Perceptual Learning Modules: Enhancing Expertise Through Information Extraction
Learning in educational settings emphasizes declarative and procedural knowledge. Traditionally, when we talk about learning, we are referring to declarative and procedural knowledge. Declarative knowledge is knowledge that can be stated, such as definitions, historical dates, ideas, rules, principles, theories, and so forth. Procedural knowledge is the ability to carry out sequences of actions to accomplish something, such as solving math problems, riding a bike, or cooking. To say you have learned something often means that you are either able to repeat that information back when asked or you are able successfully carry out the procedure that was taught.
Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning. In contrast to the literature on learning, scientific descriptions of expertise are dominated by PL effects. In describing their studies of master level performance in chess, Chase & Simon (1973) wrote: “It is no mistake of language for the chess master to say that he ‘sees’ the right move; and it is for good reason that students of complex problem solving are interested in perceptual processes.” (p. 387). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection.
Rapid, automatic pick-up of important patterns and relationships - including relations that are quite abstract - characterizes experts in many domains of human expertise. Experts tend to see at a glance what is relevant and what it is not. They tend to pick up relations that are invisible to novices and to extract information with low attentional load. Expertise is an interesting and relevant field of research to look at because experts have learned something special about their field beyond the declarative and procedural side that makes them faster and more efficient at processing information and solving problems. Specifically, experts are able to deal with information more efficiently and effectively than novices because they are able to “see” patterns and underlying structure in information.
These patterns are focused around a deep understanding of what information in a scene or a problem is relevant to the task at hand, and what is not. With lots of practice, experts learn to pay attention only to the bits of information that they need while ignoring the rest, and they also begin to see informational patterns that don’t pop out to novices. The important point here is not that experts know more than novices, but that they see problems differently.
In this article, we describe the relevance and promise of applications of perceptual learning (PL) to high-level cognitive domains. We focus on mathematics learning but we hope the relevance to other areas of learning will be obvious. Applying PL to such domains is a startling and exciting endeavor.
Defining Perceptual Learning
Perceptual learning is defined as experience- or practice-induced changes in the pickup of information. Eleanor Gibson, who pioneered the field of PL, defined it as “an increase in the ability to extract information from the environment, as a result of experience…” (1969, p. 3). In her 1969 book, Principles of Perceptual Learning and Development, Eleanor Gibson outlines three basic trends that characterize perceptual learning and development: increasing specificity of discrimination, optimization of attention, and increasing economy of information pickup. In plain English, that means that perceptual learning leads to an increased ability to decide what features are relevant and what are not, an optimal level of attention that is guided by the learner’s knowledge of what to look for, and increased speed and efficiency in identifying those key features.
These three trends can be summarized as discovery and fluency effects, where discovery is related to what features of information we attend to and fluency is related to the speed and manner of search (i.e. serial versus parallel) for those features. Table 1 summarizes some of the well-known information processing changes that can derive from PL. Kellman (2002) suggested that these can be divided into discovery and fluency effects. Discovery pertains to finding the features or relations relevant to learning some classification, whereas fluency refers to extracting information more quickly and automatically with practice.
| Characteristic | Description |
|---|---|
| Discovery | Finding relevant information in a domain |
| Fluency | Extracting information with ease and speed |
She described a number of particular ways in which information extraction improves, including both the discovery and fluency effects noted above. Of particular interest to Gibson was “…discovery of invariant properties which are in correspondence with physical variables” (Gibson, 1969, p. 81).
Assuming the relevance of PL to complex tasks, one might still wonder about symbolic domains such as mathematics. Mathematics might be thought to involve only declarative knowledge and procedures. There are inherently symbolic aspects of mathematical representations that cannot be apprehended via information “in the stimulus.” This is true, but it is also true that mathematical representations pose important information extraction requirements and challenges. Characteristic difficulties in mathematics learning may directly involve issues of discovery and fluency aspects of PL.
Moreover, in complex cognition it is important to realize that conceptual and procedural knowledge must work together with structure extraction. Both declarative and procedural knowledge depend on pattern recognition furnished by PL. Which facts and concepts apply to a given problem? Which procedures are relevant? How do we appropriately map parts of the given information into schemas or procedures?
Perceptual Learning Modules (PLMs)
Although perceptual learning seems to be the missing link between novices and experts, it’s a type of learning that has not been capitalized on in schools. The lack of PL techniques in instructional contexts owes not only to its neglect in learning research but also to the lack of suitable methods. The expert’s pattern extraction and fluency are thought to develop separately from formal instruction, as a result of experience. In our work, we implement PL principles in perceptual learning modules (PLMs).
Basically, the concept of our perceptual learning modules (PLMs) is to give participants the opportunity to interact with problems in a meaningful way without asking them to solve problems like in a traditional classroom. Although a full description is beyond our scope here, we mention some elements of PL interventions. Although we lack complete models of PL in complex tasks, it appears that information extraction abilities advance when the learner makes classifications and (in most cases) receives feedback. Digital technology makes possible many short trials and appropriate variation in short periods of time, allowing the potential to accelerate PL relative to less frequent or systematic exposure to structures in a domain.
