Maths Wars

http://commons.wikimedia.org/wiki/File:Euler%27s_formula.png

"Maths Wars" refers to the tension between instruction and construction in teaching/learning

The following interesting quote came via Artichoke

"Many of those wanting to build relational understanding with students assume that spending time on rote procedural knowledge is an important precursor for developing deeper conceptual understanding. This seems like a common sense approach – a let’s keep a foot in both camps kind of approach. However, research findings in math education suggest otherwise (Pesek and Kirshner 2000). It seems more likely that, in maths education at least, time spent building prior instrumental understanding is an interference to, not an aid to, developing relational understanding."

Interesting because Australia schools at least seem to spend a lot of time on rote procedural knowledge in mathematics.

More on Pesek and Kirshner 2000

"Students who received the procedural instruction prior to the conceptual instruction learned less than did students who received only the conceptual instruction. Somehow, exposure to routine application of formulas inhibited or interfered with students' subsequent conceptual learning."

It still seems likely to me that the best teaching will incorporate both solid procedural knowledge and problem solving in authentic and relevant contexts. This study does not destroy that belief, but it does sound a warning that you can't just mix a bit of both and always get good results.

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

The Peripatos could not have looked like that

The Design and use of simulation computer games in education Ed Shelton & Wiley
Chapter 6 "The Peripatos could not have looked like that"
Moeller, Cootey & McAllister
http://www.sensepublishers.com/catalog/files/9789087901554.pdf

Several game modding environments are mentioned as appropriate for building educational games, Half Life 2, Unreal Tournament & Neverwinter Nights.

Aristotle's Assassins was an educational game built with Neverwinter Nights at the Learning Games Initiative at Utah State University and the University of Arizona. It was designed to teach politics philosophy and music of ancient Greece. The design team consisted of a faculty member, a graduate student and two undergraduates.

They discovered that the team was learning a lot in developing this game. This unexpected learning is examined in the theoretical framework of Toward implementing distributed scaffolding: Helping students learn science from design Sadhana Puntambekar , Janet L. Kolodner and also Activity Theory

They conclude "The student design of games and simulations is a highly educational process, and the steps they take out during the design process can be helpfully interpreted using activity theory as an analytical framework".

They refer to similar findings, Learning Through Game Modding MAGY SEIF EL-NASR and BRIAN K SMITH

Learning Through Game Modding
MAGY SEIF EL-NASR and BRIAN K SMITH

They argue for the value of game making:
"During the design process, skills such as analysis, synthesis, evaluation, and revision, must be used, providing opportunities for learning content and metacognitive skills such as planning and monitoring. Students can receive ongoing feedback from peers and experts while constructing working artifacts".

They mention studies using other programming environments, Conway (Alice), Ingalls (Squeak), Repenning (Agentsheets), Resnick (?), Smith (Kidsim). References could have been made to Game Maker, Click and Play, Stagecast etc but were not.

The three modding tools they look at are Warcraft 3, Webdriver and Unreal 2.5 Engine.

"Working with Web Driver...(for) a better understanding of 3D geometry, and vector mathematics... Unreal Tournament ... (for) architecture design, texturing and sound design, lighting design and landscaping ... 3D geometry"

See student projects of Penn State College of Information Sciences and Technology you can see the design documents and then view the completed games. You can see a movie of Dungeon Girl which "included over 6020 lines of code, 5 characters, 24 weapon models, 5 original music files, and 80 sound effects and dialogue files" Watch the video, it is an example how with a relevant and authentic challenge and the right tools, students can achieve excellence.

"Through these two classes, we gained better insight on the use of game modding as a tool to promote learning. We believe that there are several skills and concepts that students learn by engaging in game design/modification, including the following:

• Software Development and Design
o team work
o building critiques and reflections on other’s work
o project scheduling
o project management
o iterations and refinement
o prototyping
• Programming Concepts
o threading and event-based programming
o Object-oriented programming
o Component-based development
o Software patterns
• Artistic Concepts
o Lighting
o Architecture design
o Character design
• Game Concepts
o Game design
o Game mechanics
o Balancing game aesthetics and game play"

They conclude "evidence ... encourages the use of game modding in classes to promote learning of several subjects and concepts. .. We believe that using game modding motivated students to learn and allowed them to apply and visualize the utility and application of the concepts".

My Conclusion
The findings of both studies (Moeller et al & El-Nasr et al) should not come as a surprise Compare EL-NASR and SMITH's list with a similar list . Read about Harel's research and a project inspired by it.

Shouldn't we base our educational systems primarily on Play?

I was asked "shouldn't we base our entire educational systems primarily on Play?", I think not, but we should use all we know about play to guide education.

School is a new invention, it is only a couple of hundred of years old. Before that, learning alongside adults also contributed to children's development. Children would learn alongside adults in the field, the kitchen and at the forge. Call it apprenticeship learning. Schools became necessary after the industrial revolution in part to free adults from childcare. Also, as society becomes more complex, some kinds of learning become too specialised to learn in a village apprenticeship way.

The points here are that

* play was never enough on its own

* school performs purposes other than learning

* the needs of society have changed since play evolved in mammals

It is time, now that technology gives us options, to reconsider the teacher at the blackboard in front of a class of children. It was only ever a stopgap compromise. We should consider what we know of play and learning and see if we can improve on the "talk and chalk" model.

Learning is best if it is authentic, like apprenticeship. It is much more motivating if you can produce something real and of value to others. Perhaps this was what Papert meant with constructionism (the N word not the V word) that learning "happens especially felicitously in a context where the learner is consciously engaged in constructing a public entity, whether it's a sand castle on the beach or a theory of the universe" http://www.papert.org/articles/SituatingConstructionism.html

Learning is best when it is relevant, when you can see that what you are learning will actually be useful to you.

There must be a balance between effort and achievement or reward. Too hard and you give up, too easy and you are bored. (I read somewhere that motivation is highest when the chance of success is 50%). You can visualise effort and achievement (reward) as two curves that have to match. We are familiar with the initial learning hump where effort is not matched by achievement/reward .

