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Introduction
How can the instructor meet the challenge of helping students develop formal reasoning skills? Can we tell students how to reason? While more capable students find lectures adequate to assist in learning, others find it more comfortable to make the move from concrete experience to abstract thinking via a carefully designed active learning exercise rather than make an intuitive leap to the use of formal reasoning. Piagetian-based education programs recognize the importance of providing students with an environment in which they can move from concrete experience to concept invention and then to application of the concept. While this type of learning is valuable, we are faced with a trade-off: do we sacrifice transmitting broad-based course content in favor of helping students develop a thorough understanding of a few concepts? and to develop the ability to focus on abstract ideas rather than factual information?
The problem of adequately helping students develop their critical reasoning skills has not gone unnoticed.
"... the existence of objective knowledge and the possibility of communicating that knowledge by means of language have traditionally been taken for granted by educators... The traditional epistemological paradigm is now being turned upside down." [Yager, Robert E., The Constructivist Learning Model, Science Teacher, p. 53 September 1991.]
Yet it seems as though there has been no widespread change in the way we educate teachers nor in the way in which course content is presented to students. By taking measured steps toward a new education paradigm we can begin to help students reason effectively.
Piagetian-based Education
"To know an object, to know an event, is not simply to look at it and make a mental copy or image of it. To know an object is to act on it. To know is to modify, to transform the object, and to understand the process of this transformation, and as a consequence to understand the way the object is constructed. An operation is thus the essence of knowledge; it is an interiorized action which modifies the object of knowledge." [Piaget, Jean. "Cognitive Development in Children: Piaget/Development in Learning", Journal of Research in Science Teaching, Vol. 2, p 176.]
Piaget's insights into cognitive development indicate that simply transmitting course content via lecture may be inadequate for students to really learn a subject. Students need to be able to touch, to manipulate, and then to predict. In his research, Piaget identified four stages of cognitive development. Up until age eight, children go from sensory-motor stage through the pre-operational stage. They first begin to develop practical knowledge for representational thought and then begin to reason on objects and start to develop language skills. When children begin the concrete reasoning stage around age eight, they start to do elementary mathematics, classification and serial ordering. Starting at age eleven some children begin to use formal reasoning skills. That is, a child will be able to reason on hypotheses. It is not yet clear how quickly children move through the final two stages -- in fact, some will argue that the transition from concrete to formal reasoning takes place continuously. In many cases adults, when faced with unfamiliar subject matter, will find it easier to move from concrete experience to formal application.
The movement from one level of reasoning to another depends upon several things: maturity, experience, social (educational) transmission, and most importantly, self-regulation. The fourth factor requires more explanation. In simplest terms, self-regulation is assimilation. For example, the student is faced with seemingly conflicting bits of information. Consider the money multiplier and the law of conservation of matter. If you had just learned that matter can neither be created nor destroyed in physics class, how can one account for a five-dollar increase in economic activity when a one-dollar bill is introduced?
Hands-on and eyes-on experiences are essential prerequisites for the development of advanced reasoning abilities. Imagine you are about to introduce the law of demand to your students. How would you begin? Would you
- draw a graph and explain that there is an inverse relationship between price and quantity demanded,
- assign a computational problem in which students must calculate the quantity demanded given certain prices,
- ask students to imagine a farmer's market in which apples are being sold and what happens when prices change, or
- send students on a fact-finding mission on the Internet to determine how businesses handle problems like shortages?
If you selected "A", you're not alone. Most economics instructors who have an arsenal of diagrams and equations to draw upon view the simple sketch of the demand curve as basic to economics. Unfortunately, the student who hasn't seen this kind of graph before and who hasn't spent time practicing plotting points and making inferences from graphs will find this presentation to be abstract.
"B" is a useful exercise to help students understand the relationship between the variables, P and Q. Unfortunately, there is no experiential base and students may fail to see its relevance.
"C" isn't a bad choice. Asking students to connect with prior experience helps them see the relevance of a concept.
"D" is the best choice when designing an exercise that effectively develops understanding. Students are engaged in real-world problem solving obtaining data from real firms. The exercise is open-ended, with little clue given about the intended outcome. Students explore, discover, and make connections.
Learning Cycles
Typically, one would begin a learning cycle lesson with an activity like the one described in 'd', above. Learning cycle lessons consist of three phases: exploration, invention, and application. If you've reviewed some of the Net NewsLine lessons, these terms will sound familiar to you.
During the exploration phase, students learn through their response to new information. They are encouraged to explore and are given little guidance. Students are apt to feel confused and sometimes frustrated during this phase. However, as they experiment and test out hypotheses, they begin the process of self-regulation. Sharing knowledge with other students via a web conference can help them gain insight into the information at hand.
In the inventions phase students typically define a new concept and invent new principle. This phase follows the exploration phase and extends the activities presented there. The instructor will encourage students to invent part of a new idea themselves before the idea is formally presented to the class.
During the application phase students find new uses for concepts or skills learned in the invention phase. These activities provide additional time and experiences for self-regulation to take place. Here the instructor reinforces, refines, and enlarges upon content of the invention phase.
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