Constructivism is a philosophy of education that says that people construct knowledge through their experiences and interactions. Essentially it says that people learn through experience, not through hearing someone give a lecture.
In a traditional setting, the teacher takes charge of a lot of intellectual work. Whereas in a constructivist classroom, teacher poses questions and problems that guides students to help them find their own answers. The primary goal of a constructivist approach is to help students learn ‘HOW TO LEARN”. The student is the person who creates new understanding for himself/ herself. The teacher facilitates learning and allows students to transform an abstract concept into a concrete one.
Constructivism is an excellent tool in Mathematics especially in introducing topics, derivation of formulae and concept building.
Featured below is an example of how constructivism can be implemented
Topic: HCF using Euclid’s Division Algorithm.
Q1 . What is the largest square that fits in 28 x 20 rectangle?
Ans: 20 x 20
Q2: How many such squares can be accommodated?
Ans: 1
Hence length can be represented as 28 = 20 x 1 + 8
Q3: What are dimensions of the new rectangle?
Ans: 20 x 8
Q4: What is the largest square that fits in 20 x 8 rectangle ?
Ans: 8 X 8
Q5: How many such squares can be accommodated?
Ans: 2
Continuing the above question pattern
Hence remaining length can now be represented as
Ans: 20 = 8 x 2 + 4
What are dimensions of the new Rectangle?
Ans: 8 x 4
What is the largest square that fits in an 8 x 4 rectangle? Ans : 4 x4
How many such squares can fit?
Ans: 2
Hence new length is
Ans: 8 = 4 x 2 + 0
Finally, what is the largest square that fits the rectangle completely?
Ans: 4 x 4
Declare 4 as the HCF
From the above activity let students observe a pattern to find HCF of two given No’s
28 = 20 x 1 + 8
20 = 8 x 2 + 4
8 = 4 x 2 + 0
Students observe that divisor becomes dividend and remainder becomes divisor and the process continues till the remainder is 0.
Student declares the divisor at this stage is the HCF .
Teacher at this stage can introduce Euclid’s Division Algorithm .