Immediate feedback. Problem solving in games works well when you can quickly test your hypothesis. The problem solving process works like the debugging process that computer programmers are familiar with. You test, arrive at a hypothesis or solution and then implement. When the implement & test part of the cycle is quick, as in programming, you spend most of your time in the cognitive conflict or cognitive dissonance part of the cycle. This is where the real cognitive development occurs. It is very frustrating but it is almost addictively motivating. Ask any computer programmer or game player whether they have still been on the computer at 3am. "I'll just fix this program bug...." or "I'll just add some more roads to my Sim City...."

Peer tutoring. Rather than locking kids into a competitive process through assessment, they should be placed in an environment where they can cooperate too. Then you can have a class full of teachers. The best way to learn is to teach something. See http://schoolgamemaker.rupert.id.au/computerclub/ Is the emphasis on assessment an attempt to motivate kids through competition in the otherwise boring environment of "talk and chalk" classrooms? I read somewhere that less than 15% of teachers use assessment as feedback to tailor how and what students learn.

An example of a cross curriculum games based project is at http://www.freewebs.com/schoolgamemaker/IT%20Course-game.doc

Instructional Simulations & Games, IDT 545, University of North Dakota

I have enrolled in Instructional Simulations & Games, IDT 545, at the University of North Dakota. It is offered as distance education and uses Adobe Connect Live Meeting for virtual face to face lectures.

You can read more on this course at http://www.idt.und.edu/index.html

Following are my reviews of the first two weeks' readings. URL's have been given where possible but some were newspaper clippings. If you are interested you should be able to access the course materials by contacting Richard Van Eck richard.vaneck@und.edu

Johnson, Everything bad is good for you. pp1..62
http://www.amazon.com/Everything-Bad-Good-You-Actually/dp/1573223077
Johnson in the foreword states that popular culture has grown more complex. I think it was Van Eck who pointed me to the Flynn Effect, that IQ is increasing with time, http://en.wikipedia.org/wiki/Flynn_effect suggesting that it might even relate to games, at least it indicates that we are not becoming dumber. (podcast)

Are computer games mindless? One of my favourite quotes “The computer is a medium of human expression and if it has not yet had its Shakespeares, its Michelangelos or its Einsteins, it will. …. We have scarcely begun to grasp its human and social implications.”
Computer Criticism vs. Technocentric Thinking By Seymour Papert
http://www.papert.org/articles/ComputerCriticismVsTechnocentric.html


Johnson talks about a baseball dice game. The baseball game story is good, it indicates that the essential features of game based learning predate even (our last week's class) text based dungeons.

He asks why kids would go to so much trouble to master games. I think the answer is that kids like to learn. They are pre-programmed learning machines.

"Games are thus the most ancient and time-honored vehicle for education. They are the original educational technology, the natural one, having received the seal of approval of natural selection. We don't see mother lions lecturing cubs at the chalkboard; we don't see senior lions writing their memoirs for posterity. In light of this, the question, "Can games have educational value?" becomes absurd. It is not games but schools that are the newfangled notion, the untested fad, the violator of tradition. Game-playing is a vital educational function for any creature capable of learning."
Crawford, The Art of Computer Game Design
http://www.vancouver.wsu.edu/fac/peabody/game-book/Coverpage.html

Give kids a relevant and authentic challenge and the right tools and you can't stop them.

McLuhan (at P15) is quoted. All new forms of media have been subjected to the same criticisms that games have, the written word, the novel, radio, film and TV. My thoughts at
http://www.schoolgamemaker.rupert.id.au/attitudes.htm

At P19 he discusses a theoretical society that discovers video games before reading. He humorously pokes fun at narrow views about games, it seems a copy of Papert's writing on the use of computers in school where the nation of Foobar which has an oral culture discovers writing. Any way I agree. http://www.papert.org/articles/ComputersInClassroom.html

His discussion of dopamine and addiction sharing a common root with enjoying games is not convincing. See my previous Crawford quote, we are pre-programmed to enjoy learning.

Much of the attraction of SimCity is in its tight debug cycle. Computer programmers know how programming is addictive.

SimCity and programming keep you in a tight cycle of: implement, test, debug. The debug part is the deep thinking part and is deliciously frustrating, we enjoy it because we are programmed to learn and solve problems. This is akin to where Gee is quoted on p44 on the probe, hypothesise cycle.

On p38 he says it is not the subject matter that attracts. I agree, Malone and Lepper are often quoted on fantasy and I am not convinced. See Habgood on fantasy. http://www.zombiedivision.co.uk/
http://www.informatics.sussex.ac.uk/users/gr20/aied05/finalVersion/JHabgood.pdf
In experiment to see if children would create a learning game with endogenous or exegonous fantasy, they created games without fantasy. Its the gameplay that counts not the fantasy.

On p40 Johnson identifies himself as a Constructivist, (References to Dewey).

Rieber, L. P. (1996). Seriously considering play: Designing interactive learning environments based on the blending of microworlds, simulations, and games. Educational Technology Research & Development, 44(2), 43-58

Rieber discusses the function of play. "play is traditionally viewed as applying only to young children. Play seems to be something you have to give up when you grow up" "the extensive research on play with children and adults in anthropology, psychology, and education indicates that play is an important mediator for learning and socialization throughout life"

I think it is possibly put better by Crawford "Games are thus the most ancient and time-honored vehicle for education. They are the original educational technology, the natural one, having received the seal of approval of natural selection. We don't see mother lions lecturing cubs at the chalkboard; we don't see senior lions writing their memoirs for posterity. In light of this, the question, "Can games have educational value?" becomes absurd. It is not games but schools that are the newfangled notion, the untested fad, the violator of tradition. Game-playing is a vital educational function for any creature capable of learning."
Crawford, The Art of Computer Game Design
http://www.vancouver.wsu.edu/fac/peabody/game-book/Coverpage.html

He says that play should be seen in the context of three general educational philosophies: essentialism, progressivism, and existentialism. Perhaps the they could be called instructionism, constructivism and radical constructivism. Does this classification artificially place progressivism aka constructivism at the centre? What of the more extreme forms of essentialism, eg. Cognitive Load Theory and the works of Kirschner, Sweller & Clark "Why Minimal Guidance During Instruction Does Not Work" http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf
and explicit instruction
http://www.k8accesscenter.org/training_resources/DirectExplicitInstruction_Mathematics.asp.

