Teaching deductive, inductive, and inferential logic through interactive online computer simulation
Thomas E. Malloy
Department of Psychology
University of Utah
The pedagogy which underlies the online teaching software demonstrated in this paper is based on a broad framework regarding the nature of learning and knowledge. I will begin with a sketch of that framework and then turn to a JAVA applet for teaching deductive, inductive and inferential logic.
1. Some Principles and Issues
A Process Learning Framework. Every process proceeds in accordance with its structure. By structure I don't mean material things like foundations and girders. I mean structure in the sense of logical structure, mathematical structure, or grammatical structure. Through repeatedly engaging a process humans learn the structure of that process. Let me restate that more fully. While repeatedly engaging external processes we structure our own internal processes in ways which enable us to relate to the structure of external processes. The classic work of Shiffrin and Shneider (1977) indicates that process learning is often, but not necessarily, highly skilled, automatic and unconscious. Every process proceeds in accordance with its structure; and, through process learning, we proceed in accordance with our learned internal structures.
Examples. Well known examples of process learning include language and music. By engaging the language which they hear, small children build internal structures which allow them to relate in useful ways to the structure of that language. The structures of Chinese, Spanish, and English are very different. By engaging the language process over many years, children learn the deep structure of their native language. The knowledge of linguistic deep structure is typically so automatic that it is brought to consciousness only with effort. People can speak; but they seldom consciously know the grammatical rules by which they speak unless or until they study grammar formally. Similarly, a civilization's music is defined by its musical scales and other musical forms. As prospective musicians repeatedly play instruments to the point of fluidity they incorporate structures within themselves which enable them to use their instruments to play the rhythmic and melodic structures of their culture's music. Depending on how they learn music, this implicit musical structural knowledge may or may not be consciously accessible.
More prosaic but still familiar examples of process learning come from the experiences of computer users. Every user has learned a favorite application (a word processing program, a draw program, a data analysis program) and an operating system (Mac OS, Windows 3.1, Windows 98, UNIX, LINUX). Moreover, we have all learned applications and operating systems over a long period of time to the point of unconscious fluidity. We have generated internal structures which allow our thought processes to relate to the structure of these programs. We think a thought and it appears on the screen with little or no awareness of the menu or key or icon structures of the program. It is as if the program has become intuitive and natural.
And, alas, almost all users have also had the experience of changing programs and operating systems. Frequently this is challenging, inconvenient, and aggravating. Why? Through process learning, we proceed in accordance with our learned internal structures and our learned structures do not relate well to the external structure of the new program. Let's look in more detail at how the process learning which results from using computers can be a powerful learning context.
Learning to structure processes. In building applications and operating systems, designers and programmers have a plan, a schema, an overall logic of how a program works and of how its various functions relate to each other. Every process proceeds in accordance with its structure; and frequently the structure of a computer program is expressed as a flow chart. Long term users of a program must in some deep sense learn to structure their internal processes to fit the program's structure. Users' structures need not be, almost certainly are not, isomorphic with the programmers' ideas, nor do they need to conform in some strict way to the flow chart. It would be a rare user who could accurately draw a flow chart of a familiar program. Nevertheless, it is proposed here that long term users must structure their internal processes in a way that lets them usefully relate to the program's structure. Notice that this sentence does not imply that their internal processes will be the same as or a representation of external structure. It says that, through learning, their internal structures come to relate to and fit with external structures imbedded in the program. This learning typically takes considerable experiential commitment.
Process learning is powerful. There are enormous advantages resulting from having learned to structure our own processes to relate automatically to the structure of some external process (Shiffrin and Schneider, 1977). But there are also disadvantages. One disadvantage is felt when external processes change and we keep proceeding by the structure of our learned processes. We proceed in ways which no longer relate well to external process. For example, sometimes circumstances entice or require us to change familiar computer applications or operating systems. Changing from Word Perfect to Word or visa versa can be demanding, even disorienting. All the internal structures that were built up over months or years no longer relate so well to the structure of the new program. Sometimes they do not relate at all. The new program can seem unnatural, counterintuitive, even stupid and certainly confusing. Switching from the Mac OS to Windows or visa versa can feel all wrong. It's not so much the specific menus and keystrokes that have to be relearned, rather it is a deeper level of how we organize our thinking in a way that fits with subtle underlying logic in the structure of the operating system which must be learned.
