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Research Clusters

We previously organized our members in clusters to bring more focused groups of researchers together to help develop the theoretical framework, to hear and critique individual research projects and new research proposals, to consider broad instructional principles that capture the results of research within and outside the PSLC, and to develop sections of the PSLC wiki. During the first four years of the PSLC, we had 3 research clusters, listed below

• Interactive communication
• Coordinative learning
• Fluency & refinement

These groups have functioned well in driving theoretical development, in establishing shared research themes, and in promoting research collaborations. A valuable cross-fertilization of ideas occurs as investigators consider other perspectives and work with others in a different cluster. Such cross-fertilization has resulted in the exploration of center-wide research questions like the assistance hypothesis raised above.

We have expanded into research thrusts that are natural extensions of our research agenda and which are important for the broader understanding of learning. We increasingly have found our empirical and theoretical analyses to border on related issues of learner factors (motivation, affect, beliefs) and social factors. More information on the current thrusts can be found on the PSLC theoretical wiki.

Slides from Sept 19, Ken & Kurt's talk can be found here: robust-learning-theory31.ppt

A video from Ken & Tom's talk on 11-28 is also available (if your browser does not support asx file try this link).

Theoretical Foundations

This section sketches the theoretical foundations of the PSLC. The first section begins by reviewing the rather rich history of theory-building that is unique to Pittsburgh. The second section discusses what kind of theory is feasible for the PSLC to develop. The third section introduces some key theoretical terms that will be used later in describing the individual research efforts and integrating their results. The fourth section highlights the theory's novel aspects, its likely scientific merit and broad impact.

The Pittsburgh theoretical tradition

A critical part of the Pittsburgh tradition is cognitive science theory and especially computational theories of human information processing (e.g., Newell, 1990; VanLehn, 1991; Anderson, 1993) and related theories of artificial intelligence and machine learning (e.g., Mitchell, 1997). Indeed, the Pittsburgh tradition is a famous example of bi-directional and multi-direction payoffs that we are proud to continue. For instance, computation models of cognition, such as ACT-R (Anderson, 1993); CAPS (Just & Carpenter, 1992) and others are a direct outgrowth of the Newell and Simon tradition (Newell & Simon, 1972; Newell, 1990) and is a part of the theoretical basis of many PSLC researchers. These same studies of human information processing led to major advances in computer science, including state-space search, theorem proving, planning, constraint satisfaction, natural language processing, machine learning, artificial neural networks and many others. In recent years, computational models of cognition have formed a bridge between neuroimaging results and cognitive experimentation. Cognitive models also played a role in the development of intelligent tutoring systems, which in turn form a bridge between psychology and technology on the one hand, and classroom social and meta-cognitive studies on the other. Figure 1 depicts the multi-direction payoffs of the Pittsburgh tradition that we expect to continue.

Figure 1 Multi-direction payoffs of the Pittsburgh tradition

Although the research of the PSLC will be based on existing theory, it will extend and create new theory. Learning in schools and colleges is a rich and complex phenomenon that centrally involves the nature of human cognition, but is also critically influenced by the social context within and outside the classroom, and that needs to be more strongly incorporated into existing theory. Although the PSLC will be open to a variety of theoretical perspectives and enriched thereby, the PSLC will have a theoretical focus that comes from a strong history of theory development in Pittsburgh and from natural affordances of the LearnLab courses and resources (e.g., intelligent tutoring systems, knowledge-coded and event-based student learning data).

What kind of theory is feasible?

Although one can formulate precise computational or mathematical theories of narrowly defined phenomena in human learning, no such theory exists that spans all the factors that contribute robust learning. Nonetheless, there are two views on the feasibility of obtaining such a theory. Allen Newell held that a precise computational theory of cognition was indeed possible; his Unified Theories of Cognition (Newell, 1990) sketched some of the properties such a theory would have. Herbert Simon held that such a theory was probably not feasible anytime soon, but an equally good type of theory was near at hand: a set of theoretic concepts that scientists can use in explanations of phenomena. For instance, given a set of concepts such as "item," "attention" and "strength," scientists can generate explanations such as "Practicing an item increases its strength so that recalling it requires less attention, thus allowing…" If we are going to have a broad theory at this point in PSLC, we must start with a Simon style conceptual theory and develop more narrow computational theories in specific areas as feasible.

Simon observed that most theorizing in psychology already consists of combining existing concepts and occasionally inventing new ones. However, psychologists generally do not try hard to economize on the terms and concepts used in their field. Yet parsimony and simplicity are important standards of any theory. In particular, the PSLC's conceptual theory should be simple and parsimonious. Thus, the main difference between the standard practice in psychology and PSLC theoretical practice is that the PSLC deliberately economizes on theoretical concepts. We intend to use center-mode power to encourage members to be more collaborative in their theorizing and to put more weight on integration with other member's theory when devising their own theoretical explanations.

