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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.

Education Education Research

Journalclub at ResearchED

I think it’s a great idea to study articles in a journalclub setting. I read the article as well and made the following annotations:

See file attached to this message

File: 00220671%2E2013%2E807491 – annotated.pdf

Annotation summary:

— Page 2 —

Seems to me to be quite a limited view of Academic Performance, including only reading.

Must keep in mind: 2000 data. Unfortunately it is quite normal to use ‘older’ data. Some of the delay lies in publication mechanisms so PISA 2012 data released December 2013 is difficult but there are other instances.

I think multilevel analysis is useful but not everyone would agree.

PISA, so contextual effects. Differences countries?

— Page 4 —

Would be good to compare with TIMSS and PIRLS.

This is the ‘standard’ PISA sampling strategy.

I’m not sure if it already was the case for PISA 2000 but now most large-scale assessments need to take into account the complex sampling design. This means sampling WEIGHTS (because of non-response) and so-called PLAUSIBLE VALUES (because not all students make all test items). There is no mention if this in the paper so either PISA 2000 was done differently or they just ‘forgot’.

According to some (e.g. Willms) this is an appropriate substitute for the actual sampling design.

— Page 5 —

In general I would want more transparency regarding missing data and the ‘model building’, see Dedrick et al. (2009) for recommendations.

— Page 6 —

With large N results will be significant very quickly. Often ‘effect size’ is mentioned.

But see how much more is explained over the models: not much more, it seems.

— Page 7 —

So only the first PLAUSIBLE VALUE was used.

Not much ‘variance explained’

— Page 8 —

Stop with ‘thus’

— Page 9 —

Cognitive Load anyone?

Important: cause and effect

So this ‘significant’ marginally interesting because of large N.


A response to a W3C priorities blog

This blogpost is a comment on this interesting white paper by Crispin Weston and Pierre Danet about setting W3C priorities. I first thought to comment on the site but it became rather lengthy so seemed more logical to post it here. Since coming to work in the United Kingdom I have not really been involved in standards for education, but the topic triggered my previous experiences. As from quite early on, 2004-ish, I did my fair share of ‘standards’ work (SCORM packages, programming the SCORM module in moodle, assessment standards for Maths via SURF) I thought it would be good to comment on the blog in more detail, not only because I disagree with some of it, but more importantly, I think any new development in this area *must* learn from previous experiences. I thought long and hard before writing this piece because I don’t want to come over, or be dismissed, as someone against innovation per se. But I must admit, even when I lived in the Netherlands, I did not really feel people really wanted too much innovation.

The context of the document

I hope that some of the claims and associations made in the first paragraph(s) will be reworded or evidenced more. At the moment one sentence combining underperforming education, PISA, MOOCs and elite courses seems far-fetched. I also wonder whether a statement saying that it’s a good time for 1:1 because touch is easy-to-use isn’t a bit too ‘easy’. On evidence I would also say that, when we run with the assumption that technology can do both good and bad, there might not be general evidence of the impact of technology on learning outcomes because it is seen as a means to and end. Like any tool, means are used correctly and incorrectly.

Three barriers

The authors of the piece see three key barriers to the emergence of a dynamic ed-tech market (why the word ‘market’?):
  • The lack of interoperability of systems and content that would allow different sorts of instructional software to work together in an integrated environment.
  • The lack of discoverability of innovative new products.
  • The institutional conservatism of many state-run education systems, which are often resistant to innovation and uncomfortable with the use of data as a management tool.
I certainly agree with interoperability (or lack thereof), which *is* the main topic of the article, as being a big barrier (some more comments later on). The second one, discoverability, is not really defined but if it leads to the conclusion that the W3C would be a good organisation to connect different players, then that’s fine as well. However, the article then primarily emphasizes how the W3C should “work with governments that are prepared to address the institutional conservatism to be found in their own formal education system.”. This is in line with the third barrier the authors define, adding that these systems “are often resistant to innovation”. I think such statements are not warranted and rather unproductive. It also neglects the role, at least on the topic of adoption of standards and interoperability, of companies that, in my view, in the last decades systematically have undermined standards, either intentional or through mis-management and neglect. In my view this thread runs from even HTML3.2 (Netscape vs Internet Explorer) to the current ePub3, Kindle and iBooks endeavours.


The paper then goes to requirements analysis. In general terms this section is ok, and I certainly see a lot of good things in Analytics and Games. I do, however, miss some analysis there. How are these aspects effective in “other businesses”?,  why is that the case?, What characteristics make it this way? What’s to say it would work in education? And, crucially, why and how would you adopt a whole paradigm? To use this then to argue that little has been done, and subsequently to propose how to go forward has a bit of a ‘light touch’.


