teachMathematics: Last blog entries
http://www.thinkib.net/teachmaths/blog
InThinking teachMathematics: www.thinkib.net/teachmaths2018 InThinking Educational Consultants. All rights reserved.Euro 2016 Fractions Decimals %
https://www.teachmathematics.net/blog/21105/euro-2016-fractions-decimals-
Fri, 10 Jun 2016 00:00:00 +0100]]>Euro 2016 Fractions Decimals %https://www.teachmathematics.net/cache/blog-thumbs/24/21105-1499084735-thinkib.jpghttps://www.teachmathematics.net/blog/21105/euro-2016-fractions-decimals-
<h1><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/21105-1499084735-thinkib.jpg" alt="Euro 2016 Fractions Decimals %" /><br /><br /></a> <a href="teachmaths/page/20577/fraction-decimal-conversion-debate" title="Number » Activities » Fraction-decimal conversion debate">Fraction-decimal conversion debate</a> “which is easier, converting fractions to decimals or decimals to fractions?”</p> <h2>Why do I like it?</h2> <ul> <li>An application that genuinely engages and interests most students.</li> <li>International awareness – as with different country’s mains voltage levels, different plug sockets etc. it’s intriguing how different nations have developed different means for solving the same problem (US, UK and continental Europe betting odds).</li> <li>A good example of how fractions, decimals, percentages and ratio are used to measure and define proportions. Students often lose sight of, or never really understand, this aspect of what fractions, decimals etc. are used/designed for.</li> <li>Betting odds are an everyday example that seem so simple, yet actually require a lot of mathematical thinking to fully understand. In particular the extension where the understanding “chance of winning” is akin to the question “how does one break even on this bet” i.e. 2/9 odds means to be a “fair” game, the bookie would expect you to win your bet (and hence £2) for 9 games, but then lose your bet (hence lose £9) in the next two i.e. lose twice in every eleven bets and win nine times (chance of winning = 9/11).</li> </ul> <p>However, it’s not a resource through which students can really “discover the mathematics for themselves”. To do this, I think you’d have to set up a simulation/game for them to play and record what happens each time and then leave it to them in pairs/groups/individually etc. to try and work out how the odds are working? I find it takes quite a bit of explanation, peer-to-peer help, and many students will need to understand the Pld, GF, GA, GD, Pts abbreviations used in the “Euro2012” pool matches tables – their sports interested peers can explain. There’s a lot of “explaining”, and discussion, required (but this doesn’t mean that by the end of it, they haven’t <em>understood</em>, <em>only memorised!</em>).</p> <h2>Why use this resource in a mathematics class?</h2> <p>So what’s the value of this resource in a mathematics classroom? As I often remind students, all of their parents are gambling, whether they see it like that or not: on their savings and investments, their pension plans, the insurance they do, and don’t, have etc. Gambling: sports, poker, is, rightly or wrongly, exciting to young people (because they know it’s not well seen in the adult world/it has an element of danger?) and glamorous – get rich quick with little effort . . (and equally easily end up on the street having lost years/decades of savings . . ). We can use this to educate more generally about risk assessment and management. It’s a context that gets them interested in relating the mathematics we’re covering in class to the world they're living in outside of class. I get a real sense of having communicated to students something that I think is essential . . and we have a lot of fun doing it! It would be great to hear from you if you use it: <a href="mailto:oliverb@inthinking.co.uk">oliverb@inthinking.co.uk</a></p> https://www.teachmathematics.net/blog/21105/euro-2016-fractions-decimals-#1465513200A favourite starter
https://www.teachmathematics.net/blog/20297/a-favourite-starter
Sun, 17 Jan 2016 00:00:00 +0000]]>A favourite starterhttps://www.teachmathematics.net/cache/blog-thumbs/24/20297-1453026566-thinkib.jpghttps://www.teachmathematics.net/blog/20297/a-favourite-starter
<h2><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/20297-1453026566-thinkib.jpg" alt="A favourite starter" /><br /><br /></p> </section> <p ></p> <p>OK, so maybe you got there already, but I didn't and I am amazed and delighted with how often this goes exactly this way in my classroom.</p> <p>So many issues wrapped up in all of this and thats why I enjoy it. Now off to further update the numberline on my classroom wall as I commit to being less 'numberist' with every passing year.</p> <p>Thanks....</p> https://www.teachmathematics.net/blog/20297/a-favourite-starter#1452988800Christmas Activities
https://www.teachmathematics.net/blog/20123/christmas-activities
Thu, 17 Dec 2015 00:00:00 +0000]]>Christmas Activitieshttps://www.teachmathematics.net/cache/blog-thumbs/24/20123-1450358347-thinkib.jpghttps://www.teachmathematics.net/blog/20123/christmas-activities
<p ><span ><span >Have a Merry Mathematical Christmas!</span></span></p> <p >So with Christmas coming around again it is time to find some activities that will entertain the students in the last week yet offer something meaningful mathematical activity. Here's some of my favourite activities that I'll be turning to in the last week.</p> <div class="pinkBg"> <h2><a href="https://www.teachmathematics.net/activities/the-great-elf-game.htm" target="_blank">The Great Elf Game</a></h2> <p><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/20123-1450358347-thinkib.jpg" alt="Christmas Activities" /><br /><br />Here’s an amazing demonstration of fractals and the Wada property that you can make with 4 reflective baubles, some scraps of coloured paper and a light source. Just beautiful!</p> </div> <div class="pinkBg"> <h2>Origami - Exploding Pyramids</h2> <p>There is a lot of potential to bring some paper folding into the classroom. I'm going to try this one with one of my classes this year. It looks like lots of fun. I just now need to find some christmassy paper to make them with...</p> <p ><iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/LlghcSz7XhY?rel=0" width="640"></iframe></p> </div> https://www.teachmathematics.net/blog/20123/christmas-activities#1450310400Museum of Mathematics
https://www.teachmathematics.net/blog/19823/museum-of-mathematics
Fri, 23 Oct 2015 00:00:00 +0100]]>Museum of Mathematicshttps://www.teachmathematics.net/cache/blog-thumbs/24/19823-1445436939-thinkib.jpghttps://www.teachmathematics.net/blog/19823/museum-of-mathematics
<p><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/19823-1445436939-thinkib.jpg" alt="Museum of Mathematics" /><br /><br /> </p> https://www.teachmathematics.net/blog/19823/museum-of-mathematics#1445554800Les Fetes des maths!
https://www.teachmathematics.net/blog/19821/les-fetes-des-maths
Wed, 21 Oct 2015 00:00:00 +0100]]>Les Fetes des maths!https://www.teachmathematics.net/cache/blog-thumbs/24/19821-1445434416-thinkib.jpghttps://www.teachmathematics.net/blog/19821/les-fetes-des-maths
<h2><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/19821-1445434416-thinkib.jpg" alt="Les Fetes des maths!" /><br /><br /></p> <p>There was alos a lovely range of exhibits, puzzles and interactivities provided by a large range of peope and we were busy from 10.30 in the morning until 18h in the evening! Like I said, what a great idea. I think it would be great to see these type of events popping up everywhere. We would love to hear about any similar events that you know about! For now, we felt we were in great company - literally, and we are already looking forward to doing it all again next year.</p> <p ></p> <blockquote class="twitter-tweet" lang="en"> <p dir="ltr" lang="en">Great to work with all these guys! <a href="https://twitter.com/Simon_Gregg">@Simon_Gregg</a> <a href="https://twitter.com/Richard_Wade">@Richard_Wade</a> <a href="https://twitter.com/bowleso">@bowleso</a> <a href="https://twitter.com/fermat_science">@fermat_science</a> <a href="http://t.co/6ZsJc4jdMS">pic.twitter.com/6ZsJc4jdMS</a></p> — Jim Noble (@teachmaths) <a href="https://twitter.com/teachmaths/status/653455461660917760">October 12, 2015</a></blockquote> <script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> <p>..</p> https://www.teachmathematics.net/blog/19821/les-fetes-des-maths#1445382000Lego Mathematics
https://www.teachmathematics.net/blog/19827/lego-mathematics
Wed, 21 Oct 2015 00:00:00 +0100]]>Lego Mathematicshttps://www.teachmathematics.net/cache/blog-thumbs/24/19827-1445464991-thinkib.jpghttps://www.teachmathematics.net/blog/19827/lego-mathematics
<p ><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/19827-1445464991-thinkib.jpg" alt="Lego Mathematics" /><br /><br />Facebook page.</a></p> https://www.teachmathematics.net/blog/19827/lego-mathematics#1445382000Changes to the site
https://www.teachmathematics.net/blog/18662/changes-to-the-site
Sun, 22 Mar 2015 00:00:00 +0000]]>Changes to the sitehttps://www.teachmathematics.net/cache/blog-thumbs/24/18662-1425834722-thinkib.jpghttps://www.teachmathematics.net/blog/18662/changes-to-the-site
<h2>What's different?</h2> <p>If you are reading this then it might be because you have noticed that many more of the activities that are on the site require a password for access. We are genuinely sorry if this has inconvenienced you in anyway and wanted to explain the rationale. The site has always had an option to subscribe, the only change is that many or most of the activities did not require a password before. The site has cost us a good deal of time and money to this point and, if we are to continue to provide, polish and publish 'lessons to look forward to' then we need to have a more sustainable model to finance the future. With an annual subscription fee of 80€ for access to all staff and students in your school we have deliberately kept the fee very affordable. You can read more about our rationale here on the <a href="http://www.thinkib.net/teachmaths/page/18245/why-subscribe" title="About Us » Why Subscribe?">Why Subscribe?</a> page, which is actually copied below. Subscribing couldn't be easier (red button on top left) and we hope to see lots of you!</p> <h1><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/18662-1425834722-thinkib.jpg" alt="Changes to the site" /><br /><br /> <h2>What is on the site?</h2> <div class="greenBg"> <p ><em>“This is one of the best websites around for teaching ideas in mathematics – it is challenging, mathematically robust, extends mathematical ideas rather than dumbing them down, is full of pedagogical sense and innovation, and ought to be available intravenously – Anne Watson, <a href="http://www.education.ox.ac.uk/about-us/directory/emeritus-professor-anne-watson/" target="_blank">Emeritus Professor Mathematics Education, Oxford University” </a></em></p> </div> <p>The holy grail of resources for us as teachers are those great, well resourced ideas that completely engage all kinds of students in rich activity that promotes mathematical thinking. The kind of activity that gets students reasoning with each other, making and testing conjectures and driven to achieve. Yes, of course that is ambitious and so it should be.</p> <p>We all know when a lesson has gone well, we know when students have had fun, we know when they have been engaged, but when we know that they have seen mathematics as it really is and really connected with it – these are the lessons we look forward to!</p> <p>That is what we are trying to do! We already have 150 + activities on the site covering large parts of typical secondary/high school Mathematics curricula and the site is growing all the time. Sometimes simple, sometimes complex, sometimes short, sometimes long, sometimes on computers and often not - always worth it!</p> <h2>Aren’t there lots of free resources already online for mathematics teachers?</h2> <p>Yes, there is a lot of stuff out there for teachers, and yes, some of it is brilliant. From our experience though, <em>most</em> of those resources can be filed under the headings of ‘Worksheets’, PowerPoint lessons’, ‘games’ and ‘puzzles’ all of which have their rightful place in a varied classroom and we are delighted that they are out there.</p> <p>What we want more than anything though are the resources described above. These are rarer! Finding, creating and employing these type of activities are the highlights for us!</p> <h2>Why pay?</h2> <p>When you consider the enormous sums of money that schools and departments willingly spend on textbooks and subscriptions, it seems odd to quibble over the small fee we are asking (80 Euros/65 GBP/ 100USD/ Year). Then consider the return on the investment! Textbooks are inefficient, quickly out of date, static and they are a model of mathematics teaching that we know is limited (note - limited, not useless).</p> <p>A classroom full of engaged students thinking about, talking about and doing mathematics? We think that is priceless.</p> <h2>Models for the future</h2> <p>Many sources on the Internet would have you believe that mathematics teaching is going through a revolution. Many mathematics educators have been arguing for and employing this revolution for decades already. Mathematical thinking is by no means a new idea!</p> <p>The debate about mathematical pedagogy rages on, but there is little doubt that while governments drive the agenda with high stakes testing, classroom resources will be geared towards those tests. We feel that the larger parts of school budgets are spent on these kind of resources produced and peddled by major publishers.</p> <p>Despite all of this, classroom teachers have been managing their classroom reality with inventiveness and innovation themselves for years. Our feeling is that this is where the emphasis should go. Our resources have been developed over a long period of time (40+ years of classroom experience between us) We use them ourselves, refine, elaborate and update them. We are always driven to create new resources and know that there is no shortage of inspiration. The emphasis is driven by educational research and practice about how people engage with mathematics.</p> <p>Real teachers, working with rich ideas inspired by educational research, informed by actual classroom practice, making resources that are polished and published on the Internet.</p> <p>For this we are asking a subscription fee of 80 Euros, 65 GBP or 100 USD (or equivalent wherever you are)</p> <p>Subscription models are obviously in vogue. Even within that though, we feel that there is danger people can get greedy and ask prices that force schools in to either/or decisions. At this price schools can afford to subscribe to multiple sources that they feel are useful.</p> <h2>What if everybody did it?</h2> <p>Well that is just the beauty of it isn’t it? In the Internet age, everybody is completely free to do so and many people are. That said, the leap from a filing cabinet full of ideas to a polished website that provides everything teachers and students need, multimedia and reflective commentary etc. has been enormous and deeply time consuming. It continues to demand a good deal of time and effort on top of a full time job too!</p> <p>It is a reasonable view for the future that teachers will be providing each other with all the resources they need and that there will be plenty to choose from.</p> <p>Rather than expect of each other that we will do this for free, why not imagine that we take back some of the enormous sums of money schools spend on other resources and spend it on resources that teachers have made.</p> <h2>Decision Time</h2> <p>Working on this site gives us an enormous amount of pleasure. We have always felt that our own students are the primary beneficiaries. Knowing that teachers and students out there are using the resources too just multiplies the pleasure. We feel that the work we do is worth a small piece of your schools budget! We hope you do to - if you are convinced, then click the red subscribe button at the top - if not, we understand!</p> <p>Thanks for reading!</p> <p>Jim Noble and the teachMathematics team</p> https://www.teachmathematics.net/blog/18662/changes-to-the-site#1426982400Polygon Proofs
https://www.teachmathematics.net/blog/18661/polygon-proofs
Sun, 08 Mar 2015 00:00:00 +0000]]>Polygon Proofshttps://www.teachmathematics.net/cache/blog-thumbs/24/18661-1425833688-thinkib.jpghttps://www.teachmathematics.net/blog/18661/polygon-proofs
<h2>Polygon Proofs</h2> <p>I have been playing with an old activity recently that was shown to me in my first year of teaching about three different ways to prove the interior angle of a polygon. In short, it involves starting with each of the three diagrams below.</p> <p ><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/18661-1425833688-thinkib.jpg" alt="Polygon Proofs" /><br /><br /></p> <p>I copied the image up to A3 and cut the triangles out. I gave groups of students a set of the triangles and asked them to make me all the regular polygons from triangle to decagon! This was not easy, but it did highlight that difference I was talking about. The hexagon and nonagon were easy because they were split in to equal triangles but the others provoked a lot more thought. I was pleased with the result!</p> <p>Once students were done I gave out a copy of the diagram below and asked them to work out all of the angles in the picture. Again, I was happy with the activity and reasoning that resulted.</p> <p>As with most classroom ideas, I had to try this one out to see what would happen and then see if has any impact on students ability to manage the proofs. I'll chew on it for a while and see what we come up with but I the idea has definitely shown potential for the kind of classroom activity I find the most productive!</p> https://www.teachmathematics.net/blog/18661/polygon-proofs#1425772800Enjoyed using these resources?
