Spanning seven orders of magnitude: a challenge for cognitive modeling.

1. Introduction

The struggle of Psychology has always been to say things of significance to the human experience that have a rigorous scientific foundation. The enormity of human experience and our strong preconceptions about that experience have made this a very difficult task. Nonetheless, among the things we want a science of cognition to address are education, training, and behavioral change. How can we arrange for experiences to make ourselves, our children, or others more capable people? Certainly, the modem, rapidly changing, technological society has increased the need to acquire new competences. This paper is concerned with the issue of how a science of cognition can address both the learning of formal, academic competences like high-school mathematics and the learning of practical, cognitive competences like air-traffic control.

The goal of effective education illustrates the dilemma of grounding significance in rigorous science. Significant changes in human potential take at least 100 hours to achieve, approximately the time investment required for a semester course. Cognitive psychologists are often concerned with effects as small as ten milliseconds. Ten milliseconds and 100 hours are seven (actually 7.556) orders of magnitude apart. This paper will argue for the Decomposition Thesis that the learning which takes place over a 100 hours can be decomposed into learning events involving small units of knowledge and occupying brief periods of cognition. Some might view the Decomposition Thesis as obviously true but there are others (Shepard, 1991) who regard it as obviously false. An alternative hypothesis is that, rather than gradual changes in small units of knowledge, learning depends on abrupt conceptual reorganizations of knowledge. In different theories such conceptual reorganizations can vary in their form from shifts of problem-solving strategy to moments of insight when large bodies of knowledge become transformed. Siegler (1996) has referred to this latter viewpoint as the theory of the "immaculate transition."

Even if the Decomposition Thesis is correct it leaves open the relevance of the 10 ms level. Is there any reason to believe that learning can be improved by paying attention to events that are measured in tens of milliseconds? Throughout science there are appropriate levels of analysis for applications. One does not design bridges using quantum mechanics (nor would one want to design education at this level). A recent panel of the National Research Council (Bransford, Brown & Cocking, 1999) was put together to address the implications of the science of learning for education. While their report does contain some discussion of biological factors it contains no discussion of events taking place over periods of 10s of milliseconds. The smallest scale events discussed took at least 10 seconds to occur. The neglect did not reflect a conscious decision on the part of the panel that such factors were irrelevant. Rather, it reflected the presupposition of those who constituted the panel that such factors could not be relevant and so were not represented on the panel. It also reflects a frequent practice in cognitive science approaches to education to begin with events on the order of 10 seconds and work upwards. This paper raises the question of whether there is a rule for events on the order of 10 milliseconds.

The paper will discuss the evidence for the Relevance Thesis, that the microstructure of cognition is relevant to educational issues. Support of a sort for this thesis can be gained by analogy to medicine where molecular biology has become increasingly important and where fine-grained measurements serve important diagnostic functions. I will review examples that show that fine-grained temporal aspects of cognition are important both to learning and to the diagnosis of learning. However, I can only point to a precious few cases where learning has been positively impacted by paying attention to the fine-grained temporal structure of cognition. This is because so little effort has been made to utilize fine-grained temporal information.

One reason for the neglect of fine-grained temporal data are technical. It has been very difficult to gather fine-grained temporal data to guide educational interventions and it has been intractable to trace out the consequences of such fine-grained information for instruction. The technical barriers to gathering fine-grained temporal data are falling as improved methods are becoming available for speech recognition, machine vision, collection of eye-movement data, and other ways of getting high-density measurements of students. However, collecting such fine-grained data are only part of the problem; one also has to find a way to use them. This paper will discuss the Modeling Thesis, which is the claim that cognitive modeling can solve the technical barrier of tracing out the consequences of such fine-grained information for instruction.

