{"id":2982,"date":"2009-09-21T19:00:32","date_gmt":"2009-09-21T11:00:32","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=2982"},"modified":"2019-12-18T15:17:43","modified_gmt":"2019-12-18T07:17:43","slug":"teaching-math-using-interactive-white-boards","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/learn-math\/teaching-math-using-interactive-white-boards-2982","title":{"rendered":"Teaching math using interactive white boards"},"content":{"rendered":"<p>Several readers have written asking me to write an article about teaching math using an interactive white board.<\/p>\n<p>You may have seen interactive white boards on TV during the election campaigns. The reporters could zoom in on particular areas in the USA map and bring up statistics on how the parties were faring. <\/p>\n<div class=\"imgCenter\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/CNN-IWB.jpg\" alt=\"CNN using the IWB\" width=\"450\" height=\"300\" \/><br \/>\nA CNN reporter using an interactive whiteboard. [Image source: NYTimes] <\/div>\n<p>These interactive whiteboards are rapidly becoming popular in classrooms around the world. <\/p>\n<p> I recently conducted an email interview with <strong>math teacher Jacky Gruszka<\/strong> on her use of the interactive white board. Jacky is an enthusiast for such interactive boards and has reported that she's become much more excited about teaching math since she began using them.<\/p>\n<p>The particular interactive whiteboad that Jacky uses is the SMARTBoard<sup>TM<\/sup>. This board allows her (and her students) to interact with objects (graphs, diagrams, Flash and java applets, etc) that are projected from her computer via an attachment that sits above the screen. <\/p>\n<div class=\"imgCenter\">\n  <img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/IWB-real-life.jpg\" alt=\"IWB\" width=\"450\" height=\"419\" \/><br \/>\n    Jacky Gruszka in action with the SMARTBoard. <br \/>\n    Note the projector above the board.\n<\/div>\n<p>Jacky writes:<\/p>\n<blockquote>\n<p>Dear Murray<\/p>\n<p>Thanks for giving me the    opportunity to talk about my use of the interactive whiteboard, specifically    the SMARTboard, which I began using in February 2009. Using the SMARTboard  has been    an engrossing, new and  exciting experience for me.<\/p>\n<\/blockquote>\n<p>On with the interview. <\/p>\n<h2>  (1) Please tell us where you teach -    and why you teach. <\/h2>\n<p>I teach mathematics at Taylors    College Waterloo, which is a large international school in Sydney, Australia. <\/p>\n<p>I really love    what I do for many reasons. <\/p>\n<ul>\n<li>Firstly, I think teaching is '<strong>giving back<\/strong>' to the    society that supports me in so many other ways so I feel good about that.    <\/li>\n<li>Secondly, I am fascinated by <strong>communication<\/strong> in general and, in    particular by the process of how to successfully communicate a complex    and abstract idea to someone else. Mathematics is the perfect subject for    that and my use of the SMARTboard this year has been very exciting for me for    that reason. <\/li>\n<li>Thirdly, it is very satisfying to me to 'turn around' the often    <strong>negative attitudes<\/strong> I find in students towards Mathematics. I have seen some    truly amazing transformations with students growing in confidence, in    charge of their Mathematics (not scared by it), and starting to feel some of    the beauty and excitement of the subject. <\/li>\n<\/ul>\n<p>I could go on and on    with this question but I'll settle on one last reason that is very    important to me - I have very rarely been bored by my job. I keep    discovering new angles, new problems, better ways of doing things and new    areas of interest.<\/p>\n<h2>  (2) Tell us about some of the things you've done with your IWB. Why did they &quot;work&quot; better than an    ordinary whiteboard lesson?<\/h2>\n<p>There are 5 main reasons why I think IWBs are a great tool for teaching mathematics. <\/p>\n<h4>(a)  Interactive graphs<\/h4>\n<p>I can present    beautifully drawn, clear and accurate graphs. Students have commented very    favourably about the graphing work and their own graphs are noticeably better    because they are always exposed to the correct shapes. I use fx-Draw3    and paste the graphs onto the Notebook pages. I can superimpose graphs    on graphs and then move one of them around to demonstrate for example, phase    shift of a trig graph or the effect of adding a constant to the equation of a    parabola.