https://www.teachmathematics.net/blog/18123/enjoyed-using-these-resources
Mon, 15 Dec 2014 03:30:00 +0000]]>Enjoyed using these resources?https://www.teachmathematics.net/cache/blog-thumbs/24/18123-1418645778-thinkib.jpghttps://www.teachmathematics.net/blog/18123/enjoyed-using-these-resources
<h3><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/18123-1418645778-thinkib.jpg" alt="Enjoyed using these resources?" /><br /><br />Take a couple of minutes to tell us what you think!</h3> <p>Hello all, we are writing to ask for your help. We would really like to collect some feedback from people who use this site. If you have ever used resources from the site and had a positive experience, please take a moment to write it down. A sentence or two to say what you think about the resources would be great. We have worked really hard to try and share some of our best ideas for teaching mathematics here and are continuing to do so. Like most teachers we love coming across really great resources and ideas that make our classrooms more engaging for students. We hope that is what we are offering!</p> <p>If this site is not your sort of thing, then no problem, if it is, please take a moment to fill in the form below. Thank you, from the Teachmathematics team, Jim, Rich and Ollie. While we are here, let us wish you a merry Christmas and a happy new year!</p> <div></div> <div><iframe frameborder="0" height="800" marginheight="0" marginwidth="0" src="https://docs.google.com/forms/d/1U72jIw8Uhs9IbVGLTc2mqpj7F9-kudJCeYfab1O8DyQ/viewform?embedded=true" width="760">Loading...</iframe></div> <div></div> Please not that we would be happy to return the favour. If you publish your resources and we are enjoying them then we would be only too happy to tell you!https://www.teachmathematics.net/blog/18123/enjoyed-using-these-resources#1418614200Seeing through these problems!
https://www.teachmathematics.net/blog/18050/seeing-through-these-problems
Thu, 04 Dec 2014 03:30:00 +0000]]>Seeing through these problems!https://www.teachmathematics.net/cache/blog-thumbs/24/18050-1417688933-thinkib.jpghttps://www.teachmathematics.net/blog/18050/seeing-through-these-problems
<div dir="ltr" trbidi="on"><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/18050-1417688933-thinkib.jpg" alt="Seeing through these problems!" /><br /><br /> No solutions here as that would spoil the fun!</div> https://www.teachmathematics.net/blog/18050/seeing-through-these-problems#1417663800Maths Journals
https://www.teachmathematics.net/blog/17036/maths-journals
Wed, 25 Jun 2014 05:20:00 +0100]]>Maths Journalshttps://www.teachmathematics.net/cache/blog-thumbs/24/17036-1403713461-thinkib.jpghttps://www.teachmathematics.net/blog/17036/maths-journals
<h3> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/17036-1403713461-thinkib.jpg" alt="Maths Journals" /><br /><br /> Mathematical Communication</a>. A year on from that first post I am reviewing a year of having played with the idea and thinking about how to push this forward into next year. I started a good debate with one of my colleagues about this and, as so often, I am left with a bunch of questions rather than answers - for now - realted to waht I am hoping to get out of this exercise. So, as a reminder, the following is what I was hoping that students could get out of the experience of keeping journals, in no partocular order.....</p> <ul> <li> Keep less of what we do but make what we keep more useful all round</li> <li> Encourage students to comuunicate about mathematics</li> <li> Provide a good exercise in review - making it</li> <li> Provide an excellent resource for revision - looking back at it</li> <li> Include lots of images and photographs that promote the idea of episodic memory.</li> <li> Students to keep something as a record of their maths that is something they take real pride in</li> <li> To have something more concise to show parents as a record of their work</li> <li> To engage students on a diferent level</li> <li> .......</li> </ul> <p> So as I go forward with this and following the debate I started with my colleague, I have the following questions...</p> <ul> <li> Is this task suited to some students more then others?</li> <li> Who, how and why?</li> <li> Does this task offer benefits for <em>all </em>students?</li> <li> If no, then who could do without it and why?</li> <li> What other tasks that take place in my classroom or in the teaching and learning of maths could I ask these questions about</li> </ul> <p> At some point I will need to commit to writing what answers I am giving to these questions and what progress I think was made against the aims set out above.</p>https://www.teachmathematics.net/blog/17036/maths-journals#1403670000Mathematical Task Design
https://www.teachmathematics.net/blog/16984/mathematical-task-design
Tue, 17 Jun 2014 06:33:00 +0100]]>Mathematical Task Designhttps://www.teachmathematics.net/cache/blog-thumbs/24/16984-1403010666-thinkib.jpghttps://www.teachmathematics.net/blog/16984/mathematical-task-design
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/16984-1403010666-thinkib.jpg" alt="Mathematical Task Design" /><br /><br /> 'The Problem with Monty Hall' </a>and of course, the whole idea behind this website that I write with my colleagues is based on rich and useful mathematical tasks.</p> <p> I'll update this post with anything that comes out of the chat..... It has already been a useful exercise for me.</p> https://www.teachmathematics.net/blog/16984/mathematical-task-design#1402983180School of Hard Sums
https://www.teachmathematics.net/blog/16937/school-of-hard-sums
Wed, 04 Jun 2014 12:53:00 +0100]]>School of Hard Sumshttps://www.teachmathematics.net/cache/blog-thumbs/24/16937-1401905525-thinkib.jpghttps://www.teachmathematics.net/blog/16937/school-of-hard-sums
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/16937-1401905525-thinkib.jpg" alt="School of Hard Sums" /><br /><br /> </iframe></p> <p> My focus is on the dancing problem. In short, if you are stood still in a dance hall and everyone kisses the person they are closest to, how can you position people so that you get the most number of kisses and what is the most number of kisses you can get? I liked this problem because I thought the context was fun - I can see playing musical statues with a class a few times. Secondly, I was interested in the three aproaches used to solve the problem, all of which were apparently different to mine. This is always the sign of a rich problem for me. As ever, it makes it more difficult to control which 'learning objective' can be taught in a given lesson, but I think that is a sacrifice worth making for the potential to get students using mathematical reasoning, testing, evidence gathering and so on. Perhaps also, there could be an activity that offers the different explanations as a starting point and asks students to discern between them. Either way there is a lot of potential and now I have more things I want to watch, do and plan! It is frustrating (lack of time) but exciting that there seems to be a never ending stream of possibilities in this profession! Thanks to the School of Hard Sums team - I am looking forward to more.</p> https://www.teachmathematics.net/blog/16937/school-of-hard-sums#1401882780Qama Calculators
https://www.teachmathematics.net/blog/16863/qama-calculators
Thu, 15 May 2014 08:16:00 +0100]]>Qama Calculatorshttps://www.teachmathematics.net/cache/blog-thumbs/24/16863-1400159907-thinkib.jpghttps://www.teachmathematics.net/blog/16863/qama-calculators
<h3> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/16863-1400159907-thinkib.jpg" alt="Qama Calculators" /><br /><br /> Qama calculators</a> to play with. I think I just needed to see one for myself and see how it worked. The basic logic is really quite simple. You enter a calculation and press 'equals'. Then the cursor moves to a new line where it expects you to make an 'estimation' for the answer. If the calculator is happy with your estimation,then it will give you the actual answer. If it is not, then you must try again. What a beautiful idea! It has clearly been a terrific effort from conception and design to manufacture and distribution and these are now really easy to get hold of a relatively inexpensive. The question is to think really carefully about how we might choose to use them in mathematics education. There are a few questions that people might think about...</p> <h4> On investment</h4> <ol> <li> Would we consider a wholesale swap and ask all our students to get one of these?</li> <li> Would we like a situation where students had one of these alongside anoher traditional calculator?</li> <li> Would we go for something like a class set that can be brought out for particular activities?</li> <li> Is it just something we might recommend for some students?</li> </ol> <p> Well, my usual take on something like this would be option 2, because this leaves all options for use open. You would need to be pretty certain that they were going to get used before you asked parents or schools to make an investment.</p> <h4> On activity</h4> <p> If this was the default calculator, then we imagine that there would be long term improvement in estimating ability and the asociated number sense, but it is worth thinking about the implications. Calculators are often a bridge that allow an activity to focus on particular skills without letting calculating skills hinder progress.</p> <ol> <li> Would permanent use of these calculators slow down activity? Does that matter?</li> <li> How would we adjust our teaching style to accomodate for the extra stage of involvement?</li> <li> What would be the implications fo increasing the emphasis on estimation from an early stage?</li> <li> Is there potential for thinking about specific activities that might make the best use of this calculator?</li> </ol> <p> I think there is a need for experimentation here and possibly picking a class to trial them with one way or another. The first question here helps me answer the first one above, in that I dont think I would want it to be a permanent replacement. I do think that it would interupt <em>some </em>teaching and learning activity. I also think there will be a significant implication for teaching style.</p> <p> Really importantly and potentially one of the most exciting implications of using these calculators is likely to be the increased emphasis on estimation as a skill. There are so many reasons to encourage this, but my favourite is because of the potential impact on understanding.</p> <h4> Specific activities</h4> <p> I think that these calculators could introduce a whole new level to activity design. Here are a few ideas that have popped in to mind in the first few days I have had this calculator....</p> <p> <em><strong>Percentage error</strong></em> - I am really curious about the margin of error that the calculator is accepting in different contexts. My colleague tried log120 and was denied with an estimation of 2.1 Quite demanding I think, but there is a lot of potential to investgiate different types of operation and the percentage error allowed.</p> <p> <em><strong>Least guesses</strong></em> - I like the idea of some activity where students have to try and estimate difficult operations in as few guesses as possible.</p> <p> <em><strong>Trigonometry</strong></em> - I had fun estimating some trig ratios. I found myself thinking about the ratio between different sides of a traingle and how it would change as the angle increased. What a great way to encourage students to think about what trig ratios actually mean.</p> <p> Again - this is just a start of lots of ideas that are bound to come from playing with these calculators.</p> <p> Thanks Qama for these - a really exciting development.</p> https://www.teachmathematics.net/blog/16863/qama-calculators#1400138160Mathemagician
