The half-way point in the CONSTRUIT! project schedule has now been reached. The aim of this Interim Review meeting, to be held at Warwick from Monday 21st to Thursday 24th March, is in part strategic and in part practical. Its primary focus is on the pedagogical aspects of the project with reference to issues that have been identified through consultation with Piet Kommers and Hamish Macleod. We shall take stock of what has been achieved in the project so far, and consider the best direction in which to proceed. We shall review the evaluation activities that have been carried out to date and that are in prospect. We shall also review prototype materials in preparation for the forthcoming C15 meeting in Athens (April 15-19) and the visit to SciFest (May 10-12). Other topics to be discussed include the status of the open online course (OOC), the prospects for virtual workshops and the plans for the final conference.
The meeting consolidates several planned visits: Hamish Macleod from Edinburgh to advise on matters of evaluation (cf. C19 on the project timetable), Tapani Toivonen from UEF (cf. C18) and Piet Kommers visiting post-C6. Rene Alimisi, Ilkka Jormanainen and Manolis Zoulias are unable to attend in person but will join in discussion by Skype.
Some brief notes on each of these topics will help to frame the agenda:
A. Strategic issues
Strategic priorities were proposed by Piet in a recent email, as presented verbatim here. Piet identifies three 'research lines' in CONSTRUIT!, which he describes in these terms:
- Optimizing the CONSTRUIT! method; in particular for students who want to acquire a further sense of what actually is learning from software constructions.
- Identifying complementary learning/teaching methods that are needed in order to make Construit! more complete and overall more successful (Construit!+ or even Construit!++).
- Making Construit!++ more self-contained not just by packaging tutorials as video lectures on the web (MOOCs or OERs), but also by superimposing the current sequence of exercises with an instructional envelope that adapts the transition from scaffolding into autonomy to student characteristics like impulsivity/failure-anxiety, memory/reasoning ratio etc etc.
Piet observes that we have so far focused entirely on the issues raised by 1, with quite modest results, and that investing in 2 and 3 may help us to resolve these issues better.
Piet's proposal can be considered alongside practical goals for the OOC, the remaining learning activities and the final conference.
B. The open online course
C. Evaluation to date and in prospect
Piet's proposal seems to put concerns about evaluation into a rather different perspective. The issue of exactly what learning objective with what audience we should be targeting when making a construal has been a vexing one from the beginning. The CONSTRUIT! proposal doesn't clarify this, as its focus is on ("O1") how effectively we are able to create resources that enable people to make construals (without being specific about who we are expecting to do this, but perhaps implicitly assuming that many people could do this in principle if our resources were appropriately developed) and ("O2") evaluating the 'six claims' about the qualities of making construals (once again without being discriminating about what makers we have in mind). The loose sense in which the term 'maker' is being invoked - which has been identified as controversial - is a further complication here. Certainly, we could envisage a fruitful collaborative interaction between human agents and a construal even though some of the participants were not engaged in 'making the construal' in the strict sense that is the counterpart of 'writing the program'. Piet's CONSTRUIT!++ suggestion seems to be giving some licence here to think about the activities that involve making construals in a less conventional way - not simply asking 'what is the topic, who are the target learners, what is the learning objective' and seeking empirical evidence, but stepping back to ask how construals can fit in a learning context, and what can be achieved in this way. This directs further attention to the question of what activities we should be venturing in learning activities.
D. Learning activities with teachers and students
Piet's reference to the 'quite modest results' of the efforts we have made to date to attract interest etc in making construals resonates in a quite uncomfortable way. We might consider the resources by way of historic construals in the old tkeden environment we presented at C1 and C5, the remakes and extensions of some of these that we presented at C5, the three elaborate presentations and construals we developed for SciFest last April, the Shopping construal/game and associated activities and the follow-up making-a-construal-from-scratch activities we prepared for C14 and in association with C2 in Athens, the solar system construal as an introductory exercise prepared for students last September, and finally the new ways of expressing and developing construals that have been explored since C6 last December. It is worth noting that far fewer people have been engaged in making construals in the latest MCE than have been in the past in previous online environments (tens of people) and in the original tkeden itself (hundreds of people). This is not necessarily a matter fror concern - there can be no question that the current environment has qualities quite beyond the range of any of its predecessors - but is something to consider in reflecting on points 2 and 3 of Piet's agenda. Certainly, we learned things related to this agenda about making construals from the extensive work with older technologies, if only in a somewhat vicarious fashion. There is a possibility that before the end of the CONSTRUIT! project, these historically useful resources will have become obsolete (for instance, the hardware that supports the Web EDEN interpreter is scheduled for scrapping in a few months time). At the very least, it would be good to be in a position to realise the potential they revealed (however inefficiently and clumsily) in new projects. This makes the question of what resources and activities to prepare next - and indeed right now - very topical.