Unlike conventional practice in solving problems, learners in PLMs typically discriminate patterns, compare structures, make classifications, or map structure across representations. In this short report, we summarize three applications of PLMs to mathematics learning, each highlighting a particular issue.
Examples of PLMs in Mathematics Learning
We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics.
Multi-Rep PLM
Mathematical representations are aimed at making concepts and relations accurate and efficient, but they pose complex decoding challenges for learners. Each representational type (e.g., a graph, or an equation) has its own structural features and depicts information in particular ways. Perceptual extraction of structure from individual representations and mapping across representations present learning hurdles that are not well addressed by ordinary instruction. We developed the Multi-Rep PLM to help middle and high school students develop pattern recognition and structure mapping with representations of linear functions, in graphs, equations, and word problems.
Students received a paper-and-pencil pretest and posttest containing two kinds of problems. Four problems required solving word problems involving linear functions. Eight translation problems involved presentation of a word problem, graph, or equation with the student being asked to translate the given target to a new representation -- specifically, to generate an appropriate graph or equation in response. There were four types of translation problem: equation to graph (EG), graph to equation (GE), word problem to equation (WE), and word problem to graph (WG).
Students in the PLM condition used a self-contained computer program that ran on a Windows platform with a point-and-click interface. The PLM consisted of short mapping trials, where students were presented with a target equation, graph, or word problem, and were asked to select among three possible choices for an equivalent representation depicting the same information. An example is shown in Figure 1. There were six types of mapping trials, comprising all possible pairs of word, equation, and graphical representations given as targets and choices. All equations were in the slope-intercept (y = mx + b) form. The program tracked responses and speed. Visual and auditory feedback followed each student response.
In a Control condition, students were asked to practice the same kinds of translation problems that appeared on the assessments. They were given packets with 32 problems including equal numbers of the four generation problem types, designed to closely resemble the translation problems on the assessments. Every time students completed a section of the practice packet, they were given an answer key to check their answers. The students used two class periods on two consecutive days to complete the pretest, the instructional intervention, and the posttest. On the first day, students completed a brief background questionnaire, the pretest, and began their learning intervention (either practice packets or PLM). On the second day, students completed their learning interventions and took the posttest.
Primary results for translation problems for the PLM and Control conditions are shown in Figure 2. There were no significant differences in pretest accuracy between the Control and PLM conditions, t(67) = 1.11, p = .27. There was a robust interaction of test by condition, F(1,66) = 21.17, indicating that the PLM group improved from pretest to posttest more than the control group.
These results, from two short sessions of PLM use, indicate that practice in mapping problems across multiple representations led to strong improvements on a transfer task - generating the correct equation or graph from a word problem, graph, or equation. In contrast, for the Control group, the translation task in the posttest was not one of transfer; it was the same task practiced during training. Pretest scores indicate that even in grade 12, the initial ability to generate correct equations and graphs is poor.
Algebraic Transformations PLM
One prediction of a PL approach is that it should be possible for a student to have relevant declarative and procedural knowledge in some domain and yet lack fluent information extraction skills. We tested this idea in work in algebra learning with students who had been instructed for half of a school year on the basic concepts and procedures for solving equations. The hypothesis was that despite reasonable student success in declarative and procedural learning, the “seeing” part of algebra is poorly addressed by ordinary methods and might be accelerated by a PL intervention focused on structures and transformations.
The PLM was tested on standard PCs using the Windows operating system in computer-equipped classrooms. The experiment was set up to assess the effects of PL techniques on learners’ speed and accuracy in recognizing algebraic transformations and the transfer of PL improvements in information extraction to algebra problem solving. A pretest was given on one day, followed by 2 days in which students worked on the PLM for 40 minutes per day. A post-test was administered the next day.
The PLM I am working with right now is called the Algebraic Transformations PLM, and its purpose is to help students understand the structure of equations and how terms can move without affecting the equality of both sides. In this particular module, each trial screen shows one complex equation and the student chooses from 4 options the correct legal transformation of that equation. They are not solving to find the value of any variables, but they do have to know and understand the rules of algebraic manipulations. As they complete the module, they advance through levels of mastery that are based on improvements in their accuracy and response times.
What is so remarkable about this module is that practice with the PLM actually cut students’ response times by two-thirds from pre- to post-test when solving algebra problems, even though they were mid-year algebra students who had been practicing solving problems for months. The other modules have shown similar improvements in accuracy related to multiple representations of linear relationships (translating between word problems, graphs, and equations) and to solving problems with fractions.
Linear Measurement PLM
In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving.
Limitations of Perceptual Learning
There are limits, however, to what perceptual learning can do, as well as to our knowledge of how much we can accomplish with technology like this. A hallmark of perceptual learning is that it is task-specific. So training on “seeing” solutions to algebra problems won’t help you with your chemistry homework (sorry). Also, perceptual learning is a process that most people can’t verbalize; even though we have evidence of significant improvement in processing information, our participants are not necessarily learning anything declarative or procedural. For these reasons, and many others, this technology will never replace real life teachers, tutors, and mentors.
There is no doubt that we need to learn declarative and procedural knowledge - we are only suggesting that perhaps a view of education that ignores the problem of “seeing” is too narrow.