Cognition: Refined (Part II)

Winn continues by covering different views of schema:

  1. Memory structures: built over time as a result of interaction with the environment and colored by encoding and recall
  2. Abstractions: placeholders to be “instantiated by recall” (schema are general; images are specific)
  3. Dynamic structures: constantly changing through assimilation (bottom-up matching followed by top-down testing) or accommodation (schema tuning or schema creation through analogy)
  4. Context: activation to set context (ambiguous information is interpreted differently, depending on the context brought by the learner).

He then applies schema to three practical applications in educational technology:

  1. Creating materials which are isomorphic to the schema
    • As images
      • because pictures are encoded as images, OR
      • because pictures impose a structure and propositions about this structure are encoded
    • As structures – making the spatial structure reflect the semantic structure; the interesting research is that artificial visual boundaries override spatial proximity in recall tests
  2. Helping learners create structural schema (information mapping)
  3. Using schema to represent information in a computer (AI)

Winn then briefly discusses mental models which are broader than schema because models also specify causal actions–how changes in one part of the model affect other parts.


Symbolic learning & the grounding problem


Harnad, S. “The Symbol Grounding Problem.” Physica D 42 (1990). 335-346.


In a short paper, the authors attempt to define symbolism as a cognitive science but find that the theory fails due to the symbol grounding problem: that symbols are composed only of other symbols and thus self-referential.

They define 6 basic learning behaviors:

  1. discriminate
  2. manipulate
  3. identify
  4. describe
  5. produce descriptions
  6. respond to descriptions

which cognitive theory must explain. Examining the first and third behaviors, the authors propose a dual representation: iconic (symbol) and categorical (internal analog transforms). However, they admit one “prominent gap:” no mechanism to explain categorical  representations. The authors thus dismiss symbolism as a sole solution and turn to connectionism as a hybrid solution: “an intrisically dedicated symbol system…connected to nonsymbolic representations…via connectionist networks that extract the nonvariant features.”


The authors likely succeed for theorists but this was a little dense given my lack of background. I think I got the idea that a symbol (for example, a swastika) exists by itself and combined with “rules” (our prior learning and knowledge that the symbol has a recent association with the Nazi Party) to produce a composite symbol (loathing). I also took away that humans, especially in groups, are too complex to be semantically interpretable, and that connectionism (based not on symbols but on pattern activity in a multilayered network) may offer some answers.

The dual representation–iconic (symbol) and categorical (internal analog transforms)–seem to suggest a symbol paired with a real-world (our experience with/background on/knowledge of) event; however, the authors later define that as an interpretation. In addition, I’m not certain why the iconic representation is not symbolic as the authors state.

The conclusion makes sense (although this is classic Vygotsky–and connectionism seems like just another word for community): if a category is defined as a symbol (image) plus our experience with that symbol, I started to believe that all our knowledge is interconnected (within a single human) with past experiences–and agree that it may not be possible to model learning in a purely symbolic (i.e., no connection to the real world) fashion.

Instance-based and rule-based learning


Taatgen, Niels A. and Wallach, Dieter. “Whether Skill Acquisition is Rule or Instance Based is determined by the Structure of the Task.” Cognitive Science Quarterly: 2.2 (2002). 163 -204.


The traditional view of skill acquisition as “a gradual transition from behavior based on declarative rules in the form of examples and instruction towards general knowledge represented by procedural rules” is challenged by instance theory. While the latter seems to explain the inability of experts to verbalize rules, research on the directional asymmetry of rules seems to support the traditional importance of rules.

ACT-R’s instance-based architecture is based on 2 key arguments:

  • the strategy to use or the memory to retrieve is based on which has the highest expected gain (optimization)
  • declarative memory is activated (and filtered) by environmental demands and past experience (which has been encoded as production rules by procedural memory)

At the symbolic level of ACT-R, procedural rules are applied to declarative chunks which store information in a proposition; chunks are either new (perceptions) or created internally by prior knowledge/experience. Each rule contains a condition- and an action-part, and declarative items are pattern-matched to the condition and applied in the action. The subsymbolic level of ACT-R deals with the choice of which rule to apply according to Bayes’ Theorem (increases base-level activation each time it is retrieved and decays over time).

The article seems to imply that if instance-based learning fails (because the problem is too time-consuming–no discernible pattern), learners will attempt to derive some sort of rule. The authors argue that instance-based learning works best when the relationships between variables is very difficult; rule-based learning (simplified cases) is more successful with a large number of cases with obvious relationships.  The authors then test this hypothesis with two detailed experiments.