What I do find interesting and appropriate is the conclusion that interoperability between the two strands, let’s concisely call them analytics and content, is an important aspect. So although I think the analysis falls short, I think there would be no harm in, even potentially serve as catalyst, to have good interoperability. But that’s not something new, of course. Getting a standard is a ‘different cookie’ (Sorry, a Dutch joke). I also like the ambition to outsmart the proprietory market and be there first.
blog2Having used SCORM myself and even having modded the SCORM module in Moodle so that it made more use of the SCORM specification, I think the lessons to learn from it, are not complete. One only needs to look at software that can create SCORM packages like Reload/Weload, Xerte, but also commercial packages to see that it has been possible to make rich content. So I’m not really sure whether it’s the lack of standardisation and tools why it has not really taken off. When I extended the SCORM module most users did not really care, they just wanted a simple scoring mechanism. But now as well: when I see current adaptive systems they are mainly multiple choice and scores. When I look at game mechanisms they mainly are Points, Badges and Leaderboards. To me, that indicates users might not really want more sophistication (yet). Now I understand this might be seen as a chicken/egg issue i.e. when we finally *can* make sophisticated stuff it *will* happen. Perhaps this is true (although history tells us otherwise) but it certainly would be smart to analyze the situation more deeply. Not in the least with regard to the role of the current edtech industry who, in my view, have sometimes frustrated attempts to formulate standards.
This also brings me to a general frustration with the fact that millions have been spent on attempts to write specifications on standards and, even worse, metadata. Over the years this has resulted in thousands of pages of documentation. Why will it be different this time? I feel that before setting out on yet such a journey, that question needs to be answered extensively. The description of the  SCORM standard shows that we are dealing with experts. Given what I said previously I think there are more important reasons for SCORM’s waning than others. Apart from asking ourselves what factors, we also need to ask ourselves how it will be prevented this time. I also wondered whether there still was any scope in assessments standards like QTI. A thread, in my view, through almost all standards is the mis-management and frustration by organisations and enterprises. If W3C leads the process, that is at least a strong start. In how far W3C can confront the largest enterprises in the world, I don’t know.
A second point risk remains hardware and software. Hardware and software becomes obsolete or deprecated. Every time when it happens we are told there are good reasons for it, often inefficiency or security (e.g. java, but that’s also, again mis-management and perhaps personal feuds), but in any case: who’s to say this won’t happen again. In my opinion it certainly ties in again with the corporate aspect. The W3C should be strong enough to address it.

SCORM was under-utilized

From a technical point of view I have always thought the CMI had not been used as well as possible. I agree that it was partly because of the SCORM specification but also unfamiliarity with it, for example the ‘suspendState’ option. A package could communicate quite a lot of information through this field, needing two things: (1) packages that would create a suspendState, (2) a VLE that would actually read that state. I remember being involved in the Galois Project, a maths algebra project, where we tried to do just that. The former was done by creating a system that could produce algebra SCORblog3M packages which utilized the suspendState for storage. The latter had indeed needed to be obtained by reprogramming a VLE, which I did for moodle’s SCORM module. The annotated SCORM module was plugged on the moodle forums. As said previously, most people simply did not see the point in doing such a thing. Now, this was just a hack, but it did led me to believe that there’s more going on in the education world, in that technology is (and probably should be) linked to the preferred didactics/pedagogy. So: maybe we don’t even need a lot of sophistication. Why am I saying this: I think it would be good to use some Rapid Application Development here: get some working stuff out there first, rather than slave for years on specs and metadata.


Having said all that, I do think, given the developments, that a follow-up for SCORM is needed. And also that it is warranted that W3C would look into something like that. It is smart, I think, to take the theme of connectivity rather than content, to make it more W3C. It also provides a good reason to include Analytics. The fact the authors mention privacy and data Protection acknowledges awareness of the politics involved with such an initiative. So overall I think this is a good initiative, but ask attention for the following:
  • Traction and commitment with enterprise. How prevent frustration of the process?
  • Rather get technology working quickly than endless specification and metadata mashing.
  • Promote a more sophisticated use of technology as well.
  • Either refrain from sweeping statements about ‘conservatism’ in education and focus only on interoperability, OR get more evidence for the various claims (I doubt you will find this).

