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Slides from researchEd maths and science

Presentation for researchED maths and science on June 11th 2016.

References at the end (might be some extra references from slides that were removed later on, this interesting 🙂

Interested in discussing, contact me at or on Twitter @cbokhove

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Games in maths education

This is a translation of a review that appeared a while back in Dutch in the journal of the Mathematical Society (KWG) in the Netherlands. I wasn’t able to always check the original English wording in the book.

Computer games for Maths

Christian Bokhove, University of Southampton, United Kingdom

51iyzu1DTlL._SX326_BO1,204,203,200_Recently, Keith Devlin (Stanford University), known of his newsletter Devlin’s Angle and popularisation of maths, released a computer game (app for the iPad) with his company Innertubegames called Wuzzit Trouble ( The game purports to, without actually calling them that, address linear Diophantine equations and build on principles from Devlin’s book on computer games and mathematics (Devlin, 2011) in which Devlin explains why computer games are an ‘ideal’ medium for teaching maths in secondary education. In twelve chapters the book discusses topics like street maths in Brasil, mathematical thinking, computer games, how these could contribute to the learning of maths, and concludes with some recommendations for successful educational computer games. The book has two aims: 1. To start a discussion in the world of maths education about the potential for games in education. 2. To convince the reader that well designed games will play an important role in our future maths education, especially in secondary education. In my opinion, Devlin succeeds in the first aim simply by writing a book about the topic. The second aim is less successful.

Firstly, Devlin uses a somewhat unclear definition of ‘mathematical thinking’.: at first it’s ‘simplifying’, then ‘what a mathematician does’, and then something else yet again. Devlin remains quite tentative in his claims and undermines some of his initial statements later on in the book. Although this is appropriate it doesweaken some of the arguments. The book subsequently feels like a set of disjointed claims that mainly serve to support the main claim of the book: computer games matter. A second point I noted is that the book seems very much aimed the US. The book describes many challenges in US education that, in my view, might be less relevant for Europe. The US emphasis also might explain the extensive use of superlatives like an ‘ideal medium’. With these one would expect a good support of claims with evidence. This is not always the case, for example when Devlin claims that “to young players who have grown up in era of multimedia multitasking, this is no problem at all” (p. 141) or  “In fact, technology has now rendered obsolete much of what teachers used to do” (p. 181). Devlin’s experiences with World of Warcraft are interesting but anecdotical and one-sided, as there are many more types of games. It also shows that the world of games changes quickly, a disadvantage of a paper book from 2011.

Devlin has written an original, but not very evidenced, book on a topic that will become more and more relevant over time. As avid gamer myself I can see how computer games have conquered the world. It would be great if mathematics could tap into a fraction of the motivation, resources and concentration it might offer. It’s clear to me this can only happen with careful and rigorous research.

Devlin, Keith. (2011). Mathematics Education for a New Era: Video Games as a Medium for Learning.

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BSRML conference – report

I have written three posts on the BSRLM day conference on November 17th, 2012.

The three posts are:

BSRLM conference part 1
BSRLM conference part 2 Alnuset
BSRLM conference part 3

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BSRLM conference part 3

The fourth session by Ainley reported on the Fibonacci project, integrating inquiry in mathematics and science education. It was good to hear that the word ‘utility’ that was used, did not refer to a utilitarian view of maths, i.c. that everything should have a clear purpose. I mention this as discussions about utility often tend to end in comments like ‘what’s the point of doing algebra’? Actually, I think that does have a purpose, amongst others ‘analytical thinking’ but I prefer steering clear from these types of pointless discussions. The best slide, I though, was a slide with science, statistics and mathematics in the columns and rows with a distinction in, for example, their purpose.

It formed a coherent picture of STEM. The two examples for integrative projects were ‘building a zoo’ which I didn’t like when it concerned the context of fences that had to be built. It’s the lack of creativity that often is in textbooks as well. the second project, on gliders, was more interesting but the mathematical component seemed to belong more in statistics used. I would loved to have seen a good mathematical example.

The fifth session by Hassler and Blair was about Open Educational Resources. The project, funded by JISC, acknowledged three freedoms: legal, technical and educational. It is a project that boasted a website with educational resources, free to use, keywords and with pdf creator. Although nicely implemented, to me, it seemed to be a bit ‘yet another portal’. The individual elements weren’t that novel either, with for example a book creator also in the Activemath project. The most interesting thing was the fact that the materials were aimed at ‘interactive teaching’.