One possibility we might consider is investigating alternative ways in which making construals can be situated in the learning context. Influenced by ideas from Steve Russ and our Thai visitor Hengmath Chonchaiya ("Heng"), I had been thinking about three different kinds of classroom activity that perhaps can be seen as deploying construals (in some ways similar / closely related construals). Here are some links to prototype resources that could perhaps be adapted for this purpose (the most appropriate version of the MCE to use - in preference to construit.c6 - is http://jseden.dcs.warwick.ac.uk/nick/ - which is a more up-to-date version. To load scripts (aka 'agents') see the instructions on the MCE page:
- A single construal can support a broad topic area. For instance, when I am thinking about elementary number theory, whether the specific topic is modulo arithmetic, relative sizes of numbers, basic arithmetic operations, prime numbers etc I have an underlying geometric model in my mind. This is something that I first learnt as a sequence of tokens "one, two, three, four, ... " / "un, dau, tri, pedwar, ,,," and later came to relate to patterns (as in "twenty one, twenty two, twenty three, twenty four, ...") that are associated with decimal representation. I'm imagining that this geometric construal is part of the background mental furniture when I'm considering any activity that involves whole numbers, even when I'm not explicitly paying attention to this (as in rote learned 'times tables'). Different number representations are different ways of imposing pattens on this plain sequence. To see construals of representations in base 10, 2, 3 and 6 (somewhat crassly implemented where the deliberately naive use of 'when-clauses' is concerned), load and run the script wmb/numberreps. Characteristic questions and activities here might involve back-and-fore interpreting that relates abstract operations with number and concrete interactions with the construal. (Developing basic mental arithmetic skills and principles - when is a decimal number divisible by 3? etc, visualising hailstorm sequences, or the principles of the RSA algorithm are on our agenda.)
- The concept of 'whole number' can be invoked in conjunction with many different kinds of referent. For instance, numbers can be construed both as periods of time and quantities of money. We appeal to number when we consider notions such as relative size, ratio and proportion. In thinking about ratio and proportion, Steve framed an exercise concerning time devoted to watching TV during waking hours. A construal put together by Jonny Foss and myself (that doesn't - yet? - represent an appropriate solution to the exercise as stated) can be viewed by loading and running the script sbr/ratioSimonSophieEx. This construal adapts the hexary representation of numbers to derive a linear model of the day that is linked to Jonny's visually challenging timecircle. The time display function adopts the principles that we use in giving change (see Steve's guidance on the givingchange construal) - something similar should also be used to unify the way that numbers are displayed in all the numbereps construals. Some definitions from sbr/ratio.experimental have also been used. Another context in which a number representation has been adapted for use in a construal is in the MENACE construal - see c6/menace/worksheetPt1. The project repository (still in a somewhat raw form) helps to demonstrate the potential for the kind of assembling of construals from simple components and pirated subsets of definitions that can be practised. Characteristic questions that might be associated with this kind of concretisaton through interpretation in a referent would involve exercising the construal in a way that reflects changes in the real-world referent situation.
- The 'metaphorical' relationship experienced between a construal and its referent can perhaps be used to surreptitiously prime the learning of abstract topics such as number theory by creating game-like activities that involve appropriate skills of manipulation and interpretation. I think one possible way to implement this for the basic arithmetic / elementary number theory domain would be to adapt a puzzle that recently appeared in a UK newspaper (see the Listener Crossword No 4386 Hailstorm puzzle, by Elap). This is a fun puzzle if you like reasoning about arithmetic - and the only arithmetic operatons involved are multiplication and addition of positive integers. A construal (though it involves very little but the representation of the crossword clues as a definitive script) can be loaded from wmb/puzzles/hailstorms (the plural forms here are not really appropriate!). To trace the solution of the puzzle (as far as completing the grid is concerned) you can inspect the content of the script wmb/puzzles/hailstorms/answers. Note that decoding the 'observables' a,b,c etc is a separate action from entering digits in the grid - which you do by setting the values of observables of the form g11, g12 etc. My idea, as yet only partially developed, is that solving ths puzzle can be reinterpreted in terms of a detective-style activity in which you attempt to identify the home locations of 32 criminals in a street with about 200 houses who work in pairs and who hide the goods they steal in a vault with about 2000 locations. Once the locations of the responsible criminals have been identified, the clues in the crossword provide recipes (somewhat Logo-like, but in one dimension only) that can be used to locate a stolen item. The decimal representation in wmb/numbereps was originally developed as a visual representation of the street on which the criminal gang lives - it makes it possible to refer to digits as colours and to interpret arithmetic operations in terms of movement. The visualisation can be adapted to represent the locations in the vault where the loot is stored. The hailstorm sequence provides relationships you can use to determine which criminals are paired. The thought would be to dress all this up into a narrative that is laced with pretexts for making elementary construals - for instance, we can write a few definitions to determine whether the criminals who live at particular addresses can be partners in the gang etc. What's attractive here is that students could come up with their own proposals for how to make helpful construals - potentially giving the exercise the open-ended flavour that suits making construals. A major issue for this whole concept is whether you can disguise the fact that the underlying principles are just 'boring maths' and some basic formula evaluation, as you may sense yourself if you try to follow the reasoning set out in my solution. But this approach might work, and fits Piet's notion of potentially complementary learning methods.
One suggestion for a theme for our meeting might be the preparation of a submission for the ALT-C annual conference, to be held from 6-8th September at Warwick this summer. It may well that Piet's agenda - and how we can respond to this - would make a good topic for a one hour panel/symposium/workshop session. For this purpose, we could perhaps explore and differentiate possible learning activities such as 1, 2 and 3 above.