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Teaching Maths through real-life situations

Discussion in 'Mathematics' started by lizdoig, May 14, 2011.

  1. Hi. Had a few discussions with teachers recently and one argument came up time and again.
    I think that all maths can, and should, be taught with real-life examples and practical tasks. I have had much more success teaching this way rather than teaching the maths skills as an isolated objective. Many teachers say that they don't have time to 'do it' this way, which I appreciate as we are all on a very tight timescale to get everything 'taught' to everyone.
    In my most recent assessments the 'LA' students have by far exceeded their expectations - 45% of the class raised their levels by more than 2 sub-levels since the mid-year assessments in February.
    I have no idea how you would teach cos, sine and tan to students as a real-life situation although I do remember the saying & formulas even now! Our teacher used pirates to if remember rightly. Now I think about it, I remember a wooden barrel being brought out - maybe I should get intouch with him!
    Any suggestions for teaching this way?
    Liz
     
  2. alabaster

    alabaster New commenter

    I agree that putting things into context should be used wherever possible. Sometimes I struggle to put things into a context that is simple enough not to confuse the kids though. For example - off the top of my head I can't think of a simple real life situation to teach vectors in. Trying to link them to force diagrams in physics in likely to confuse my students - most of them won't have come across anything that complicated in physics.
    Also - off the top of my head I can't think of a simple real life situation where the Alternate Segment Theorem would be handy for me!
     
  3. Here's a real life situation for cos: A low flying military aircraft using radar cannot compute the range to a target directly. It can only compute the slant range which provides the radar echos and is extended due to the aircraft's height. The situation can be very easily sketched. To compute the actual range (across the earth's surface) the radar multiplies the cosine of the angle of the aircraft's radar scanner depression by the slant range to produce the actual range. The radar scanner, the slant range and the actual range form the vertices of a right angled triangle. I can give you many other engineering applications for trig as a whole which are too numerous to mention here. You could also use simple applications from AS level mechanics such as resolution of forces.
     
  4. To my mind, this statement is too general. Perhaps it's just symantics, but I don't think that there are many areas of maths that can (let alone should) be taught with real-life examples.
    I like assessing, securing and extending the learning through real-life examples wherever possible. Many of my lessons will start with a "real-life" question, we'll discuss how to solve it, identify that we need some "new maths", so I'll teach it, they'll practise it, then go back to answer the original question. But that's a different thing in my mind.
    Your trig example demonstrates what I mean by this. I don't think that we, as maths teachers, should be scared of teaching a topic exactly as and for what it is. By all means, then assess, secure and extend the topic through real-life settings (I think, when I was at school, these were often referred to quite simply as "worded questions").
     
  5. I teach my students to mock the examiner if they try too much to put the question into context
     
  6. Some maths should be taught for the sake of teaching it and enjoying its beauty rather than trying to justify it to pupils who are not engaged.
    The intrinsic satsifaction of solving problems in pure maths for many pupils is something that should not be watered down.
    I believe the curriculum should change rather than having to water topics down to make them appeal to pupils. Some foundation pupils (at GCSE) will benefit from 'real world maths' but sometimes the response to "why do we bother learning this?" should be met with "Because its maths and its nice" rather than trying to find a flimsy link to justify it.
    "Why do we have to do circle theorem? when we we ever use it?" is a typical top set disengaged pupil question......."Because there is something very pretty about it" rather than having to take a rope out to the playground and sell them a story about some far fethced situation where it occurs beyond the class.
    I agree with some maths being taught for a practical reason, some certainly not.
     
    crashMATHS likes this.
  7. DeborahCarol

    DeborahCarol New commenter

    At school I often used to wail 'Why do I have to know about cosin, sin and tangent? What good will it be in my life?' Well, no, I didn't have to use cosin, sin and tangent in life UNTIL I had to brush up on it to....teach children cosin, sin and tangent!
    I suggest telling students that, even if they're not going to be taking A-level Maths, that circle theorem, trig etc, are excellent brain training for them. It's about being given some information, but not all, and using what one already knows to work out what the missing information is. It's about bravery when facing problems, about working hard to build up a sufficient arsenal to vanquish all mental foes (eg that little voice telling us 'I can't do this!'). Tell them the brain (and our self-esteem) thrives on this sort of activity and it's good training for all sorts of situations we might meet in life.


