Constructivist Teaching Approach In Mathematics

The purpose of this study was to determine what influence a constructivist teaching approach in a mathematics course had on developing students’ reasoning ability. This review of literature includes: constructivist teaching approach, reasoning ability, open-ended problems and cooperative learning.

Constructivist Teaching Approach

Confrey (1990) described constructivism as “a theory about the limits of human knowledge, a belief that all knowledge is necessarily a product of our own cognitive acts”. Johnston (2005) described constructivism as an approach for teaching and learning based on the premise that cognition (learning) is the result of "mental construction." In other words, students learn by fitting new information together with what they

The Open-Ended Problem is based on the research conducted by Shimada which is called "The Open-Ended Approach". The Open-Ended Approach provides students with "experience in finding something new in the process" Akihiko, 2005 as cited in Shimada 1997). The Open-Ended Approach started in 1970s. Since then, Japanese teachers have developed many open-ended problems and lesson plans using open-ended problems. These problems are being used in mathematics lessons ranging from elementary through high school grades, and the lessons are called the Open-Ended Problem Solving. Open-ended problems are also used as assessment tasks because "In responding to such (open-ended) items, students are often asked not only to show their work, but also to explain how they got their answers or why they chose the method they did" (Akihiko,2005 as cited in Schoenfeld,

1) Students participate more actively in lessons and express their ideas more frequently. The Open-Ended Problem Solving provides free, responsive, and supportive learning environment because there are many different correct solutions, so that each student has opportunities to get own unique answers. Therefore, students are curious about other solutions, and they can compare with and discuss about their solutions each other. As students are very active, it brings a lot of interesting conversation to the classroom.

2) Students have more opportunities to make comprehensive use of their mathematical knowledge and skills. Since there are many different solutions, students can choose their favorite ways toward the answers and create their unique solutions. Activities can be the opportunities to make comprehensive use of their mathematical knowledge and skills.

3) Every student can respond to the problem in some significant ways of his / her own.

4) The lesson can provide students with a reasoning experience. Through the comparing and discussing in the classroom, students are intrinsically motivated to give reasons of their solutions to other students. It is a great opportunity for students to develop their mathematical