Goals - Part 1

My goals in helping children with arithmetic are simple. I want them

  • to be good at solving all different types of word problems,
  • to like solving word problems,
  • to understand the problem solving methods (shortcuts) that they use and
  • to be able to communicate their reasoning to others.

1. What Is A Word Problem?

This is a word problem:

Rose had 2 lollipops. Trixie gave her 3 more. How many lollipops does Rose have now?

Here is the corresponding equation.

2 + 3 = □

The arithmetic problems that arise in day-to-day adult life are word problems - not equations. At the playground I need to know if I have enough cash to buy my grandchildren ice cream. In the car, I often want to know how many miles are left until I reach my destination, and how long it will take to get there. In the kitchen, I sometimes need to know how to double a recipe. It seems obvious that instruction in arithmetic should emphasize problems in the form that children will need to understand.

In spite of this, parents and teachers often over-emphasize calculation at the expense of solving word problems. Children get lots of practice with equations like 2 + 3 = □ and with "problems" like this


but often don't know how to apply these skills to the kinds of real problems that adults need to be able to solve. Even cell phones have built-in calculators so it makes no sense to spend a lot of time on skills that are no longer necessary at the expense of ones that are.