The sixth and last session was a presentation by Kislenko from Estiona. She described how in Estonia a new curriculum was implemented for educating teachers in mathematics and natural sciences. It was an interesting story, although I was wondering how ‘new’ it was, as the title had the term ‘innovative’ in it.

Together with some networking these sessions made up an interesting and useful day in Cambridge.

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BSRLM conference part 2 Alnuset

The third session I attended was more a discussion and critique session, led by Monaghan and Mason, on the topic of ‘cultural affordances’. The basis was the work of Chiappini, who -in the ReMath project- used the software program Alnuset (see here to download it) to look at (its) affordances. Monaghan described the work (a paper on the topic, there will be a publication in 2013, was available) and then asked some questions. Chiappini distinguishes three layers of affordances: perceived, ergonomic and cultural. Engestroms cycle of expansive learning is used, as I understood it, to use activities as drivers for transformation of ergonomic affordances into cultural affordances. Monaghan then asked some critical questions, under which whether the theory of Engestrom really was necessary, wouldn’t for example Radfords work on gestures be more appropriate? Another comment pondered whether the steps for expansive learning were prescriptive or descriptive. I think the former: as the author has made the software with certain design elements in mind it is pretty obvious that they have a preconceived notion of how student learning should take place.  It was pretty hard to discuss these more philosophical issues in detail. I’m not really sure if I even understand the work. Although this could be solely because I haven’t read enough about it, I also feel a bit as if ‘difficult words’ are used to state the obvious. I could only describe what I was thinking off. The article that I took home afterwards gave some more pointers. To get a grasp of this I downloaded the software, that reminded me a bit of the Freudenthal Institute’s ‘Geometrische algebra’ applets, and tried out the software. I liked the idea behind the software. In this example I’ve made three expressions, and I can manipulate x. The other two expressions change with x. Some comments:

  1. I like the way expressions are made and the look and feel, as well as the way dragging changes the expression. Also ‘dividing by zero’ causes expressions to disappear. However, why does x=0 disappear as well when I drag x to 0? (see figure)
  2. I don’t see how the drawback of every tool that allows ‘dragging’, namely just pointless dragging, in this case just to line up the different expressions, is solved. Maybe this isn’t the main goal of the software.
  3. I think that the number line should be used in conjunction with tables and graphs, thus forming a triad expression-table-graphs. The addition of things like an algebraic manipulator and a Cartesian plane seems to indicate that the authors also like more than one representation.
  4. It has far too limited scope for algebra. The 30 day trial is handy here, as in my opinion the software doesn’t do enough to warrant the price.
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BSRLM conference part 1

On Saturday November 17th I visited the second day of the BSRLM conference (British Society for Research into Learning Mathematics). I’ve become a member as it’s ‘the place to be’ for maths education research. This time the conference was in Cambridge, and apparently I was the only one tweeting #bsrlm.

The first session I attended was by Anne Berit Fuglestadt from the university of Agder (soon, homebase of a Dutch researcher I know). She reported about teachers discussing inquiry-based teaching with digital tools.

The second half of the session consisted of discussions on instrumental and documentational genesis (The French School, Trouche is an important name). This was fitting, as one PhD student I (co-)supervise is studying instrumentation as underpinning framework for her study.

The second session was an interesting take on use of the Livescribe pen. At first it seemed as if the study, done by Hickman and Monaghan, seemed a bit of a waste of the livescribe pen. Emphasis was put on the audio recording facilities.

Luckily, as I could have expected, they did more with the pen. The pens were used to record student work while ‘thinking aloud’ and these materials (a sort of screencasts of what was written) were used for a combination of stimulated recall and task-based interviews (e.g. Goldin, 1997). Hickman showed some discourse by primary students that was recorded with the pen. It was nice to see student work being ‘constructed’ instead of just having static scans of their work. It also was nice that we could try out the pen ourselves. I did think more can be done with even the older generation of pens. For example, Dragon Naturally Speaking does doe a decent job of transcribing voice, just as long as it is trained to recognize it. It will certainly cut the amount of time you need for transcribing an hours worth of audio.

Another application to use would be Myscript, from the same company that brings a great online equation recognizer. The latest version of the pen also boasts Wifi and Evernote integration, so it looks interesting. It will certainly be worthwhile to check out this for our SKE+ group. A follow-up discussion could be whether these devices will eventually become obsolete if tablet technology with styli, like the Galaxy Note, takes off.