by Roman Taraban, PHD, Texas Tech University
“Just Do It” has been a great slogan for selling athletic equipment and has also spawned some humorous spinoffs, like Bart Simpson’s “Can’t someone else just do it?” And is it not how we sometimes solve problems: “Don’t think, just do it?” Although just doing it (or getting someone else to do it) may have some visceral appeal, models for teaching argue against just doing it when it comes to solving problems.
One of the most influential problem-solving models is Polya’s (1957) 4-step model: i) understand the problem, ii) develop a plan, iii) carry out the plan, and iv) look back. On this model, solvers don’t “do it” until the 3rd step. What is really striking about this model is that it is mostly about critical thinking and metacognitive processing. The principles of understanding the problem, planning one’s approach to solving the problem, and reflecting on the solution after “doing it,” all require critical thinking and metacognition (Draeger, 2015). STEM disciplines have generally embraced the Polya model, suggesting that commitments to metacognitive thinking by researchers and instructors are widespread and well-entrenched. Two disciplines will be considered here to make that point: mathematics and engineering.
In a research study in mathematics, Carlson and Bloom (2005) collected and analyzed the problem solving behaviors of twelve expert mathematicians. The data showed that the mathematicians engaged in metacognitive behaviors and decisions that were organized within a general problem-solving framework consisting of Orienting, Planning, Executing, and Checking. One of the phases, Executing, is where one “does it” – the others are more metacognitive. Researchers have developed comparable models for problem-solving in engineering. These models preface equation-crunching with understanding the problem and planning a solution, and follow up with reflection on the solution. This is exemplified in the six-step McMaster model: Engage, Define the Stated Problem, Explore, Plan, Do It, and Look Back (Woods et al., 1997).
In spite of teachers’ best intentions, might students still just do it? Certainly! An alternative to metacognitive planning before doing, and monitoring, regulating, and reflecting, is to apply a purely rote strategy (Garofalo & Lester, 1985), also termed a “plug and chug” method (Maloney, 2011). Plug and chug in physics and engineering involves a mental search for equations that will solve the problem, but with little conceptual understanding of the nature of the problem, little strategic decision-making, and little metacognitive self-reflection and regulation of the solution process. In disciplines not involving equations, various matching and cut-and-paste strategies could qualify as plug-and-chug. James Stice, a distinguished professor in chemical engineering, described part of his own engineering training (Stice, 1999) that suggests how plug-and-chug may come about:
“When I was an undergraduate student, many of my professors would derive an equation during lecture, and then would proceed to work an example problem. They would outline the situation, invoke the equation, plug in the numbers and arrive at a solution. What they did always seemed very logical and straightforward, I’d get it all down in my notes, and I’d leave the class feeling that I had understood what they had done. Later I often was chagrined to find that I couldn’t work a very similar problem for homework.” (p. 1)
Much of the motivation for research on how experts solve problems, like Carlson and Bloom (2005), has led to developing didactic models for the classroom, like the six-step McMaster model (Woods et al., 1997) in engineering: Engage, Define the Stated Problem, Explore, Plan, Do It, and Look Back. These didactic models have been developed largely in response to the absence of metacognitive thinking among students.
Although teaching methods could account for some of the absence of metacognitive thinking in beginning students, domain-specific knowledge may also be a factor. Few would disagree that domain-specific knowledge plays a key role in successful problem solving. Indeed, Carlson and Bloom attributed the expertise of their mathematicians, in part, to “a large reservoir of well-connected knowledge, heuristics, and facts” (p. 45). Can a novice student readily access domain-related facts, organize information within the problem, muse, imagine, and conjecture over possible strategies, apply heuristics, and effectively monitor progress? Of course not. Obviously, the absence of domain-specific knowledge in beginning students enables and motivates the teaching of domain-specific knowledge. But I would like to argue that the absence of domain-specific knowledge also enables and motivates teaching students metacognitive processes. This may seem illogical, but it’s not. The point is that an absence of domain-specific knowledge provides instructors with a great opportunity to teach the domain-specific knowledge but also how to think about thinking about that knowledge, that is, how to be metacognitive while learning facts and procedures.
Getting students to “Think, then Do It” will require more than working examples for them on the blackboard in order to convey domain-specific knowledge. Instead, within a framework like that provided by Carlson and Bloom, the metacognitive processes at each step of solving the problem should also be modeled. Some students may show metacognitive behaviors early on, and all successful students will eventually catch on. However, to truly be a pedagogical principle, it needs to be part of the learning situation. A model of metacognitive instruction (Scharff, 2015) for the student could be guided by the work on scaffolding metacognitive processes proposed in the seminal work of Brown and Palinscar (1982). The point is to take the domain-specific knowledge that you are trying to convey and to model and scaffold it to students along with the metacognitive decisions and control that go with expert problem solving, and to do it early on in instruction. It is worth mentioning that James Stice, who was taught to plug and chug, became a follower and proponent of the six-step McMaster model as professor of chemical engineering.
There is an old Jack Benny joke. Jack Benny was a comedian known for being a cheapskate. One night a thug stopped him – “Don’t make a move bud, your money or your life.” After a long pause, the thug, clearly annoyed, repeated – “Look bud, I said….Your money or your life.” Jack Benny: “I’m thinking it over.” Just to be fair, sometimes we should just Do It and not think too much about it. When it comes to teaching and learning, though, thinking about thinking is better.
References
Brown, A. L., & Palinscar, A. S. (1982). Inducing strategic learning from texts by means of informed, self-control training. Tech Report No. 262. Urbana: University of Illinois Center for the Study of Reading.
Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45-75.
Draeger, J. (2015). Two forms of ‘thinking about thinking’: metacognition and critical thinking. Retrieved from https://www.improvewithmetacognition.com/two-forms-of-thinking-about-thinking-metacognition-and-critical-thinking/ .
Garofalo, J., & Lester Jr., F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163-176.
Maloney, D. P. (2011). An overview of physics education research on problem solving. Getting Started in PER..Reviews in PER vol. 2. College Park, MD: American Association of Physics Teachers. http://opus.ipfw.edu/physics_facpubs/49
Polya, G. (1957). How to solve it. Princeton, NJ: Princeton University Press.
Scharff, Lauren (2015). “What do we mean by ‘metacognitive instruction?” Retrieved from https://www.improvewithmetacognition.com/what-do-we-mean-by-metacognitive-instruction/
Stice, J. (1999). Teaching problem solving. In Teachers and students – A sourcebook (Section 4). University of Texas at Austin: Center for Teaching Effectiveness. Retrieved from
http://www.utexas.edu/academic/cte/sourcebook/teaching3.pdf
Woods, D. R., Hrymak, A. N., Marshall, R. R., Wood, P. E., Crowe, C. M., Hoffman, T. W., Wright, J. D., Taylor, P. A., Woodhouse, K. A., & Bouchard C. G. (1997). Developing problem solving skills: The McMaster problem solving program. Journal of Engineering Education, 86(2), 75–91.