Interestingly, it seems like the more of these kinds of switches from one program to another that we make, the easier switching gets. I assume that this is because switching repeatedly forces users to learn higher-order logic that are common to the structures of all programs.
I want to address how the structural knowledge resulting from the use of computers can be used to great educational benefit. But first, I want to make a couple more conceptual distinctions and agree upon some terminology.
Old Media. In the electronic context, I use "old media" to include written text, pictures, illustrations, recorded music, movies, videos, television, and animations. Text, pictures, and illustrations are best for static concepts; videos and animations are best for dynamic concepts where movement is crucial. What characterizes the old media is that the audience can change little, if anything, about the information coming at it; the audience is receptive, even inclined to be passive. Whether it be from watching endless hours of television or from sitting, still and quiet, in a classroom listening to lectures for eight to sixteen years, one of the consequences of old media process learning is the development of learning strategies which are passive and which produce the perception of knowledge as external to the learner and passed down from experts. When a person uses old media to quench the desire for knowledge, the internal structures which result are primarily receptive. Another consequence of learning through old media is the atrophy (or at least the lack of opportunity to develop) active discovery processes as a basis of learning. Any activity on the part of the person (a library or Internet search) comes before reading the book or watching the video. The medium is the message at the deepest levels: Old media audiences structure their learning processes to be receptive, and at times even passive. Like people changing operating systems, they can find it challenging, inconvenient, and aggravating to engage processes which require them actively to seek and to discover knowledge. Frequently students accept reading an assigned chapter in their text but dislike choosing, even don't know how to choose, their own topic and do an active library search. This is one deep form of learning accomplished by processing old media.
Multimedia. In the electronic context, educators frequently combine different types of old media as a way of gaining educational advantages. For example, Mayer and Anderson (1991) found that combining media produced better subsequent problem solving than the use one medium alone.
New Media: Interactive Simulations. The emerging new media are based on the interactive nature of computers. My candidates for the defining examples of new media are found among scientific computer simulations models. More and more frequently, simulation is being used as a powerful scientific tool enabling discoveries that were impossible with other methods. But I include in new media also computer games, draw programs, word processors, the Internet as a whole, any sort of program whose interactivity allows the user to be active and creative and to change the output of the program. The direction I want to take this discussion is that if computer simulations can be used as scientific discovery processes, then surely they can be used in a parallel manner by students to learn to develop their own discovery processes. This paper will focus on exploring how new media, especially interactive simulation, can be a powerful method for teaching the deep structure of ideas.
Audience versus User. The term "audience," so appropriate with old media, no longer seems right with new media; we prefer terms like "user," "player," or "gamer," and so on, depending on the specific medium. The difference between "audience" and "user" points at a crucial difference between old and new media. An audience receives experience. Users create experience by interacting with the medium. More accurately, an old media audience creates the highest quality experience for itself by being attentive and receptive to input. Users of new media create the highest quality experience for themselves by attending to and actively altering input to fit their own goals and desires.
Computer Games. Computer games constitute a special case of computer simulation. Alex Garland (1998) in The Beach, p. 139, describes (to those who play little or not at all) what video gamers all know, "In video games, play occurs in levels of increasing difficulty. The term 'boss' refers to the ultimate challenge a player meets, blocking the way to the next level of play. Until you get past the boss you cannot play the next level. Most bosses have a pattern; crack the pattern, kill the boss. A typical pattern is illustrated by Dr. Robotnik during his first incarnation in Sonic One, Megadrive version, Green hills zone. As he descends from the top of the screen, you jump at him from the left platform. Then, as he starts swinging toward you, you duck under and jump at him from the right. As he swings back, you repeat the process in reverse until, eight hits later, he explodes and runs away. That's an easy boss." From Garland's description, it is clear that learning the game's strategic structure is as important as eye-hand coordination. In fact, eye-hand coordination is not enough; a very fast and accurate player can't win without learning strategic game structures. One of the themes Garland explores in The Beach is the darker consequences of some of the subtle strategies learned by video gamers.