https://www.teachmathematics.net/blog/16199/mathemagician
Thu, 16 Jan 2014 12:32:00 +0000]]>Mathemagicianhttps://www.teachmathematics.net/cache/blog-thumbs/24/16199-1389897614-thinkib.jpghttps://www.teachmathematics.net/blog/16199/mathemagician
<h2> A Mathematics Trick</h2> <p > <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/16199-1389897614-thinkib.jpg" alt="Mathemagician" /><br /><br />Andrew Jeffrey</a> performs magic shows based on mathematics. I was lucky enough to ‘participate’ in one of his shows in Lisbon a few years ago. He has put together an e-book of mathemagical tricks and will send it to you for free if you sign up to his newsletter. All the tricks are based on mathematics and trying to work out why they work can be the basis for some rich mathematical work! Now where did I leave that rabbit?</p> <p><strong>Tags:</strong> <em>magic; mathematics; fun; problem solving</em></p>https://www.teachmathematics.net/blog/16199/mathemagician#1389875520Christmas Mathematics Lessons
https://www.teachmathematics.net/blog/16130/christmas-mathematics-lessons
Sun, 08 Dec 2013 16:02:00 +0000]]>Christmas Mathematics Lessonshttps://www.teachmathematics.net/cache/blog-thumbs/24/16130-1386541248-thinkib.jpghttps://www.teachmathematics.net/blog/16130/christmas-mathematics-lessons
<h2> “Can we do something fun today?”</h2> <p > This is the question that irks me most when we approach the end of Christmas term. Of course, I would want to reply that all lessons are fun! However, the forthcoming Christmas break always presents with me with a challenge for lessons: How to embrace the festivities and excitement, yet offer something worthwhile where some real learning takes place? Finding this type of resource and planning these lessons always seems to take three times longer than a classic lesson. To help, I’ve built up a series of lessons that I can dip into depending on the class and mood. I thought I’d share them with you to save you some time too.</p> <div class="pinkBg"> <h4> <a href="https://www.teachmathematics.net/activities/the-great-elf-game.htm" target="_blank">The Great Elf Game</a></h4> <p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/16130-1386541248-thinkib.jpg" alt="Christmas Mathematics Lessons" /><br /><br /> <a href="http://www.mei.org.uk/files/ppt/Twelve-Days-of-Christmas.pptx" target="_blank">PowerPoint for the 12 days of Christmas</a>. These are great for posting one per day on your classroom door. Chocolate prizes go down well for the first correct answers!</p> </div> <p> <span ><span >Have a Merry Mathematical Christmas!</span></span></p> <p><strong>Tags:</strong> <em>christmas</em></p>https://www.teachmathematics.net/blog/16130/christmas-mathematics-lessons#1386518520Ideas to Activities
https://www.teachmathematics.net/blog/15929/ideas-to-activities
Sun, 06 Oct 2013 13:02:00 +0100]]>Ideas to Activitieshttps://www.teachmathematics.net/cache/blog-thumbs/24/15929-1381076817-thinkib.jpghttps://www.teachmathematics.net/blog/15929/ideas-to-activities
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15929-1381076817-thinkib.jpg" alt="Ideas to Activities" /><br /><br /></p> <p> Happy creating!</p> <p><strong>Tags:</strong> <em>ideas,activities</em></p>https://www.teachmathematics.net/blog/15929/ideas-to-activities#1381060920Mathematical Communication
https://www.teachmathematics.net/blog/15890/mathematical-communication
Sun, 15 Sep 2013 11:40:00 +0100]]>Mathematical Communicationhttps://www.teachmathematics.net/cache/blog-thumbs/24/15890-1379263928-thinkib.jpghttps://www.teachmathematics.net/blog/15890/mathematical-communication
<p > <span ><em><span ><img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15890-1379263928-thinkib.jpg" alt="Mathematical Communication" /><br /><br /> 3D uncovered activity</a> and came up against some similar issues. The whole point of this activity is about students extracting 2D planes from 3D constructions and then applying trigonometry. In most cases, it was near impossible to trace a students conclusion back to the question because thay had written little or nothing along the way to help.</p> <p> I tried to make my point with students with two examples related to writing,</p> <ol> <li> If asked to do a piece of writing, would students write the words in random unsequential places on the page and expect the teacher to just 'know' what order they are supposed to come in?</li> <li> What use would a book be if you were only offered the first and last chapters?</li> </ol> <p> I know analogies can be dangerous and distracting, but instinctively I suppose I was just observing how there is so much to do to teach people to communicate properly and how that is actually an integral part of strengthening understanding.</p> <p> I am thinking about a couple of ideas for placing more emphasis on this in the future</p> <ol> <li> Some kind of classroom display that shows examples of good and not so good communication.</li> <li> An activity that encourages students to examine this for themselves. This would involve getting students to llok for the missing bits of communcation.</li> <li> Perhaps some peer assessment aimed at getting them to see how difficult it can be to follow each others' work if it is not properly communicated.</li> </ol> <p> ...</p> https://www.teachmathematics.net/blog/15890/mathematical-communication#1379241600A Balanced Mathematical Diet
https://www.teachmathematics.net/blog/15655/a-balanced-mathematical-diet
Sat, 10 Aug 2013 22:00:00 +0100]]>A Balanced Mathematical Diethttps://www.teachmathematics.net/cache/blog-thumbs/24/15655-1376072770-thinkib.jpghttps://www.teachmathematics.net/blog/15655/a-balanced-mathematical-diet
<h3> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15655-1376072770-thinkib.jpg" alt="A Balanced Mathematical Diet" /><br /><br /><a href="http://www.cimt.plymouth.ac.uk/projects/mep/intrep00.pdf" target="_blank">Centre for Innovation in Mathematics Teaching,</a> <a href="http://www.cimt.plymouth.ac.uk/projects/mep/intrep00.pdf" target="_blank">University of Exeter</a>, p.4] </p> <p><strong>Tags:</strong> <em>computer based math,understanding,memory</em></p>https://www.teachmathematics.net/blog/15655/a-balanced-mathematical-diet#1376168400Digital Memories
https://www.teachmathematics.net/blog/15516/digital-memories
Sun, 14 Jul 2013 08:25:00 +0100]]>Digital Memorieshttps://www.teachmathematics.net/cache/blog-thumbs/24/15516-1373291211-thinkib.jpghttps://www.teachmathematics.net/blog/15516/digital-memories
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15516-1373291211-thinkib.jpg" alt="Digital Memories" /><br /><br /> </iframe></p> <p><strong>Tags:</strong> <em>video; demonstration; proof; pythagoras theorem</em></p>https://www.teachmathematics.net/blog/15516/digital-memories#1373786700Adding life to old problems!
https://www.teachmathematics.net/blog/15449/adding-life-to-old-problems
Tue, 25 Jun 2013 04:49:00 +0100]]>Adding life to old problems!https://www.teachmathematics.net/cache/blog-thumbs/24/15449-1372155142-thinkib.jpghttps://www.teachmathematics.net/blog/15449/adding-life-to-old-problems
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15449-1372155142-thinkib.jpg" alt="Adding life to old problems!" /><br /><br /></p> <p> There are so many lovely hidden challenges like 'finding the centre of rotation' in these puzzles. The puzzles themselves provide the motivation for students to pursue solutions. I am a great advocate of the notion that 'practice can be found in rich tasks' and here is a prime example of that as well as 'Adding life to old problems'.</p> <p> *Autograph - The landscape for mathematics education software is rapidly changing with Geogebra calling the shots, but there are still numerous occasions when I reach out for Autograph and I would not want to work in a department without it!</p> <p><strong>Tags:</strong> <em>challenge,ICT,transformations,translations,rotations,reflections,congruence</em></p>https://www.teachmathematics.net/blog/15449/adding-life-to-old-problems#1372132140Mathematics Scrapbooks
https://www.teachmathematics.net/blog/15429/mathematics-scrapbooks
Wed, 12 Jun 2013 09:58:00 +0100]]>Mathematics Scrapbookshttps://www.teachmathematics.net/cache/blog-thumbs/24/15429-1371033390-thinkib.jpghttps://www.teachmathematics.net/blog/15429/mathematics-scrapbooks
<div dir="ltr" style="text-align: left;" trbidi="on"> <p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15429-1371033390-thinkib.jpg" alt="Mathematics Scrapbooks" /><br /><br /> </p> <ul > <li> What activity that students do, do they really need to keep records of?</li> <li> How many of our students regularly, or indeed ever, look at those records?</li> <li> How many parents ever look at it and if they do, how much do they get out of it?</li> <li> How much of our activity do we keep ourselves?</li> <li> How much do we look at?</li> </ul> <div> I suspect that in the vast majority of cases, paper and pages in a book get filed away never to be seen by anyone again. The more time passes, the less sense the bits of papers make because the context has passed. In truth only summary documents are likely to be of any use, tests for example. Personally, I keep so much more than I ever look at. Yes, I will often find a gem in amongst some piles of paper (or amongst an archive of files) but I often wish I had been clever enough to file it under 'Gems' at the time and not bothered with the other stuff. I think I will argue that the more we keep, the less useful it is, but that if we have nothing physical to show for our efforts it somehow feels wrong.</div> <div> </div> <div> Here is an idea I am playing with to take things on a little...</div> <div> </div> <div> A Mathematics journal!</div> <div> </div> <div> I am sure this is not a new idea and would be really glad to hear from anyone that has experimented with this.</div> <div> </div> <div> Forget everything else and just get students to keep a journal to chronicle their experiences discoveries and any bits of information they want to hold on to. Rather than include everything they did why dont we get them to pick out the highlights? Take pictures and paste them in, take screenshots of digital work, get students to tell stories about what we did in class and what they got out of it. The end result would be a kind of scrapbook of the key moments and best bits. A mixture of images, diagrams and words that will serve to make and preserve memories of experiences that help them to make sense of what they have done, why they did it and what they concluded at each stage. Because it is not everything, students might be inspired to take pride in making something fabulous that they have ownership over.</div> <div> </div> <div> My only, although tricky, dilema is the best format. Even as a technophile, I am drawn towards the creation of a physical book that might be of a similar ilk to the 'Art sketchbook' or the 'Design technology portfolio'. This, though, feels somehow like a step backwards. Its funny though that people want to make prints and books of their digital photos these days as well as sharing them digitally. The other alternatives I have been playing with are perhaps a blog or an ongoing google presentation.</div> <div> </div> <div> Anyway, this has been occupying my thoughts today and I think I will pick some small groups of students and experiment a little to see what happens! All thoughts and suggestions welcomed!</div> <div> </div> <div> Thanks.....</div> </div> https://www.teachmathematics.net/blog/15429/mathematics-scrapbooks#1371027480Wrong, right, misleading?