     
  8. Many dont want to train their brains though and say "thats boring"
    My point focuses on the idea that we should not have to justify why we are teaching them anything even if they may never use it again as other may on some level.
    Things I learned at school:
    • How to play the triangle with a bit of string tied to a chunk of metal
    • The subtle differences between written words in German grammar
    • How to draw the school building with a technical drawing kit
    • The French revolution in the 18th century
    plus many many other things I will never do again.
    None of this is remotely useful to everyday life for the majority yet the teachers of the subjects involved rarely have to justify why they spent large parts of a school year doing it.
    I believe we as maths teachers should not have to justify or water down a beautiful subject to spark motivation or control behaviour. We are doing it because we are doing it.

     
  9. PaulDG

    PaulDG Occasional commenter

    I believe that too.
    As a teacher who "had a life" before teaching, I've used all the maths I did at school (and a lot more) professionally and I can give the kids examples of where pretty much everything we do is used or can be used.
    When I started, I thought that being able to do that would be a great asset.
    It's not really.
    "Where will I use this" isn't a real question; it's a distraction technique. Some kids might genuinely be interested but they can find out for themselves pretty easily and anyway, all KS2/3/4 textbooks include wordy questions that give actual contexts for everything so they can see possibilities there.
    No, the kid that asks "where will I use this" is looking to kill a bit of time in the hope you'll expect them to do less work this lesson - and if they're really lucky they'll even get you to legitimise their intent not to do the work.
    "Where will I use sines and cosines?"
    "Well, I don't know where you'll use them as who knows what the future brings. What I can tell you is they're used in electronics, mechanical engineering, video game design, audio processing, construction, navigation and all sorts of other things".
    "Yeah, but I'm going to be a car mechanic / hairdresser when I leave school, where am I going to use them?" (Hoping you'll now get into some sort of careers discussion with them which will involve them talking about their favourite subject - themselves - and them completely getting out of doing any work this lesson.)
    It doesn't work.
    The answer to "why are we doing this" is:
    "Because it'll be in your test at the end of term."
     
    mathsmutt likes this.
  10. alabaster

    alabaster New commenter

    I agree, and I am fed up with the kids that have a target of A at GCSE trying to justify their not bothering to do any of the work because they can't see how it will help them in the future.
     
  11. Anonymous

    Anonymous New commenter


    Wouldn't hurt though to use a bit of real life stuff to sparkle some motivation? Or don't you want motivated children in your class?
    As for vectors - yes, I enjoyed the mathematical aspects of it. Then when I was 23, I did a diving course and a course on navigation. Had to use tide charts to work out speed and direction of tides, plot a route, take into account the tide. Fascinating.
    I think the RAF have some resources on using maths in real life situations.
    And yes - there is plenty of stuff I learnt at school that has no use now and I did it because I had to. Luckily I knew the value of education so I worked hard. Some people might not know the value and anything we can do to motivate them and interest them is not a bad thing, is it?
     
  12. You guys are great!
    Thank you for the informative and supportive suggestions you've made! Such a relief to have secondary teachers who DO try to 'make it real' for their students! Even if you've exhausted all other replies and there are still questions - "It's on your test" - that's real! No psycho, happy-clappy stuff going on in this forum!
    If you don't mind, I'm going to send the link to this forum to our Secondary Teachers in case they have anything to add...
    Again - You Are Great!
    Liz
     
  13. Hi arsinh. I'm not sure how you feel about this, but I generally find that quoting small sentences from a long article obscures much of their original context. I didn't choose to have to justify not letting students come up with their own usernames. Perhaps you could read the whole story and check out the video before passing judgement?
    On the other hand I'd agree that perhaps it would be best not to give trolls the responses that they're looking for, so perhaps the first half of that reply should have been left out.
    We live and learn, don't we?
     
