## Monday, August 18, 2014

### Can Calculators Boost Number Sense?

Once when my stepdaughter was in fifth grade her teacher assigned her a page of fractions to be converted to decimals using long division.  This touched off one of the most memorable kitchen table homework battles.  She insisted that her teacher said she couldn’t use a calculator.  I shamelessly bribed her with one M&M for each problem completed.  The assignment was finished and turned in.  I vowed I would never give a similar assignment.  My stepdaughter hated math, still hates math, and is choosing a college/career path where she will no longer take math classes. (Probably not because of this one assignment, but it didn’t help.)
When I teach conversion from fractions to decimals, I want my students to see the pattern.  I show them how to enter the fraction as a division problem.  They fill out a similar sheet to the one my stepdaughter was given using a calculator.  We discuss what they see for a particular fraction.  For example: 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6 and so on.  By having a clear lesson focus, seeing the patterns, I can determine when my students should use calculators and when they should not.
In every fourth grade classroom, I have a group who struggles to become fluent in multiplication and division facts.  This gets compounded when I want them to multiply and divide large numbers.  For some, I teach the process and let them use multiplication tables for the facts they haven’t memorized.  Others have such a lack of number sense, that they don’t see the following pattern: 8 X 4 = 32, 80 X 4 = 320, 80 X 40 = 3200.
I showed one student this process with a calculator.  What didn’t make sense for her when she saw someone else’s completed table, made more sense when she used the calculator and wrote down the answers.  I want to emphasize the guided aspect of this process:  she was making the calculations and writing the answers.  She could begin to predict how large the products would be based on the number of zeroes in the factors, because she was doing the work with a calculator as a tool.  I wanted her to notice those patterns by looking at accurate answers.
This year my whole class struggled with measurement.  I developed several lessons and stations for practicing length, volume, and weight.  One of the activities involved reading food labels and computing the volume and weight of the contents.  Because my focus was on learning the relative amounts of these measurements, I let them use calculators for the computations.  I knew they were not strong enough to multiply decimals and fractions without a tool.
When teaching students process and strategies for computing numbers, I don’t let them use calculators.  I am clear with my students, their parents, and myself, when I am testing them on computation and when I want them to go beyond and study patterns and develop more complex problem-solving strategies.  After all isn’t that when we use calculators as adults?

What do you think? How do you use calculators in your classroom?