By: Doktor Prax Evad | Contributing AOJ journalist
Learning theories that center around cognition seem very appropriate to human learning and appear particularly useful when examining problem solving. Even some behaviorists attribute cognition as an important element of learning. E. C. Tolman (1948) believed that behavior was guided by purpose. Organisms selectively take in information from the environment and build up cognitive maps as they learn. From cognition learning and associated theories, such as schema theory, it can be hypothesized that cognitive maps or schema are enhanced by learner errors. The contribution of error making to learning is the subject of this paper. Parts of various theories are directly impacted by error making with respect to the learning process. These theories are identified and expounded upon with regard to error making; thereby, arriving at new theories or insights to previous theories.
Errors Relate New Information to Existing Schema by Specifying Differences
Encoding is an aspect of cognitive theory and memory that is directly impacted by a learner making errors during the learning process. “Encoding refers to the process of relating incoming information to concepts and ideas already in memory in such a way that the new material is more memorable. Left to their natural inclinations, humans will always try to make things meaningful, to fit some new experience into the fabric of what they already know.” (Driscoll, 2000, p. 91). Errors make new experiences more meaningful by relating differences between what already is in memory and providing guidance on what a thing is not. For example, suppose a child already has in memory that a dog has four legs and then encounters a horse. The child may refer to the horse as a dog. This error might be corrected by the parent causing the child to identify differences between a horse and a dog, such as size or a mane. The new definition of a horse now has greater meaning to the child.
The example given in the previous paragraph describing how errors lead to identified differences and similarities also relates to the theory of correlative subsumption. When defining subsumption Driscoll (2000) stated that “The principal way of adding information to cognitive structure, in Ausubel’s view, is to attach new ideas and details in a subordinate fashion to the anchoring ideas already present…More typical of the way most learning occurs, according to Ausubul, is correlative subsumption. This process refers to elaboration, extension, or modification of the previously learned concept or proposition by the subsumption of the incoming idea.” (p. 120). Part of cognitive structure is also what things are NOT. Differences are often more meaningful than similarities and making errors allows identifying differences. Interestingly, when engaged in a process where errors occur and a learner’s concept or result proves true, rather than in error, more confidence in the result and a stronger connection to the concept or result is made thanks to previous errors.
When existing schemata evolve to become more consistent with experience, then tuning has occurred. Rumelhart and Norman (1978) suggested that this process accounts for the minor schema modifications that come with new exemplars of concepts and principles. This indicates that errors help tune schema and are not only used by novices while instituting trial and error techniques, but are also used by experts to tune current schema.
In tuning schema, errors help assure that the new information added to your current schema is uniquely relevant to and suitable to the learner. Errors allow you to gather more information that more appropriately fits your schema than delivered reception, such as information delivered directly from a teacher. These errors are also the errors to which you may personally be prone, and therefore, need to learn. Dispositions and one’s unique schemas change how you will react to learning and new information. Errors assure that new information is customized to the learner’s disposition. “Encoding performance does not occur in a vacuum: perceptions are framed in context and result from a dynamic interaction between characteristics of the performance context and individual dispositions” (Iigen, 2000, p. 3).
Problem Solving Requires Exploration and Inherent Mistakes
Exploration is a technique of learning that has proven very effective and is particularly apt when problem solving is required. For novices, exploration is often accomplished through trial and error since without a base of knowledge it may be difficult to at first form specific goals and intentions. At the other extreme, experts perform exploration using a systematic approach where hypotheses are tested against expected and non-expected results (errors). “Systematic exploration is an optimal pattern of behavior that leads to the highest probability of successful task completion. The term systematic refers to the process in which a person forms goals and intentions based on hypotheses about how the task should be done. These hypotheses are tested in a logical manner and outcomes are evaluated in order to plan further behavior” (Van Der Linden, Sonnentag, Frese, & Van Dyck, 2001, p.190). Errors or mistakes in the learner’s hypotheses are expected as they progress through the process, and these errors force the learner to continuously reevaluate and sharpen their hypotheses. No other learning technique provides as much guidance as systematic exploration due to its nature of constantly evaluating mistakes and errors, as well as the (typically less frequent) successes.
Reception learning is essentially the same as what commonly occurs in expository instruction, where learners are told information rather than discovering it for themselves. Science textbooks, for example, state principles and provide examples of their applications. Errors in reception learning play a small role in achieving understanding. By contrast, discovery learning is accomplished where students derive understanding from their exploration, such as through experiments from which they derive the understanding of scientific principles. The benefits of discovery learning over receptive learning are based on the ability to make mistakes from which one can easily learn and the broader understanding inherent in testing your schema against unknown variables and conditions.
