Blog 2 - Constructivism

Having considered the question, how students learn mathematics through terms like constructivism and understanding, how do these theories and perspectives compare with what you have thought prior to this course? What do you think are the implications for constructivism in the classroom -- what would it look like?

Prior to this course, I thought that an effective way of learning was by using the 'show-and-tell: teacher-directed approach'. This way, the students were shown how the teacher wants the problem solved, and are guided in this manner. The students aren't able to construct their own ideas. No reasons are offered as to why you approach a problem in this manner, rules are assumed to be obvious, and the teacher receives no input on the ideas students have. The teacher can only find out if students are able to follow directions. However, many students who solve the problems correctly really don't understand and will be reinforced that math is a collection of rules to be learned.

Constructivism is much different; it is a student-centered approach. Students are free to develop their own ideas by using prior knowledge to give meaning to the problem solving strategy they develop. Once students have been given time to work on the problem and connect ideas to construct new ideas and develop an understanding, there is a discussion phase where ideas continue to grow. Students may hear new ideas that they hadn't thought of. Teachers begin where the students are - with their ideas. Students are allowed to solve problems in ways that make sense to them by using their own ideas.