https://www.teachmathematics.net/blog/15427/wrong-right-misleading
Sat, 08 Jun 2013 10:47:00 +0100]]>Wrong, right, misleading?https://www.teachmathematics.net/cache/blog-thumbs/24/15427-1370707039-thinkib.jpghttps://www.teachmathematics.net/blog/15427/wrong-right-misleading
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15427-1370707039-thinkib.jpg" alt="Wrong, right, misleading?" /><br /><br /> British Transfer fees</a></p><p><strong>Tags:</strong> <em>handling data,interpeting data,presenting data</em></p>https://www.teachmathematics.net/blog/15427/wrong-right-misleading#1370684820Mathagogy, one question lessons and making cones
https://www.teachmathematics.net/blog/15403/mathagogy-one-question-lessons-and-making-cones
Mon, 27 May 2013 08:48:00 +0100]]>Mathagogy, one question lessons and making coneshttps://www.teachmathematics.net/cache/blog-thumbs/24/15403-1369648563-thinkib.jpghttps://www.teachmathematics.net/blog/15403/mathagogy-one-question-lessons-and-making-cones
<h3> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15403-1369648563-thinkib.jpg" alt="Mathagogy, one question lessons and making cones" /><br /><br /> The Mathematical Experience</a>.</p> <h4> The Mathagogy project</h4> <p> I just wanted to end by saying what a wonderful idea I think this project is and how keen I am to watch and hear what so many other maths teachers around the world have to say. I also hope that those teachers will help me develop these ideas in this blog post further! Thanks.</p> https://www.teachmathematics.net/blog/15403/mathagogy-one-question-lessons-and-making-cones#1369640880Mr Men Mathematics
https://www.teachmathematics.net/blog/15369/mr-men-mathematics
Wed, 15 May 2013 06:45:00 +0100]]>Mr Men Mathematicshttps://www.teachmathematics.net/cache/blog-thumbs/24/15369-1368529988-thinkib.jpghttps://www.teachmathematics.net/blog/15369/mr-men-mathematics
<h3> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15369-1368529988-thinkib.jpg" alt="Mr Men Mathematics" /><br /><br /></p> <p> Through all of this, I am remided of how foolish it was of Mr Gove to dismiss an idea out of hand without any exploration. So often, the more you explore, the more potential you see. That is the business of teachers! As I write, I am certain that I am not the first to have these ideas and resolve to look for existing ideas before I go any further.</p> <p><strong>Tags:</strong> <em>Mr Men,Ideas</em></p>https://www.teachmathematics.net/blog/15369/mr-men-mathematics#1368596700Mr Men teaching in Toulouse
https://www.teachmathematics.net/blog/15366/mr-men-teaching-in-toulouse
Mon, 13 May 2013 13:23:00 +0100]]>Mr Men teaching in Toulousehttps://www.teachmathematics.net/cache/blog-thumbs/24/15366-1368470023-thinkib.jpghttps://www.teachmathematics.net/blog/15366/mr-men-teaching-in-toulouse
<p> <img src="https://www.teachmathematics.net/cache/blog-thumbs/24/15366-1368470023-thinkib.jpg" alt="Mr Men teaching in Toulouse" /><br /><br /> Dancing Vectors</a> the best. Mathematics teaching is a critical field, fighting against years of misconception about the subject, what it is, why we learn it and what it can be for different people. Our job is hugely important and any suggestion that we are making it trivial with our attempts to engage students, indeed misses the point. Any suggestion that our efforts are aimed at anything other than raising confidence, expectation and improving a generation’s understanding of the role mathematics plays in our world is, sadly, very wide of the mark. The point is this; nothing is more inspiring or rewarding that creating opportunities that promote engagement, enquiry, enthusiasm and critical thinking. Anyone with any experience of that will know that, and those without cannot and should not be directing the future of education. As we think about posting resources to this site, this is our mantra and our goal. It may be that it doesn’t always work for all teachers or all classes (ours included) but is our goal all the same.</p> <p> I am a Mr Man teacher and proud!</p> <p><strong>Tags:</strong> <em>Mr Men,International School of Toulouse</em></p>https://www.teachmathematics.net/blog/15366/mr-men-teaching-in-toulouse#1368447780The homework debate!
https://www.teachmathematics.net/blog/14368/the-homework-debate
Tue, 13 Nov 2012 11:38:00 +0000]]>The homework debate!https://www.teachmathematics.net/cache/blog-thumbs/24/14368-1352829442-thinkib.jpghttps://www.teachmathematics.net/blog/14368/the-homework-debate
<h3> <img alt="" class="left noborder" height="100" src="/files/teachmaths/files/Blogs/homework.jpeg" width="100">Homework - Yuck or Yay</h3> <p> The following blog post is a quick response the question above that has been posed by the <a href="http://twitter.com/search?q=%23globalmath&src=hash" target="_blank">#globalmath</a> group on twitter who are having a debate on this topic this evening based on some responses to this <a href="http://docs.google.com/spreadsheet/viewform?formkey=dHNvQm9sQnhNTk5ULWNoRl85V2JVbVE6MQ" target="_blank"><img class="ico" src="/img/icons/connection.png"> Questionnaire</a>. I love this debate and like many good ones can see lots of different points of view. It often helps to try and come off the fence though and in this case I have written some thoughts about why I would be happy to see the end of homework as we know it. This view is not necessarily shared by my colleagues that help write this website and is really just designed to spark further debate. Few issues are black or white! I should probably add that I have been influenced by <a href="http://www.alfiekohn.org/books/hm.htm" target="_blank"><img class="ico" src="/img/icons/connection.png"> The Homework Myth</a> by Alfie Kohn. The thoughts are about homework in secondary schools in general, but from the perspective of a maths teacher.</p> <h4> Quality of life</h4> <ul> <li> Big cause of tension and conflict in homes.</li> <li> Students day is long enough if spent productively.</li> <li> Odd to expect longer days from teenagers than of many working adults.</li> <li> After school and evening times should be for family, sports, leisure and hobbies - all very valuable pursuits from which people can learn huge amounts.</li> <li> There has to be time in the day for students to be doing things <em>they</em> have decided they are going to do. Progress in these fields is likely to be more significant than that which is obliged.</li> <li> We should encourage learning to be voluntary and self driven.</li> </ul> <h4> The case for homework?</h4> <ul> <li> Where is the evidence supporting the case for homework?</li> <li> I would argue that evidence presented is assumed.</li> <li> Homework is a long standing feature of education - it is there because it always has been, not because of strong evidence that it should be.</li> </ul> <h4> The case for no homework</h4> <ul> <li> Equally, scrapping homework is largely untried. I think it is time to try it for the reasons above. </li> <li> School days must become more productive but students should be more receptive during the day if homework is off the table.</li> <li> Too much emphasis is placed on amount of time rather than quality of time. Too much on coverage, rather than nature of time spent.</li> </ul> <h4> The nature of homework</h4> <p> This is the crux of the matter for me. Any time spent working at home in the evening is infinitely more valuable when students do it of their own volition rather than out of compulsion. The types of things that students could be doing are many and varied and I think it would be great to be providing possibilities and provoking an interest. Of course, for this to work, the key would be getting home culture to match the schools which is unlikely but we can only really offer possibilities. As its stands, the success of homework as we know it is already highly dependent on the culture of students' homes. To support learning in maths I would be suggesting/encouraging - just a first draft</p> <ul> <li> Regular playing of logic/strategy games that encourage critical thinking and discussion</li> <li> Individual Puzzle solving, giving students practise of working idependently</li> <li> A shared stream of interesting and relevant links etc about the subject, encourage an exchange about these via a tool like fb or edmodo or blogs or the like</li> <li> Offer various projects that students could volunteer for and offer support with them.</li> <li> Offer tasks that involve creativity.</li> <li> Have ongoing things like photos of maths in the real world, sudoku competitions etc.</li> <li> Keep an eye out for relevant documentaries - give students the chance to respond to these.</li> </ul> <p> <br> If this sort of advice was being offered across all subjects then would be no shortage of things on offer for students to enrich their school based studies.</p> <p> Anyway, I am looking forward to the debate, both as it unfolds this evening and continues.</p>https://www.teachmathematics.net/blog/14368/the-homework-debate#1352806680Using Games in Mathematics
https://www.teachmathematics.net/blog/14140/using-games-in-mathematics
Wed, 24 Oct 2012 18:46:00 +0100]]>Using Games in Mathematicshttps://www.teachmathematics.net/cache/blog-thumbs/24/14140-1351123499-thinkib.jpghttps://www.teachmathematics.net/blog/14140/using-games-in-mathematics
<h2> Expanding Double Brackets</h2> <p> <img alt="" class="left" height="145" src="/files/teachmaths/images/Blogs/Games.png" width="200">Generally students enjoy playing games (who doesn't). Whilst we can find many attractive and fun games online I'm often disappointed with the quality of the questions. If it's fun, but the students don't really learn much mathematics what's the point?</p> <p> I'm keen to create some games and have found a useful platform from <a href="http://www.classtools.net/">http://www.classtools.net</a></p> <p> Here are a couple of games to practise expanding double brackets. In the first game the students have to save the world by shooting invaders. In the second they have a choice of which game they prefer including an old classic Manic Miner!</p> <p> I aim to create a whole actvity on factorising brackets and these games will provide a warm-up.</p> <p> Enjoy the games and let me know what you think.</p> <h3> Round 1</h3> <p align="center"> <code><iframe frameborder="0" height="320" scrolling="no" src="http://www.classtools.net/widgets/quiz_25/Expanding_Double_Brackets_Round_1_wBdmF.htm?400?300" width="408"></iframe></code></p> <p align="center"> <a href="http://www.classtools.net/widgets/quiz_25/Expanding_Double_Brackets_Round_1_wBdmF.htm">Click here for larger version</a></p> <h3> Round 2</h3> <p align="center"> <code><iframe frameborder="0" height="320" scrolling="no" src="http://www.classtools.net/widgets/quiz_15/Expanding_Double_Brackets_Round_2_xcdqf.htm?400?300" width="408"></iframe></code></p> <p align="center"> <a href="http://www.classtools.net/widgets/quiz_15/Expanding_Double_Brackets_Round_2_xcdqf.htm">Click here for larger version</a></p> <p align="center"> </p><p><strong>Tags:</strong> <em>quadratics,expanding brackets,algebra</em></p>https://www.teachmathematics.net/blog/14140/using-games-in-mathematics#1351100760Visual Sequences
https://www.teachmathematics.net/blog/14075/visual-sequences
Mon, 22 Oct 2012 17:27:00 +0100]]>Visual Sequenceshttps://www.teachmathematics.net/cache/blog-thumbs/24/14075-1350945419-thinkib.jpghttps://www.teachmathematics.net/blog/14075/visual-sequences
<p> <img alt="" class="left" height="150" src="/files/teachmaths/files/Blogs/sequences 1.jpg" width="150"></p> <h3> Building and summing sequences with cubes!</h3> <p> This has come up a couple of times recently and seeing a twitter discussion on 'brilliant activities using manipulatives' I decided to write this down quickly. This is a beautiful and simple activity to teach arithmetic sequences using manipulatives. Of course this could be done in lots of ways and so this blog is really only giving the outline. What is nice about this activity is the possible age ranges it could be used with!</p> <p> 1st - ask students to make a visual representation of the sequence 1, 5, 9, 13 .... and so on depending on howmany cubes you have. you can get all sorts of different shapes. I have been doing this activity for years and always see something new! The picture on the left is one possible answer, the one below another.</p> <p > <img alt="" height="400" src="/files/teachmaths/files/Blogs/sequences 2.jpg" width="300"></p> <p> 2nd - ask how many cubes it will take to build the next, 10th, 100th pattern etc which is really asking students to think about the structure of the sequences and work towards a formula that is built on intuition.</p> <p> 3rd - ask how many terms of the sequence you can build with the cubes you have - you get some wild answers! Test it by building them</p> <p> 4th - Once they are built arrange them like the picture below...</p> <p > <img alt="" height="240" src="/files/teachmaths/files/Blogs/IMG_1365.jpg" width="320"></p> <p> 5th - Carefully get students to demonstrate how this can be made in to a rectangle like the the picture below...</p> <p > <img alt="" height="240" src="/files/teachmaths/files/Blogs/IMG_1366.jpg" width="320"></p> <p> and that the area of this rectangle is the sum of the sequence and that the formula for the sum is easily derived from the way this was put together.</p> <p> As I said, this is just a quick blog to sow the seeds of an idea. There is so much going on here, so many alternate paths that it has become for me an essential activity!</p> <p><strong>Tags:</strong> <em>number,sequences,algebra,manipulatives</em></p>https://www.teachmathematics.net/blog/14075/visual-sequences#1350923220Craig Barton Recommends Teachmathematics
https://www.teachmathematics.net/blog/14051/craig-barton-recommends-teachmathematics
Wed, 17 Oct 2012 19:30:00 +0100]]>Craig Barton Recommends Teachmathematicshttps://www.teachmathematics.net/cache/blog-thumbs/24/14051-1350521304-thinkib.jpghttps://www.teachmathematics.net/blog/14051/craig-barton-recommends-teachmathematics
<p> It's always nice to know that other mathematics teachers appreciate the site so it was a proud moment for the site to get a glowing testimony from Craig Barton AKA <a href="http://www.mrbartonmaths.com" target="_blank">MrBartonmaths</a> and the main man behind mathematics resources in the <a href="http://www.tes.co.uk/" target="_blank">TES</a>.</p> <p> Here's Craig's short video:</p> <p > <iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/SSoxN713NMQ?rel=0" width="420"></iframe></p> <p> Here are the three activities and the training resources that Craig mentioned in his video</p> <p> <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/ALGEBRA/angry birds/main.jpg" width="100"></p> <h3> <img class="ico" src="/img/icons/activities.png"> <a href="http://www.teachmaths-inthinking.co.uk/activities/angry-birds.htm" target="_blank">Angry Birds</a></h3> <p> <strong>Age: 15+ Time 1 hr</strong>. This set of games asks students to find the correct equation of the parabola in order to hit the pig! Three set of coordinates are given and students are required to calculate the equation of the parabola. They will be required to understand the equation of a quadratic, in particular the form y=a(x - p)(x - q) would be helpful. Great fun!</p> <p> <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Geometry/3D Perception/3Dperception100x100.jpg" width="100"></p> <h3> <img class="ico" src="/img/icons/activities.png"> <a href="http://www.teachmaths-inthinking.co.uk/activities/3d-perception.htm" target="_blank">3D Perception</a></h3> <p> <strong>Age: 12+ Time 1h </strong>The aim of this resource is to develop student’s association of nets, hence surface area, with 3D solids, hence volume. The activity starts with a matching activity, nets and solids, some of which work, some don’t, students can cut and fold to check. Two virtual manipulative websites are then used, one aimed at inspiring them with a wide, and unusual range of 3D shapes.</p> <p> <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Statistics_Probability/Roll em/main_image.jpg" width="100"></p> <h3> <img class="ico" src="/img/icons/activities.png"> <a href="http://www.teachmaths-inthinking.co.uk/activities/roll--em.htm" target="_blank">Roll 'em</a></h3> <p> Roll, roll, roll… This carefully structured activity aims to get students to discover that experimental probability approaches theoretical probability as we increase the number of trials. We often overlook the importance of carrying out games of chance to build up an intuition for probability. In this case we roll a dice then use a lifelike simulator on Excel to produce up to 2000 rolls. <strong>Age:</strong> 11+ <strong>Time:</strong> 1h</p> <p> <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Conferences/ECIS 2011/geogebralogo.jpg" width="100"></p> <h3> <a href="http://www.teachmaths-inthinking.co.uk/conferences/tsm---july-2012.htm" target="_blank">TSM - July 2012 - Introductory Geogebra</a></h3> <p> <strong>Objectives</strong> - To support workshop participants to get to grips with geogebra software and demonstrate its uses in the mathematics classroom.</p> <p> <strong>Aims</strong> - Participants should observe potential, get practice, be inspired to use it in the classroom!</p> <p> <strong>Content</strong> - Learn the basics of creating geometrical figures, measurement and calculation; coordinate geometry and functions for elementary and advance topics.</p> https://www.teachmathematics.net/blog/14051/craig-barton-recommends-teachmathematics#1350498600Five great ideas for visualising number!