Discussions during our class illustrated the differing philosophies. Discussion on the possible uses of Tetris for education ranged from essentialist "put the letters of the alphabet on the blocks to make words" to "use the game to learn concepts of shape and area".

Rieber states "the benefits of play are long-term - enabling intellectual and social
growth over many years . If, on the other hand, one is primarily interested in short-term gains on performance tests of narrow objectives, such as standardized achievement tests, the value of play becomes less evident" Playful learning is well suited to higher level tasks like problem solving and metacognitive skills. Evidence of short term gains of near transfer will be harder to find. Nevertheless there is some evidence,

http://www.psych.ucsb.edu/~mayer/fifth_dim_website/HTML/res_reports/final_report.html The Fifth Dimension Cognitive Evaluation, Final Report

Microworlds are discussed, of course Logo and Geometer's Sketchpad and Interactive Physics. Missing from the list are Game
Maker www.gamemaker.nl, Scratch scratch.mit.edu and eToys http://wiki.laptop.org/go/Etoys

Rieber invokes Piagetian Learning Theory as a theoretical foundation of Self-Regulated Learning Within a Microworld. The concept of Epistemic conflict has been discussed by Forster and Gesthuizen "Games and Constructivism"
http://www.groups.edna.edu.au/file.php/81/ICTEV/Games_and_Constructivism_v2.ppt as a motivating cycle of implement-test-debug similar to when computer programming and ascribe much of the motivation and cognitive gains to a tight cycle.

Gee is also quoted on a probe, hypothesise cycle in Johnson "Everything bad is good for you".

The implement-test-debug cycle also aligns well with Csikszentmihalyi's Flow theory.

The author states "a simulation-as-microworld must meet the "simplest case" principle. Of course, the simulation should be designed so that ideas expand as the learner is ready for them", this is the motivation behind reprogrammable learning objects, http://schoolgamemaker.rupert.id.au/samples3

Three systems are postulated in a simulation, the target system; the user's mental model; and a "conceptual" model of the target system. For more investigation of mental models and higher order thinking, see " Higher order thinking - a thought experiment" http://tonyforster.blogspot.com/2007/08/higher-order-thinking-thought.html

There is more on Endogenous Fantasy (Lepper & Malone) and I refer to Habgood on fantasy. http://www.zombiedivision.co.uk/
http://www.informatics.sussex.ac.uk/users/gr20/aied05/finalVersion/JHabgood.pdf
In an experiment to see if children would create a learning game with endogenous or exegonous fantasy, they created games without fantasy. Its the gameplay that counts not the fantasy.

See for example, the physics game Linerider
http://linerider.com/play-line-rider-online it is clearly not the fantasy that makes this a highly engaging game.

The author notes "Anthropologists have long viewed games as but one aspect of expressive
culture, or how people in a culture project their psychological dispositions" computer games have been used to support indigenous culture whilst providing a bridge to western culture,

eg. see www.acmi.net.au/game_nibby.htm
'Nibby' means sleepy lizard in the local language. The school garden project at Koonibba Aboriginal School served as the inspiration for the making of this game.
Created by:
Roxanne Dodd, Stephanie Dudley & Ian Martin
Koonibba Aboriginal School
Koonibba Community via Ceduna, South Australia

and http://waveplace.com/
Project Waveplace's mission is clear: to create a thriving new industry in the Virgin Islands independent of tourism, one requiring no physical imports, no clearing of land, no retail space, no condos. This new industry will be a digital one: animation, illustration, photos, music, software. There's a world of media buyers on the Internet ready and willing to pay fair licensing fees for the right talent. Our plan is to teach Virgin Islanders to create with computers, so they can export their most stunning resource, their creativity.


Does Easy Do It? Children, Games, and Learning
By Seymour Papert
http://www.papert.org/articles/Doeseasydoit.html

This is one of a number of articles by Papert at http://www.papert.org/works.html
All are well thought out, well written and well worth reading. Papert excels as a communicator and a deep thinker well ahead of his time. Considering the amount of resources that were directed into LOGO in the 1980's, the only disappointment is the lack of results. Though there are many case studies, they are strong on advocacy but weak on analysis.

The lack of analysis, ie. experimental data with controls is not surprising. Consider the views of Rieber, (Seriously considering play) "the benefits of play are long-term - enabling intellectual and social growth over many years . If, on the other hand, one is primarily interested in short-term gains on performance tests of narrow objectives, such as standardized achievement tests, the value of play becomes less evident".

In this article, Papert launches a full frontal attack on the Essentialist or Instructivist use of computer games for drill and practice calling them Shavian reversals—offspring that keep the bad features of each parent and lose the good ones. He notes that good play and good learning are not easy, it is hard but fun.

The terms "hard fun" and "choc coated broccoli" have often been used to characterise the constructivist and instructionist use of computer games.


Van Eck
“Digital Game- Based Learning It’s Not Just the Digital Natives Who Are Restless”
March/April 2006 EDUCAUSE review
http://www.educause.edu/ir/library/pdf/erm0620.pdf

In a thought provoking paper, Richard Van Eck suggests that proponents of digital game-based learning (DGBL) should move from the promotion of DGBL to a critical analysis of DGBL. “Like the person who is still yelling after the sudden cessation of loud music at a party” we now have the world’s attention and its time to do critical analysis of what exactly we are promoting.

He identifies three kinds of DGBL:

* have students build games;
* have educators and/or developers build educational games; and
* integrate commercial off-the-shelf (COTS) games into the classroom


He believes that student built games are not likely to be widely accepted because:

* not all teachers have the skill sets needed for game design,
* not all teach in areas that allow for good content,
* not all can devote the time needed to implement this type of DGBL,
* and many teach within the traditional institutional structure, which does not easily allow for interdisciplinarity.


