In the article “Solving Word Problems” in the December 2007 issue, Kamala Mukunda stressed the importance of forming Mental Models. I would like to take this process further and suggest some mental models for the primary classes, where a firm foundation in basic operations needs to be given. Using mental models, students can easily master these operations, and they can mix and match these models in the higher classes to understand and solve more complex problems.
The four basic operations to be ‘understood’ in the primary school are Addition, Subtraction, Multiplication and Division. These operations are mathematical abstractions of a wide variety of real-life processes. Students need to be exposed to a range of these real-life situations to help construct mental models in their mind so that they can relate the real-life problem with the arithmetic operation.
I describe here a few models for Addition and Subtraction before taking up the issue of how to teach them in the classroom.
The author is the Principal, Atul Vidyalaya, Gujarat. He can be reached at firstname.lastname@example.org.