<\/p>\n<div class=\"imgCenter\">\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/IWB-graph.jpg\" alt=\"graphs on the IWB\" width=\"450\" height=\"404\" \/><\/p>\n<p>Jacky describes the asymptotes on her SMARTBoard  <\/p>\n<\/p>\n<\/div>\n<h4>(b)  Dynamic Visualisations<\/h4>\n<p>It is easy    to embed dynamic visualisations into the Notebook pages. (A &quot;Notebook&quot; is the SMARTBoard application that allows the user to create geometric objects, and to integrate these with images and text into a lesson.) <\/p>\n<p>This saves    me having to jump around the room clumsily attempting to mime some dynamic    mathematical concept or entreating students to imagine this or that.    For example, <a href=\"https:\/\/math.dartmouth.edu\/~klbooksite\/appfolder\/206unit\/SecTanLine.html\">this simple Tangent animation<\/a> which I use for the introduction to differentiation was very successful.  You can move the    vertical slider at the right and show variable <em>h<\/em> approaching zero. The students can more easily see how the secant appraches a tangent at the limit. <\/p>\n<p>A male student came up    to me after that particular lesson and with visible emotion thanked    me in a very heartfelt way. He was trying to find the words to say how blown    away he was by having maths ideas presented in this way and how he was    starting to really see what Calculus and its underpinnings of the notion of    limit was all about. These moments are so rewarding.<\/p>\n<p>Some (not a lot) of    the Gallery items (built-in interactive and multimedia items) in the    Notebook software are useful for Senior maths lessons. For example, I can get    coloured dice up on the screen (as many as I like and as large as I like) and    they can be rolled. Random results are generated. No more having students    noisily throwing dice on the desks and having half the class on the    floor under the desks looking for the dice they lose. I have used the    interactive protractor a lot and the electronic timer for quick quizzes.<\/p>\n<p>I can make    things fade in &amp; out, spin, fly in... fly out ..although the novelty of    this has faded somewhat for both me and my students. Fade in and Fade out    have been good stayers.<\/p>\n<h4>(c)  Visually appealing<\/h4>\n<p>Visually, interactive whiteboards   are a huge improvement over a static whiteboard. The instructor can ensure more brightness, colour, clarity, movement and    pictures. <\/p>\n<p>I have a giant picture of the calculator which I can bring up at    the click of the mouse for example. <\/p>\n<p>When we did Rates of Change,    we talked about an example where  a swimming pool was    &quot;being drained for cleaning purposes&quot;. Showing the students a photo of a real pool being drained meant the<strong> meaning of the    question<\/strong> immediately becomes much clearer. <\/p>\n<p>Someone has actually attempted to    put the grains of rice on the chessboard to show the power of a geometric    sequence and photographed the result and    I show that to my students too. (For background on this, see this <a href=\"https:\/\/www.intmath.com\/series-binomial-theorem\/series-introduction.php\">Fairy Story<\/a>.) <\/p>\n<div class=\"imgCenter\"> <img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/3216429791_f1ff84b202.jpg\" alt=\"rice on a chessboard\" width=\"333\" height=\"500\" \/><\/p>\n<div xmlns:cc=\"http:\/\/creativecommons.org\/ns#\" about=\"http:\/\/www.flickr.com\/photos\/audreypenven\/3216429791\/\">Source: <a rel=\"cc:attributionURL\" href=\"http:\/\/www.flickr.com\/photos\/audreypenven\/\">http:\/\/www.flickr.com\/photos\/audreypenven\/<\/a> \/ <a rel=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/2.0\/\">CC BY-NC-SA 2.0<\/a><\/div>\n<\/p>\n<\/div>\n<p> Sometimes I incorporate classic art eg for a    problem about maximising yield for an olive farmer I used one of Van Gogh's    pictures of an olive grove. <\/p>\n<p>I have Elvis Presley, one hand holding the    microphone the other pointing out to his audience reminding them not to    forget the &quot;+ c&quot; when they integrate! <\/p>\n<p>I'm trying to get mathematics    out of the <strong>sterile bubble<\/strong> students seem to put it in and into the flow of the    world. So for non-English-background students and visual learners the    SMARTboard has been wonderful.