At http://learningevolves.wikispaces.com/Review%2C+digital+natives I question these reasons for overlooking student made games and argue that they are the area with the most prospects.


Designing Online Games Assessment as “Information Trails”
Christian Sebastian Loh
Curriculum & Instruction, College of Education & Human Services
Mail code 4610, Southern Illinois University Carbondale,

Loh argues for data tracking to be built into games to "help ... reconstruct users’ gaming decisions" and "to measure its effectiveness, or the return of investment" He notes that data tracking is increasingly technically feasible.

He talks of "Trails and Nodes" and data tracking when the learner meets key nodes. As I read the article, I am increasingly aware that he is considering instructionist or essentialist learning where there are predetermined items of content that must be learned. This is "learning on rails" even though the rails form a mesh like a non linear novel and the learner has choice which rails are followed in which order. Even though he states the approach can be used for "Open-ended and non-linear (constructivist approach) to close-ended and completely linear (instructivist approach)" it is difficult to see how it really does apply for constructivist learning. Constructivist learning is more than the non-linear progression through a set curriculum, it is about developing versatile thinkers, self directed learners and problem solvers.

When assessing self-directed constructivist learning, it is rarely the product (and hence the nodes) which can be usefully assessed, it is the learner's personal journey which matters. The most productive assessment are often the learners reflections, either in diary, blog or video form. A learner could put in a lot of deep thinking while traversing a few nodes.

The worked example uses Bejewled, it is clearly a drill and practice exercise.

While the paper is clearly an advance in demonstrating how data tracking in educational games could be used, there is a risk that, if such data mining became expected by the educational establishment, there could be pressure for games to concentrate at the lower levels of Bloom's Taxonomy (http://web.odu.edu/educ/llschult/blooms_taxonomy.htm) and be used to teach
information and not achieve their potential for deep thinking and problem solving.

Is It Age or IT: First Steps Toward Understanding the Net Generation
Diana Oblinger
EDUCAUSE
James Oblinger
North Carolina State University

The authors outline how the "Net Generation" differ from the other generations. They note that "age may be less important than exposure to technology".

The characteristics include:

the Net Gen is able to intuitively use a variety of IT devices and navigate the Internet
the Net Gen is always connected
the Net Gen is fast. They multitask
the Net Gen prefer to learn by doing rather by being told what to do
the Net Gen is a prolific communicator
The Net Gen often prefers to learn and work in teams
The Net Gen is very achievement oriented
the Net Gen is oriented toward inductive discovery
The Net Gen is more comfortable in image-rich environments than with text.
The Net Gen readily takes part in community activities.

Teachers, particularly IT teachers are often suspicious of these generalisations, holding that the Net Gen is not that different from preceding generations. Prensky holds more extreme views including claims that Net Gen's have brains that are wired differently. Prensky popularised the term "Digital Natives". Oblinger quotes extensively from Prensky. Prensky has been criticised by

Kerr http://learningevolves.wikispaces.com/nativesImmigrants
Siemens http://connectivism.ca/blog/2007/10/digital_natives_and_immigrants.html
Mc Kenzie http://fno.org/nov07/nativism.html
Livingstone http://learninggames.wordpress.com/category/twitch-speed/
and http://learninggames.wordpress.com/2008/01/23/google-generation-is-a-myth/
and others http://knowledgegarden.usq.edu.au//tiki-index.php?page_id=622

Many of these criticisms also cast doubt on how different the Net Gen really are.

Voters Support Teaching of 21st Century Skills
Meris Stansbury

The author reports on a poll which she claims as evidence that momentum is building for the teaching of "21st Century Skills". The author's comments seem to indicate that the poll supports constructivist or progressivist views.

"88% of voters say they believe schools can and should incorporate 21st Century skills such as critical thinking and problem solving, communication and self direction and computer skills into the curriculum"

The author omits the fact that the strongest response was for reading comprehension which is not exclusively a 21st century skill.

This article appears to be based on a press release from the Partnership for 21st Century Skills which appears to be a lobby group for educational computer technology suppliers. http://www.21stcenturyskills.org/documents/p21_pollreport_2pg.pdf

Dropout Factories?
Nancy Zuckerbrod

The author says that there are 1700 High Schools in the US that fit the description of "Dropout Factory" with no more than 60% making it to senior year.The highest concentration is in large cities or high poverty rural areas in the south and southwest of USA.

Dropouts are a problem in high poverty areas around the world but the US has surprisingly low educational performance considering its high income. http://www.pisa.oecd.org/document/2/0,3343,en_32252351_32236191_39718850_1_1_1_1,00.html

PISA is a triennial survey of the knowledge and skills of 15-year-olds. It is the product of collaboration between participating countries and economies through the Organisation for Economic Co-operation and Development (OECD), and draws on leading international expertise to develop valid comparisons across countries and cultures. US performance is significantly below OECD average.

Concern about poor performance has contributed to the NCLB (no child left behind) policy which has shifted policy towards instructionist or essentialist learning. A keyword search indicates a considerable shift towards instructionism when compared to Australia, It also shows a higher interest in educational games in Australia. There is a swing towards instructionist or essentialist learning in Australia evident now, we lag behing the US in most things.
http://tonyforster.blogspot.com/2006/05/interest-in-game-programming-by.html

The author lists Four Winds Community High School in North Dakota USA as fitting the profile of a "dropout factory".

