The International Online Journal of Science and Mathematics Education

The academic community has been engaged in the last decade in the debate between socioconstructivism versus behaviorism as contrasting views on mathematics education. These major psychological stances, acting as macrobeliefs, have in turn influenced the way students, teachers, schools, and the education system in general have thought about what mathematics is and how it should be taught and learned.

Socioconstructivism, which for the sake of brevity will be called constructivism, gives recognition and value to new instructional strategies in which students are able to learn mathematics by personally and socially constructing mathematical knowledge. Constructivism considers that reality is implicit, internal to the individual, and can only be constructed but not instructed. Learning therefore depends on the way the learner looks at a situation, as people determine their own knowledge (Biggs & Moore, 1993). Constructivists do not consider knowledge a commodity that can be transferred but cognition is seen as an adaptive and experiential process (Phillip, 1995). Constructivist strategies advocate instruction that emphasizes problem solving and negotiation of meaning through reflective and exploratory learning. These strategies also recommend group learning, plenty of discussion, informal and lateral thinking, and situated learning (Murphy, 1997). Clements and Battista (1990) and Wood, Cobb, and Yackel (1991, p. 591) characterize best the basic tenets of the constructivist paradigm which include:

Knowledge is actively created by children and is not passively received from the environment.
Children create new mathematical knowledge by reflecting on their physical and mental actions. In addition, children’s actions are viewed as rational to them and reflect their current understanding.
Substantive learning occurs in periods of conflict and confusion, surprise, and other long periods of time.
Learning is a social process in which children grow into a community.
Mathematical ideas are cooperatively established by the members of a culture.
Opportunities for learning occur during social interaction involving collaborative dialogue, explanation and justification, and negotiation of meaning.

On the other side, the pedagogical principles of the behaviorist paradigm focus on manipulating external factors to modify behaviors (Elliot, Kratochwill, & Travers, 1996). Some of its main pedagogical principles can be outlined as follows:

Students are required to master basic tasks before they move to more advanced tasks.
Reward and reinforcement are indispensable to secure student learning.
Desired behavior in the classroom is clearly characterized at the completion of the task.
Correct answers are rewarded instead of partially correct responses.
Learning tasks are arranged in a continuum from low- to higher-order thinking activities.

Accordingly, behaviorist practices emphasize transmission of knowledge and stress the pedagogical value of formulas, procedures and drill, and products rather than processes. Behaviorism also puts great value on isolated and independent learning, as well as conformity to established one-way methods and predilection for pure and abstract mathematics (Wood, Cobb, & Yackel, 1991). Leder (1994, p. 35), for example, stated that in the behaviorist movement “the mind was regarded as a muscle that needed to be exercised for it to grow stronger.” Behaviorism has been criticized because of its process/product- oriented and teacher-centeredness tendencies to teaching and learning that have been prevalent in classroom teaching and in teacher education programs in the twentieth century (Marland, 1994).