<\/p>\n<h4>(d)  My lessons are better organised<\/h4>\n<p>My lessons    are much better organised now that I am using the IWB. <\/p>\n<p>Everything is there and more. I can skip pages if    time is short. I can go back to previous pages again, even previous lessons    from months ago at the click of a mouse or the touch of my finger. The    examples are all up there. <\/p>\n<p>I very rarely have my <strong>back to the class<\/strong> so I find    that their attention is much more focussed (on me!) I have a page at the end    of each lesson with the headings LANGUAGE, FORMULAE, HOMEWORK. Time is saved    by having this all written out. I can be dealing with a student's    question while the rest of the class is copying down that last page. I can    run through the lesson privately with a student who might have been away sick    or was late to class (for a legitimate reason). I can use any of the lessons    for revision at any time. Students come up to the board after the lesson and    scroll back to get material they might have missed. I can revise my lessons if    certain things did not 'work' as I intended them and make them better and better. <\/p>\n<h4>(e)  Enjoyment<\/h4>\n<p>I am enjoying    using the SMARTboard so much. It really is fun! <\/p>\n<p>There are some great    interactive games such as:<\/p>\n<ul>\n<li>The classic &quot;<a href=\"http:\/\/nlvm.usu.edu\/en\/nav\/frames_asid_117_g_4_t_2.html?from=grade_g_4.html\">Switch or Stay<\/a>&quot; game <a href=\"http:\/\/nlvm.usu.edu\/en\/nav\/frames_asid_117_g_4_t_2.html?from=grade_g_4.html\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a> <\/li>\n<li>Another  game I used successfully was the &quot;<a href=\"https:\/\/www.intmath.com\/integration\/millionaire-calculus-game.php\">Who Wants To Be A Millionaire<\/a>&quot;  Calculus game <a href=\"https:\/\/www.intmath.com\/integration\/millionaire-calculus-game.php\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a> from IntMath (sound  is important).          <\/li>\n<\/ul>\n<p>But  really, the main fun for me has been the <strong>creativity<\/strong> that this form of teaching  has pulled out from me - creativity that I hardly knew I possessed.  And for a maths teacher, being creative is a bit of a novelty.<\/p>\n<h2> (3) What are some of the best resources that you  have found to use with your IWB?  How did you use them?  <\/h2>\n<p>IWBs are an easy to use device for collecting resources which can then be inserted and used appropriately throughout a lesson - a wonderful big toolbox for the teacher and student to pick and choose from.<\/p>\n<p>For Senior Mathematics, I  believe that the concepts of simulation and mathematical modeling are important  ideas to get across. <\/p>\n<p>Just yesterday I showed my classes your <a href=\"https:\/\/www.intmath.com\/exponential-logarithmic-functions\/world-population-live.php\">Current World  Population Counter<\/a> because we are doing  Exponential Growth &amp; Decay. Of all the dynamic things I show these days  with the Smart board, this got the most vocal response. They were <strong>rather  shocked<\/strong>. One student said spontaneously &quot;Oh, stop it. We have to stop  it!&quot;. They asked &ldquo;Is this real time? How can they get this information?&rdquo;  and this gave me the opportunity to talk about using an equation that models  the real life situation using population data from previous years.<\/p>\n<p>I have been  using some really good dynamic simulations of <strong>rates of change<\/strong> lately such as a <a href=\"http:\/\/lectureonline.cl.msu.edu\/~mmp\/applist\/decay\/decay.htm\">simulation of radioactive decay<\/a>.<\/p>\n<p>I have not said much about  videos, probably because its been hard to find good ones. <\/p>\n<p>The <a href=\"https:\/\/www.youtube.com\/watch?v=H_7lNT9oDzI\">quadratic formula song<\/a> took the students by surprise  although it was a bit long <\/p>\n<p>  The trig video from your  IntMath site <a href=\"https:\/\/www.intmath.com\/\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a> was  good although the ideas came thick and fast and it is best used after the topic  has been taught. <\/p>\n<div class=\"videoBG\">\n<iframe title=\"YouTube video player\" width=\"480\" height=\"303\" src=\"https:\/\/www.youtube.com\/embed\/FUMpGuLIQ5M\" frameborder=\"0\" allowfullscreen><\/iframe>\n<\/div>\n<p> Possibly the most enthralling one to watch (works  well with students) is the <a href=\"https:\/\/www.youtube.com\/watch?v=rEIpewOvAMc\">melting ice cube<\/a> Youtube video.  Wonderful music (esp. after you've watched it a zillion times like I have).<\/p>\n<p>A  comment posted on the Net about this latter video proved to be absolutely  true - &quot;whoever would have thought that watching an ice cube melt would be  so enthralling!