Cognitive modeling depends on the use of cognitive architectures. Cognitive architectures not only allow us to model the fine-grained temporal structure of cognition, but they also allow us to span parts of cognition that have traditionally been treated as separate in cognitive psychology. Educational applications do not respect the traditional divisions in cognitive psychology. For instance, high-school mathematics involves reading and language processing (for processing of instruction, mathematical expressions, and word problems), spatial processing (for processing of graphs and diagrams), memory (for formula and theorems), problem solving, reasoning, and skill acquisition. To bring all of these aspects together in a cognitive model one needs a theory of the cognitive architecture (Newell, 1990). A cognitive architecture both specifies what is constant across these many domains and how the components from these various domains are integrated. A number of cognitive architectures have been used for education or training purposes including Soar (Newell, 1990), Cognet (Zachary, LeMentec & Ryder, 1996), and our own ACT-R (Anderson & Lebiere, 1998).

In summary, this paper will discuss three propositions of successively greater specificity. The first is the Decomposition Thesis that learning on the large scale is composed out of learning on the small scale. The second is the Relevance Thesis that greater educational effectiveness can be achieved by paying attention to fine-grained temporal detail. The third is the Modeling Thesis that these gains can be achieved by modeling cognition within a cognitive architecture. While it would be convenient rhetorically if one could simply argue that each proposition is true or false (and simpler yet if one could argue for the same conclusion to all three propositions), the current state of knowledge does not allow for such simple conclusions. To appropriately qualify our conclusions requires that we articulate the different time scales at which cognition occurs. Newell (1990) proposed such an articulation that the next section of the paper describes.

2. Newell's bands of cognition

Table 1 reproduces Newell's rendition of the four bands of cognition--the Biological, the Cognitive, the Rational, and the Social. As the table indicates each successive band captures the human experience at roughly 3 orders of magnitude greater than the previous. Ten millisecond effects are at the upper level of Newell's Biological Band while educational effects of consequence are firmly in his Social Band. Newell thought a theory of cognitive architecture was most relevant to the Cognitive Band. Newell thought that issues of cognitive architecture became relatively unimportant at the Rational Band and were completely irrelevant at the Social Band. Nevertheless, this paper will argue that fine-grained temporal factors at the Biological Band do influence higher-level outcomes and that education can be made more effective by paying attention to the lower level.

Bruer (1998) has argued that trying to link biology to education would be a "bridge too far." He suggests that cognitive psychology serves as an "island" to link research on the brain with research on instruction; that is, there should be one bridge from biology to cognitive psychology and another bridge from cognitive psychology to education. His discussion is really concerned with the choice between psychological and biological explanations and not with time scales. Most of what he describes as cognitive psychology would be situated in the upper end of the Newell's Biological Band, the Cognitive Band, and the lower end of the Rational Band. It certainly includes simple laboratory tasks, where 10 millisecond effects are measured. Thus, in part his argument depends on the plausibility of building a bridge from 10 msec effects to complex educational outcomes. Without taking a stance on whether a bridge from the discipline of biology to the discipline of education is a bridge too far, this paper will consider the issues involved in bridging the time scale required for his cognitive psychology-to-education bridge.

The paper will examine the plausibility of three "bridges" of successively longer spans. It will first consider spanning the 4 orders of magnitude in going from what are called unit tasks (the top end of Newell's Cognitive Band, taking on the order of 10 seconds) to educational outcome in courses taking on the order of 100 hours (a "long" bridge). Then the paper will discuss how these unit tasks can be broken down into primitive actions (Newell's Deliberate Acts) taking hundreds of milliseconds and assess whether instruction can be enhanced by paying attention to these primitive actions (a "longer" bridge). Then the paper will show how parallel, subsymbolic processes control 10 millisecond differences in these primitive actions and consider whether differences in these subsymbolic processes have significant impact for educational achievement (the "longest" bridge). The paper will show that the Decomposition Thesis has strong support all the way down. The existing evidence for the Relevance Thesis weakens as we go down to the subsymbolic level. There remain technical barriers to establishing the Modeling Thesis below the unit-task level.

3. The long bridge: from unit tasks to instruction

Card, Moran and Newell (1983) noted that there was a strong tendency for people to decompose the performance of a task into unit tasks that took less than a minute to complete. People focus their attention on solving one of these unit tasks, ignoring for the moment the larger task structure. For instance in text editing, the editing of an entire page would be divided up into a set of tasks like inserting a new line or correcting a word. There is a similar unit-task division in academic tasks. For instance, students solving algebra equations tend to treat each transformation (rewriting) of the equation as a unit …