https://www.teachmathematics.net/blog/13991/five-great-ideas-for-visualising-number
Sun, 07 Oct 2012 05:42:00 +0100]]>Five great ideas for visualising number!https://www.teachmathematics.net/cache/blog-thumbs/24/13991-1349608661-thinkib.jpghttps://www.teachmathematics.net/blog/13991/five-great-ideas-for-visualising-number
<h3> <img alt="" class="left" height="133" src="/files/teachmaths/files/Blogs/Pop pyramids.jpg" width="200">The power of visualising</h3> <p> The abstraction of numbers is a fascinating topic for debate and discussion and the root of much confusion in secondary school matehmatics students, not to mention many of the worlds adults! As teachers, our challenge is to keep developing successful activities that help people to develop their powers of abstraction and understand ideas in different ways. Visualisation is a key tool in this process and, as such, I am always on the look out for new, and successful old ways of building activities around the idea. In the digital age, it is easy to forget the value of physical manipulatives and practical activity. Here are five number based activities that invite students to create their own visualisations using manipulatives and practical activity!</p> <table align="left" border="0" cellpadding="5" cellspacing="0" style="width: 630px; "> <tbody> <tr> <td > <img alt="" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Number/MultipleFactors/MultipleFactors100x100.jpg" width="100"></td> <td> <h3> <a href="http://www.teachmaths-inthinking.co.uk/activities/multiple-factors.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Multiple Factors</a></h3> <p> <strong>Age</strong> 9+ <strong>Time</strong>: 1h. Students form interesting groups using their bodies to get a physical appreciation for factors and multiples. They then create a wide range of imaginative designs using counters, beads, collage etc. to represent numbers in terms of their factors for other groups to decipher. Finish with the multiple factors game. Be prepared for a lot of fun!</p> </td> </tr> <tr> <td > <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Number/Recreating%20Ratios/RecreatingRatios.jpg" width="101"></td> <td> <h3> <a href="http://www.teachmaths-inthinking.co.uk/activities/recreating-ratios.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Recreating Ratios</a></h3> <p> This lesson requires students to produce a range of images for a given ratio. The aim is to draw out the equivalence of different ratios and how, and why, they can be simplified. The more creative and imaginative students are in creating different images to fit a given ratio, the clearer the true concept of ratio becomes (great opportunity for display work). It also provides a good lead in to sequences and graphs. <strong>Age:</strong> 11+ <strong>Time:</strong> 1h+</p> </td> </tr> <tr> <td > <a href="http://www.teachmaths-inthinking.co.uk/activities/rounding-what-for.htm" style="color: rgb(255, 255, 255); background-color: rgb(0, 51, 102); " target="_blank"><img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/files/Number/Art%20of%20Fractions/AoF.jpg" width="100"></a></td> <td> <h3> <a href="http://www.teachmaths-inthinking.co.uk/activities/the-art-of-fractions.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> The Art of Fractions</a></h3> <p> Create some great art and display work whilst practising calculating fractions of different quantities. This activity involves the repeated splitting of rectangles into carefully chosen proportions defined by a single fraction and can lead to some lovely 'Mondrian inspired' pictures! <strong>Age: </strong>11+<span > </span><strong>Time: </strong>1 hr</p> </td> </tr> <tr> <td > <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/images/4tothe4.gif" width="100"></td> <td> <h3> <a href="http://www.teachmaths-inthinking.co.uk/activities/visualising-indices.htm=cl"><img class="ico" src="/img/icons/inthinking.png"> Visualising Indices</a></h3> <p> 'Squared' and 'Cubed' can be explained by using 2 and 3 dimensions. The area of a square with length 5 is 5<sup>2</sup>, volume explains cubed, so how can we represent 5<sup>4</sup>? This activity explores visual representations of indices and draws on a little creativity! <strong>Age: </strong>14+<span > </span><strong>Time: </strong>1 hr</p> </td> </tr> <tr> <td > <img alt="" class="left" height="100" src="http://www.teachmaths-inthinking.co.uk/files/teachmaths/images/rice.gif" width="100"></td> <td> <h3> <a href="http://www.teachmaths-inthinking.co.uk/activities/the-rice-show.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> The Rice Show</a></h3> <p> This acivity is inspired by <a href="http://www.stanscafe.co.uk/ofallthepeople/index.html%20"><img class="ico" src="http://www.teachmaths-inthinking.co.uk/img/icons/connection.png">'Of All The People in All the World' </a>from 'Stan's Cafe'. Use grains of rice to represent different numbers of people! How can we make a pile of rice with 1,000,000 grains in it? Do the estimation then use some statistics to make a powerful display! <strong>Age: </strong>10+<span > </span><strong>Time: </strong>1 - 3hrs</p> </td> </tr> </tbody> </table> <p><strong>Tags:</strong> <em>number,visualising,ratio,multiples,factors,fractions,squares,cubes,roots,indices</em></p>https://www.teachmathematics.net/blog/13991/five-great-ideas-for-visualising-number#1349584920Visualising Indices - new direction
https://www.teachmathematics.net/blog/13911/visualising-indices-new-direction
Sun, 30 Sep 2012 08:35:00 +0100]]>Visualising Indices - new directionhttps://www.teachmathematics.net/cache/blog-thumbs/24/13911-1349012823-thinkib.jpghttps://www.teachmathematics.net/blog/13911/visualising-indices-new-direction
<p> <img alt="" class="left" height="150" src="/files/teachmaths/files/Number/Visualising Indices/VI 3.jpg" width="200"></p> <h3> Stop animation video!</h3> <p> This activity comes around year after year for me and I love that each time you do an activity you come up with new ideas about how to develop it. It is even better when those new ideas come from students! The activity is <a href="http://www.teachmaths-inthinking.co.uk/activities/visualising-indices.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Visualising Indices</a>. This year, one of my students decided to create a stop motion video to represent a particular power. I think this is a brilliant development of the idea and have added the video to the activity page and embedded it below as well with some more images of this years efforts and a link to a <a href="http://pinkmathematics.blogspot.fr/2012/09/visualising-indices.html" target="_blank"><img class="ico" src="/img/icons/connection.png"> school blog entry about it! </a>The whole thing also got me interested in the use of stop motion video for this type of thing and so I got straight in to <a href="http://boinx.com/istopmotion/ipad/" target="_blank"><img class="ico" src="/img/icons/connection.png"> iStopmotion</a> for iPad and iPhone which is fabulous and highly recommended. The iPad runs the show and works with the iPhone as a remote camera so that the camera can stay in the same place.</p> <h4> Stopmotion video</h4> <p > <iframe allowfullscreen="" frameborder="0" height="360" src="http://www.youtube.com/embed/I1FftZV5_i0?rel=0" width="480"></iframe></p> <h4> Some more photos</h4> <p > <embed flashvars="host=picasaweb.google.com&hl=en_US&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2F101222321750151631432%2Falbumid%2F5791740531263163809%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_US" height="267" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://picasaweb.google.com/s/c/bin/slideshow.swf" type="application/x-shockwave-flash" width="400"></p> <p><strong>Tags:</strong> <em>visualising,practical,indices</em></p>https://www.teachmathematics.net/blog/13911/visualising-indices-new-direction#1348990500Natural medium
https://www.teachmathematics.net/blog/11751/natural-medium
Wed, 08 Feb 2012 19:22:00 +0000]]>Natural mediumhttps://www.teachmathematics.net/cache/blog-thumbs/24/11751-1328739776-thinkib.jpghttps://www.teachmathematics.net/blog/11751/natural-medium
<h3> <img alt="" class="left" height="150" src="/files/teachmaths/files/Geometry/Indestructible Quads/SOQ.gif" width="150">Are computers a natural medium for mathematics?</h3> <p> One of the reasons I both love and hate twitter! I am casually flicking through some pages over breakfast and I happen on this <a href="http://blog.mrmeyer.com/?p=12782&utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+dydan1+%28dy%2Fdan+posts+%2B+lessons%29" target="_blank">blog post from Dan Meyer</a>. In fairness the blog post seemed mostly to point out how helping mathematics education has not ever risen to the top of silicon valley's priority list. Whilst this is an interesting question, it was the question phrased in the title above that caught my attention. I love this because it is great when some one else's writing makes you stop and think - I hate it when the question pre-occupies your mind when you are trying to do other things. The result is that I am writing this long after I should be asleep, getting ready for tomorrow. Anyway, I think the below can stand alone, but can be put in to context by reading the blog post linked above. This was the response I left on the blog post.</p> <p> As #57 says, who is still reading! I find though that putting these thoughts and reactions in writing is mostly only for my own benefit! In this case, it is beacuse, whilst I understand and sympathise with the general view being expressed, I think I actually disagree with the statement about 'natural medium'! I read most of the responses and scanned the rest but the response from David Wees came closest to my reaction when he said '</p> <p > <em>'There are some tasks for which computers are perfectly suited in terms of mathematics'</em></p> <p > and</p> <p > <em>'What you have suggested is that they are less than ideal for the quick communication of mathematics, and for deeper assessment of what mathematics students understand.'</em></p> <p> Regarding the first point....</p> <p> My relatively short teaching career (13 years) has spanned 'almost no access to computers' to 'working with a one to one program at my current school'. There is no doubt in my mind that computers have had a hugely significant effect on the way mathematics can be taught and, more importantly, discovered, <em>beacuse</em> they provide a considerably <em>more</em> natural, able and versatile medium. A lengthy description of cases could follow, but I will limt myself to just a few...</p> <p> <em><strong>Dynamic geometry</strong></em>, as has been mentioned by some already. This tool has done amazing things for helping teachers to create opportunitites for students to make discoveries on their own and thus enage with mathematics. It can go beyond the teaching of geometry as well. Examples of activities <a href="http://www.teachmaths-inthinking.co.uk/activities/indestructible-quadrilaterals.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Indestructible Quadrilaterals</a>, <a href="http://www.teachmaths-inthinking.co.uk/activities/circle-theorems.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Discovering circle theorems</a>, <a href="http://www.teachmaths-inthinking.co.uk/activities/trig-calculator.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Making a trig Calculator</a> allof these activities involve students creating mathematical objects in the medium of dynamic geometry.</p> <p> <em><strong>Graphing software</strong></em> - largely by labour saving, but also through dynamic functionality - these tools as well have created new opportunities for exploring relationships. Examples of activties <a href="http://www.teachmaths-inthinking.co.uk/activities/olympic-records.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Olympic Records</a>, <a href="http://www.teachmaths-inthinking.co.uk/activities/straight-line-graphs.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Straight line Graphs</a></p> <p> <em><strong>Data Handing</strong></em> - This has come to life through computers with access to real, live data, the functionality to collect it and the ability to process it. All this means that the nature of data handling tasks can now vary in new ways. (I will not say 'more mathematical ways' although that it is what <em>I</em> think.) Examples of activities <a href="http://www.teachmaths-inthinking.co.uk/activities/predict-the-future.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Predict the future</a>, <a href="http://www.teachmaths-inthinking.co.uk/activities/dynamic-scatter-graphs.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Dynamic Scattergraphs</a></p> <p> As suggested, I could go on and will in my head!</p> <p> Regarding the second point....</p> <p> Yes I agree that progress is slow on more able and intuitive user interfaces for communicating mathematics. I think that this has worked in our favour as teachers though. For example, taking the fractions, modern calculators now make it much easier to input and work with fractions than it used to be and this may have resulted in a poorer understanding of what fractions actually mean. The fact that computers dont find it easy to accept fractions means that users have to think about what the fraction actually means in order to input it. A fraction is easily written on a piece of paper with no understanding of its meaning.</p> <p> Likewise, when programming with dynamic geometry (and I do consider constructions a type of programming), there is no 'rectangle tool', in order to construct one you have to know that a rectangle is made by two pairs of parallel sides intersecting at right angles. When you program it correctly it will always be a rectangle regardless of which points are moved. The process of drawing a rectangle on a piece of paper is not at all the same.</p> <p> In summary, dont get me wrong, I estimate that computers are used for about 50% of our lesson time and I am a committed believer in variety of tasks that range from the pencil and paper, to the practical, to the virtual. That said, I am a passionate supporter of what computers have done for mathematics education. I am also a relatively new blogger and always have a sense of fear when 'submitting' such responses. I think most bloggers understand that expressing your views and reactions is the best way to develop them, so thanks Dan for making me think! Apologies if I have missed the point somewhere along the line, I feel better for writing this down either way.</p> https://www.teachmathematics.net/blog/11751/natural-medium#1328728920Optimal Cuboid
https://www.teachmathematics.net/blog/11072/optimal-cuboid
Sun, 13 Nov 2011 09:25:14 +0000]]>Optimal Cuboidhttps://www.teachmathematics.net/cache/blog-thumbs/24/11072-1321187114-thinkib.jpghttps://www.teachmathematics.net/blog/11072/optimal-cuboid
<h3 style="text-align: center; "> Optimising understanding with 3D shapes - A quick idea for playing with cubes and cuboids</h3> <h3 style="text-align: center; "> <img alt="" height="350" src="/files/teachmaths/files/Geometry/Optimal 3D Shapes/y10.jpg" width="350"></h3> <p> This blog post is just a quick way of sharing an idea that is developing. I love it when ideas pop in to your head as you are teaching and you just go with them. Its a risk, but some times brilliant things happen and great ideas are born. I tried this in class this week and it got me thinking about a series of questions and challenges that could be really engaging and help students to get to grips with 3D shapes.</p> <h4> Objectives</h4> <ul> <li> For students to play with different nets for a cube.</li> <li> For students to explore the nets and thus the surface area of cuboids.</li> <li> For students to consider what is an appropriate measure of 'bigness' and thus consider the idea of volume.</li> <li> Students think about 'Optimisation'.</li> </ul> <h4> The Task</h4> <ul> <li> Students are given a piece of A4 card from which they must do the following;</li> <li> Draw the net, cut out and make a cube 5cm by 5cm by 5cm</li> <li> From the card that remains, students must draw the net, cut out and make the 'biggest' cuboid that they can!</li> </ul> <h4> The thinking!</h4> <p> The following are some of the thoughts and observations related to this activity that came out as we did it. They are in no particular order!</p> <ul> <li> Students straight away wanted to know if their nets had to be a single piece - i answered yes so as to stick with the definition of a net and make it more of a challenge. I was pleased that students seemed to recognise a key point early on.</li> <li> Students had to think about the different nets for a cube so they could choose one that left a maximum area of card for the cuboid. </li> <li> What does 'biggest' mean? And so surface area and volume are born as ideas!</li> <li> There is no substitute for building 3D shapes for understanding how the nets work and which sides have to correspond.</li> <li> Students are thinking about optimisation at an early age! A super concept to introduce.</li> <li> Most importantly, students were engaged from start to finish with solving the problem and all of the objectives listed above.</li> <li> On a technology note - I had just had a new document camera delivered to my room and it was perfect to be able to use it to show the class all the cuboids up close so we could decide which one was the biggest.</li> <li> The ensuing debate was terrific.</li> </ul> <p> The more I think about this, the more possibilities I see and I want to go away and devise a series of questions involving more complex shapes! Watch this space - I plan to post a resourced activity on this idea in the future! Thoughts and suggestions welcome!</p><p><strong>Tags:</strong> <em>quick idea,geometry,challenge,3D,cubes,cuboids,</em></p>https://www.teachmathematics.net/blog/11072/optimal-cuboid#1321176314Education Revolution
