter as well as igniting passion for the subjects themselves. I would love to talk more about how we could possibly work together to develop a pedagogy around this concept, or introduce this concept in to a particular teaching style.
    • Mar 8 2011: Thank you for your interest, William.
      Where can I read or know more about Dope Science Movement?
      I hope to hear from you.
  • Mar 4 2011: A good example:

    See: http://www.khanacademy.org/

    - Khan was introduced by Bill Gates, who curated the entire Knowledge Revolution session — a new guest curation experiment at TED

    Read more: http://www.brainpickings.org/index.php/2011/03/03/ted-2011-highlights-day-2/#ixzz1FeWOELJa
    • Mar 4 2011: Very good recommendation!! thanks!!
      Khanacademy is fantastic, I have watched some of his videos since I discovered it, It seems to be the future.

      I will explore brainpickings...
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    Feb 25 2011: I'm surprised no one has already mentioned Dan Meyer's talk:
    www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

    It contains the majority of things I find wrong with math classes. The remainer is in Conrad Wolfram's talk:
    http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html

    Basically - let computers do the calculation, and focus on the "what" and "why" instead. Teach methods first, and formalize them with new terminology afterwards, not the other way around. Try to make students gradually reach up to the "how" based on the "what" and "why". That is not to say "don't tell them any formula" or "don't teach any algoritms", just... being less helpful, answering questions with questions that lead directly to the answer, instead of the answer itself.
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    Mar 23 2011: I think the question is not so much about the teaching of maths at different levels of education, but rather the teaching of maths at the different levels of learning. The current system of pushing out instruction has to be turned on its head - we have to learn how to invite learners into forms that enables us to learn from each other all that is known - and is being discovered. Including that which is known of math.
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    Mar 23 2011: Well, i mean the teaching of maths at any level should pay more attention to let the students know how they can use it in their life, not only in their exams. From my point of view, it is a good way to make them intrested in maths, and also, it can change the people's minds that the math is so difficult to learn but useless in our life.
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    Mar 23 2011: Dr. Ryan Honomichl did a beautiful and eloquent comparative analysis (in his lecture for a class on adolescent psychology) on the teaching styles in math and science in the US and East Asia.
    In the US, teacher show solutions and teach problems, fix errors quickly, go over large volumes of material, and have more of a dictating role, focusing on what's the right way to solve a problem.

    In East Asia teachers assign students into groups, then they are supposed to come up with solutions and present to the whole class - explaining their own thoughts certainly is a huge difference maker in how much understanding of the material they gain. Then teachers step in and focus on errors, which they consider crucial. Figuring out why certain solutions go wrong exploses the students to many different ideas and a context for the right solution - why it works, how it works. Discussion rather than power point and note taking are the tools. The pace is slower in East Asian math compared to US math. As Dr. Honomichl said, the math textbooks in Singapoure are strikingly different, and one does not need to read them to notice it. THEY ARE VERY THIN!

    Covering little material over a long period of time equals solid foundations. In the US, teachers rush through the material. How do you build a house without having solid site preparation, without digging deep foundation.

    One last thing - research shows that American high schoolers spent 4-5 hours a week on average on doing homework, while East Asian students spend more than 4 hours a day on homework. (they engage in sufficiently smaller amount of extracurricular activities, and in general East Asian students rarely have student jobs)
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    Mar 23 2011: Ola Jone!

    Here's my 2 cents: At any level (and at any discipline), it's fundamental to talk about the subjet (as in conversation), play with the subject, know the history about it and be creative on the subject (with metaphors & other analogies) on how/where/when/why. After all, we all have this ability to abstract (and we do pretty serious 'calculations' from an early age, if you care to notice) but, most of the time, we're pretty 'lazy' at focusing and reasoning about a subject without a motivation, a catalyser of attention, of awe even! Imagine trying to teach musical composition without an instrument...

    Of course, this demands a huge effort from any teacher, passion, talent to communicate and the awareness that there's a lifetime to learn, that neither students and teachers are "geniuses" and that, more often than not - in communication - an appealling approach leads to a fruitful content. ;)

    Sorry if I sounded too paternalistic. Not my intent, anyway.


