Thursday, February 14, 2008

Problem solving - creating runnable mental models

Game creation is gaining recognition as a valuable learning activity. I have justified it in the past on 3 grounds

  • transferable cognitive skills,
  • metacogitive skills and
  • affective benefits

and my attention for transferable cognitive skills has mainly been on near transfer,
  • Cartesian coordinates
  • negative number
  • position, speed, acceleration
  • and many more like this
I would like to argue the case for generalised problem solving skills in the visual domains like mathematics and physics through improved competence at creating and using runnable mental models.

Bloom' Taxonomy (note 1) is not particularly helpful for understanding higher order thinking and problem solving in visual thinking so I have already had a try at describing problem solving in visual domains as the creation and running of mental models.

Last year I described how one could solve problems like eg. the forces in structures, from first principles with a bit of prior knowledge by building, validating and running a mental model

There is a bit of literature on mental models, Betrancourt & Chassot refer to a "runnable mental model" in Mayer, R. E. (1989). Models for understanding. Review of Educational Research but I can't download that. Jonassen 1 2 refers to runnable mental models:

He says:
(1) Mental models are internal representations.
(2) Language is the key to understanding mental models; i.e.. they are linguistically mediated.
(3) Mental models can be represented as networks of concepts.
(4) The meanings for the concepts are embedded in their relationships to other concepts.
(5) The social meaning of concepts is derived from the intersection of different individuals' mental models.
These assumptions, we believe, are probably necessary but not sufficient for defining mental models....

Generally, mental models are thought to consist of
  • an awareness of the structural components of the system and their descriptions and functions,
  • knowledge of the structural interrelatedness of those components,
  • a causal model describing and predicting the performance of the system (often formalized by production rules),
  • and a runnable model of how the system functions
Jonassen's mental might be a bit different to my concept, mine are visual rather than linguistically mediated. Jonassen also states that mental models are multi-modal so the meaning of linguistically mediated is unclear. Jonnasen also seems to lump together mental models that are a community mental model that is socially negotiated with the construction of a problem space inside a problem solver's head.

I like the words in Dunn quoting Jennifer Wiley: students’ “active construction of a runnable mental model” significantly improves their comprehension of any dynamic system.

To give another example of creating, validating and running mental models, consider my manual transmission car which has a noise. Assume I have a vague recollection of the function of the clutch to break the drive train and remove forces from the gearbox. I produce two visual images of engine-clutch-gearbox-wheels and engine-gearbox-clutch-wheels as possible mental models of the car. To validate them I run them, test their output for what I know of the behaviour of cars. Only the first model is consistent with double declutching (remember having to do that? You are old). I can now use my validated model to diagnose my noise, the noise is present, stationary in neutral , but not with the clutch depressed. Run the model, only the gearbox input shaft meets these conditions.

My belief is that there are generalised problem solving and higher order thinking skills that relate to the ability to build complex and robust mental models and then interrogate or run them. Good problem solvers are good at building and running mental models. These skills can be exercised when programming, particularly in the syntax-free iconic languages such as Scratch, Etoys and GameMaker, also when playing problem solving games. The higher order thinking is the debugging where you compare the behaviour of your program and the mental model of your program. Good learning environments keep learners in a tight cycle of test-implement-debug.

Care should always be exercised when talking about generalised higher order thinking skills, one can make sweeping claims without ever defining what higher order thinking is. Pea & Kurland (ON THE COGNITIVE EFFECTS OF LEARNING COMPUTER PROGRAMMING) criticised similar claims about Logo: whether "spontaneous experience with a powerful symbolic system will have beneficial cognitive consequences, especially for higher order cognitive skills. Similar arguments have been offered in centuries past for mathematics, logic, writing systems, and Latin" That is why I think it is important to have a clear understanding of what higher order thinking is.

I'm thinking about the mental model you have of a computer program as you write the program and the debugging process in the context of cognitive conflict or cognitive dissonance. How helpful is it to view a mental model of a program in the dimensions of the Event Indexing Model - time, space, protagonist, causality, and intentionality? For example, think about event driven programming vs linear, with causality indexing for event driven vs temporal for linear.

Finally, you add the magic ingredient of games: a relevant and authentic challenge, the right tools and a collaborative environment which encourages peer tutoring, flow and the ZPD.

Note 1, Reeves "Kyllonen and Shute (1989) have proposed a taxonomy that represents the spectrum of internal states with which cognitive psychologists are concerned. Their taxonomy begins with simple propositions (e.g., stating that Japan sells more electronic products than any other nation), proceeding through schema, rules, general rules, skills, general skills, automatic skills, and finally, mental models (e.g., analyzing the potential of a trade war between Japan and the United States based on an analysis of balance of trade trends). The latter type of knowledge seems particularly important because mental models are the basis for generalizable problem-solving abilities (Halford, 1993)."

more to come.. work in progress

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Anonymous rob said...

Hi Tony

have you read Gee, "What Video Games Have to Teach Us About Learning and Literacy" ?

has lots of interesting ideas on role of games, and mental models

not research as much as self observations but pretty interesting n

Tuesday, March 04, 2008 9:47:00 PM  
Blogger Tony Forster said...

Haven't bought the book but I have an idea what he is talking about. See

Wednesday, March 05, 2008 12:56:00 PM  
Blogger Tony Forster said...

I meant

Wednesday, March 05, 2008 12:58:00 PM  
Blogger Bill Kerr said...

great post tony

I've been having another look at idit harel's work on teaching kids the deep meaning of fractions using an instructional design approach.

One thing she found was that some kids initially had absurdly rigid ideas of what fractions were, eg. "a fraction is just the shaded semi circular part of a whole circle, the unshaded part is not a fraction, it is nothing"

Then after a month (sic) of discussing and building fractions with logo, the same student started to see fractions everywhere in the world - and built a logo screen showing fractions in a house, cars and the moon.

So the factors here would be play with the right tools in the right environment using a relaxed time frame - pretty much the opposite to how maths is taught in school most of the time.

The notion of situated knowledge rather than generalised higher order thinking is also covered by Papert and Harel in a later summary of this work (this in response to the Pea criticism). Although the popularisation of the word "situated" was done by others (Suchman, Lave, Brown) Papert / Harel argue that the idea of situatedness is an important theme in the development of logo based constructionism - along with the idea of fluency (another important word here)
Software Design as a Learning Environment by Harel and Papert, 1990, page 22 ( I just looked on line, it is referenced but doesn't seem to be available)

Visual thinking, situated knowledge and fluency are all connected concepts, I think

Another thought I had is that competitive chess is a great way to teach runnable mental models, with the enforcement of the touch and move rule. Chess players are continually testing alternative mental models, some win and some lose, so the penalty of getting it wrong is high. The debugging has to be done mentally before committing the "code", not after.

Monday, April 21, 2008 10:05:00 AM  
Blogger Tony Forster said...

Imaginary Worlds
John B. Black
Teachers College, Columbia University

Learning Newtonian mechanics with an animation game:
The role of presentation format on mental model acquisition
Margaret S. Chan and John B. Black
Teachers College, Columbia University

Thursday, June 26, 2008 9:18:00 PM  

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