Operational Fluency

< 11.2 Arithmetic Operations | Topic Index | 11.4 Addition >

Apart from understanding the logic behind arithmetic operation procedures, students are also expected to achieve mastery in performing them. Instead of the term, mastery, we will use the term fluency which gives a better understanding. Fluency implies both speed and accuracy in computations.

The Practice of Drilling

Currently, the general understanding in schools is that fluency is achieved by a lot of practice. But as we will see, fluency needs practice with understanding. Without understanding, mere practice becomes boring and mostly does not lead to any learning but on the contrary, leads to a loss of motivation to learn. This practice is called &ldquo;drilling&rdquo; in schools, possibly mirroring the idea of a military drill. But my teacher, PKS used to say that drilling most likely produces holes!

Procedural Fluency 

Attaining fluency in operational procedures is made up of 3 different elements.

Teachers who believe in &ldquo;drilling&rdquo; are aware only of steps 1(b) &amp; 2. This is not enough. Math computations have so many variations &amp; exceptions that a student can get confused &amp; lost if she remembers them only as a series of steps. It is better to understand the concepts underlying the procedure and the procedure itself as a coherent story where one step follows the other. While a computation is being done, the underlying story should unfold in the mind as the spool of a music tape. A combination of steps 1 to 3 is what leads to procedural fluency.
 * 1) Mastery of the algorithm as in 				what is the logic underpinning the algorithm?what is the sequence of steps?
 * 2) Recalling computational facts like what is 8 X7?
 * 3) Number Sense - The ability to mentally split &amp; rearrange numbers &amp; use inter-related properties of the 4 operations.

Happy Drills

An alternative to &ldquo;drilling&rdquo; is the idea of giving &ldquo;happy drills&rdquo; to students. Math has a special area called &ldquo;recreational math&rdquo; (Section 22) which deals with math games, puzzles and explorations. These activities are fun to do and learn through them.

The use of games &amp; puzzles engages students in practicing with joy and without realizing that they are practicing math skills. These activities provide mathematical skills while at the same time provide mental pleasure.

They are easy &amp; mentally engaging and accessible to students in Primary School. This is especially important in the Primary classes where students are not mature enough to motivate themselves to work hard for an easy tomorrow. Hence these should form a part of the mathematics curriculum.

Using Fingers

Another issue in many schools is the idea that math is a mental subject and hence memory is important. A related idea is that use of fingers should be discouraged. Teachers who discourage the use of fingers have not understood their value. What needs to be understood is that math has to be &ldquo;constructed&rdquo; in the mind and not &ldquo;memorized&rdquo;. Using fingers is an excellent way for &ldquo;constructing math&rdquo; in our minds. Fingers are available with us anywhere and anytime! Using fingers will also give visual &amp; kinaesthetic pictures of numbers &amp; procedures and deepen understanding of what is happening in that operation. This will provide visual and kinesthetic images which will help &ldquo;remember&rdquo; the facts. Consequently, the ability to mentally perform these computations will also develop. As the visual images are internalized, the need for using fingers will gradually reduce.

While looking at ways of improving fluency, we will be focusing on many techniques which use fingers, for improving number sense as well as performing computations.

< 11.2 Arithmetic Operations | Topic Index | 11.4 Addition >