Many people have noticed pretty much the same thing that Alex Garland described. By playing or, more likely in many cases, by watching our children play computer games we noticed that players must learn strategic ways of thinking to succeed at the game. Much recent media analysis has focused on media content; but there are important societal consequences of what people learn from media processes as well. A game's structure is as important as, perhaps more important than, that game's content. Players are learning HOW to think as much as learning WHAT to think.
The cognitive distinction between "how" and "what" is important. Recent trends in cognitive research have focused on memory for different types of knowledge. Roediger & McDermott, (1993) distinguish between explicit memory (conscious recall of information) and implicit memory (unconscious activation revealed in changes in task performance). Squire, Knowlton & Musen (1993, p. 457) make the distinction "between conscious memory for facts and events [declarative memory] and various forms of nonconscious memory, including skill and habit learning [nondeclarative memory]..." They define skills as motor, perceptual or cognitive procedures for operating in the world. Thus nondeclarative memory is sometimes referred to as procedural memory and, as such, refers to memory for learned processes.
For the educational purpose of this paper let's use the following definition: Process learning is the structuring of our internal processes in ways that allow us to relate to external processes. Both implicit memory and procedural memory can reflect those changes of structure that result from process learning. Based on phenomena such as implicit and procedural memory, one intriguing question, a question which is prior really to memory for process, is to ask is how to change the structure of process? What I am proposing is that educators can take advantage of process learning. We can identify structures of thought that we believe are valuable. We can then structure interactive computer programs in ways which set the context for people to learn those thought structures we value.
Designers of computer-based instructional programs are espousing similar approaches to the one outlined above. For example, Judkins (2000) argues that "the real power in multimedia is with active simulation and training." Brown (1999) focuses on the need to simulate research as a way of learning research principles. Brown's Wildcat World allows students to design various types of research projects. Washburn (1999) has developed a program which gives students experience in distinguishing interpretation from findings in a research methods class. In a different educational context, Martin and Reese (2000) use computer interactivity to stimulate critical deliberation about realistic case studies in a medical ethics curriculum. Martin and Reese make use of the unique interactive properties of computers to engage students in active learning of principles by presenting them with realistic situations that simulate their students' future life contexts. Underlying all these computer programs is a commitment to active learning through simulation which emphasizes the discovery of principles (or the discovery of what I call structure).
I will now examine the meta-structure of the Difference to Inference game. Depending on your learning style you may prefer to gain game experience (see section 3, below) before reading about the game's structure. Others may prefer to read about the meta-structure of the game before playing. In that case just read on.
2. The Difference to Inference Game: Using deductive and inductive logic to make theoretical inferences
Meta-structure. In the Difference to Inference Game students plan a strategic series of two-group experiments whose data will discriminate among five theories. Students must choose which of five theories (visual patterns) best describes an unseen visual pattern hidden behind a screen.
Deduction. First they must make deductions from the level of theory to the level of research design. They must deduce how to construct crucial experiments which will eliminate some theories but not others. This is done by critically examining the five theories and determining where the theories make different predictions.
Induction. Second, after collecting research data, students must use inductive logic to go from the data back to theory. Theories make predictions about data; the data obtained from research studies may or may not be inconsistent with each theory's predictions. Students run empirical studies and then must decide if they can eliminate one or more theories on the basis of the research data.
Inference. Finally students must make theoretical inferences based on all this deductive and inductive logic. They must conduct a series of research projects until they discover one and only one theory which remains consistent with all the known data.