    Cheers!
  • Mar 23 2011: Like my career in tevevision productions of all kinds, I would target the right "audience". As a "right brained" creative person, I needed a creative and motivation-driven teacher especially in "left brain" subjects that I had no talents or abilities in. I got great grades with teachers who were creative and motivating and who could make the subject clear to me. The use of technology today to illustrate no tonly the subject, but why teh subject is amazing would help motivate students to learn I believe. Show them "Why" as well and "How".
  • Mar 22 2011: Hi everybody,
    These are the last hours of this talk and I want to thank you for your contributions.
    I hope I will read you hear soon!!
    Thanks!!
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    Mar 21 2011: to tell u the truth i think only basic maths should be taught across the field, since many things taught at present one would see or hear about them again in their life. thus it should be up to a person depending on their career path should be able to chose, if they want to continue in any advance maths.
  • Mar 18 2011: hi, i can say maths have to teach not in different levels, it's depends on the student.i learned like that only. my sir used to teach maths differently from others to me. so at some point i liked algebra.
    here some steps
    1.observe the student closely, may it will take some time but give some easy problems....give some 100 i can say..same type easy way......he feels that it's easy. if possible give some live example for that problem.he feel it's interesting.
    2.next after that slowly increase the level of hardness....but same method.....no of problems...and live example....
    3.after all type of problems from particular topic , now give the practical application as problem.....definitely he solves that...
    4.next ask him prepare some problems and give it to other students...like that mutual exchanging of ideas, thoughts through discussions.
    every thing can be expressed in and for language of mathematics...i hope it can help.....thank you
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    Mar 16 2011: I believe that the biggest problem with teaching maths is that it is seldom made concrete enough for people to grasp. Most people need to understand what on earth this formula solves in the real world. I was in graduate school before anyone bothered to tell me why i needed to know the slope of a line and that, I feel was far too late. Once I understood the why teaching my own kids became much easier. If we get kids to understand why this is important they will have an easier time grasping it.As an example. When my kids were little, I did not want to fight them to eat veggies so I translated the 'super power' that each veggie had into a story of the way their bodies worked and why they as "kings and queens of their own little country' had to support their citizens (cells). Game over. I never fought with them over veggies.I'm sure that this sounds like amateur hour but I can't help but think it can be related to maths as well. In preschool I could teach them positive and negative numbers with little cars on the kitchen floor going so far from home one way and so far from home in another. They get it if we give them the opportunity and bring it down to where they can see it.
  • Mar 6 2011: As a (retired) secondary school Maths teacher, I am painfully aware that many of my pupils had not been enthused with the subject by their primary school teachers (grades 1-6) - who were themselves often victims of the same problem. Changing the situation is going to need major effort: but in the same way that Jamie Oliver has made people aware of the importance of good food, and Bill Gates is working on various fronts, it can be done: to enthuse teachers and their pupils (and their parents) .about a subject
  • Feb 28 2011: I agree with you, Vi Nguyen, I think that the best teacher is that who feels the students in front of him/her and knows how to communicate with them, it´s basic.
  • Feb 28 2011: I had tried some visual methods (animation, slides, funny movies...) to learn math but they seem not help. What I suggest is to encourage pupils or students to compete with each other in every lessons. My math teacher divided us into many groups which had both the good and bad students. Then, each group had to solve a problem, may be a hard formula. It really helped me a lots. I was inspired to learn more quickly and efficiently.
  • Feb 26 2011: Thanks Vasil, both talks are very good. It´s some months since I watched them and they made me think.
    They propose very good topics!
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    Feb 26 2011: Change the education system, then build new math approach.
  • Feb 25 2011: All your comments are welcome.

    I feel responsible about the teaching of maths in the schools and Universities because I am math teacher. I always try to teach as clear as I can because I know that there may be a lot of students in front of me that they lost on the way of trying to understand a new math concept or a problem.

    I am also conscious that when you teach in an institution you are forced to follow a curricula, and sometimes It´s not easy to teach something in the way you feel more natural and fluent in the context where you are teaching. I know that I could do things better, but at this moment this is how a feel.
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    Feb 24 2011: I hated math in school because my teachers taught me it in a wrong way. I have suffered this lack all my school life. Math should be taught in a dynamic and fun way from child. Also each of us develop different skills. It's not right to force people doing what they don't like.
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    Feb 24 2011: I bought Euclid's Elements awhile back. It wasn't quite what I was expecting. There were no metaphors, no words problems, no exposition on the principles at play, just proof after elegant proof. I could follow along to most of them, but I didn't really understand what was going on for all but the some of the first proofs. For the ones I understood, the proofs were elegant, simple, sublime. For those that I didn't, those proofs were mostly confusing.

    But than again, Euclid didn't write a text book. He wrote a book about geometry. Those who taught with it were not subject to standards, for education wasn't wide spread. The teacher knew the concepts, their applications, and how to teach them. Todays text books can almost be read on their own, sans teacher. Maybe simplified textbooks offering just proofs, cross referenced with the theory behind each proof (Maybe in a different section, or a different book, or right with the proof). Then, if a teacher finds that focusing on theory in class works best, then the text book becomes a source of verification and example. Almost like a dictionary of math. And if the teacher wishes to focus on the proofs then that teacher can leave the theory for homework (maybe essays on the proof learned that day, or writing and solving their own word problems.) Sort of like a cliff notes for math.

    Either way could be done, the books can be designed to have the knowledge necessary to meet national standards; it's up to the teacher to make sure that the students learn. I was bored much of the time in math class because the teacher was saying pretty much the same thing as our textbooks. The teacher seemed just like a mouthpiece, there was no life to the lesson. But if a teacher has to decide for herself exactly how to phrase the lesson, how to structure it, how to tailor it to the individual characteristics of that class, then he can teach as a person, and not simply as a mouthpiece.
  • Feb 23 2011: Sorry, I wanted to say "not to find" in my second sentence.
  • Feb 23 2011: I agree with you, Jonathan and Harald. For me it´s difficult to find maths interesting, I always have loved it and work in it.
    But It´s good for me to know what people think about it, because it can improve the way I usually teach to my students.
    I have never been interested in applications, I only wanted to know different math concepts and I was happy with it. But know, teaching to different people, I realize that I need to know more practical and applicative math problems, more connected to the real life.
    There also are very magical and interesting behaviors with numbers and natural patterns, and I think that this could be a way to make maths more interesting in class.
    Thank you for your comments!!
    • Mar 7 2011: The application of math was the only way I could find concepts in calculus like differentials and integration to be understandable. In my particular case, I was fascinated by creating models of viral replication - these terms could simply be altered by increasing a variable to increase rate. Similarly, the graphs of host and prey dynamics intrigued me. Obviously, I was more interested because of the direct application to another subject I loved (Biology), but I think the creative challenge that lies ahead would be to link math to a favorite subject.

      Linking math to the less obvious subjects such as to art or music or social studies (if they are so inclined) would be a formidable feat, but I believe it would be amazingly rewarding for students.
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    Feb 23 2011: I agree with Jonathan. I hated math in school because it was just to dry and boring. If math teaching would be based on more real life applications then many would find more love for it.
  • Feb 23 2011: Perhaps math should be taught with more examples of how it can be used in the real world - mostly in middle / high school. I think it's a hard subject to follow for most people because it's so abstract, especially as you reach higher level education.