In 2003, Professor James Paul Gee, a cognitive scientist who at that time was a professor of reading at the University of Wisconsin, published a thought-provoking book titled What Video Games Have to Teach Us About Learning and Literacy. That same year, I and two colleagues at Stanford University organized a three-day research workshop titled Gaming2Learn, aimed at bringing together leading education researchers and successful game developers to examine the prospects for developing good video games that provide good learning. It was my encounter with both Gee and his book, together with what I learned at that workshop, that in due course led me to co-founding BrainQuake.
Dr, Gee, who trained in linguistics and education theory, got into video games by trying to help his young son play them. He discovered that not only were they quite hard, they seemed to be constructed around sound principles of learning. So he decided to make a study of them.
In his book, Gee lists 36 principles of good education that can also be found in good video games. Although his book refers occasionally to math, mathematics education is not his focus. Rather, his 36 principles are the ones that video game designers unconsciously follow in order to produce compelling games that will sell to a fickle and demanding audience in a highly competitive market.
In my book about the design of mathematics learning video games Mathematics Education for a New Era: Video Games as a Medium for Learning, published in 2011, I listed Gee’s 36 design principles for good learning games and divided them into three categories.
I marked 24 of them as Highly Relevant to Learning Basic Mathematics, another four as Moderately Relevant to Learning Basic Mathematics, and the remaining eight as Not Particularly Relevant to Learning Mathematics, providing discussions of many of them, with reasons to support my category assignments.
Since writing that book, I have decided that all 36 of the principles are in fact highly relevant to mathematics learning. What happened to change my mind so dramatically?
It came down to two things. One was my experience in working with a talented and experienced team of educators, education designers, game developers, and system engineers at BrainQuake to actually design and build math-learning video games, and conducting studies to see how they work (or do not work as hoped). The other was that a lot of my research activity at Stanford moved from mathematics to mathematics education, which brought me into contact with some of the world’s best mathematics education scholars, from whom I learned a lot.
Basically, the twelve Gee design principles I did not view as highly relevant to the design of video games for math learning were all about psychological, social, and cultural issues.
It’s not that I thought those issues were not relevant to doing and using mathematics. I did, after all, spend much of the decade following the September 11, 2001 attack on the World Trade Center working for three successive branches of the US Department of Defense on projects to try to improve intelligence gathering and analysis and save lives (both of civilians and of the military who are on the front lines of defense).
Those projects were all focused on how to take mathematics originally developed for the inanimate worlds of physics and engineering and use it effectively in the far more messy world of people, of organizations, and of nations. The twelve Gee principles I had felt comfortable ignoring in my earlier video game learning work were all front and center in my DoD research.
But, even though I was engaged in that work when I was writing my video-games book, I felt that when it came to designing educational video games, those human factors really could be put to one side, and perhaps accounted for later if necessary, much as we ignore friction in mathematical mechanics. Gee’s book was written to provide advice to mathematics teachers, based on the design principles video game developers use implictly to ensure their products are engaging. My book was aimed at educators and others who wanted to design and build math learning video games.
In the case of our own game design work at BrainQuake, ignoring the “social/cultural friction” turned out to be reasonable for a while. But as we got deeper into our game design work, it became clear to me that we could no longer ignore the social/cultural “friction”, at least if we were to take advantage of the maximum benefit video games can offer to mathematics learning.
In particular, one huge benefit that (suitably designed) video games bring to mathematics learning is their potential to be inclusive. They can be designed to require no prior literacies and to be free of social or cultural bias. But note that word “can” in that last sentence. I did not say “will (automatically) be so designed.” To pull it off is not easy. And that’s where Gee’s remaining principles come in.
As our video game development progressed, it became increasingly clear to me that we should take account of all of Gee’s principles, not just the 24 (“friction-free”) principles I originally singled out in my book.
For the record, I present Gee’s list as an appendix. I have left in my original classification, but with you should view them subject to the rider that they are all important factors to take account of in the design of math learning video games created to yield good learning. The list is probably of most relevance to potential designers of math-learning video games and teachers who want to make use of video games in their classrooms.
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The numbering is Gee’s original one; the three-part classification is mine. I have given the three categories different titles from those in my 2011 book to account for the experience obtained since that was written. While this classification is likely useful in setting out the timeline for designing a new math-learning video game, all 36 should be taken account of for the resulting video game to be as effective a learning tool possible, given the medium.
First-Order Game Design Features Relevant to Learning Basic Mathematics
 Active, Critical Learning Principle All aspects of the learning environment (including ways in which the semiotic domain is designed and presented) are set up to encourage active and critical, not passive, learning.
 Semiotic Domains Principle Learning involves mastering, at some level, semiotic domains, and being able to participate, at some level, in the affinity group or groups connected to them.
 “Psychological Moratorium” Principle Learners can take risks in a space where real-world consequences are lowered.
 Committed Learning Principle Learners participate in an extended engagement (lots of effort and practice) as extensions of their real-world identities in relation to a virtual identity to which they feel some commitment and a virtual world that they find compelling.
 Self-Knowledge Principle The virtual world is constructed in such a way that learners learn not only about the domain but about themselves and their current and potential capacities.
 Amplification of Input Principle For a little input, learners get a lot of output.
 Achievement Principle For learners of all levels of skill there are intrinsic rewards from the beginning, customized to each learenr’s level, effort, and growing mastery, and signaling the learner’s ongoing achievements.
 Practice Principle Learners get lots and lots of practice in a context where the practice is not boring (i.e., in a virtual world that is compelling to learners on their own terms and there the learners experience ongoing success). They spend lots of time on task
 “Regime of competence” Principle The learner gets ample opportunity to operate within, but at the outer edge of, his or her resources, so that at those points things are felt as challenging but not “undoable.”