The game structure of Difference to Inference requires students to integrate deductive, inductive and inferential logic to choose the best of five theories.
Game format. To begin, students receive a research grant amounting to 500 grant bucks. The game is an important assignment in a university class; to get full course credit they must earn more grants until they have a minimum of 2000 grant bucks. Various research activities such as collecting data, analyzing data, and submitting incorrect theoretical conclusions cost grant bucks. In the long run these costs can be reduced by carefully deducing an efficient series of studies to isolate the "correct" theory (i.e., that one theory among the five which, in the game's simulated reality, will be consistent with the results of all possible studies). When students think they have figured out which theory remains consistent with data across many studies, they submit their conclusion. If they are wrong it costs them grant bucks. If they are right they receive another grant. The game can then be played again with five new theories. By repeatedly playing the game with new theories, students can build up their grant bucks toward the 2000 grant bucks required as a minimum for their course grade. Moreover, the login names of the students with the top 10 grant buck earnings are posted automatically by a JAVA applet interacting with an Oracle database. Publicly posting the top 10 earnings allows those who wish to do so to compete with other students. Inevitably there is a large group of students who earn well above the minimum course requirements as they attempt to get the top grant buck score. (Any resemblance to the scientific community is purely coincidental.)
Game Story. Computer games typically provide a game story or other framework to give the game activities meaning. The Difference to Inference gives a player a choice of two stories, one based on the work of the seminal statistician, R. A. Fisher, and the other based on hurricane damage and deforestation. The game plays exactly the same whichever framework the player chooses. I will describe only the first framework here.
Historical Note. In the 1920's mathematician R. A. Fisher developed the statistical procedures known as the Analysis of Variance. The F test is named for him. Fisher worked in Britain and developed many of his procedures while working with farmers on agricultural yield. He developed inferential statistics which allowed him to determine if different plots of ground yielded different amounts of food. I probably shouldn't mention this because I probably won't hear the end of it, but Fisher worked a lot with the effects of fertilizers on yield. For that reason the statistics he developed, for example ANOVA, have sometimes been called, especially by critics, "manure pile statistics."
A Historically Based Puzzle. The current Difference to Inference puzzle will be based (with substantial changes in methodology) on this part of the history of inferential statistics. Let's say the dependent variable (DV) is the amount of corn in bushels per acre. The independent variable (IV) is placing or not placing a certain fertilizer on a plot of ground. There are 5 fields, each one divided up into a 7 by 7 grid of 49 plots. In each field the fertilizer was placed on a subset of these 49 plots during the growing season. Now it is harvest time. The shape of the area with fertilizer is a little different from field to field and is shown in red. The area in each field that has no fertilizer is shown in green. Here's the puzzle. There are 5 different fields. You have maps of the 5 fields showing the shapes of the fertilized areas in red. The yields should be higher in the red areas (fertilized) and lower in the the green areas (unfertilized). The problem is that the records indicating which map goes with which field have been lost. You are standing in one field. You know that one of the 5 maps applies to this field. Your job is to measure crop yields in this field to discover which map applies to it.
Game Strategy. Like most games, Difference to Inference offers strategic advice to players about game play.
Inference from difference. You are standing in a field looking for the edge of the pattern which divides fertilized (red) from non-fertilized (green) plots. To do this, you will be able to use a Horizontal or Vertical Tool to collect samples of data on crucial adjacent plots. Use the data from the samples to decide if there is a difference in yield in the two adjacent plots. After you collect data a few times you should be able to infer, from the differences you find (or don't find), which of the 5 maps applies to the field in which you are standing.
Seek the edge. Remember one of the fundamentals of human pattern perception: The important information is at the edge of the pattern.
Seek difference. Use the Horizontal Tool or Vertical Tool to determine if the yields (expressed as samples of numbers indicating bushels of corn per acre) of any two adjacent plots are the same or different. If they are different, then you've found an edge of the pattern. But difference alone is not enough. There are other challenges.