&quot;<\/p>\n<h2> (4) What have been some of the struggles that  you have faced? <\/h2>\n<p>Getting a good looking  <strong>mathematical expression or equation<\/strong> up there is a bit of a pain, especially  fractions. They have to be constructed virtually bit by bit and then  grouped as a single object. I can't use MathType which would be my wish. Having  said that, with the simple toolbox provided by the Notebook software it is  possible to create anything mathematical, even definite integrals and I make it  a bit easier for myself by editing previous expressions that I have made or  just doing a copy and paste of something I have already created, such as <em>dy\/dx<\/em>.<\/p>\n<p>I would like to have  access to a store of <strong>good quality dynamic demos of maths concepts<\/strong> that I can  copy and paste directly onto the pages of a Notebook file. Simple, clear  animations without too much text around them (hopefully none!). Access to  the internet is great but it is still not immediate enough for me.<\/p>\n<p>I would like more videos  created for <strong>students with non-English speaking backgrounds<\/strong> ie shorter videos  presenting just one main idea (perhaps a real world application) where the  presenter speaks slower and more simply but speaks to his\/her audience as young  adults not children. It would be great to then be able to embed these in an  ongoing lesson.<\/p>\n<p>I also struggle a bit  intellectually with the knowledge that my SMARTboard lessons are very much  <strong>teacher-centred<\/strong>. My level of control in the classroom has dramatically increased  I would say and I am aware of the criticism from the teaching fraternity about  this. Of course it is good for students to not just be passive recipients of  education but I don't think this means running up to an IWB popping balloons  and moving tangram pieces around with one finger, especially the senior  students that I teach who are in the 18-20 age group. <\/p>\n<p>I am also continually  under <strong>time pressure<\/strong> to get through the content of the course and having  students interact with the board (even in a meaningful way) is about 10 times  more time consuming. This is something I am still thinking about.<\/p>\n<h2> (5) How often do you use your IWB? <\/h2>\n<p>I use it for every lesson.  At our school we are very fortunate that about half the classrooms have an IWB  set up linked to a computer on a podium. All I bring to the classroom is my 6  GB flash drive except for ONE occasion this year when I forgot it! I had to do  an ordinary whiteboard lesson which was a big comedown. We are also lucky to  have good IT support as the IWB software, Adobe Flash and JAVA etc need to  be upgraded quite often.<\/p>\n<h2>  (6) What software applications do you use with your IWB?<\/h2>\n<p>The lessons are all fully  prepared in advance with examples written up but there are deliberate  points at which I would actually do the solution real-time on the board.  Or a student might ask a question that needs a written explanation. On these  occasions I hand write. I have a small problem with the thickness of the pen.  It's too thick for a complex algebraic expansion (you lose fine definition when  writing say, e^(-1\/x)) and I know how to make the line thinner but it  won't stay thin as soon as I do something else like draw a rectangle or a set of  axes. But I think this is just a matter of delving into the Help Manual.<\/p>\n<div class=\"imgCenter\">\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/IWB-writing-with-digital-pen.jpg\" alt=\"writing with digital pen\" width=\"450\" height=\"312\" \/><br \/>\nHandwriting using  the digital pen.<\/p>\n<\/div>\n<p>I have found out how to  get my <strong>PPT files<\/strong> up there and have done that earlier in the year but my  preference is to convert everything to use within the Notebook application from SMARTboard. The style of PPT is  different to that of an IWB, the former working like a hammer, the latter like  a Swiss army knife (to use an excellent tool analogy I got from a  conference recently).<\/p>\n<p>I have used <strong>Excel<\/strong>  occasionally and intend to use it more. It's more a problem of the Senior High  School Maths syllabus I think, that spreadsheets do not jump out as  being immediately useful. They should be! I use them so much in my  everyday life I feel instinctively that they should be a much more  integral part of our current maths syllabus. <\/p>\n<p>I use <strong>websites<\/strong> quite often.  