The results:

  • Previous research showed no learning through observation without direct rules (explicit relationships)
  • Subsequent research, indicated that exploratory participants did better than observers, but that observers could better verbalize and construct a causal model.
  • This research shows evidence of learning by observing even without rules; and participants seem better able to answer questions about old systems than new. Both results support instance-based learning.


ACT-R seems to offer tremendous explanatory power. However, instance theory seems related to the concept of expert (tacit?) knowledge:

  • know when to apply
  • gets better over time (more instances)
  • gets better with use
  • additive for community

Because production rules that propose new declarative rules are not accounted for in the ACT-R architecture, this “missing link” may be the elusive transfer element; the authors propose partial-matching in ACT-R retrieval as a solution.

In instance theory, encoding and retrieval seem more closely linked to temporal/spatial reality than to attention as the authors claim; however, the view of memory as evolving from algorithmic processing to memory-based processing succinctly describes expert knowledge.

The recommendations for design strategies seem profound:

  • Instance-based learning takes over from rule-based over time
  • Creating declarative rules is the most important (first) step
  • Analogy works best at the start but declines quickly
  • Declarative rule works well at start and persists
  • Instance continues to improve over time to become best

Conditions-based Theory

Ragan, Tillman J. and Smith, Patricia L. (2004) “Conditions Theory and Models for Designing Instruction.” In D. H. Jonassen (Ed.), Handbook of research on educational communications and technology. Mahwah, NJ: Lawrence Erlbaum Associates. 623-649.

The incredible value of this article is in so clearly summing up Gagnés work and relating it to other theories: learning outcomes vary across contents, contexts, and learners; distinctive cognitive processing demands can be supported by different methods, strategies, and conditions. An early discussion of the background for Gagné noted that instructional design effectiveness varied among rote learning, skill learning and problem solving; however, the authors express doubt in a hierarchy of skills (and report that aside from the intellectual category, Gagné later moved away from his original taxonomic chain).

Rule-using (intellectual) skills are stored in hierarchical structures: verbal learning stored as propositional networks or schemata; rules stored as “if…then” productions; problem-solving are interconnections of schemata and productions. Gagné differentiated problem-solving (and concept formation) from other types in that PBL does not include any portion of the solution in the problem itself. One of Gagné’s contributions was to tie external events or instruction to internal events of learning; the latter he suggested were most impacted by prior knowledge; manner of long-term encoding; and requirement for retrieval and transfer to new problems.

The article’s coverage of multiple additions to Gagne’s work was equally clear. Merrill’s Component Display Theory categorizes learning objectives as a performance level (remember, use, or find) and a content type (fact, concept, principle, or procedure). Five operations (based 4 memory structures: associative, episodic, image, and algorithmic) can be conducted on subject matter:

  1. identity (facts)
  2. inclusion (concepts)
  3. intersection (concepts)
  4. order (procedures)
  5. cause (principles)

Reigeluth’s Elaboration Theory proposes three structures: conceptual (parts, kinds, matrices); procedural (order, decision); and theoretical (descriptive, prescriptive). Smith and Ragan argue that a middle ground exists between instruction-supplied and learner-initiated events. Tennyson describes three storage processes (declarative, procedural, and conceptual) and three retrieval processes (differentiating, integrating, and creating). Declarative knowledge is stored as associative networks or schemata; procedural knowledge is related to intellectual skills; and contextual (is this the same as conceptual?) knowledge is related to problem-solving. Finally, Ellen Gagné contributes the idea that declarative knowledge can be represented by propositions, images, linear orderings, or schemata (composed of the first three, while procedural knowledge is represented as a production system.

After agreeing with the fundamental premises (of conditions-based theory, the article demonstrate the lack of a proven link between learning categories and external conditions:

  • competition may be superior when a task is simple, but cooperative goal structures are more effective in problem-solving
  • explicit organization affected achievement although sequence modification did not
  • punishment is more effective than reward for discrimination learning
  • introductory students benefited more from direct guidance while advanced students performed better with more opportunities for autonomy
  • novice learners need more explicit learning guidance in employing cognitive strategies

The call for additional research is apropos although the need for additional knowledge of the relationship between internal learner conditions and subsequent learning is complicated by the difficulty in determining those internal (private) conditions.

Rejection of PBL – Rejected

Kirschner, Paul, Sweller, John, and Clark, Richard. “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching.” Educational Psychologist 41.2 (2006): 75-86.
The authors’ extensive citations of research studies suggest their premise—that minimally-guided instruction doesn’t work—is based on data. In reality, the authors misrepresent constructivist theory and PBL, and they continuously commit logical fallacies. For example, the authors claim that the PBL approach implies “instructional guidance that provides or embeds learning strategies in instruction interferes” with learning; one sentence later, the actual PBL approach is described (the emphasis is mine): “large amounts of guidance…may impair later performance.” The real intent of the article is buried several paragraphs after the introduction: PBL is too difficult for teachers to implement.