Initial Theoretical Concepts of Robust Learning

This section presents our current set of theoretical concepts. It is merely defines them without trying to connect them to our other work, and to the PSLC empirical studies in particular. Technical terms are italicized.

We use robust learning to refer to an outcome, that is, a desirable result of instruction. As mentioned earlier, learning is robust if it meets traditional 3 criteria: (1) the knowledge or skill is retained for long periods of time; (2) it transfers, that is, it can be used in situations that differ significantly from the situations present during instruction; (3) it accelerates future learning.

Figure 2 A taxonomy of robust learning processes. P1 through P8 are place-holders for specific learning processes.

Robust learning processes are cognitive processes that operate during instruction and cause robust learning. There are many robust learning processes, and part of the theory's job is to formulate a useful taxonomy for them. The current taxonomy is illustrated in Figure 2 and described below:

• Sense-making. These are cognitive processes wherein students try to understand the instruction or engage in higher-level thinking to create knowledge independent of instruction. We distinguish two types of sense-making processing.
  
  • Co-training: When students go beyond direct instructional feedback to learn on their own by integrating results more multiple input sources, representations, or reasoning strategies, we say they are engaged in co-training. The term is borrowed from a celebrated result in machine learning (Blum & Mitchell, 1998), but we are using it in a more general way to include multiple representations and strategies not just multiple input sources.
  • Dialogue: When the student takes turns with another agent, they share initiative during the instruction, and may explore an idea at arbitrary depth then we say they are engaged in dialogue. We mean to include natural language dialogues between a student and a peer or a tutor as well as other non-verbal (e.g., computer interface mediated) forms of dialogue.
• Foundational skill building. Some knowledge and skill must be mastered in order to provide a foundation for subsequent learning. The learning processes involved in obtaining such mastery appear to be somewhat different than those involved in obtaining an initial understanding of the knowledge or skill.
  • Refinement: These processes are responsible for making modifications to the knowledge itself and more importantly, to refining the conditions under which the knowledge should be accessible. In particular, students should associate the knowledge with deep features rather than shallow ones.
  • Fluency: Cognitive processes that achieve fluency or automaticity are engaged at all times when learning a piece knowledge, but as the knowledge becomes well-understood and its information content is not changing much, these processes continue to act, leading not only to correct performance, but eventually to fast and effortless performance. Part of the study of fluency-building processes is determining how they enable further learning. Although it is widely believed that mastery of the parts facilitates more efficient understanding of the whole, it is not clear exactly how this acceleration works.

Most robust learning processes are controlled by the student. No matter what kind of instruction is given to students, they can usually find a way to get through it without learning. Thus, part of understanding what is going on during instruction is understanding the student's self-regulative or metacognitive strategies. Thus, all these taxonomic categories involve studying processes that are a mixture of cognitive and metacognitive processing. We tend to think of the sense-making processes as having a higher degree of metacognitive involvement than the foundational skill building processes, but that remains to be seen.

We assume that learning results from the acquisition of knowledge (and skills, which we consider a subclass of knowledge), and that knowledge is decomposable into a very large number of small knowledge components. Many knowledge components are abstract, in that they can be applied by the student in many situations. For instance, a word's pronunciation is a knowledge component, and knowing it allows the student to say the word on many occasions.

A knowledge event is a time interval in the life of the student, usually lasting a few seconds or a minute, wherein the student applies or constructs a knowledge component. For instance, the following are all knowledge events involving the same geometric knowledge component:

Figure 3 Supplementary angles defintion including an example.

• reading a definition of supplementary angles, such as the one at the top of Figure 3.
• studying an example of supplementary angles, such as the one at the bottom of Figure 3.
• using supplementary angles in a proof
• explaining supplementary angles to another student
• incorrectly selecting a supplementary angle pair from set of angle pairs, getting feedback from a tutor, and then correctly selecting the supplementary pair.
• Starting to write a definition of supplementary angles, realizing that one is uncertain of the distinction between supplementary angles and complementary angles, looking supplementary angles up in the textbook, and writing a correct definition for supplementary angles.

A single knowledge event often mixes application, construction and/or refinement of the knowledge component.

The PSLC is primarily concerned with learning as it occurs in instructional settings with long-term implications for life and future academic success. In instructional settings, knowledge events often come in one or more of three forms 1) a verbal description (e.g., definition, rule, or principle) of a knowledge component, 2) an example of a knowledge component's applications, or 3) an opportunity to practice a knowledge component's application. This three-part distinction is an important refinement of the well-known explicit vs. implicit learning distinction (Dienes & Perner, 1999; Reber, 1967). The sole source of explicit learning is verbal description, whereas implicit learning can occur during either an example or a practice opportunity.