Differences that make a difference. One challenge is that various fertilizer patterns share the same shape on parts of their edges. Study the 5 maps noticing those crucial places where the shapes of the patterns are different. These places--where the 5 theories differ in their predictions--are where you should put your attention and do your research. These are the differences that make a difference. These are the crucial differences at the edge.
3. Links to the Difference to Inference Game
Below are three links relevant to the game. The first takes you directly to the game itself. The second takes you to an in depth web lecture about the game. The third link takes you to the the registration page of an Introductory Statistics Course at the University of Utah. This extensive course uses many JAVA-based interactive learning tools, including the Difference to Inference game, as well as an online statistical text.
Play the Game. When you click the Difference to Inference link below you can play the game directly without logging in to the StatCenter site. The program will associate your score with the name "Guest" in the database. So you will see your score change as you earn grant bucks; your score will be saved on the database as the score for "Guest." Be advised that every guest player will replace the score for every other guest, so your score is not permanent. If many guests are playing at once the score will change every time any one of them earns a new score.
Suggestion: On the game interface, you must choose an effect size before you begin. Choose "Easiest (Large Effect Size)." You can play the "Easiest" level of the game using inductive, deductive, and inferential logic without integrating statistical reasoning into game play. Harder levels of the game require more and and more use of statistics and statistical reasoning. This paper does not address the teaching of statistical reasoning processes, even though the game does teach statistical reasoning also.
Hint: At the easiest level of play the red areas will have much larger scores than the green areas.
Difference to Inference game
Web Lecture. It may be worthwhile reading more detailed information on the game than is included in this paper. This paper focuses on the critical thinking and logical reasoning structures of the game. But the game is also structured to teach statistical reasoning. The web lecture explains the pedagogical background which integrates statistical reasoning with deductive, inductive, and inferential logic. The web lecture can be read online; but if you choose to print it, you will get about 17 pages of hard copy.
Web Lecture for Difference to Inference game
StatCenter. When you click the link below you will be able to log in as a guest to an Introductory Statistics class which is part of set of online learning resources called StatCenter. Once you log on as a guest and see the Main Menu, double click Interactive Learning. On the Interactive Learning page scroll down to Difference to Inference and double click.
The advantage of the StatCenter link is that it allows you to explore the full online statistics class into which the Difference to Inference game is embedded. You can see many other interactive features as well as some 1500 pages (when printed) of online text. To use the entire site fully, you will need Adobe Reader and Macromedia's Web player for Mac or PC. To go to Macromedia's download site, click Web Player for PC or Mac on the right hand panel of the Main Menu.
StatCenter at the University of Utah
The Difference to Inference game presents five visual patterns within a story which construes the patterns to be five candidate theories. Players engage a challenge requiring them to deduce how to design a two group study whose data might eliminate one or more the candidate theories. This simulates an important and rewarding aspect of science--deducing implications of competing theories and designing research to test those implications. Next, players must induce from the data they collect which theories, if any, are eliminated by the data. After conducting some number of such research studies players infer which theory is the best choice in the sense that it alone remains consistent with the known data. In short, players learn holistic, interrelated thinking processes (deduction, induction, and inference) for empirical theory testing.
Note that the structure of the game in no sense leads players to think about "proving a theory." Rather it requires players to choose a theory because it is the single theory among the five candidate theories which is most consistent with the data. This last point is important. The Difference to Inference game gives students experience which allows them to learn one important and deep structure of scientific thinking. They learn to think in terms of eliminating theories and not in terms of proving theories. Students learn to prefer theories which are consistent with data. Anyone who has tried to teach the point that science does not prove theories but rather that it seeks theories which are consistent with data knows that this way of thinking is very difficult to teach in a way which connects deeply to students' experience. Students typically come in to a class wanting to prove the truth of theories. Difference to Inference engages students in processes which structure their thoughts to eliminate theories on the basis of data.