https://www.teachmathematics.net/blog/10831/education-revolution
Sun, 25 Sep 2011 16:49:46 +0100]]>Education Revolutionhttps://www.teachmathematics.net/cache/blog-thumbs/24/10831-1316976586-thinkib.jpghttps://www.teachmathematics.net/blog/10831/education-revolution
<p> <img alt="" class="left" height="138" src="/files/mathstudies/images/blog/ER2.png" width="145"></p> <h3> Just some thoughts on the topic!</h3> <p> In this entry I am writing down some of the thoughts I have following two things that I have paid attention to this week. The first is the <a href="http://www.tedxlondon.com/first" target="_blank">TEDxLondon</a> event on the theme ‘Education Revolution’. The second is <a href="http://www.conservatives.com/News/News_stories/2011/08/~/media/Files/Downloadable%20Files/Vorderman%20maths%20report.ashx" target="_blank">Carol Vorderman’s report</a> to the UK government on the state of mathematics education in the UK (BTW this is interesting reading wherever you live and work). </p> <p> As in most cases with blogs, I suspect that the primary beneficiary of this exercise will be me! Articulating thoughts, reactions and emotions in to coherent statements takes me far too long, but can be satisfying. Importantly, I reserve the right to change my mind in the future based on subsequent thoughts and reactions!</p> <h4> The current State of Education</h4> <p> I have a great fear that those who speak so clearly, well and influentially on the current state of education are not familiar enough with it and thus not qualified enough to do so. Whilst this does not invalidate their arguments it does begin to undermine them. Far too many sweeping statements are made about the terrible things that happen in current education. Most are very careful not to blame teachers, but rather government and micro management, but all tend to imply that teachers follow enforced strategies blindly.... most teachers, from my experience, are educators and capable of taking directives, standards and tests etc in their stride, whilst remembering that their primary role is to provide an education for their students. As such, what happens in classrooms is seldom the blind delivery of someone else’s plan. Maybe I am lucky, but that has been my experience of teachers to date. For interest you can read here about our philosophy on creating <a href="http://www.teachmaths-inthinking.co.uk/about-us/the-mathematical-experience.htm" target="_blank">'mathematical experiences'</a>.</p> <h4> Sage on the stage</h4> <p> Much is spoken of how the ‘Sage on the Stage’ idea is outmoded and it is time for change. This relates to what I have said above. I ask, who is teaching like that? There is no way I could ‘lecture’ for the 19 hours a week I spend with my classes. Apart from being pretty dull for all of us, I would not have the energy. I just don’t think this is happening. One of my colleagues, <a href="http://twitter.com/#!/russeltarr" target="_blank">@russelltarr</a>, pointed out the irony of the format of TED events in this context and I was reminded of this from <a href="http://www.youtube.com/watch?v=rTOLkm5hNNU" target="_blank">Jeff Jarvis</a> on the same topic. It is not rocket science, but worth remembering that variety is a huge tool in sustaining engagement and interest. This is as true of a group of adults as it is students. Sometimes I enjoy listening to the sage on the stage – sometimes I enjoy trying to be it, but this makes up a small proportion of what happens.</p> <h4> Revolution/Evolution</h4> <p> I am increasingly leaning towards evolution in this debate. Again, we could easily get caught up in semantics here, but I think I have achieved some clarity on this point. Education – that which happens in schools – has a constant need to ‘evolve’. From my experience it does so all the time. If it didn’t, my job would be easy but dull. Constant reflection, openness and willingness to engage with new ideas and the views of others are key ingredients. How individuals are judged by the wider world as a result of their ‘education’ is quite possibly in need of a revolution. This is perhaps best illustrated by the fact that what happens in schools evolves despite the stranglehold exam boards have on the notion of ‘terminal assessment’. Many courses offer a very sound philosophical basis and then use a horribly blunt assessment tool that does match that philosophy. For example, while schools are embracing technology, we still seem light years away from technology being used in assessment. Mathematics education and technology are deeply interwoven, but students still sit terminal exams without a computer. Revolution is required at that end to allow the natural evolution to happen in schools.</p> <h4> Success and Failure</h4> <p> Related to the above is a need to revise perceptions of success and failure. It is true that success in most schools is still measured mostly by academic achievement and this really does need to change. I believe that lots of schools do a fabulous job of providing a broad range of opportunities for students to succeed but still there are lots of students who leave schools as very able, broad, caring and considerate people with little to show in the way of ‘Official success’. Sure exam results open doors, but being a successful person is about so much more and I would like to see teacher references for students carry a lot more weight than they do at present. I could tell you more about my students than any set of exam results.</p> <h4> Play Vs Work</h4> <p> A colleague tweeted during the TedxLondon event that ‘School leaders need to learn not to see playing and learning as mutually exclusive’ and I could not agree more. I do subscribe to the point of view that ‘play’ is a fantastic way to learn but want to be careful not to imagine it as the only or the best way of learning. It is important here not to get caught up in semantics and I think the word play can be defined very broadly, but on its own can easily be misinterpreted. I much prefer engagement as a term and I base this on my own experiences as a learner. On the one hand we can see that students will be more likely to engage when what they are doing is not perceived as work. On the other hand would it not be better to change the perception of ‘work’?</p> <h4> Technology</h4> <p> There is far too much to discuss here to even think about adding a ‘paragraph’ that sums it up, so I will try and do it in a sentence. Technology it seems is generally considered, toylike, frivolous, flashy, dangerous and unnecessary etc until proven otherwise. This needs to be reversed!</p> <p> For example - If you are a player in the ‘twittersphere’ then you will not get this impression because of the obvious bias of those most likely to engage with each other about education through social media, but Facebook and Twitter are still dirty words in most educational establishments. I am not unaware of the risks, but it is unbelievable to me that we take the ‘communication tools of choice’ for most of our students and brand them too dangerous and frivolous to use for education.</p> <p> As suggested already, there is so much to discuss here regarding hardware, software, access and philosophy, but the world around us will change and move on and schools and education simply cannot afford to be left behind.</p> <h4> Cultural Importance….</h4> <p> The Vorderman report does talk about the differing cultural importance of mathematics in different countries and concedes that we can’t just take the methods used in other places and expect them to work. It would be a lot to expect that the report offers suggestions for how we can change the cultural perception of mathematics, but I feel the point is rather glossed over. I can’t speak for other subjects but I feel strongly that the general understanding and perception of mathematics as a subject is often misguided and its cultural value is very low in the UK. These two things are of great significance to the future of mathematics education.</p> <h4> Talking and Doing…</h4> <p> I am in danger of finishing this piece ironically. I have been prompted to write this by both the TEDxLondon event and the the Vorderman report on the state of mathematics education. Whilst this has been very good in helping me reflect on some of these issues, I can't help but feel that so much is spoken and written about what needs to change in education, whilst most teachers are in the practice of simply doing it! On that note I am going to stop writing and do some planning.....</p>https://www.teachmathematics.net/blog/10831/education-revolution#1316965786Physical Manipulatives
https://www.teachmathematics.net/blog/10718/physical-manipulatives
Sun, 11 Sep 2011 11:06:23 +0100]]>Physical Manipulativeshttps://www.teachmathematics.net/cache/blog-thumbs/24/10718-1315746383-thinkib.jpghttps://www.teachmathematics.net/blog/10718/physical-manipulatives
<p> <span ><img alt="" class="left" height="150" src="/files/teachmaths/files/Blogs/Manipulatives.jpg" width="150">Pick it up and move it around!</span></p> <p> This is a brief reflection on my experiences this week in thinking about the merits of physical Vs virtual manipulatives. Working in a school with a one to one laptop programme always invites You to think about what a computer can add to an experience. The number of virtual manipulatives available is staggering and some of them have really helped the evolution of teaching methods in mathematics. Having that programme really allows us to take advantage of them. With that in mind, please don't consider this blog post an 'anti technology' entry.</p> <p> Task design happens in a number of different ways. It is probably fair to say that most of us start by thinking about what it is we want to teach. At that point we either go looking for existing resources or start thinking of new ways to do it. Being that it is the start of a new term, I am prone to the latter given the energy I have after a summer break. I would like to think that I am disciplined enough not to overlook some fabulous existing ones either. The trouble with coming up with new ideas is that they usually involve the creation of new materials! As an optimist, I will always go and look on the internet to see if what I am looking for is already out there, but this is really the wrong way round. The internet is like a garage sale - go in search of something in particular and you are likely to be disappointed, go with some money in your pocket and you will probably find something useful!</p> <p> Having done some work on introducing the concept of tree diagrams, I decided that what I wanted was some online, interactive tree diagrams where the probabilities were listed but not put in the right place so that the task was to move them into the right places! This would just remove one area for possible error and in the early stages of an idea, I find it a very useful checking mechanism to know that if you have one left over that doesn't make sense then you may well have made a mistake. Anyway, I looked and I looked and I couldn't find it anywhere - I wondered about how long it would take me to program something like this using flash, but resolved that this was not the best use of my time at this time of year. I then decided that I really believed that in this case the 'physical manipulative' would be better. (I am not sure it saved me any time). A consequence of having technology at our disposal is that the benefits of the physical manipulative can be overlooked.</p> <p> The result was the creation of this resource <a href="http://www.teachmaths-inthinking.co.uk/activities/probability-trees.htm" target="_blank"><img class="ico" src="http://www.mathstudies-inthinking.co.uk/img/icons/inthinking.png" style="border-style: initial; border-color: initial; "> Probability trees</a> in which students work in groups with cut out bits of paper to solve problems where they have the answers and just need to put them in the right order. The physical manipulative really helped the group work aspect because more than one person can be involved in the arranging, and the absence of the computer screen allowed both more space and encouraged conversation and reasoning between the group members. In my search I had hoped that I would find something that was 'self-checking' so that students would get instant feedback on their efforts. This is a principle that can be very helpful, but is not without its faults. When no answer is instantly available, students need to reason with each other and reach some kind of consensus before settling on an answer. None of this is to say that the physical manipulative was 'better' in this context, but rather to say that there are lots of benefits to experiences based around physical manipulatives. Below are some pictures of the bits of paper!</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2F&set_id=72157627519034031&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2F&set_id=72157627519034031&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p> <p> On this note, the following are just a few examples of similar activities where physical manipulatives are used.</p> <p> <a href="http://www.teachmaths-inthinking.co.uk/activities/meeting-functions.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Meeting Functions</a></p> <p> A classification exercise with different functions, domains and ranges.</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157626075774355%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157626075774355%2F&set_id=72157626075774355&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157626075774355%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157626075774355%2F&set_id=72157626075774355&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p> <p> <a href="http://www.teachmaths-inthinking.co.uk/activities/oxo.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> OXO</a></p> <p> Using Multilink cubes to relate algebraic sequences to physical situations.</p> <p > <iframe allowfullscreen="" frameborder="0" height="345" src="http://www.youtube.com/embed/8fksgviuVlU?rel=0" width="420"></iframe></p> <p> <a href="http://www.teachmaths-inthinking.co.uk/activities/quadratic-links.htm" target="_blank"><img class="ico" src="http://www.mathstudies-inthinking.co.uk/img/icons/inthinking.png" style="border-style: initial; border-color: initial; "> Quadratic Links</a></p> <p> Linking the different representations of a quadratic function together.</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2F&set_id=72157624445351321&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2F&set_id=72157624445351321&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p> <p> Using multilink cubes to look at linear sequences!</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2F&set_id=72157623076372881&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2F&set_id=72157623076372881&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p><p><strong>Tags:</strong> <em>task design,group work,manipulatives,reflection</em></p>https://www.teachmathematics.net/blog/10718/physical-manipulatives#1315735583CAS - which way to go?
