A Technical Memo
Stephen W. Draper
Department of Psychology
University of Glasgow
Glasgow G12 8QQ U.K.
Link to ITFORUM.
Link to list of ITFORUM participants.
Since that time the term has been extended: "The concept of mathemagenic activities expresses exactly the idea that there are activities the learner can carry out that will result in their learning." (Laurillard, 1993).
Laurillard went on to coin the term "Anathemagenic", meaning "activities which
give birth to loathing" which encompass, in educational technology:
To which we could add, in the present context:
When mathemagenic behaviors are controlled or manipulated by specific design attributes of instruction (such as inserted questions in programmed learning), the result could be a reductive approach to learning (Jonassen, 1984a). Learners become "active performers", responding to activities imposed by the lesson rather than "active learners" where learners impose their own metacognitive activities to produce the desired learnin outcome.
I think there is a continuum of learner generated/instruction generated
mathemagenic activities which largely depends on:
- the type of learning outcome;
- learner characteristics and entry skills; and
- the type of instructional strategy used.
Laurillard (1993 p.103) takes up this notion and proposes a model in which there are 12 mathemagenic activities. These apply to all subject areas. The basic approach is that no software to date covers all 12 activities, so any complete approach will combine software (multimedia, etc.) with other activities. This model is not without its problems: to explain how learning occurs without overt support for and observation of some activities, I have to hypothesise that these may be internalised. This leads to further predictions that have not yet been properly tested e.g. that learners will report these internalised activities when interviewed, and that study skill training would equip learners to perform such activities internally without further support. Nevertheless, I find this model to have real predictive power. That is, rather than studying the effects of media or of interactive modes on learning, I vote for studying these mathemagenic activities as primary factors determining learning.
The issue here is: what is the nature and limitations of the notion of M-act
(mathemagenic activity), on which the Laurillard model is based? For maximum
utility we would like to identify an element that caused learning directly AND
could be manipulated by designers directly. Tough.
However there seem to be four ways to develop the notion of M-act, generated by two two-way choices.
Mathemagenic just means "likely to induce learning". You can't be sure of their importance a) because learners may never get it; b) because able learners may not need an activity to induce the processing that causes learning, but do it by reflection or automatic inference.
For instructional /ped. design, we want it to be a teacher action or at least an overt activity. Then we design courses by designing the M-acts; we can do like Laurillard and categorise CAL by M-acts. But actually external acts don't cause learning reliably. But if M-acts are invisible (internal) then they may be causally correct but are almost useless as you can't know when they happen and they don't help much in designing ped. In other words, there seems a tension between developing the concept for theory (can make it true, but not useful and almost without strong predictions for observations), or make it practical but false.
M-acts must really be defined as internal mental acts; although often with behavioural (observable) aspects e.g. student writing notes or essays or speaking. Whether an M-act occurs depends as much on learner as on the CAL / educational intervention.
The right position is probably (1) that M-acts are internal, but you can get fairly reliable / direct evidence of them simply by asking students (talouds, SSI right after). E.g. Alec standing outside a chemistry lab asking students what the lab was about and finding that they clearly didn't really know (at conceptual level). (2) But we can also classify CAL or other ped. design by whether there is any direct support for each M-act. (3) And furthermore, classify that support as weak or strong. E.g. providing a notepad is weak support for M-act-2: it shows designer has thought about it and provided for it, but it is entirely possible (and empirical studies show it is in fact usual) for students not to use this. In contrast, pre-labs requiring students to calculate parameter values before they can start the lab is strong support for M-act-10.
Are all the 12 M-acts necessary for learning? On the face of it, clearly not because people can learn from hearing something once with no visible re-expression activities. Are they sufficient: forgetting suggests not.
But my position might be:
Learning is directly caused by hidden mental actions / tasks. The M-acts are a bit higher level, and should be thought of as structuring these actions such that it is very likely but not certain that they occur and so learning occurs. Forgetting might then come later. Thus M-acts are approximately sufficient.
M-acts may be internalised, in which case you won't see them unless you get the
right data i.e. ask students at the time. Are they necessary? Approximately,
in that it is conceivable but unlikely that some other activity would drive the
necessary lower level mental actions.
Actually, no they aren't necessary. I think that if you are interested and prepped right, then you would process stuff as it comes in, making the right links and learning. Re-expression is an activity likely to exercise this in most students, but isn't necessary for everyone. On the other hand, it can only help. So I see M-acts as a blunderbuss approach, each activity likely to cause learning, but only partly necessary depending on what other activities that learner has really engaged in.
Furthermore, within the conceptual level there is no binary learned/not-learned. The more connections you have made a) the longer retention is likely, b) the more new/transfer tasks you are likely to be able to do and/or do fast. The M-acts promote these connections, but on the one hand there is no limit to the number of connections you might make (cf. Einstein working out more), on the other, very slender connections can be enough for later processing at test time.
Rothkopf,E.Z. (1970) "The concept of mathemagenic activities" Review of
educ. research vol.40 pp.325-336