A search reveals that it serves an Indian community
http://www.fourwinds.k12.nd.us/education/sctemp/c141f72d9b5f3269f1bf452929130206/1200468276/StudentParent_Handbook.pdf

It lists its goals as:
1. To provide a responsive and flexible educational program.
2. To develop student's feelings of positive identity and self-worth.
3. To develop an awareness of and pride in the Dakota heritage, values, language,
and culture.
4. To develop skills necessary for healthful and productive living.
5. To provide accessibility to the parents and community as well as recognition of
the vital role the parents and community play in learning.
6. To require high expectations of all staff that shall be sensitive to the unique
needs of all students.
7. To provide students, not only intellectual growth, but also physical, social, and
moral growth.
8. To heighten expectations of students to require strong basic skills which will
result in their ability to continue learning in all academic and other settings

These are goals for which game making has been suggested in other indigenous communities.
http://learningevolves.wikispaces.com/indigenous

"Keep our diverse languages and cultural traditions by excelling in education and digital technologies, the only means of arresting the decline of our ancient and oral traditions" Noel Pearson, Australia

"Much trouble has come from people forgetting the land, the spirit. Many people are sick and have lost their spirit. The white government has cut their culture; we grieve for them. But we can all learn and make our spirit strong. My teaching is about opening your spirit, working together to build understanding. Opening our way, opening our hearts to share the spirit of the land with all who want to learn.” Nganyinytja an elder of the Pitjantjatjara people of Central Australia.

Programming computer games about traditional stories can be an excellent way to "develop student's feelings of positive identity and self-worth and develop an awareness of and pride in the heritage, values, language, and culture" while "excelling in education and digital technologies"

Read how game making was introduced into a predominantly aboriginal school, GameMaker at Gillen, Alice Springs by Kym Urquhart, http://learningevolves.wikispaces.com/gillen

and see the award winning game by Koonibba Aboriginal School
www.acmi.net.au/game_nibby.htm
'Nibby' means sleepy lizard in the local language. The school garden project at Koonibba Aboriginal School served as the inspiration for the making of this game.
Created by:
Roxanne Dodd, Stephanie Dudley & Ian Martin
Koonibba Aboriginal School
Koonibba Community via Ceduna, South Australia

See also the Waveplace proposal http://waveplace.com/proposal/
"Project Waveplace's mission is clear: to create a thriving new industry in the Virgin Islands independent of tourism, one requiring no physical imports, no clearing of land, no retail space, no condos. This new industry will be a digital one: animation, illustration, photos, music, software. ... Our plan is to teach Virgin Islanders to create with computers, so they can export their most stunning resource, their creativity. "

See also the proposal for the OLPC ($100 laptop) for Vanuatu

http://tonyforster.blogspot.com/2007/08/thoughts-on-olpc-100-laptop.html
and
http://tonyforster.blogspot.com/2007/09/rom-dance-north-ambrym-vanuatu.html

Back to the article under review, the author continues under "finding a solution" to talk of punishing schools for low test scores, more reporting, data tracking and goals. Frankly this stuff depresses me for its lack of vision.

Higher order thinking - a thought experiment

This is a repost of a blog of mine from February, which has been in draft till now:

I was challenged by the Connectivism conference to clarify what HOT (Higher Order Thinking) is. I was challenged by the perspective that Higher Order Thinking is not really distinct from other forms of thinking, it just consists of deeper levels of understanding, making more and better connections.

Bloom's Taxonomy helps a little but I suspect Bloom was a writer, a verbal reasoner, not an engineer. His highest level, Evaluate (assess, judge in relational terms), sounds a bit like making connections, it doesn't really ring true for the hard sweat of deep thinking for me.

So I decided to observe deep thinking in the only laboratory I have, inside my own head. To conduct a thought experiment. The big risk here is that we all think differently, we already know that there are verbal and visual thinkers, I'm definitely visual. Does my mental model building hold true for other visual thinkers?

So I decided to observe my thinking and document it. I wanted to analyse deeper thinking, problem solving, the example that came to mind was the truss, I don't know why, nor do I know why it came to me while riding my bicycle.

The word "truss" is stored along with a visual image of a truss, it looks something like this,

except that I can't visualise all the bars at once any more than I can concentrate on them when looking at them now.

I searched my memory for all connections and came up with the words "statically determinate", from that I was able to to retrieve a kind of visual image of a structure where, if you took out one member it would fall apart but if you added another, the braces would fight each other and you wouldn't be able to calculate the forces in the structure. Also the image of the triangle came up as the building block of statically determinate structures.

A visual image of the members being hinged or pinned at the joints came up like this.


Ok it's looking good, there's quite a bit of retrieved data and the problem is, in theory, solvable. But so far there's no higher order thinking, I have been bouncing round Bloom's lower order: 1. Recall data 2. Understand 3. Apply (use). Its all retrieval, making connections, so far.

Now time for the deep thinking, I build an animated visual image of the truss under gravity in my mind. I know it will sag, everything does, this is another connection, data by association. I allow the visual image to sag and observe it, a bit like this:

I observe that the top bars must shorten and the bottom bars lengthen, those visual images trigger the words "compression" and "tension". Yes I think the top bars are compressed and the bottom compressed.

Let's check that, let's run the mental simulation with a top bar removed, it plays in my mind like this.


Yes the top was definitely being compressed.

Now run the mental simulation with the bottom bar removed, it runs like this.

What about the diagonal braces, take one from the middle like this. I imagine it like this.

The structure doesn't know which way to fail, it could twist just as easily either way. I'm thinking that the force in the brace is near zero.

Does this hold for all braces? Try for an end brace like this.

No. So I'm thinking that the forces in the braces are zero in the middle and increase towards the sides. I've got a feeling that they will alternate between tension and compression but this mental simulation is getting taxing and I am at risk of falling off my bicycle.

What have I achieved here? I am satisfied that lower order thinking can be thought of as making connections, as information is recalled and cross checked against other data, checked for consistency, understood.

When the higher order thinking takes place, problem solving, the thinking is qualitatively different. It uses the "virtual serial machine built on top of the hard wired evolved natural predominant parallel processing" of our brain.

Mental models are built, understandings are constructed. The language of constructivism better describes the thinking process. HOT is different.


The simulations were run with sodaconstructor and captured with Cam Studio, then uploaded to Google Video.

Is this where Logo fell over?

In the 70's and 80's, Logo was put forward by its supporters as a silver bullet for education. It was enthusiastically promoted as an exceptionally good educational tool. Yet its mass introduction to schools was less successful, with a general perception that it had "not delivered what it promised".

