# The two sides of a coin

Sundaram S

One of the purposes of learning mathematics in school is to apply the concepts and procedures of mathematics to “quantify and understand” real life situations. These situations are usually presented to students in simplified versions as “word problems” at two levels – the learning level and the application level.

In primary and lower middle schools, students need to master the basic concepts and procedures of mathematics. For this they are given “raw problems” like 3+4=? as well as word problems reflecting simple life situations where these concepts and procedures can be used. We can call this the learning level, as the main objective here is to master computations and procedures. A problem such as, “If a shop has 8 baskets with 10 apples in each basket, what is the total number of apples in the shop?” is an example.

By upper middle school, students are expected to have mastered all the basic concepts and procedures of basic mathematics. They are now exposed to a variety of life situations which can be understood and explored using all the mathematics that has been learnt until then. We can call this the application level which may also need and nurture higher order thinking skills. A problem like, “If Rs. 10,000 is deposited in a bank account, what interest would it earn if the interest rate is 8%?” is an example.

These application level situations can be broadly classified as

• Situations needing measurement of physical aspects of objects and shapes like length, volume, and surface area with appropriate units of measurement.
• Physical situations like speed, time and distance as well as work, wages, and time taken.
• Commercial situations involving income, expenditure, sale, purchase, savings, banking, investment, etc.

This gradation in the use of word problems (learning vs application) has not been brought out very well in the current syllabus. Word problems related to both “learning and application levels” occur at random stages in many chapters without a unifying theme. For example in class 8, many commercial applications of mathematics come in a chapter called “Comparing Quantities” (Ch 8). Lack of a unifying theme could also be a factor in making the problems difficult for students to understand. A unifying theme like “Application of Mathematics to Life” at the middle school stage could enable better focus and understanding.

The author started his school career, lasting 24 years, with the Rishi Valley School. He has worked as a Principal, Teacher Trainer and Educational Consultant in several schools in India. His areas of interest are primary mathematics, school leadership, and quality in education. He conducts workshops for teachers of primary and middle School on the theme of “Understanding Primary Math for Effective Teaching”. He can be reached at sundaram48@yahoo.com.