In this and other ways, Difference to Inference is an example of new media interactive simulation which encourages discovery-based strategic learning. While the game does teach statistical and scientific conceptual content and jargon, its focus is more deeply oriented toward learning how to deduce research design from theory, how to use data inductively to eliminate theories, and how to choose a theory based on consistency with known data.
At the process level, the medium is the message. Old media teach students to learn receptive internal structures appropriate for processing old media. Computer simulations, in contrast, teach students to learn to structure their internal processes to relate to the structure of the computer program. This process learning offers a double edged challenge. One edge is promising because educators can use process learning to pass on culturally valued ways of thinking. The other edge is problematic because the structures of simulation programs (e.g., computer games) are frequently driven solely by profit with little consideration of the consequences of the structures that players must learn to succeed at the game.
Some qualifications. The distinction between new media (the use of computers and computer simulations to promote active learning and discovery of process) and old media (passive reception of information) is aimed at discussions of electronic media. It is not meant to imply that educators do not have important choices among what would otherwise be considered old media. For example, writing presupposes the use of some sort of media. And writing assignments at their best provoke active discovery on the part of students; in fact, I believe writing is one of the finest and most active discovery processes we have available. Writing is among the oldest uses of media; and I do not mean to discount it by my old versus new media distinction. Nor do I want to imply by my focus on computer simulations that other educational processes such as collaborative learning, service learning, the Socratic method and so on can't be active discovery processes.
What I do want to say is that among the electronic media, computers have introduced options (new forms of media) which teachers can use to great educational advantage because the new media allow them to teach the principles and deep structures of their disciplines. In the context of computers and electronic information then, the new versus old media distinction is a useful short hand.
Summary. Whatever the educational activity might be (quietly listening to a lecture, actively working in the the community in service learning, writing an essay, watching television, or using a computer simulation), students are learning process as well as content. Process learning is the structuring of our internal processes in ways which allow us to relate to external processes. In this paper I have argued for the careful consideration of the structure of the processes students must learn in order to succeed in their classes whatever the class format may be. As we enter a new millennium, our society is engaged in a lively public discussion of the effects of media content on the national character. I believe it is crucial to expand this discussion to the kinds of internal processes which various forms of media encourage. The Difference to Inference game is one concrete example of what I mean by a computer simulation game whose structure provokes students to learn to structure their thinking in useful ways.
Every process proceeds in accordance with its structure; and, through process learning, humans proceed in accordance with their learned internal structures. Whatever media they use in teaching, educators have a profound influence on how their students proceed through life.
Brown, MF. Wildcat World: Simulation programs for teaching basic concepts in psychological science. Behavior Research, Methods, Instruments, & Computers. 1999, 31 (1), 14-18.
Garland, A. The Beach. Penguin Putnam, 139, New York, NY, 1998.
Judkins, K. Interactive animation in medical education. Journal of Information Technology in Medicine. http://www.J-ITM.com. (2000)
Squire, LR, B Knowlton and G Musen. The structure and organization of memory. Annual Review of Psychology. 1993 44: 453-495.
Martin RM and AC Reese. Computer assisted instruction as a component of a comprehensive curriculum in medical ethics. Journal of Information Technology in Medicine. http://www.J-ITM.com. (2000)
Mayer, RE and RB Anderson. Animations need narrations: An experimental test of a dual-coding hypothesis. Journal of Educational Psychology. 1991, 83 (4), 483-490.
Roediger, HL and KB McDermott. Implicit memory in normal human subjects. In F. Boller & J. Grafman (Eds.), Handbook of Neuropsychology. Vol. 8. (pp. 63-131). Amsterdam: Elsevier, 1993.
Shiffrin, RM and W Schneider. Controlled and automatic human information processing: II Perceptual learning, automatic attending, and a general theory. Psychological Review. 1977, 84, 127-190.
Washburn, DA. Distinguishing interpretation from fact (DIFF): A computerized drill for methodology courses. Behavior Research, Methods, Instruments, & Computers. 1999, 31 (1), 3-6.