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

  48
+23 

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.

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