In multiple illustrations, the authors discuss how experts perform: chess masters are better able than novices to reproduce board configurations of real games (the emphasis is mine) but not random ones; experts develop mental models and strategies through experience. These distinctions seem to prove the validity of using real problems. The argument that working memory cannot hold the large amount of information required for problem-construction and problem-solution may have validity but ignores a PBL goal of problem-construction as an end unto itself.

Pejorative and unsupported claims abound: PBL proceeds, “as though working memory does not exist;” constructivism believes that, “learning is idiosyncratic” which ignores the social component; PBL rejects, “instruction based on the facts, laws, principles and theories” of a discipline. At the same time, salient points are sufficiently interspersed as to give the article an aura of validity: content knowledge (of a discipline) is different from pedagogical content knowledge (how to teach the knowledge of a discipline); the behaviors and methods of experts are different from those of students; novice learners may need more guidance than accomplished learners.

The article attempts to paint PBL as a pure-discovery method when in fact, PBL is a collection of techniques. And the authors further beg the question by equating the rejection of Kolb’s LSI instrument as a rejection of learning styles. Despite these limitations, the authors actually provide an answer (although they probably did not intend to do so) in citing Kyllonen and Lajoie’s work: “‘strong treatments benefited less able learners and weaker treatments benefited more able learners.'” This finding, paired with the observation that the advantage of worked-examples, used as an exemplar of guided instruction, “disappears and then reverses as the learners’ expertise increases” argues that scaffolding from guided to unguided instruction provides not only a solid foundation for novices but also an open field of learning opportunities.

How do I remember? Let me count 3 ways.

I found the Gagné chapter pretty cool. I’d heard of the 9 events but didn’t realize the underpinnings of the 3 types of knowledge (in memory).

  1. Propositions are declarative and form into networks; they are composed of argument (general)-relation (narrower) pairs although it took me a while to “count” them correctly. What was interesting is that we remember them as ideas not as exact sentences–maybe because we take in the sentence and then adapt it to our schema based on our history. They are easier to acquire but slower to retrieve. Propositions are organized in hierarchies and underlie the ability to reproduce information.
  2. Productions are procedural and form into systems; they are composed of if (condition)-then (reaction) pairs and are more reactive with the environment. They are slower to acquire but faster to retrieve (automatic) because they don’t need to be brought back into short-term memory. Productions are organized into if-then pairs and underlie the ability to operate on information.
  3. Images are different from both and pack more information into a smaller space. Images are used to represent spatial information because of ST memory limits. Images are continuous (analog) while propositions (and procedures?) are discrete (digital).

Here are some things I questioned:

  • 45% correct if 2 ideas are in working memory at the same time vs. 35% if the 2 ideas are separated: doesn’t seem like a huge difference but is used to justify bringing recalled knowledge into short-term memory and immediately connecting it to new knowledge.
  • Declarative knowledge is useful for novel situations while procedural knowledge is important for familiar ones; this seems incongruous with Wiggins’ contention that PBL is best for new situations (or perhaps PBL builds declarative knowledge).
  • Images may be represented  in long-term memory as propositions or as images and propositions; they could be represented only as images (is there research on whether image recall is as fast as procedural recall?).


What the article doesn’t specify is the delay between memory formation and recall. One of the articles we read last week said short-term memory temporal capacity was 15 seconds, so if the delay was longer than 15 seconds, this phenomenon may apply to long-term as well as working memory.

On the surface this research would seem like a vindication for the  cognitive school with its emphasis on memory schema (although there’s nothing in constructivism that denies the important role of memory–only that memory is viewed through the lens of the individual’s culture and experience). Maybe I need to think of behaviorism as applicable to fundamental (physical) learning. So, we first have to learn a topic behaviorally (get the definitions down– sort of like the lower levels of Bloom’s taxonomy) before we can learn the same topic cognitively (see the patterns–the middle levels). And once we’ve spent enough years on the planet (20?), we have accumulated enough history and acculturation that we will (whether we want to or not) learn the same topic constructively (apply our own values which have formed by and over that period of time). For example, a 10 year old can learn historical dates but can’t learn (see) a pattern of colonialism from those dates; a 15 year old can learn (visualize) that pattern but can’t be horrified (or proud); a 20 year old, having grown up in a culture that prizes human rights, can learn to abhor a pattern of conquest (or, having grown up in a culture that values “manifest destiny,” can learn to rationalize war as a national imperative).