It appeared to pass the test of enthusiastic teachers delivering to kids but fail where enthusiastic teachers delivered to rank and file teachers who in turn delivered to kids.

See Computer Criticism vs. Technocentric Thinking for an analysis by Papert on why it was perceived by some to have failed.

Is this the point we are at with the new drag&drop tools such as GameMaker? Over the past 4 years, a small group of teachers have recognised game making as a powerful constructivist tool for learning, a sandpit for higher order thinking. They persuaded their reluctant schools to let them teach game making.

Now its changing, game making is being adopted at school level and novice teachers are being told that they will "teach GameMaker". Unless the understanding is there that it is the journey and not the destination that matters, that it is a learning tool not a teaching tool, one for self-directed learning, then maybe its mass implementation will fall short of what we know it can deliver.

Will Game Maker fail the test of mass implementation like Logo did?

Higher order thinking - a thought experiment

I was challenged by the Connectivism conference to clarify what HOT (Higher Order Thinking) is. I was challenged by the perspective that Higher Order Thinking is not really distinct from other forms of thinking, it just consists of deeper levels of understanding, making more and better connections.

Bloom's Taxonomy helps a little but I suspect Bloom was a writer, a verbal reasoner, not an engineer. His highest level, Evaluate (assess, judge in relational terms), sounds a bit like making connections, it doesn't really ring true for the hard sweat of deep thinking for me.

So I decided to observe deep thinking in the only laboratory I have, inside my own head. To conduct a thought experiment. The big risk here is that we all think differently, we already know that there are verbal and visual thinkers, I'm definitely visual. Does my mental model building hold true for other visual thinkers?

So I decided to observe my thinking and document it. I wanted to analyse deeper thinking, problem solving, the example that came to mind was the truss, I don't know why, nor do I know why it came to me while riding my bicycle.

The word "truss" is stored along with a visual image of a truss, it looks something like this,

except that I can't visualise all the bars at once any more than I can concentrate on them when looking at them now.

I searched my memory for all connections and came up with the words "statically determinate", from that I was able to to retrieve a kind of visual image of a structure where, if you took out one member it would fall apart but if you added another, the braces would fight each other and you wouldn't be able to calculate the forces in the structure. Also the image of the triangle came up as the building block of statically determinate structures.

A visual image of the members being hinged or pinned at the joints came up like this.


Ok it's looking good, there's quite a bit of retrieved data and the problem is, in theory, solvable. But so far there's no higher order thinking, I have been bouncing round Bloom's lower order: 1. Recall data 2. Understand 3. Apply (use). Its all retrieval, making connections, so far.

Now time for the deep thinking, I build an animated visual image of the truss under gravity in my mind. I know it will sag, everything does, this is another connection, data by association. I allow the visual image to sag and observe it, a bit like this:

I observe that the top bars must shorten and the bottom bars lengthen, those visual images trigger the words "compression" and "tension". Yes I think the top bars are compressed and the bottom compressed.

Let's check that, let's run the mental simulation with a top bar removed, it plays in my mind like this.


Yes the top was definitely being compressed.

Now run the mental simulation with the bottom bar removed, it runs like this.

What about the diagonal braces, take one from the middle like this. I imagine it like this.

The structure doesn't know which way to fail, it could twist just as easily either way. I'm thinking that the force in the brace is near zero.

Does this hold for all braces? Try for an end brace like this.

No. So I'm thinking that the forces in the braces are zero in the middle and increase towards the sides. I've got a feeling that they will alternate between tension and compression but this mental simulation is getting taxing and I am at risk of falling off my bicycle.

What have I achieved here? I am satisfied that lower order thinking can be thought of as making connections, as information is recalled and cross checked against other data, checked for consistency, understood.

When the higher order thinking takes place, problem solving, the thinking is qualitatively different. It uses the "virtual serial machine built on top of the hard wired evolved natural predominant parallel processing" of our brain.

Mental models are built, understandings are constructed. The language of constructivism better describes the thinking process. HOT is different.


The simulations were run with sodaconstructor and captured with Cam Studio, then uploaded to Google Video.

Thinking about thinking

"Consciousness - our brain contains a virtual serial machine built on top of the hard wired evolved natural predominant parallel processing."

I like this quote from learningevolves, it encapsulates the higher order thinking that is missing from Connectivism. The virtual machine uses symbol systems, often but not always language. The symbols can be visual images too but they do run serially.

Visual thinking can consist of constructing a mental model or simulation and running that simulation in our head. The simulation runs serial mode. We observe this thought experiment and then use language to extract conclusions.

By comparison, making connections and data retrieval run parallel.

External storage, be it pencil and paper or delicious bookmarks or the scrabble letter rack expand our limited working memory and assist both our parallel and serial processing.

I once had a dumb cow and a smart cow. If I stood on the other side of the fence with a bale of hay, the dumb (Hereford) one would move as close as possible and then stand and bellow.

The smart one (Jersey) would process for a few seconds then run away from the hay, out through the gate and back. Was it making connections, running back through all the stored chess moves triggered by fence and hay till it retrieved a success scenario? Was it running an A* path finder algorithm on a visual map model in its brain?

Bad navigators use a 1D map representation in their head, probably stored as linguistic symbols "first right then turn left at the shops, first right at the railway line" Good navigators store a visual representation of a 2D map. Probably both run in the virtual serial machine.

Then there's autopilot mode. Ever ended at home when you intended to go somewhere else? The good old Connectivist parallel processor recognised landmarks along the way and fired up the drive home connections.

OCC2007 Constructivism, Constructionism and Connectivism

Vicki : Perhaps the reason connectivism is gaining such steam is that educators feel the current (learning theories) as presented are missing out on some vital aspects of effective, engaging teaching. Are you saying that connectivism is in other theories and so then would you say that perhaps those theories are not being taught correctly to educators?

This question was asked during the Kerr session of OCC2007. Bill Kerr writes that "a political movement is needed" that Constructionism battled with schools in the 80's and that school won. Schools are power structures and empowering students threatens schools' entrenched values. The battle is being fought again, this time its about games and blogs and flickr and myspace.

