Does Your Elementary Mathematics Methodology Class Correspond to Constructivist Epistemology?

Article excerpt

This study examines whether the instruction of an elementary mathematics education methodology course corresponds to constructivist learning. The participants were pre-service teachers in their senior year at a college in the southern part of the U.S. They were 49 students (3 men, 46 women) enrolled in three sections of a teacher certification course, one in the K-4 program and two in the K-8 program. During the first half of the semester, the instructor taught all students via direct instruction and during the second half by using a strategy involving hands-on activities, group work, and empowerment of students. The researcher administered the Constructivist Learning Environment Survey (CLES) at the beginning and at the end of the treatment. The investigator of this research will use the CLES to examine whether or not the instructor maintains a classroom that promotes a constructivist learning environment. Results showed that the classroom learning reflected a constructivist environment in four of six sections of the survey.

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The U.S. Department of Education (2005) reported that of 12 nations (Hungary, Austria, Latvia, Japan, Hong Kong, Italy, Russia, Netherlands, New Zealand, Belgium, and Norway) that participated in a mathematics assessment, U.S. fourth graders ranked 8th and U.S. eighth graders ranked 9th, indicating below average scores. The report also stated that when teaching mathematics, American teachers tend to focus on procedural computation, rather than conceptual understanding of a lesson.

The National Council of Teachers of Mathematics (1989) has developed standards for teachers of mathematics that promote deep understanding of mathematical concepts, while advocating for student-centered instruction. Several of these standards include using concrete materials, modeling, engaging students in the classroom, encouraging communication in the classroom, involving students in discussion, initiating problem solving, moving toward understanding instead of memorization, respecting students' ideas, and being sensitive to students' experience and culture.

Increasingly, teacher education programs in colleges and school districts are adopting a constructivist theory of learning even though it is difficult to change teachers' beliefs (Richardson, 1997; Richardson, 1996). Van De Walle (2004) has stated that providing a constructivist learning environment, which is an effective method of teaching, will help improve student understanding of mathematical concepts. Van De Walle states:

   The most widely accepted theory known
   as constructivism, suggests that children
   must be active participants in the development
   of their own understanding.
   Constructivism provides us with insights
   concerning how children learn mathematics
   and guides us to use instructional
   strategies that begin with children rather
   with ourselves. (p. 22)

Troutman and Lichtenberg (2003) have found that students do not learn concepts by memorizing isolated facts, by watching the teacher explaining a lesson, by reading definitions, or by using abstract symbols. These researchers state that students learn concepts by actively participating in learning activities. Also, the importance of mathematics knowledge for teachers has been emphasized by the National Council of Teachers of Mathematics (1989, 1995, 2000). NCTM promotes standards that correspond to a constructivist approach to teaching. Moreover, NCTM (1991) emphasizes the teacher's role in creating a classroom in which students can learn to think mathematically by exploring, questioning, and justifying mathematical problems. Instructors as role models could influence students because research has shown that most people will teach the way they were taught (Lortie, 1975).

Piaget and Vygotsky are two important contributors in the development of constructivist learning (Henson, 2003; Olivia, 2005). Piaget's constructivism focuses on an equilibrium theory that states that when a student encounters contradictory information, the learner tries to reach equilibrium (Brooks & Brooks, 1993). …