  14. Learnalot ... my earlier reply has been deleted as it quoted your opening post. So, to summarise, I like the look of the site and think that it has its place in what I earlier referred to as "assessing, securing and extending" the learning done in class. (That's just my opinion, obviously, others may rate it higher and others lower.)
    That said, as someone with years of sales (much of it IT related) experience behind me ... when you're selling something be proud of it and don't hide behind veils of "I'm just providing a link to some resources .... whether I work for the company or not is immaterial" (I'm paraphrasing, but I don't believe I've changed it too much.)
    Following on from that, don't get into spats with potential clients. If every customer tells 7 friends, and they tell 7 friends ...
    Your site looks really good and I, for one, am going to mention it to my HoD, but don't ruin the good work by appearing a little ... what's the word ... teenager-on-a-forum-ish.
     
  15. Hi Paul
    Thank you so much for the positive comments. I was beginning to think the forum was an online representation of the village of the damned so it's nice to be addressed without being accused of something. Cheers.
    With regards to hiding behind a veil, I think that's the exact opposite of my first post which was, sadly, unceremoniously deleted for violating TES code of practice. I was singing from the rooftops about what we have achieved with our potal and how many of you could see measurable gains from using it with your students and I proudly proclaimed my involvement. Unfortunately some users took issue to that and the post was gone.
    I take on board what you say about trying to get on with people, irrespective of their tone or comments. Having been online pretty much every day since 1996 though, sometimes it's just a little difficult to find the patience. Still, I will try harder because, as you say, it would be a shame to overshadow the work that we have achieved and the positive results that it is having on maths students.
    I'll keep an eye out for your HoD's trial application and be sure to give them an extra week!
     
  16. arsinh

    arsinh New commenter

    You seem to attach a great deal of importance to portion size. "Another disappointment considering that we were in a "steak house" was that the only fillet steak available was a mediocre 8oz, so both my father and I ordered 12oz sirloins instead." I see you have now deleted the restaurant review (something I said?) but, never fear, it will live long in the heart of Google cache.
    While there, I was suprised to come across these comments about your ertswhile customers (long quote this time to keep you happy):
    "As time has progressed since our launch almost two months ago another pattern in the use of the portal has started to emerge: teachers who post low scores on resources or games seem to log in less than those who post higher scores.
    Firstly, a possible explanation for this is that those who are inherently more interested in maths and/or competitive gaming are not only more likely to log into a related service more often but are more likely to be good at it as well. On the other hand, there’s little excuse for poor performance caused by incorrect answers from maths teachers on maths resources. Surely the vast majority of maths teachers have at least a passing interested in the subject?
    I’m trying to decide if the teachers who post low scores are consciously avoiding the portal because it’s exposing their weaknesses (and we know such weakneses exist) or if they’re subconsciously avoiding the portal because they believe their poor performance is down to issues with the software rather than their poor knowledge/skill in the subject.
    We’ve received “bug” reports from teachers – some of them quite aggressive I might add – when upon investigation the reality was that they either had errors in their methods or simply hadn’t read the question properly. One teacher in particular claimed there was a bug in Britain’s Got Power because one of the questions didn’t give him the answers after he submitted an incorrect guess!
    The fact that so many students (some as young as 10 years old) are posting such high scores clearly demonstrates that there is no built-in problem with the software because if there was, everyone would be affected. Only a small number of teachers who have posted low scores have come to us with bogus “bug” reports though so without getting individual feedback it’s difficult to say if this is a common misconception.
    Either way, it’s a shame if some students aren’t going to be allowed to use the resources in school because their teachers are afraid of posting low scores. I think it might even be worth pointing out that they don’t have to post a score at all: it’s possible and perfectly acceptable to simply create student accounts and monitor their progress from your teacher account without ever posting a score at all, so don’t let that fear keep your students away from software that is having a tremendous effect on their maths skills. An alternative idea of course is that you use the resources and games yourself to improve your skills!"
    Could your complete lack of respect for your professional colleagues ("we have seen some concerning behaviour from some teachers to be honest") be one of the reasons why you have parted company with six mathematics teachers (or is it more now?) in a year?
    Finally, I note that these resources are Bowland rejects. Our profession didn't rate the resources they did release particularly highly but at least they were free. As a gastronomic adventurer, I'm sure you will agree that it is rather cheeky to charge top dollar for what amounts to little more than leftovers.
    "The reason for their decision was apparently the pedagogy behind the resources and that maths just wasn’t taught in that way yet, which was very strange considering we had two full-time maths teachers on board designing them for us!
    Perhaps our resources were just too forward-thinking for such an organisation?
    Not to worry. We’ve had such good feedback on the resources that we’ve decided to make our own portal, called Learnalot. The resources that Bowland turned down – plus a lot more besides – will find a home there instead."
     
