Reasoning at the level of formal operations
The stage of formal operational thought provides the individual with the capacity to handle hypothetical and theoretical possibilities and reason in terms of verbally stated hypotheses. To reason hypothetically and to deduce the consequences that the hypotheses necessarily imply is a formal reasoning process. Hypothetico-deductive reasoning, or the whole causal reasoning process, is not possible before the formal operational development stage is reached (Inhelder & Piaget, 1958). Hypothetico-deductive reasoning is a crucial part of many problem-solving situations. Research results have indicated that the problem-solving process, which involves identifying an appropriate question as the object of investigation and the ability to generate one or more hypotheses, is a challenging one, but also contributes significantly to individuals’ success (Kuhn, lordanou, Pease, & Wirkala, 2008). Later in the reasoning process, during the phase of analyzing and establishing conclusions, cognitive abilities are needed to evaluate, compare, and combine different claims and solutions (e.g., such reasoning patterns as probabilistic, proportional, and correlational reasoning) (Lawson, 2004).
Causal reasoning activates relevant sub-processes: 1) exclusion and control of variables, 2) constructing and using formal models, and 3) logical reasoning (Adey & Shayer, 1994). The key element in the causal reasoning is the construction of experiments, which means that one chooses pairs of experiments for further analysis. This reasoning pattern is an important part of advanced “variable-centered reasoning” and it requires the ability to hold several independent variables and one dependent variable in mind, and consider the possible effects of each independent variable on the dependent variable. This schema of “exclusion and control of variables” includes the exclusion of irrelevant variables that requires the identification of variables that do not have any effect. The schema plays an important role in causal reasoning, especially in the natural sciences, but also implicitly or explicitly in all experiments or critical investigations in social sciences as well (Adey & Shayer, 1994). Its importance is in its ability to isolate the factors which may possibly have an effect on an event, to consider each of them in turn and all together, and to make rational assessment of their relative contributions to the effect (Adey & Shayer, 1994). A precondition for the schema which controls the variables is an understanding of combinatorial variables. It is important to be able to make a logical deduction of the role of every variable based on the experiments and to demonstrate if a certain factor is a causal agent, and which other variables have no effect (Inhelder & Piaget, 1958).
An example of a natural-scientific question measuring formal thinking is the Pendulum question (Figure 3.1; see Kallio, 2016). The question demonstrates
- (1) A pendulum
- (2) Two weights of different sizes
- (3) Two strings of different lengths The pendulum can be given
a strong or weak push and the amount of swings per minute counted.
Which factor(s) have an influence on the movement of the pendulum when it is pushed for the first time?
FIGURE 3.1 Pendulum task in formal operational thinking research (Kallio, 2016; see Inhelder & Piaget, 1958; Kallio, 1998; Seppala, 2013). Printed with permission. Copyright The Finnish Educational Research Association that, content-wise, the originally used methods are natural-scientific in nature. The research subjects have to assess the influence of three different variables on the fast or slow movement of the pendulum: the length of the string, the size of the weights, and the force of the push given to the weights. The question is which variables have an effect on the pendulum’s measured movement within a certain period of time. There is only one correct answer, which means that this type of question is a closed, well-defined problem.
Furthermore, the ability to construct and use formal models is an important element in reasoning. The model that has to be imagined has different parts which move and hold the same relationships to one another. A challenge of the formal model is that their construction requires mental manipulation of many variables together (Adey & Shaver, 1994). Logical reasoning involves the ability to analyze the combinatorial relations present in the information given. The logical operations - implication and the denial ofimplication - are examples of logical reasoning (Adey & Shayer, 1994).
According to Piaget (1976), a developmental change occurs when contradictory and different experiences that are in contrast to already-formed ways of action are confronted. The process is called reflective abstraction and it occurs when an individual is prompted by contradictory feedback (in the physical environment or in social interaction with other people) and the result is that the individual gains declarative knowledge and becomes more aware and conscious of this knowledge. According to Piaget (1972), the development of thinking and the differences between individuals depend on the social environment, acquired experience, and intellectual stimulation besides the aptitudes, personal interest areas, and professional specializations of the individuals. It is argued that there are great differences between individuals in the skills of formal thought depending on these factors.
Based on current research knowledge, it seems that, unlike Piaget assumed, not everyone can fully master fonnal thinking in adulthood. For example, not all Finnish adolescents and young adults master it extensively, not even the ones studying at a higher education institute (Hautamaki, 1983; Kallio, 1998; Seppala, 2013). Research findings from the last decades indicate that even among university students only 60-80% reach the stage of fonnal operational thinking (see Kallio, 1998; Seppala, 2013, 2016; Shibley, Milakofsky, Bender, & Patterson, 2003).
According to Dasen (1994), lower-level concrete operational thinking seems to be found across cultures, for example, among Australian aboriginal and Inuit (Eskimo) children. He favors Piaget’s claim that the developmental stages are universal. Empirical studies conducted mainly at the end of the 20th century however, indicated that the fonnal stage is not a universal developmental stage in all cultures (Feldman, 2004). There has not been much research on adults’ formal thinking lately, and it has been mostly connected to natural-scientific thinking abilities and academic success (Haider, 2016), and with lower-age subjects (e.g., Thuneberg, Hautamaki, & Hotulainen, 2015). The latest important development is connected to the creation and usage of standardized questionnaires related to formal thinking skills (Adey & Shayer, 1994; Kuhn et al., 2008; Seppala, 2013).