Guided Error Learning Compared To Exploration
Errors can be made intentionally as directed by instruction and as part of the learning process using a technique referred to as guided error learning. Guided error learning is not as effective as explorative learning that produces errors because the learner attributes guided errors to something that was supposed to happen. Since the error was intended, there is little surprise to focus learner attention and fewer opportunities to develop metacognitive skills. In addition, guided errors probably are not the same errors that a learner would naturally make, and therefore, are less applicable to the learner’s schema or tuning that schema.
Simulators and games offer an environment where guided error learning or explorative error learning can take place and where theory is closely connected to real-life experiences without fear of real-life consequences (Henry, 1997). For the reasons stated in the previous paragraph, simulators and games are better tools for learning if there are non-prescribed errors, which implies explorative error learning. While teaching classes at New York Power Authority using a power system simulator, I have observed the benefits of explorative error learning over guided error learning. The students were given labs to complete with guided errors included. The students had difficulty identifying why the errors were important and relating the errors to how they actual use the system. During free-time (explore the simulator program on your own) after a lesson, the students gained significant proficiency in using the program if I was available to answer the questions as they explored and made mistakes. Note that the students all had different questions using the computer in reference to the lesson previously provided. The differences indicate that they all have unique schema that are tuned with unique information; hence, explorative error learning was superior to guided error learning.
Simulation or games are good methods of teaching problem solving because they allow schema transfer through application, which is the next subject to be covered. Application is critical due to its explorative nature where one feels or finds their way to the solution by making mistakes. These mistakes or errors guide the learner to the solution keeping the learner on a proper path for that specific learner.
Invoking Relevant Schema
Errors make one raise the question, “why is an answer inappropriate?” and facilitate transfer or application of schema. It is crucial that schema not only be properly formed, but also that the proper schema are applied to new problems through a process known as transfer. Errors in explorative learning enhance the learner’s ability to invoke relevant schema in new situations. “Schema theory is more comprehensive than meaningful reception learning in being able to account for how learners bring to bear what they know on solving problems. But neither theory is focused particularly on how people learn when to use their knowledge. Although transfer may be a matter of invoking relevant schema, determining when a schema is relevant turns out to be no easy task.” (Driscoll, 2000, p.149) Perhaps, people learn when to use their knowledge under various schema based on errors indicating when the knowledge is inappropriate to the situation.
Working on problems or looking at problems from multiple angles with multiple examples helps students learn why mistakes are made and ultimately develop a proper schema for the problem type. “It is possible that when errors are present the performer has to create hypotheses about how to correct them and, thus, adopts a selective learning strategy. When errors are absent, there is no need to test hypotheses because the movement is effective (successful). Therefore, participants who do not make errors may adopt an unselective mode of learning by default.” (Maxwell, Masters, Kerr, & Weedon, 2001, p. 1052)
Errors and Motivation
Making errors can have a dubious effect on one’s motivation, which is also critical to the learning process. However, errors can be made with positive effects when the learner is placed in a positive learning environment since a learner understands they are to make mistakes in such an environment. It is important to let the learner know that such mistakes are expected and encouraged as part of the learning process. As an instructor, consider treating wrong answers as successes and expected outcomes during the learning process. At work when teaching a new employee to develop training material, the employee seems to do better over the several draft iterations when I warn them upfront that I will almost undoubtedly markup their drafts extensively while they learn our process and that this is to be expected. Since these mistakes are expected, they have less of an impact on motivation than in a non-learning environment.
Errors can help a learner become more motivated through increased attention. For example, task complexity or difficulty is a factor that influences selective attention. An indication to the learner of task complexity or difficulty is making mistakes or errors while working on the task. Selective attention helps take information from sensory memory and transfer it to working memory.
Striving to succeed and treating errors as motivational allows the learner to focus on achieving difficult answers. I refer to this concept as the obsession factor. When I am working on a task, such as installing software, I become more focused on my task as I encounter more problems (mistakes or errors in my schema). To tune my schema and adapt, I focus harder on the problem to overcome it. If a task is simple, less learning usually results due to less attention and less input of new information through errors to my schema. Beware of striving for unobtainable goals in learning or the learner will lose confidence and/or hit frustration. “When learners encounter instruction that makes no sense to them, it becomes an impossible task to call upon prior knowledge, because there is no way to judge what knowledge will be relevant.” (Driscoll, 2000, p.144)
Errors Give the Learner Confidence in the Correct Answer
Errors give the learner confidence in the correct answer by assuring that feedback is working properly. An example is the time I taught an energy management system computer course. The subject on which the learners performed worst was emergency rotating load shedding. This subject was taught in simulation mode but the simulation was not working properly and feedback was not given, such as a switch open symbol after opening a switch. Without this feedback, the learners had no idea whether they were doing tasks properly or improperly.