My take on a new College of Teaching

A lot has already been said about the proposed new College of Teaching (CoT). Up until now I have only devoted tweets to the topic, and because it might almost seem as if I’m against such a college, I thought it would be good to write this post. Let’s say I’m positive but politically skeptical. One thing that certainly has become apparent that there is quite some momentum it seems, within the teaching community itself. I even became very enthusiastic about the passionate posts by David Weston and Tom Bennett

Initial depicting Boethius teaching his students from folio 4r of a manuscript of the Consolation of Philosophy (Italy?, 1385)
Initial depicting Boethius teaching his students from folio 4r of a manuscript of the Consolation of Philosophy (Italy?, 1385)

(and more at Claim your College). Also, the run-ins I had with Andrew Old were helpful, and showed a drive to make it work. The main discussions center around who could join the CoT and what the CoT would do.

Who could join?
There was some discussion about what teachers were envisaged. Although I initially thought a broad group of teachers should be able to join, after all teaching takes place at many levels, I was convinced by the argument that indeed some sub-groups already have opportunities or can create opportunities themselves. For example, although I have been a secondary school teacher for 14 years, now I’m a teacher/lecturer in HE. Well, the Higher Education Academy is for me then (unfortunately, their funding has been cut considerably), and they provide CPD and certification. So, yes, I can see a good case for a professional body for only schoolteachers, and it could contribute to a stronger professional identity within the sector. It could also certainly play a strong role in CPD and other professional development.

Dangers exaggerated
Mind you,  I think the dangers of allowing a wider group of ‘teachers’ to join have also been exaggerated. I’ve seen words suggesting that outside groups might ‘dominate’ the CoT. I firstly wonder on what evidence this statement is based, as it does fit too easily in a caricature of an educational establishment trying to keep education in a hold.  A caricature which is often ‘proven’, ironically, by providing anecdotal evidence which doesn’t stand the test of reasonable social science research. More importantly, I think that even if this was the case I think the presence of lobby groups will not be any less with or without these groups, just different. I think most organizations eventually will ‘suffer’ from lobby or dominant groups. I don’t think it will be any different in a CoT. Vocal bloggers express their opinion? They might very well be dominant. Some teachers are Google teachers, Apple educators etc. They might very well be overly positive towards technology and be influential. I think any organization gets the audience it deserves.

Teacher Training (Education!) and politics
My main point of political skepticism concerns the function of the CoT. Most people who wrote about it assumed that the CoT would be a ‘professional body’. I, however, am a bit concerned that some groups, especially the government, will see the CoT as something more. In the consultation document by the government the foreword explicitly mentions initial teacher training. Under initial functions in 2.9 it mentions “This might include functions that are presently exercised by the Secretary of State, or other roles undertaken by the Department for Education or the National College for Teaching and Leadership (NCTL) in relation to teacher training and development.”. Especially, the ‘in relation to’ at the end begs the question what functions are meant. The NCTL has the following responsibilities:

nctlNow, if the first two bullets are representative of what the government means with ‘in relation to teacher training and development.’ then to me it’s clear that more stakeholders than ‘schoolteachers’ are involved. Especially the allocation of teacher training places surely is a joint responsibility. I think it would be very undesirable if a new CoT would decide over this unless the brief and membership of it would include all the relevant stakeholders. It would also fly in the face of what Sir Carter mentions in the introduction of the recent Carter review of initial teacher training: “The truth is that partnership is the key.”. The review mentions more critical points for the future, for example in recommending that a future CoT might “develop a framework for core content for ITT”. Again, I would feel it inappropriate if a professional body of only teachers would decide on this when multiple routes into teaching need to be represented.  If anything, the government’s response to the Carter Review seems to agree with a big role in all of this for a new CoT. It is this prospect of perhaps some formal decision powers on Teacher Training which might cause the  CoT to become a political pawn. It is no secret that a school-led teacher training has been the main focus of the government, and this has led to the closure of some university providers. I think a CoT should try to prevent being used as a political pawn and should clearly state that they acknowledge that Teacher Training is a partnership affair which doesn’t mean that a professional body of schoolteachers alone decide on it.

So to summarize:

  • I’m positive about a professional body for schoolteachers. I agree that a restricted scope of ‘members’ could help build the profession and build a professional identity.
  • I’m skeptical about statements which imply that a restriction of membership is needed to prevent some forces to become too dominant. Like any organization this will happen any way.
  • If the College of Teaching gets formal powers (from the NCTL for example) for Teacher Training, then the scope should be broadened and include all stakeholders involved in Teacher Training.

Other comments
The current, most extensive blueprint for the CoT is based on documents from the Prince’s Teaching Institute.
The Teacher Development Trust also has written plans.
Both look pretty extensive and good but don’t really address the point of Teacher Training.
I also think that one critical point will be whether such a CoT would have anything to do with prescribing Standards or not. Maybe more on this in later posts (then again, maybe not).