CONSTRUCTIVIST VIEWS OF LEARNING

How do we learn? For example how did we learn that ‘if it is 8 am now and it will be 2 pm six hours later.’? In order to make calculations in the clock arithmetic, is it necessary to know some knowledge of modular arithmetic? The example might seem exaggerated but that’s the underlying mentality of the classical educational system! Most of us learn the clock arithmetic in the childhood without any prior knowledge of modular arithmetic. We learn this through our experiences. We learn it when we adjust our sleeping time or decide when to return home.

Constructivism views learning as a process in which the learner actively constructs or builds new ideas or concepts based upon current and past knowledge. In other words, “learning involves constructing one's own knowledge from one's own experiences” (Ormrod, J. E., Educational Psychology: Developing Learners, Fourth Edition. 2003, p. 227). But what our educational system does is to assume that the students have no current or past knowledge; rather, they are seen as empty pages. Especially in mathematics education, students are expected to memorize. They learn by memorizing that 2+2=4; which is not always correct.

2 + 2 is not always equal to 4

At a first glance, it seems as if it is quite difficult to apply the constructivist paradigm to mathematics education. In a literature class, each student can have his/her own understanding of Shakespeare for example; but in mathematics 2 + 2 = 4, and how can we change this basic fact in another way?

Here is a list of questions, a constructivist mathematics teacher might have asked:

• What is the mathematical setting we are working with?

• How many elements does our space have? In particular, does it include 4?

And the following ideas might have helped him/her:

• If we use the daily arithmetic then the answer to 2+2 is 4;

• But if our space only includes the numbers: 0, 1, 2 and 3 then our answer cannot be 4 since it is not in our space.

• The numbers that are needed to count the days of the week are 1, 2, 3, 4, 5, 6 and 7. If today is Saturday, it is the 6^th day of the week and 2 days later it will be the 1^st day of the next week. Then in weekly based arithmetic 6+2=1 (modulo 7). And if a week were to consist of 3 days then 2+2 would be 1 in this system.

Constructivism suggests that knowledge of mathematics results from forming models in response to the questions and challenges that come from actively engaging with the problems and environments - not from simply taking the given information, nor as merely the blossoming of an innate gift (Mathematics Ed.: Math Forum @ Drexel). So emerging from the interaction of people and environmental problems, the knowledge should be interactively learned.

Teacher's Role in a Constructivist Classroom

Contrary to the criticisms by some educators, constructivism does not dismiss the active role of the teacher or the value of expert knowledge. Constructivism modifies that role, so that teachers help students to construct knowledge rather than to reproduce a series of facts (Educational Broadcasting Corporation: http://www.thirteen.org). A constructivist teacher should always make extra researches about the subject being taught. S/he should know the relevancy of the subject with daily life; also should create or find activities for the students. The teacher should make the classroom atmosphere participatory with questions, which helps to keep the students motivated.

In my opinion the desire of the students for participation and knowledge is innate. If you observe the children before and after they begin the school, you will see that the current education usually hinders their curiosity. They usually ask more questions before beginning the school. Thus the problem is to decide what is more valuable for us? “If we want students to value inquiry, we, as educators, must also value it.” (Brooks, 1993; p.110). If we ask questions with only one and unique answer, such as what is the general term of Fibonacci sequence, then we cannot expect the students to calculate the population growth of bees, or at least have the idea that Fibonacci created this sequence to calculate the population growth of rabbits. Because if all the teacher wants is some general formula, then the students will not try to explore the rest.

As a result, teachers should not forget that we are living in a changing world; even 2+2 is not always 4.