The intellectual property proponents and the "old school" schools are both working to limit children's access to the creative opportunities of the web.

“The computer is a medium of human expression and if it has not yet had its Shakespeares, its Michelangelos or its Einsteins, it will. …. We have scarcely begun to grasp its human and social implications.”
Computer Criticism vs. Technocentric Thinking By Seymour Papert

Bill writes of Article 13, UN Convention on the Rights of the Child

“The child shall have the right to freedom of expression; this right shall include freedom to seek, receive and impart information and ideas of all kinds, regardless of frontiers, either orally, in writing or in print, in the form of art, or through any other media of the child's choice.”

The "rights" of children were infringed when schools denied children the creative opportunities of the computer in the 80's, now their rights are again being infringed as they are denied the creative opportunities of Web2.

Constructionism , the N word is similar to Constructivism the V word. "It then adds the idea that this happens especially felicitously in a context where the learner is consciously engaged in constructing a public entity, whether it's a sand castle on the beach or a theory of the universe." The bold emphasis is mine. Constructionism anticipated the creative opportunities ofWeb2 self-publishing.

Constructivism, like Connectivism offers a strategy for education when there is education abundance, teaching students to be life long learners.

So to return to Vicki's question, current learning theories have not been widely implemented in schools. Where they are implemented they definitely result in engaging teaching. Are they effective teaching? That's harder to judge, standardised testing is good for fact recall but does not indicate whether students are equipped to be lifelong learners.

Online Connectivism Conference OCC2007

The Online Connectivism Conference - OCC2007 will be held online 2-9 Feb or (3-10 Feb if you are in Melbourne), generally at 17:00 GMT, which is 4am Melbourne time or whatever day and time it is in your time zone.

I have agreed at Bill Kerr's request to be a Context Filter.

My chosen context is engagement in relevant and authentic tasks. I came to this conference through my involvement in students creating their own computer games, a highly engaging, relevant and authentic task.

What do computer games and Connectivism have in common? Quite a lot.

• I would never have found Game Maker without the internet
• I would never have met teachers equally enthused as I without the internet
• I web published our students games on the internet
• I am self-taught about game pedagogy through the internet
• I am self-published on the internet
  
• Through the internet I am in real-time dialogue with the worlds experts on games and learning
  

A Constructivist (my) perspective and a Connectivist perspective both try to come to terms with an increasing body of knowledge, sitting at our fingertips, Google now indexing 10 zillion pages. Both perspectives agree that the rote learning of facts is becoming less important in school. Constructivists believe that students will need the skills to construct understandings of new knowledge, Connectivists believe that they will need the skills to connect with new knowledge.

For me the debate is not whether Connectivism has the necessary depth to be called a learning theory, whether it deserves to be an -ism. For me the important issue is what can be learnt about living and learning in a connected world when 1000 people from round the world connect in a way which was previously impossible.

If I can master the technology and sleep deprivation I'll filter.

The Filters

Tony Forster
http://tonyforster.blogspot.com/
engagement in relevant and authentic tasks

Graham Wegner
Student initiated curriculum

Sheryl Nussbaum-Beach
http://21stcenturylearning.typepad.com
Voice for the Voiceless

Mel Chua
Student/younger generation

Vicki Davis
http://coolcatteacher.blogspot.com/
K-12

Virginia Yonkers
Business and workplace education/training

Chris Sessums
http://elgg.net/csessums/weblog/
Issues of Poverty

Clarence Fisher
Rural K-12
http://remoteaccess.typepad.com/

Jo McLeay?
http://theopenclassroom.blogspot.com/
Personal teaching experiences

Darren Kuropatwa
K-12 – Senior High School
http://adifference.blogspot.com/

Michael Hotrum
http://choicelearning.blogspot.com/
Higher Education

Marilyn Martin
Consultants view

Sharon Peters
Women of Web 2.0

Review of “Digital Game- Based Learning It’s Not Just the Digital Natives Who Are Restless"

The original paper is by Richard Van Eck, Associate Professor at the University of North Dakota and published in March/April 2006 EDUCAUSE review http://www.educause.edu/ir/library/pdf/erm0620.pdf

This review is a discussion paper for Games in Learning Symposium - ACEC, Cairns, Tues Oct 3, 1:20 - 2:25, here is the link to abstracts of all Games in Learning and Games Programming Cairns papers)

In a thought provoking paper, Richard Van Eck suggests that proponents of digital game-based learning (DGBL) should move from the promotion of DGBL to a critical analysis of DGBL. “Like the person who is still yelling after the sudden cessation of loud music at a party” we now have the world’s attention and its time to do critical analysis of what exactly we are promoting.

He identifies three kinds of DGBL:

• have students build games;
• have educators and/or developers build educational games; and
• integrate commercial off-the-shelf (COTS) games into the classroom

He believes that student built games are not likely to be widely accepted because:

• not all teachers have the skill sets needed for game design,
• not all teach in areas that allow for good content,
• not all can devote the time needed to implement this type of DGBL,
• and many teach within the traditional institutional structure, which does not easily allow for interdisciplinarity.

The skill sets needed for game design

I believe that student built games are the kind of DGBL with the most promise.

Though teachers may not have good game design skills, it is wrong to assume that teachers need to have strong game or IT skills to run an effective class. Many of today’s and tomorrow’s students will have IT skills which surpass their teachers. In a world where content has an ever decreasing half life, an important role of the teacher is to provide an environment where students can engage in constructivist self-directed learning. The teacher has in important role in providing and maintaining this environment and in teaching higher order cognitive and metacognitive skills but is less and less a teacher of content down a one way pipeline. The teacher can no longer expect to be the expert in the content but is still an expert in learning.

Areas that allow for good content

Though not all areas of old curriculum fit easily with game creation, many do. Games: student made, edugames or COTS will never cover all areas of education.