 Probing Principle Learning is a cycle of probing the world (doing something); reflecting in and on this action and, on this basis, forming a hypothesis; re-probing the world to test this hypothesis; and then accepting or rethinking the hypothesis.
 Multiple Routes Principle There are multiple ways to make progress or move ahead. This allows learners to make choices, rely on their own strengths and styles of learning and problem solving, while also exploring alternative styles
 Situated Meaning Principle The meanings of signs (words, actions, objects, artifacts, symbols, texts, etc.) are situated in embodied experience. Meanings are not general or decontextualized. Whatever generality meanings come to have is discovered bottom up via embodied experiences.
 Text Principle Texts are not understood purely verbally (i.e., only in terms of the definitions of the words in the text and their text-internal relationships to each other) but are understood in terms of embodied experiences. Learners move back and forth between texts and embodied experiences. More purely verbal understanding (reading texts apart from embodied action) comes only when learners have had enough embodied experience in the domain and ample experiences with similar texts.
 Intertextual Principle The learner understands texts as a family (“genre”) of related texts and understands any one such text in relation to others in the family, but only after having achieved embodied understandings of some texts. Understanding a group of texts in a family (genre) of texts is a large part of what helps the learner make sense of such texts.
 Multimodal Principle Meaning and knowledge are built up through various modalities (images, texts, symbols, interactions, abstract design, sound, etc.), not just words.
 Incremental Principle Learning situations are ordered in the early stages so that earlier cases lead to generalizations that are fruitful for later cases. When learners face more complex cases later, the learning space (the number and type of guesses the learner can make) is constrained by the sorts of fruitful patterns or generalizations the learner has found earlier.
 Concentrated Sample Principle The learner sees, especially early on, many more instances of fundamental signs and actions than would be the case in a less controlled sample. Fundamental signs and actions are concentrated in the early stages so that learners get to practice them often and learn them well.
 Bottom-Up Basic Skills Principle Basic skills are not learned in isolation or out of context; rather, what counts as a basic skill is discovered bottom up by engaging in more and more of the game/domain or game/domains like it. Basic skills are genre elements of a given type of game/domain.
 Explicit Information On-Demand and Just-in-Time Principle The learner is given explicit information both on-demand and just-in-time, when the learner needs it or just at the point where the information can best be understood and used in practice.
 Discovery Principle Overt telling is kept to a well-thought-out minimum, allowing ample opportunity for the learner to experiment and make discoveries.
 Transfer Principle Learners are given ample opportunity to practice, and support for, transferring what they have learned earlier to later problems, including problems that require adapting and transforming that earlier learning
 Dispersed Principle Meaning/knowledge is dispersed in the sense that the learner shares it with others outside the domain/game, some of whom the learner may rarely or never see face-to-face.
 Affinity Group Principle Learners constitute an “affinity group,” that is, a group that is bonded primarily through shared endeavor, goals, and practices and not shared race, gender, nation, ethnicity, or culture.
 Insider Principle The learner is an “insider,” “teacher,” and “producer” (not just a “consumer”) able to customize the learning experience and domain/game from the beginning and throughout the experience.
Second-Order Game Design Features Relevant to Learning Basic Mathematics
 Semiotic Principle Learning about and coming to appreciate interrelations within and across multiple sign systems (images, words, actions, symbols, artifacts, etc.) as a complex system is core to the learning experience.
 Metalevel Thinking about Semiotic Domains Principle Learning involves active and critical thinking about the relationships of the semiotic domain being learned to other semiotic domains.
 Ongoing Learning Principle The distinction between learner and master is vague, since learners, thanks to the operation of the “regime of competence” principle listed [as principle 14], must, at higher and higher levels, undo their routinized mastery to adapt to new or changed conditions. There are cycles of new learning, automatization, undoing automatization, and new reorganized automatization.
 Subset Principle Learning even at its start takes place in a (simplified) subset of the real domain.
Third-Order Game Design Features Relevant to Learning Basic Mathematics
 Design Principle Learning about and coming to appreciate design and design principles is core in the learning experience.
 Identity Principle Learning involves taking on and playing with identities in such a way that the learner has real choices (in developing the virtual identity) and ample opportunity to meditate on the relationship between new identities and old ones. There is a tripartite play of identities as learners relate, and reflect on, their multiple real-world identities, a virtual identity, and a projective identity.
 “Material Intelligence” Principle Thinking, problem solving, and knowledge are “stored” in material objects and the environment. This frees learners to engage their minds with other things whole combining the results of their own thinking with the knowledge stored in material objects and the environment to achieve yet more powerful effects.
 Intuitive Knowledge Principle Intuitive or tacit knowledge built up in repeated practice and experience, often in association with an affinity group, counts a great deal and is honored. Not just verbal and conscious knowledge is rewarded.
 Cultural Models about the World Principle Learning is set up in such a way that learners come to think consciously and reflectively about some of their cultural models regarding the world, without denigration of their identities, abilities, or social affiliations, and juxtapose them to new models that may conflict with or otherwise relate to them in various ways.
 Cultural Models about Learning Principle Learning is set up in such a way that learners come to think consciously and reflectively about their cultural models of learning and themselves as learners, without denigration of their identities, abilities, or social affiliations, and juxtapose them to new models of learning and themselves as learners.
 Cultural Models about Semiotic Domains Principle Learning is set up in such a way that learners come to think consciously and reflectively about their cultural models about a particular semiotic domain, without denigration of their identities, abilities, or social affiliations, and juxtapose them to new models about this domain.
 Distributed Principle Meaning/knowledge is distributed across the learner, objects, tools, symbols, technologies, and the environment.