https://www.teachmathematics.net/blog/10569/cas-which-way-to-go
Mon, 22 Aug 2011 09:52:21 +0100]]>CAS - which way to go?https://www.teachmathematics.net/cache/blog-thumbs/24/10569-1314013941-thinkib.jpghttps://www.teachmathematics.net/blog/10569/cas-which-way-to-go
<p> <img alt="" class="left" height="157" src="/files/teachmaths/files/Blogs/CAS.jpg" width="150">This blog entry was written as part of a reflection on the ICTMT 10 conference held in July in Portsmouth, UK.</p> <p> CAS for schools is tricky decision at the moment, but I must confess that this conference has helped me to narrow down some of those decisions. <a href="http://www.wolfram.com/mathematica/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Mathematica</a>, <a href="http://www.maplesoft.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Maple</a> and <a href="http://education.ti.com/calculators/products/US/os-update/" target="_blank"><img class="ico" src="/img/icons/connection.png"> TI-Nspire</a> are the names that seem to rise to the top and I am interested in all three. The first two are probably more capable then we actually need for secondary school. At our school, we still use and enjoy an old version of Derive that we have on our system at school and have been looking at ways to get TI Nspire for all our computers. We have been playing with single user licenses and like what it does, but we don’t want to invest in the handheld technology. We have the luxury of 1 to 1 computers and I am still of the view that advances in smartphone technology will take over handheld calculators as soon as exam boards catch up. This is no small point however, and the exam boards are the ‘joker in the pack’ as one teacher put it, for CAS enabled calculators as the leap into allowing smartphones or effectively computers into exams is huge and one that will cost exam boards a large amount of time and money and so they are likely to hold out as long as they can. More frustrating than this is that TI appear, not surprisingly, much more interested in selling the handhelds than they do the emulator software. As a result, I feel priced out of all three of those top runners, TI, Mathematica and Maple.</p> <p> I was then, fascinated to learn more about the development of the freely available <a href="http://maxima.sourceforge.net/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Maxima</a> from Chris Sangwin. Even better than this is the collaboration with <a href="http://www.geogebra.org/cms/" target="_blank"><img class="ico" src="/img/icons/connection.png">Geogebra</a> to integrate maxima thus creating one great tool that will combine so many of our needs in secondary schools. CAS, graphing and dynamic geometry all integrated and linked! A beta version of this software is available <a href="http://www.geogebra.org/trac/wiki/GeoGebraCAS" target="_blank"><img class="ico" src="/img/icons/connection.png"> GeogebraCAS</a> and the official launch is due this month. I for one am looking forward to it. Of course, the next discussion is to think in more detail about how to get the maximum benefit from this software in the classroom. See <a href="http://www.teachmaths-inthinking.co.uk/activities/investigating-quadratic-factors.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png">Investigating Quadratic Factors</a> and <a href="http://www.teachmaths-inthinking.co.uk/activities/finding-factors.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Finding Factors</a> for examples of investigations, using CAS (with "how to" video help for Geogebra 4.0 CAS, WolframAlpha, TiNspire Derive), that offer the opportunity for students to 'discover' for themselves the concept of factorising. Watch this space for further applications ....<br> </p><p><strong>Tags:</strong> <em>CAS,ICT,conference,</em></p>https://www.teachmathematics.net/blog/10569/cas-which-way-to-go#1314003141ICTMT 10 - Portsmouth
https://www.teachmathematics.net/blog/10568/ictmt-10-portsmouth
Mon, 22 Aug 2011 09:29:01 +0100]]>ICTMT 10 - Portsmouthhttps://www.teachmathematics.net/cache/blog-thumbs/24/10568-1314012541-thinkib.jpghttps://www.teachmathematics.net/blog/10568/ictmt-10-portsmouth
<p> <a href="http://ictmt10.org/" target="_blank"><img alt="" class="left" height="53" src="/files/teachmaths/files/Blogs/ICTMT 10.jpeg" width="150"></a>This blog is a short reflection on my experience of the ICTMT10 conference in Portsmouth 5 – 8 July 2011. I will not attempt a complete review of the conference for two reasons. Firstly, it would be impossible because of the number of parallel sessions on offer and secondly because I would not do it justice. As a secondary school mathematics teacher, the most useful thing for me to do is record some of the highlights and, perhaps most importantly, the resulting points of action that I have. Rather than publish this all in one go, I will publish a series of blogs over the next few weeks on some of the main themes. The following serves as an overview of what may follow.</p> <p> It is worth noting from the start that the conference is aimed at a mixture of educational researchers and practitioners from secondary and tertiary education and the sessions are a mixture of keynotes, presenting research and workshops. As such it is a rich mixture of possibilities for all kinds of people. I attended the previous conference, ICTMT9 in Metz, 2009 and I would be lying if I said I wasn’t a little disappointed that there were quite a few less secondary school teachers in Portsmouth and a considerably smaller North American presence. That said, there was a truly international feel to the conference and enough of my peers for some really rich exchange, not to mention some good company and good times.</p> <p> There were keynote speeches from Richard Noss, Paul Drijvers, Colin White and Collette Laborde all of which were thought provoking. One theme that seemed to run through all of these was that there seems to be a general disappointment that progress with ICT in Mathematics teaching has not achieved the potential that was thought to exist 20 - 30 years ago. Having only taught for 13 years I am not able to comment on this, but do think I can reflect on some significant changes during those 13 years!</p> <p> There was research presented on the benefits of using technology as a modeling tool and motivator, particularly in tertiary education. One example was given in the study of sports science where students did not necessarily have a strong mathematical background, but could make progress with modeling tools such as 'Matlab'.</p> <p> There was a particularly interesting workshop on students making videos of themselves solving problems and using these videos of getting students to reflect on their 'working out' and the stages they went through.</p> <p> There was much discussion of various electronic assessment tools and, in particular, their ability to give relevant feedback where mistakes were made. This technology is clearly advancing and does have a place in secondary schools.</p> <p> Handheld technology, mobile apps, GDCs and screen sharing software were all on show and this has prompted me to think about how to move forward with this in my school.</p> <p> Which CAS technology should we be embracing? This is a tough call but I became aware of some very interesting developments with Geogebra and Maxima, that may make this choice a little easier.</p> <p> With London 2012 on the horizon, sport and mathematics was a running theme through the conference and without too many concrete ideas, I am determined to think about strengthening this link in my school.</p> <p> We were treated to an excellent talk from Richard Noble about the 'Bloodhound project' that made me think about the whole land speed thing in a new way. As well as this we had dinner on the HMS Warrior - a 150 year old battle ship restored in all of its glory to round off an excellent week.</p> <p> As I said, I could not do the whole conference justice in one blog entry and so only aimed to give a brief summary. Many of the issues deserve to be returned to in future weeks in more depth.</p> <p> We, from the International School of Toulouse, offered 2 sessions during the conference, the details of which can be found here;</p> <p> <a href="http://www.teachmaths-inthinking.co.uk/conferences/future-curriculum.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Future curriculum</a> 'Use of technology to significantly enhance the development, engagement and skillset of students in the third industrial revolution.</p> <p> <a href="http://www.teachmaths-inthinking.co.uk/conferences/animated-questions.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Animated Questions</a> 'New types of question afforded by developments in technology'</p><p><strong>Tags:</strong> <em>Conference,ICT</em></p>https://www.teachmathematics.net/blog/10568/ictmt-10-portsmouth#1314001741An incentive to generalise
https://www.teachmathematics.net/blog/10302/an-incentive-to-generalise
Sun, 17 Jul 2011 12:21:14 +0100]]>An incentive to generalisehttps://www.teachmathematics.net/cache/blog-thumbs/24/10302-1310912474-thinkib.jpghttps://www.teachmathematics.net/blog/10302/an-incentive-to-generalise
<p> <img alt="" class="left" height="150" src="/files/teachmaths/files/ALGEBRA/Tower of Hanoi/ToH.jpg" width="150">I recently attended the <a href="http://ictmt10.org/" target="_blank">ICTMT10 conference</a> in Portsmouth. Amongst the many presentations was a thought provoking keynote from Richard Noss in which one of the themes was considering the merits of different representations for complex and abstract mathematical ideas. He discussed a particular example of a ‘typical’ sequences question in which students were expected to draw the next two patterns of a given tiling sequence and deduce the algebraic generalisation that gave the number of tiles required for any given term of that sequence. The discussion went on to look at ‘typical’ responses where students will spot a term to term rule and mistakenly try to express this algebraically rather than considering a position to term relationship. It was then noted that teachers will try to help students move on by asking them to predict the number of tiles for the 100th term. This may achieve some success, but will draw, from some students, the reaction of counting the number of tiles in the 10th problem and multiplying it by 10.</p> <p> The example was one of many that alluded to the notion that numbers have different meanings in different contexts with different representations that is both testimony to the richness of numbers and algebra and the ease with which a student can be confused. This was amusingly demonstrated with a picture of two buses, one the number 9 and the other the number 18, which was twice as long, but half as high!</p> <p> Sticking with the first example and being aware of the problems based on my own classroom experience, I wanted to add that another factor that contributes to general confusion is the lack of ‘incentive to generalise’. For my money a good activity will stop students from asking ‘Why do we need to do or learn this’ not by answering the question directly, but by engaging students with activity and incentives that pre-occupy them before they think to ask. A simple example of this is ‘Sudoku’. Why does anyone need to do that? I could come up with lots of good answers but millions of people worldwide never ask! With this in mind I wanted to share some examples of activities that I think provide that engagement and incentive to generalise.</p> <p> These activities involve real physical situations in which students are actively involved in solving problems that can be modeled algebraically. The puzzle provides engagement and incentive by appealing to a natural puzzle solving instinct and better yet, it provides a physical, structural link from which students can generalise, thus taking the edge off the otherwise abstract nature of the process. Each of the links below is to a teaching activity ready to go for classrooms or ready for twisting and turning by teachers and students alike. The activities come with descriptions, resources and teacher notes to help think about how to get the most out of them.</p> <p> <img alt="" class="left" height="60" src="/files/teachmaths/files/ALGEBRA/Tower of Hanoi/ToH.jpg" width="60"><a href="http://www.teachmaths-inthinking.co.uk/activities/tower-of-hanoi.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> The Tower of Hanoi</a></p> <p> The classic puzzle that can be modeled by an exponential sequence which means that only a small increase in the number of discs would make the problem unsolvable within our own lifetimes! Get a real one and let students physically do it themselves.</p> <p> <img alt="" class="left" height="60" src="/files/teachmaths/files/ALGEBRA/Frogs/frog.jpg" width="60"><a href="http://www.teachmaths-inthinking.co.uk/activities/frogs.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Frogs</a></p> <p> Truly one of my favourite lessons year after year. There is so much going on with this puzzle, not least of which is a nice example of a quadratic sequence. Get students hopping and sliding around the room to get under the skin of this one.</p> <p> <img alt="" class="left" height="60" src="/files/teachmaths/files/ALGEBRA/SBP/sbp.jpg" width="60"><a href="http://www.teachmaths-inthinking.co.uk/activities/sliding-bus-puzzle.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> The Sliding bus puzzle</a></p> <p> Another good one for physical activity and packed with a couple of nice surprises. It’s a linear sequence that can be broken down into smaller ones. It is really accessible and good fun!<br> </p>https://www.teachmathematics.net/blog/10302/an-incentive-to-generalise#1310901674Data is out there!
