Drawing Pictures/Counting Fingers

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. -S. Gudder

What a true statement!  While we need to learn math facts and rules, they are not an end unto themselves.  Math is about discovering new ways to think about numbers.  Counting fingers and drawing pictures are two ways that help children up through adults to understand what numbers mean.

Counting Fingers

When most children learn to add and subtract, they use their fingers to count.  They could use any objects, but “fingers are tools you always have with you.  You can’t replace them.”

Although there is a debate about whether to allow finger counting or not, it is definitely appropriate to use when children are learning about numbers.  However, to continue to use this method for years to come has many drawbacks.  As the Mathnasium of Littleton says, “…counting by ones beyond the early primary years in school, is like building a dog house with just a hammer and nails. It can be done; however, if one has screws, a drill, screwdrivers, a saw, a level and other tools in their toolbox, the dog house will be much stronger, and it can be built more efficiently.”

While children may start learning math by counting on their fingers, a transition to using other strategies does need to occur.  Relying solely on finger counting can prevent children from developing their mental math capabilities.  If given an equation such as 36-9, a child may visualize it as (36-10)+1.  Learning to do mental math is a more efficient way of solving math problems.

Drawing Pictures

Many people, not just children, encounter some difficulty with problem solving.  Drawing or sketching a problem helps to understand what the problem is asking and how to solve it.  For example:  If a farmer has some land that measures 8′ by 4′, how many 2×2 garden plots can he make?

This is what some students might draw.

Drawing isn’t just limited to lower grade students.  Middle school teacher, Andrew Stadel, asked his students in essence to create three different zip line rides…one for certain death, one boring, and one just right.  After giving his students materials and price lists, they began.  In part here’s what one group came up with.

A visual representation is a good starting point for solving all kinds of problems.  It helps students to begin thinking like a mathematician.  Also, drawing is a way to engage students in their learning.  Most leap at the chance to create.

The good news is that as children age they develop more strategies for solving math problems.  As their brains mature so do their abilities as long as they are shown how and encouraged to use different methods to figure out problems.