Sometimes these can be slow to load up which I don't like at all as it  interrupts the energy of the lesson. Lately I have been searching for Flash  animations that I can just copy and paste onto a SMARTboard page. They are  already moving when you open the page and I really like that. I have found two  excellent ones that show a tangent moving around a concave up curve and another  where the tangent moves around a concave down curve. They are simple diagrams  but the tangent is moving and it is much easier then to see that the  gradient is increasing, therefore rate of change of dy\/dx is positive and is  defined as d<sup>2<\/sup>y\/dx<sup>2<\/sup> etc. <\/p>\n<div class=\"imgCenter\">\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/09\/IWB-volume-of-solid-of-revolution.jpg\" alt=\"IWB - volume fo solid of revolution\" width=\"450\" height=\"285\" \/><\/p>\n<p>Using a lesson on volume of solid of revolution from IntMath<\/p>\n<\/div>\n<p>I spend a lot of time  trawling the Net looking for <strong>mathematics applets<\/strong> only to be frequently  disappointed by the visual presentation of many applets. They are small,  faint with thin spidery font and thin, spidery animations and they would  &quot;work&quot; too quickly!  <\/p>\n<p>I did find one really  excellent one though which was a demonstration of the classic  maximising volume  problem  of cutting out square corners from a sheet<br \/>\n  If you scroll down the  bottom of this page and click on Launch Presentation you get an easy to see  animation (that you can control the speed of). You can even make it Full  Screen. I look for more work by the same designer, Thomas S. Downey. This is  the best interactive maths aid I have found this year.<\/p>\n<h2>(7)   What do the students think of lessons presented this way?<\/h2>\n<p>The students have given me  very <strong>positive feedback<\/strong>. This is the main factor that keeps me going. I  surveyed them after using the SMARTboard for 6 weeks and asked them to compare  lessons done this way with the old whiteboard way.<br \/>\n  85% felt that their <strong>understanding and enjoyment of a  maths lesson<\/strong> and their attention in class was &quot;better&quot; or  &quot;much better&quot;. 91% said that their interest in the Smartboard  lesson was &quot;better&quot; or &quot;much better&quot; than it was for an  ordinary whiteboard lesson.<\/p>\n<p>I have students from other classes <strong>asking to sit in on my  lessons<\/strong> as extra. 98% of the time I see 26 faces totally focussed on the  lesson. No-one is looking bored or playing with a mobile phone or talking to  their neighbour. I have had emails from students saying things like :<\/p>\n<blockquote>\n<p>&quot;I have never seen this before. I never thought you can use this  kind of technology this way to teach Mathematics&rdquo; <\/p>\n<\/blockquote>\n<p>Another said:<\/p>\n<blockquote>\n<p>&quot;I'd like to say thanks a lot for your help  last semester. before moving to your class, I lost my confidence but thanks to  your help, I could enjoy and find confidence.I was so happy to be your student  :)&quot;<\/p>\n<\/blockquote>\n<p>And one more:<\/p>\n<blockquote>\n<p>&quot;I  want to tell you that I really enjoy your maths class, to be honest with you ,  I do not like maths when I was in China, however, you made me begin  to got interested in learning maths.&quot; <\/p>\n<\/blockquote>\n<h2>Conclusion <\/h2>\n<p>Jacky concluded with the following:<\/p>\n<blockquote>\n<p>The SMARTBoard has taken up    huge amounts of my time this year but it has been a labour of love. <\/p>\n<p>While the IWB provides lots of opportunities for enhancing lessons, it's important to remember that the teacher is  still the \"magic\" in the classroom.<\/p>\n<\/blockquote>\n<p>Thank you so much Jacky for your valuable contribution! <\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/learn-math\/teaching-math-using-interactive-white-boards-2982#comments\" id=\"comms\">13 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here's an interview with a math teacher who is very enthusiastic about interactive white boards.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[102],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2982"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=2982"}],"version-history":[{"count":4,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2982\/revisions"}],"predecessor-version":[{"id":12349,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2982\/revisions\/12349"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=2982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=2982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=2982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}