https://www.teachmathematics.net/blog/10148/data-is-out-there
Sun, 19 Jun 2011 17:27:12 +0100]]>Data is out there!https://www.teachmathematics.net/cache/blog-thumbs/24/10148-1308511632-thinkib.jpghttps://www.teachmathematics.net/blog/10148/data-is-out-there
<p> <img alt="" class="left" height="150" src="/files/mathstudies/images/blog/Data.png" width="150">The longer I teach mathematics, the more apsects of it I enjoy teaching. My preferences vary from group to group and course to course, but just at the moment, I think it is really exciting to teach statistics. It is well documented that students can respond particularly well to the rooting of ideas in concrete contexts and statistics are a fantatstic way to do just that. I should add that I don't subscribe to the view that ideas always have to be rooted in concrete contexts, but that is a whole other conversation.</p> <p> So it has probably always been true that use of context has been very possible in the teaching of statistics, although it is remarkable how much fictional, semi real data is still used. This is particularly true of textbooks and exams, and whilst I believe that the nature of both of those things should change on a big scale, I can't be sure how long that will take. In the classroom however, we are free to move with the times and the use of real, current and intriguing data is more possible than ever. Technology allows the data to be easily shared and for large amounts of it to be analysed with relative ease. For example, the whole question of climate change can be be tackled in classrooms now. Just today, I picked up this <a href="http://www.guardian.co.uk/news/datablog/2011/jun/10/data-store-drought" target="_blank"><img class="ico" src="/img/icons/connection.png"> 100 years of UK rainfall data</a> from one of my favourite data sources, <a href="http://www.guardian.co.uk/news/datablog" target="_blank"><img class="ico" src="/img/icons/connection.png"> The Guardian Datablog</a>. I grabbed the data really quickly and used <a href="http://www.autograph-math.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Autograph</a> to make a scattergraph as shown in the image below. What conclusions can I draw? The point of this blog is the ease with which data can be gathered and processed and because it is real data, it makes one keener to play with it some more to see if there is anything in the data that is not shown in the scattergraph.</p> <p > <img alt="" height="232" src="/files/mathstudies/images/blog/UK rain.png" width="450"></p> <p> Above all this though, what I find particularly exciting is the increasingly high profile that popular media is giving to data analysis. The following are just a few examples</p> <p> <a href="http://www.netflixprize.com//index" target="_blank"><img class="ico" src="/img/icons/connection.png"> The Netflix prize</a> - This is a great example of a project that was put out there for anyone that wanted to enter!</p> <p> <a href="http://www.kaggle.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Kaggle</a> - This website is based on a similar idea - real statistics projects/competitions for anyone that can.</p> <p> <a href="http://www.informationisbeautiful.net/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Information is Beautiful</a> - David McCandless brings information to us in increasingly inventive and interesting ways with his infographics. In doing so he reminds us how our understanding of the world around us depends in no small part on our ability to understand statistics and their representations.</p> <p> <a href="http://www.coolinfographics.com/blog/2011/6/6/datavis-contest-from-postgrad-and-david-mccandless.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+CoolInfographics+%28Cool+Infographics%29&utm_content=FaceBook" target="_blank"><img class="ico" src="/img/icons/connection.png"> Visulaisation prize</a> - This is just another link I picked up through twitter that is a competition to create an infographic with some data they haven't had time to look at at 'information is beautiful'. To help, here is a blog I found on <a href="http://www.makeuseof.com/tag/awesome-free-tools-infographics/?asid=c228f21b" target="_blank"><img class="ico" src="/img/icons/connection.png"> Tools for making infographics</a>. </p> <p> <a href="http://www.gapminder.org/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Gapminder by Hans Rosling</a> - As many readers will know, Hans Rosling has done a huge amount to help get data in to the public domain and given us tool to help understand it.</p> <p> All this really helps to convince students of the relevance of what you are trying to teach them and the place of these skills and techniques in our world. I particularly like the quote from David McCandless in his <a href="http://www.ted.com/talks/david_mccandless_the_beauty_of_data_visualization.html" target="_blank"><img class="ico" src="/img/icons/connection.png"> TED talk</a> that 'Data is the new soil' and the illusion that much of our future development may depend on our ability to use data to accurately understand the present! It is all very exciting, particularly for mathematics teachers.</p><p><strong>Tags:</strong> <em>statistics,popular,data,internet</em></p>https://www.teachmathematics.net/blog/10148/data-is-out-there#1308500832Poker Machines and Percentages
https://www.teachmathematics.net/blog/10025/poker-machines-and-percentages
Sun, 29 May 2011 11:05:22 +0100]]>Poker Machines and Percentageshttps://www.teachmathematics.net/cache/blog-thumbs/24/10025-1306674322-thinkib.jpghttps://www.teachmathematics.net/blog/10025/poker-machines-and-percentages
<p> <img alt="" class="left" height="113" src="/files/teachmaths/images/Poker Machine.jpeg" width="150"></p> <h3> Are percentages that basic?</h3> <p> This blog entry is really just designed to ask the question above and not to answer it. The hierarchy of mathematical sub-topics has always fascinated me and I have never really been clear on what I would view as 'the basics'. Equally I have never really been clear on why fractions and percentages often fall into that category when defined by people in discussion. In fact, students' failings with percentages appear to upset fellow teachers regularly and we as maths teachers are often asked by colleagues 'When do you do percentages?' and 'Why can't your students do them in my lessons?' and questions like these. At the risk of of being irritating I might often respond by asking, 'What do you mean 'do' percentages?'. Almost like probability, percentages are a topic that can escalate from simple to difficult very quickly indeed. How about the following classic problem,</p> <p > <em>'Start with 2 glasses of wine of equal size, one red, one white. Take a 10% sample from one of the glasses and put it in the other. Now extract the same size sample from the second glass and put it back in the first. What percentage of each glass is white wine?'</em></p> <p> That problem can be developed in many different ways very quickly and all of a sudden, many of the people who refer to percentages as basic are struggling. The aim is of course not to make people struggle, but to stop and think about the whole idea of percentages in a bit more depth. Many times I have started lessons on percentages by talking about the 10 % pay rise followed by the 10% pay cut and the associated counter intuitive response. Repeated percentage change, percentage error, reverse percentages and so on are some of the most difficult things that happen in my classroom. I know of students who can apply differential calculus in context, but come unstuck with reverse percentages or in a discussion about why 'Jedi Knight' is the fastest growing religion in the world according percentage growth between surveys. So I am not sure that percentages should be generalised as mathematical basics.</p> <p> This view was reinforced this week when I read this article, <a href="http://www.abc.net.au/unleashed/2733166.html" target="_blank"><img class="ico" src="http://www.teachmaths-inthinking.co.uk/img/icons/connection.png" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-top-color: rgb(153, 153, 153); border-right-color: rgb(153, 153, 153); border-bottom-color: rgb(153, 153, 153); border-left-color: rgb(153, 153, 153); border-style: initial; border-color: initial; display: inline; vertical-align: bottom; "> Poker Machine Maths,</a> about poker machines in Australia. In short, the law states that poker machines should give a return of between 85 and 90%. A lady gambles $300 in a day at the machine and walks away with nothing, but the machine stayed within the law. Follow your instinctive reaction to that statement then read the article. Then, if you really fancy a challenge, imagine how you explain that to a class of your students and the other mathematics that is involved with this problem?</p>https://www.teachmathematics.net/blog/10025/poker-machines-and-percentages#1306663522Animated questions
https://www.teachmathematics.net/blog/9869/animated-questions
Sun, 08 May 2011 10:34:26 +0100]]>Animated questionshttps://www.teachmathematics.net/cache/blog-thumbs/24/9869-1304858066-thinkib.jpghttps://www.teachmathematics.net/blog/9869/animated-questions
<p> <img alt="" class="left" height="100" src="/files/teachmaths/files/Geometry/Magic Mirror/Magic Mirror.png" width="100">Dynamic geometry and similar dynamic software have been a major influence on my own understanding of mathematics and consequently my own teaching. Start with the notion that all squares actually meet the minimum requirements to qualify as all other quadrilaterals<img class="ico" src="/r/f1.png"></p> <meta charset="utf-8"> <p> National variations in the definition of a trapezium or trapezoid do provide an interesting challenge to this notion<img class="ico" src="/r/f2.png">. How often does this notion upset students who somehow want rectangles and squares to be discretely different from each other? I suggest that a mathematical object or phenomenon is best described by its properties and that these properties can best be explored in a dynamic environment. The ability to bend, stretch, and explore a dynamic situation demands that we consider generalities and their limits where static representations provide us only a particular case. Why then, are so many questions in mathematics classrooms asked through a static, fixed and often printed medium? Developments in technology have prompted me to explore the setting of ‘Animated questions’ where students are shown short animations of particular mathematical phenomena and asked to explore and define them by attempting to recreate them. In this workshop I propose to engage the audience with a number of examples of these ‘animated questions’ exploring geometry, functions, sequences and more. In exploring the problems I hope the group is prompted to recognise the benefits of asking questions in this way in terms of exploring generality, engagement and problem solving.<br> <br> I work in a school where students carry their own laptops with them at all times, which aids such experimentation, but this is not a prerequisite for being able to ask these questions. What it does do is make me increasingly curious about how long it will be before external assessment tools for mathematics will be set using technology as a medium and thus allowing a broader, more versatile style of questioning of which these ‘animated questions’ are just an example.<br> <br> The above is the abstract for a session I am planning to run at the <a href="http://ictmt10.org/" target="_blank"><img class="ico" src="/img/icons/connection.png"> ICTMT 10</a> conference in Portsmouth in July.</p> <h4> Examples</h4> <p> The following are a few examples of such animations as described above. In each case, the question is essentially quite simple. Can you recreate the animation?</p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/TTLoseMKpgY?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/KohHmcjlnV4?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/Q1JkBViqVQo?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/twRF3f4HT7g?rel=0" width="560"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/S8p5XyNARZ0?rel=0" width="425"></iframe></p> <h4> Activities</h4> <p> Please follow the links below to see some examples of how this can be done in the classroom.</p> <p> <a href="http://www.teachmaths-inthinking.co.uk/activities/quadratic-movers.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Quadratic Movers</a> - Learning about quadratics in a dynamic environment</p> <p> <a href="http://www.teachmaths-inthinking.co.uk/activities/kaleidoscope.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Kaleidoscope</a> - Investigating rotation in a dynamic environment</p><p><strong>Tags:</strong> <em>ICT,innovation,conference,dynamic geometry</em></p>https://www.teachmathematics.net/blog/9869/animated-questions#1304847266