  17. Anonymous

    Anonymous New commenter

    You don't get it. I hope you don't work in marketing because even though any publicity is helpful, being rude and antagonistic towards customers is not going to work.
    Basic rule of marketing - you do something good and the customer tells 1 person. Do something bad and the customer tells 10 people. Probably got my sums wrong - I would guess it's 20 / 80 as these things usually are.
    The point is - this is a board for maths teachers. There are hundreds of companies out there who would love to sell their products and use all kinds of marketing to do it. But actively promoting your product on a board is spam.
    Second point - don't criticise customers. We've all learnt your company name and you aren't exactly selling yourself by your attitude.
    Marketing 101 I think.
     
  18. DM

    DM New commenter

    Typical maths teacher then by the sound of it.
    [​IMG]
     
  19. Anonymous

    Anonymous New commenter

    Just in case it's not clear.
    "You may not upload, post, email or otherwise transmit any unsolicited or
    unauthorised advertising, promotional materials, "junk mail," "spam,"
    "chain letters," "pyramid schemes," or any other form of solicitation,
    except in those areas (such as shopping rooms) that are designated for
    such purpose; "

     
  20. All in all, it's abundantly clear that the TES forums are a very hostile and unfriendly environment. Clearly a clique. If you weren't born here, you're not welcome.
    Initially I thought it was just me getting off on the wrong foot for daring to promote a great resource that I just happen to be involved with, but having read some of the other threads going back several months it's obvious that there is a small number of users here who's sole purpose on this forum is to try to put down everyone else's great work.
    Whether this is because their own work leaves a lot to be desired, I don't know, but whatever the reason it certainly isn't a fertile place for new ideas and new ways to engage students to thrive.
    I'm concerned about the effect that such personalities are having on young teachers who are new to the profession who come here looking for help and advice. Whether getting shot down for daring to suggest involving real-life scenarios in their lessons or getting chastised for using facilitators in online demonstrations, it seems any possible threat to the old guard is vehemently put down.
    And to those who think I came here merely to market my product, don't be so naive. It would be simplicity itself to harvest email addresses from the forum and send marketing emails to them all, but that's not being involved and I have no intention of doing that. I registered on here because I wanted to be involved in a 2-way communications process. I wanted to ask for your input in exactly the same way I asked for input from our beta schools. Little did I know that outsiders are burned at the stake at TES.
    Of course, I know not everyone here is like this. I've had a good number of private messages from users who prefer to stay in the background and avoid confrontation with the bullies and from the welcome I've had here I can completely understand why. I appreciate the warnings and I respect you for continuing to come here despite the hostility - but I don't think this is for me. I was looking for a fertile and positive place to discuss ideas and share best practice; not somewhere I'd have to defend myself and my work with every post.
    I'd wholeheartedly recommend that some of you get out more. There's more to life than putting other people down - especially people who have spent two years of their lives and their entire savings making a portal that tries to make life easier for teachers and make maths more interesting and exciting to children.
    Why did we all bother?
     

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