Problem Solving, Reasoning, and Analytical Thinking in a Classroom Environment

Article excerpt

The analysis of learning outcomes (Tiemann & Markle, 1983; 1990) combined with instruction founded on sound design principles (Markle, 1990) empowers educators to teach the most complex of cognitive skills. At Morningside Academy, a small private laboratory school, the faculty fully believes and works toward the radical notion that intelligence can be taught, that intelligence is not static nor determined at birth (see Whimbey, 1975).

Today's Morningside classroom integrates instruction in effective problem solving, reasoning, and analytical thinking, drawing primarily from the investigation of problem solving processes pioneered by Bloom (1950), Dewey (1933), Skinner (1957, 1969), Samson (1975) who credits Albert Upton's methods of 1933, Whimbey (1975), Whimbey and Lochhead (1991), Markle and Droege (1980), Heiman and Slomianko (1988), Robbins, Layng, and Jackson (1995), and Robbins (1996).

That students should be skilled problem solvers, reasoners, and analytical thinkers is not in dispute. Most educators agree that teaching students to be good thinkers is important and that rote memorization, although having value, must augment not replace, the ability to problem solve on one's own. However, there is no consensus about how to teach these skills. A longitudinal study was conducted at McMaster University, by Donald Woods, a professor in the Department of Chemical Engineering, (Woods, 1998) to investigate approaches to teaching problem solving. The study provides evidence that three approaches often used to teach problem solving don't work. To summarize from the McMaster report [italicized text not in original]:

Ineffective approach #1: Give students open-ended problems to solve. This approach is ineffective because the students get little feed back about the process steps, they tend to reinforce bad habits, they do not know what processes they should be using and they resort to trying to collect sample solutions and match past memorized sample solutions to new problem situations.

Ineffective approach #2: Show students how you solve problems by working many problems on the board and handing out many sample solutions. This, we now see, is ineffective because teachers know too much. Teachers demonstrate "exercise solving". Teachers do not make mistakes; they do not struggle to figure out what the problem really is. They work forwards, not backwards from the goal. They do not demonstrate the "problem solving" process; they demonstrate the "exercise solving" process. If they did demonstrate "problem solving" with all its mistakes and trials, the students would brand the teacher as incompetent. We know; we tried!

Ineffective approach #3: Have students solve problems on the board; Different students use different approaches to solving problems; what works for one won't work for others. When we used this method as a research tool, the students reported "we learned nothing to help us solve problems by watching Jim, Sue, and Brad solve those problems!"

Many teachers will recognize these approaches. Whereas the goal of creating good problem solvers seems to be shared by nearly everyone, there is less clarity about how to achieve the goal. However, there are some promising approaches, one of which is the McMaster Problem Solving Program. This program improves the problem solving, reasoning, and analytical thinking skills of college students. Almost all successful approaches (as described by Gustafson and Pederson, 1985, Heimann and Slomianko, 1988; Whimbey and Lochhead, 1991) share two characteristics, 1) they are relatively unknown, and 2) they were developed for high school age students and above. This paper will summarize some of the effective strategies that can help a teacher shape the qualities described by Whimbey and Lochhead, and how the author and her colleagues at Morningside Academy and elsewhere, have designed effective programs to teach these vital problem-solving, reasoning, and thinking skills to children much younger than college students. …