Misconceptions in Mathematics

 

Misconceptions in Mathematics

Mathematics is the gate and key of all the sciences! 

This statement confirms the importance of Mathematics but still there is a fear about Mathematics in the mind of most of the students! Why is this fear so difficult to minimize or fade off?

The major barriers in learning mathematics are lack of understanding the concept and importance given to exams rather than understanding the concept. So, when the concepts are not learnt correctly, or students have access to incomplete/ half-truths or ingrained with some pre-established ideas in their mind, or sometimes poor reasoning skills and the faulty teaching practices that does not motivates the students; all these develops misconceptions in Mathematics.

Misconceptions can be described as a mistaken idea or view resulting from a misunderstanding of something.

For example, the teacher is explaining an image of a tree and student's perception of a tree can be completely different, just as shown in the below picture.

But why should we worry about? What is the effect of misconceptions? 

As we can observe in the right-hand side example.  Most of the students believe that the horizontal line or the line which is on the ground is the base. Hence the if I need to find out the area of the triangle, I need to find the height. However, if we just orient the figure as shown in the below figure it shows the base and height is already there. Hence, this kind of misunderstanding continues in failure of understanding the new built-up concepts. Students starts committing mistakes and scoring low in the exams. And the gradual effect of misconceptions could become so extreme that the students will start disliking the subject and develop a fear for it. 

How can we change the misconceptions?

Changing the misconceptions is not an easy task. It is deeply rooted in their mind and hence difficult to change it just by saying or giving some examples. They need to believe in it and develop a trust in what the actual concept is about!

So, when I shared the below example with teachers most of the teachers said that the answer is option A or B for sure. It was hard for them to believe that the answer is actually option C. How it is true? Can you also think about the option C with proper justification? 

Misconceptions can be surely changed:

• By changing the conceptual framework of students.
• Building on new concepts based on strong foundations.
• Change a frame of mind.
• Change in own belief system.
• Own cognition has to be changed.
• Opportunities for them to realize themselves where they are wrong.
• Developing self-confidence and courage in solving problems.
• By being Adaptable

How can I identify that a student is having a misconception?

There are some repeated mistakes.

Common mistakes most of the students do.

By being Vigilant 

                        Assessment tasks- especially formative assessment tasks

 As you can observe in the above example where students first start deleting the x to get the value of y in the following manner however this is not possible when there is an addition operation. So, it is essential to point out to students where they might go wrong!

Some topics from VIII-X standard, that are attracted towards misconceptions!

As a teacher, what can I do?

I firmly believe that the teacher has the key to unlock all the doors of concepts and clear misconceptions. Teacher needs to have clear concepts himself/herself first and then follow the following ways!

In my next blog I will be discussing various strategies that will be useful for the teachers to tackle the major challenge of handling misconceptions.