The trial and error technique works on the same principle of requiring feedback of errors or successes so that the learner has confidence in the correct answer. Illustration of this principle is shown in some of Thorndike’s research. Thorndike was particularly interested in discovering whether his animals could learn their tasks through imitation or observation (Kentridge, 2001). He compared the learning curves of cats who have been given the opportunity of observing others escaping from a box with those who had never seen the box being solved and found no differences in their rate of learning. He obtained the same null result with dogs and, even when he showed the animals methods of opening a box by placing their paws on the appropriate levers and so on, he found no improvement. He fell back on a much simpler trial and error explanation of learning. Occasionally quite by chance, an animal performs an action which frees it from the box. When the animal finds itself in the same position again it is more likely to perform the same action again.
Proper Feedback Is Critical to Learning from Errors
As alluded to in the previous section on confidence, proper feedback is critical to learning from errors. Errors without feedback are less instructive than errors with feedback. Feedback can be achieved through self monitoring or provided externally. Feedback has been found to be an important instructional variable in improving student achievement. Research by Clark and Dwyer (1998) shows that “in computer-assisted instruction, feedback is a very important external condition that can be manipulated to positively effect the learner’s performance…Kulhavy found feedback after incorrect response to be effective in facilitating learner achievement…When confidence is high in an error response, feedback acts as a strong corrective device, and the resulting facilitation tends to maintain itself over a retention interval” (p. 1).
Based on the separation between the error itself and the error consequence it is useful to differentiate between three types of error consequences as identified by Van Der Linden, Sonnetag, Frese, & Van Dyck (2001). First, negative consequences for direct goal attainment (e.g. errors that block further effective behavior or errors that destroy earlier constructive work). Second, non-effective actions: erroneous actions that do not have any direct effect at all (e.g. pushing non-active buttons or other worthless attempts). Finally, actions which are in essence wrong (do not lead to the intended goal) but might lead to insight in solving the task being performed (positive error consequence).
Note that errors can teach dysfunctional behavior if goals are specified incorrectly or with lack of precision and consequently reinforcers are applied. This theory is based upon Thorndike’s Law of Effect: “When a modifiable connection between a single situation and a response is made and is accompanied by a satisfying state of affairs, that connection’s strength is increased. When made and accompanied by an annoying state of affairs, its strength is decreased.” (1913, p. 4)
Suggested Additional Components to Improve My Errors Enhance Learning Theory
To improve my existing theory, a study of the weighted relationship between errors and successes would prove useful. This information would provide insight to the degree which errors influence learning. The analysis would need to be with regards to different types of learning, such as rote, problem solving, etc.
Another way to improve the theory would be to add a component on optimal angles from which to approach a problem. The optimal angles or contexts would need to address how errors interrelate from these various angles of attacking a single problem or performing a single task. I am curious to know if there is a non-linear increase in understanding based on a multiple angles approach.
Based on research performed by
others and anecdotal evidence of my own experiences, performing errors and
making mistakes during the learning process enhances a learner’s schema. Errors add additional information to the
schema that is tailored to the individual learner and more readily fits into or
adjusts their schema. Additionally,
errors can be a positive motivational factor by focusing selective attention in
the proper learning environment. Perhaps
the most important benefit of errors and mistakes is in the area of applying
relevant schema to new tasks and problems.
Errors make one raise the question, “why is an answer inappropriate?”
and facilitate transfer or application of schema.
Clark, K. & Dwyer, F. M. (1998). Effect of different types of computer-assisted feedback strategies on achievement and response confidence. International Journal of Instructional Media, 25, 55-63.
Driscoll, M. P. (2000). Psychology of learning for instruction (2nd ed.). Needham Heights, MA: Allyn and Bacon.
Henry, J. M. (1997). Gaming: A teaching strategy to enhance adult learning. The journal of continuing education in nursing, 28, 231-234.
Iigen, D. R. (2000). Bearing bad news: Reactions to negative performance feedback. Applied Psychology, 49, 550-566.
Ivancic, K. & Hesketh, B. (2000). Learning from errors in a driving simulation: Effects on driving skill and self-confidence. Ergonomics, 43, 1966-1984.
Kentridge, R. W. (2001) Operant conditioning and behaviorism – an historical outline. Paper was restructured from a lecture.
Maxwell, J. P., Masters, K. E., & Weedon, E. (2001). The implicit benefit of learning without errors. The quarterly journal of experimental psychology, 54A, 1049-1068.
Rumelhart, D. E., and Norman, D. A. (1978). Accretion, tuning and restructuring: Three modes of learning. In J. W. Cotton and R. L. Klatzky (Eds.), Semantic factors in cognition. Hillsdale, NJ: Erlbaum.
Thorndike, E. L. (1913). Educational psychology. Vol. II. The psychology of learning, New York: Teachers College, Columbia University.
Tolman, E. C. (1948). Cognitive maps in rats and men. Psychological review, 55, 189-208.
Van Der Linden, D., Sonnentag, S., Frese, M., & Van Dyck, C. (2001). Exploration strategies, performance, and error consequences when learning a complex computer task. Behaviour & Information Technology, 189-198.