Although a knowledge component is a piece of information, and can exist anywhere information does (e.g., on a page; in a computer; in a human brain; in a conversation), when it is stored in a human brain, the probability of successfully recalling it is roughly proportional to the strength of the knowledge component's encoding in memory, and the feature validity of the way in which it is encoded. The feature validity of a knowledge component measures how well the features associated with the mental representation of the knowledge component match the features present during all situations where the component should be recalled. Strength is roughly proportionally to the number of times an encoding of a knowledge component was accessed and how recently it was accessed.

These two concepts, strength and feature validity, are meant to be broad and yet consistent with many lower-level theories of human memory, attention, reasoning, and problem solving. They are clearly only a crude theory of memory, but they should suffice for our purposes. Just as chemistry theory can be built on physics theory or mechanics built on relativity theory, we may want to link robust learning theory to such more detailed cognitive and neuro-cognitive theories. However, just as chemistry and mechanics theory are necessary in their own right, so to is robust learning theory. Lower level computational and neuro-biological theories alone are not sufficient to yield understanding of higher-level learning and instruction.

Both sense-making and fundamental skills building can lead to robust learning. That is, they can increase retention, transfer and acceleration of future learning. In order to exercise the terminology and to preview some of the explanations that accompany specific studies, let us consider first how each process can cause robust learning.

Sense-making can yield robust learning: 1) by allowing students to apply domain fundamentals to re-derive partially forgotten knowledge at long retention intervals, 2) by providing conceptual understanding that can be adapted or transferred to novel situations, 3) by allowing students to more quickly learn new material by having well-practiced meta-cognitive strategies (like systematic discovery strategies) to make sense of it and learn on their own. Although all three pathways to robust learning-rederivation, adaptation and self-supervised learning-can be used by individual learners, we hypothesize that they can be significantly enhanced through certain collaborative processes, including instructional dialogues and peer collaboration.

Foundation-building activities involve practice with attention to appropriate deep features and to the point of fluent execution. This can yield robust learning by allowing students 1) to develop strong, well-practiced mental connections that survive long retention intervals, 2) to encode and represent instructional situations in terms of well-learned and general features that support transfer to novel future situations, 3) to have acquired connections to a level of automaticity that reduces cognitive load during new learning, leaving "headroom" to apply sense-making strategies that accelerate new learning. In contrast to the three pathways of the sense-making path, which are primarily meta-cognitive or social, these three mechanisms, strengthening, deep feature perception and headroom, here are primarily cognitive.

Novelty, scientific merit and broad impact

The novelty of this kind of theory does not lie in the theoretical concepts themselves - we are building off of past research and theoretical developments. What is new is the attempt to describe a rather diverse set of phenomena and interpretations in the same terms. Whether it has been done accurately remains to be seen, as most of the predictions have not been tested yet.

The scientific merit of the PSLC theory also remains to be determined. We believe the theory can meet standards for parsimony, and it can both explain observations and predict them. Because it has been constructed to cover a large variety of studies, including all those done by the PSLC, it should be quite general. However, a huge amount of work remains before we are satisfied with the scientific merit of the theory. In particular, we would like the theory to be able to explain the details of individual studies but to remain parsimonious and simple. It is not clear how far we can push this embryonic theory while still maintaining its chief property, which is that it covers all studies of robust learning.

Because sense making and foundational skill building are the top levels of our taxonomy of robust learning processes, we hope to have broad impact on the "education wars" mentioned earlier. Debates in the "education wars" tend to contrast a traditional focus on drill and practice of basic skills versus a reform effort to provide more constructive experiences toward conceptual understanding and higher level thinking. Both sides of the debate would agree that what we call robust learning is the goal for student learning, but each promotes student learning in restricted ways that fail to produce robust learning.

Although there are important non-scientific dimensions to the educational wars, there is an important scientific issue that can and should be addressed by the science of learning. The education wars mistakenly set in opposition two paths to robust learning that, in fact, are complementary and-in our theoretical perspective-essentially interwoven with one another. In our theory of robust learning we refer to these as the sense-making processes and the foundation skill building processes . Our theoretical starting point is a broad hypothesis that robust learning requires both sense-making and foundation-building. Again, this is something that most the education warriors agree on, but they differ on the relative importance each. Our theory is intended to show how and when these 2 kinds of processes are important both for robust learning and for each other's operation. This is a key scientific issue that a science of learning can and should address in order to adequately inform the ongoing debate.