The skills which have been identified as necessary for a digital age are not necessarily those of the old curriculum. The Essential Learning Standards recognises that:

“In our rapidly changing and globalised world, with the pervasive influence of high speed, interactive information and communications technology (ICT), knowledge is a major resource. ….. This is accompanied by the realisation that students can no longer prepare for one career in life and therefore need to develop a commitment to life-long learning in all occupations and facets of life, and a capacity to manage change…The Essential Learning Standards consciously seek to reduce the crowding of the curriculum to give students time to explore the underlying concepts of tasks and problems they are set, to process information they gather or receive, and to make connections to other information they already possess.”

Though student game creation may be a poor match to some areas in the old curriculum, it is a good match for the kind of learning needed for the future.

The time needed to implement student game creation

With a game programming tool like Gamemaker students are creating their first game within an hour. From the outset, they are highly motivated and are involved in deep learning which spans literacy, numeracy and generalised higher order cognitive skills.

The traditional institutional structure does not allow for interdisciplinarity

Interdisciplinary learning has been identified as one of the key features of education, see the Essential Learning Standards. If schools are not offering interdisciplinary learning, they should be.

COTS games

Van Eck suggests that COTS games can be extended into the classroom through instruction and projects which preserve the context of the game. The idea being presumably that the motivation and “flow” will be carried back to the classroom if there is a close parallel between the game and the class work.. So the real learning is taking place outside of the game and the game is mainly setting the students into an appropriate state for learning. If time in game is not time on task, can COTS games be that effective?

He quotes Malone and Lepper who identify fantasy (endogenous and exogenous) as one of four main areas that make games intrinsically motivating. Hence the transfer of motivation from the game to the class relates to the preservation of the fantasy which is endogenous to the game. Recent research questions the importance of endogenous fantasy.

The study, “Intrinsic Fantasy: Motivation and Affect in Educational Games Made by Children. M. P. Jacob Habgood”, http://www.informatics.sussex.ac.uk/users/gr20/aied05/finalVersion/JHabgood.pdf found that children create games with extrinsic fantasy, both for “curriculum” and “non-curriculum” games. This questions the importance of endogenous fantasy to children.

Much more important than fantasy is having a sense of ownership. When students can influence the set task and can create an object of real value and relevance to their peers, then they are really motivated.

For these reasons, I believe that student created games is the area with the most promise in DGBL

Tony Forster,
ASISTM Computer Game Design, Programming, Multimedia and Mathematics Cluster. forster at ozonline dot com dot au

Interest in game programming by country

Here is an analysis of the interest in the educational use of computer game programming by country using Clustrmaps http://clustrmaps.com

	total	Australia	UK&Ireland	USA
Pop million		20	60	283
http://www.mindtools.tased.edu.au/gamemaker/default.htm	8780	3070	550	6640
hits/million pop			9	23
http://www.freewebs.com/schoolgamemaker/	887	765	55	575
hits/million pop			0.9	2.0
http://www.gamelearning.net/	2955	270	550	1405
hits/million pop		13.5		5.0

It is obvious that you cannot use a site's map to gauge relative interest in a topic in its host country, there's a strong "home town" effect. It is interesting that the 2 Australian sites both found that interest per capita was twice as high in USA as UK. Then, based on one site, Australian interest per capita was almost 3 times as high as USA.

Another analysis can be done with http://www.google.com/trends . Note that statistics for search terms are normalised on a % of searches basis. If a city rates highly its not because it has more searches of that term but that term is more likely to be used in its total of searches.

Search gamemaker:

1.	Brisbane Australia
2.	Amsterdam Netherlands
3.	Adelaide Australia
4.	Perth Australia
5.	Auckland New Zealand
6.	Melbourne Australia
7.	Stockholm Sweden
8.	Sydney Australia
9.	Helsinki Finland
10.	Seattle, WA USA

Note that Estonia wins on a per country basis and Australia comes third (I dont understand)

Australian cities, notably Brisbane win on Constructivism, Metacognition and Pedagogy. Interestingly if you search instruction or instructional, USA fills all 10 top places but for instructional design, India wins.

I also had fun with war/peace, love/hate etc. Its also fun to look at time trends

I have been thinking why I teach game programming. I do not expect that my students will make Gamemaker games when they grow up or become game programmers. Most won't even become computer programmers. The benefit is not in the specific programming skills but in more generalised higher order skills.

I have found the cognitive/metacognitive divide useful. http://www.education.auckland.ac.nz/learning/tech/ict/education/it6.asp Metacognition can be described simply as learning how to learn. A key component of metacognition is the opportunity to reflect on how a problem was solved and whether that strategy can be generalised.

Teaching for Transfer D. N. Perkins and Gavriel Salomon http://www.lookstein.org/integration/curriculum_transfer.htm talks of near and far transfer and the transfer mechanisms “low road/high road” model of transfer. High road transfer is a beast like metacognition and requires time to reflect and abstract general principles from the activity of game programming.

The paper suggests "Hugging" for near transfer and “Bridging” for far transfer. Bridging "means teaching so as to meet better the conditions, for high road transfer. Rather than expecting students to achieve transfer spontaneously, one “mediates” the needed processes of abstraction and connection (Delclos et al. 1985, Feuerstein 1980). For example, teachers can point out explicitly the more general principles behind particular skills or knowledge, or better, provoke students to attempt such generalizations themselves"

Finally, I have found Bloom's Taxonomy useful in identifying what the higher order cognitive skills might be for which we seek "far, high road transfer" http://www.nwlink.com/~donclark/hrd/bloom.html

Bloom breaks up the cognitive domain into 6 categories: Knowing Comprehending Applying Analysing Synthesising Evaluating

I think the skills we seek are in the last 2 categories, synthesis and evaluation. Fortunately this is where students spend most of their time in the debugging cycle of implement/test/debug.

Which brings me back to cognitive conflict. Cognitive conflict is an essential part of the debug cycle, its also an important aspect of Metacognitive theory. So I think that Metacognitive theory, high road transfer and Bloom's taxonomy are pretty much talking about the same thing.

And the take home message: allow students to spend as much time as possible in a state of cognitive conflict as they synthesise and evaluate solutions while giving them the opportunity to abstract generalised rules from the exercise.