It is common for girl scouts to follow marching orders like with the boy scouts. For a troop to commence with its marching stance, there need to be a clear understanding of the whole procedural flow. Otherwise, the marching line will be in disarray from the beginning.

            The same is true in the stages of learning math. By the time a learner gets confused in understanding of procedures, the problem solving process will be a problem by itself. It becomes academic that the needed solution is not to be arrived at.  Learning about numbers draws everything from the diligent understanding of the procedures involved together with their proper application. Skills enhancement will not be possible if void without comprehension. 

            Mathematical comprehension refers to the understanding of the problem with the   knowledge of when and how the procedures are to be used appropriately, efficiently, and accurately.

            There are learners who are good even with mental calculations given routine problems.  When it comes to non-routine problems where procedural applications are required, the natural thing to do is to get a pencil and paper to solve them. It is because with non-routine problems the learner will not immediately know the usable solution method to be applied. This situation requires the productive thinking of the learner to understand and provide way to solve the problem.

            A classic example would be a math puzzle from a local daily which goes like this: A cycle shop has a total of 36 bicycles and tricycles on stock. Collectively, there are 80 wheels. How many bicycles and how many tricycles are there?

            One approach is to reason out that both the bicycle and a tricycle at the least have two

wheels. With the 36 vehicles collectively on stock multiplied by two (2) will arrive at 72 wheels. Since, there are 80 wheels in all; the eight (8) additional wheels must belong to eight (8) tricycles making 28 as the number of bicycles in the shop.

            Actually there are other methods to solve the given problem which with understanding can aid the solver to find the appropriate procedural application to solve it like the “ guess and check ” approach or through the more sophisticated algebraic approach. Either way, the answer to the math puzzle will be 28 bicycles and 8 tricycles are inside the cycle shop.

            The key in enhancing one’s skills in Mathematics is to have fun in understanding it. With that in mind, enjoy the while.

By: ELAINE V. CUADRA | Teacher I | Bataan National High School | City of Balanga, Bataan