Assuming you have your driver's license, think back to when you first learned how to drive. What were the stages that you went through? Did you take a class (e.g., Driver's Ed)? Did your parent take you to an abandoned country road and turn over the wheel? Did you learn to drive a car with a manual or automatic transmission? (Lawyers may object to the next couple of questions because I might be "leading the witness.") In the first few months behind the wheel, were you allowed to listen to the radio? Could you carry on a conversation and drive at the same time? Did you talk to yourself when trying to recall which pedal was the gas or which gear you were in?
Learning to drive is complex because it is a mixture of motor learning (e.g., when to disengage the gas, engage the clutch, and shift gears) and verbal learning (e.g., the traffic laws). After several years of practice, driving becomes second nature. How, then, did we go from a nervous teenage driver to an expert on the road? Acquiring this complex skill requires that we traverse several stages of development.
The Three Stooges, er...Stages!
Acquiring a motor task of sufficient complexity must undergo three stages [1]. An example of a motor task might be learning to serve overhand in volleyball or learning the breaststroke. These tasks are complex because the person must synchronize the timing of various muscle groups. When a novice begins to learn how to serve overhand, the first stage, called the cognitive stage, is best described as verbal. The person learning the task benefits from hearing a verbal articulation of the steps needed to complete the task. The learner might even recite the steps to themselves while practicing. Then the learner transitions to the second stage, the associative stage, where some of the motor subroutines become more fluid. The individual commits fewer errors and relies less on verbal articulation. The final stage, the autonomous stage, is when performance is nearly error free and completely fluid. You know that the learner has entered the autonomous stage when she can now do the task and carry on a conversation. This indicates that a verbal representation of the task is no longer needed and does not interfere with performance.Given its usefulness in describing the development process for learning motor tasks, this 3-stage framework was adapted to describe how one goes about acquiring a complex cognitive skill [2]. Examples of complex cognitive skills are learning multi-column addition or learning how to balance a checkbook. Like a motor task, the acquisition of a cognitive skill is theorized to undergo three stages. The first stage is the declarative stage where information is represented as declarative chunks. Like the associative stage, the declarative stage can be articulated verbally, and the problem solver is very deliberate when attempting to practice the skill. The second stage, the knowledge compilation stage, takes place when the declarative chunks are "compiled" into procedural representations. Again, there are fewer errors when an individual reaches the second stage, and the problem solver relies less on verbally stating the rules. The final stage, the procedural stage, is similar to the autonomous stage in that all of the declarative chunks have been successfully converted over to procedural rules. Performance is smooth and much faster than the first two stages.
The mapping between the two theoretical frameworks can be summarized as follows:
Steps or Waves?
I've described both frameworks in terms of discrete stages that transition from one stage to the next. This is a step-wise theory of development, as represented in Figure 1. Is this an accurate depiction of how we acquire a complex skill? |
| Figure 1: A step-wise, schematic representation of development. |
While this looks good on paper, life is not so simple. Stages of development are rarely discrete [3]. Instead, there can be forward progress on one day, but then a regression back to the old way of doing things on a different day. This would be more like an overlapping set of functions, as represented in Figure 2.
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| Figure 2: A schematic representation of discontinuous development. |
A good example of the contrast between the step vs. wave model of development is watching kids learn how to add. At first, their performance on this task is heavily dependent on a physical representation of the number system. In other words, kids like to add by counting their fingers. If I ask a child, "What is three plus four?", one strategy he could use is to start counting, using his fingers as placeholders:
1, 2, 3 [holds up three fingers]1, 2, 3, 4 [holds up an additional four fingers][Goes back to the beginning and counts all of the raised fingers] 1, 2, 3, 4, 5, 6, 7Three plus four is seven!If kids do this enough, they begin to realize that they can jump start the counting by holding up three fingers and start the counting from there:
4, 5, 6, 7 [holds up another finger for each new number]Three plus four is seven!But when we up the ante and give the child a more difficult problem (e.g., one that goes beyond ten), he may fall back to his first strategy or come up with an entirely different strategy altogether.
A similar observation can be made in the driving example. When traffic is normal, we might be motoring along with no problems (i.e., Stage 2). But then something unexpected happens, and we suddenly find ourselves needing to turn off the radio or interrupt a conversation so we can focus on the current situation (i.e., regress back to Stage 1).
The STEM Connection
Take a minute to solve the following problem. While you are working through each step, keep track of what is currently in your working memory and where you must guide your attention. For bonus points, see if you can supply a mathematical justification for each step.
614
438
+ 683
The goal of this little exercise is twofold. First, I want to simulate what it was like to be a novice back in Stage 1. As a novice, most of your knowledge is stored declaratively, so that means you need to think about what to do in terms of the verbalizable chunks of information stored in long-term memory. Second, I also wanted interrupt your pre-compiled procedures for this task. You have been doing multi-column addition for so long that you have probably automatized the steps. That means you might not have access to those declarative representations anymore. Asking for a justification is my attempt to get you to "un-compile" your knowledge.
To teach a complex cognitive skill, it is informative to try and answer the following questions:
- What is my current goal?
- Which pieces of information should I focus on?
- How did I know which action to take?
- What information can I ignore after I am done with this step?
Share and Enjoy!
Dr. Bob
For More Information
[1] Fitts, P. M. (1964). Perceptual-motor skill learning. Categories of human learning, 47, 381-391.[2] Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological review, 89(4), 369.
[3] Siegler, R. S. (1996). Emerging minds: The process of change in children's thinking. Oxford University Press.
