### A 'Fractional' Understanding

As a teacher (not of math but of science) I happen to think the issue with fractions is similar to issues with multiplication and division. I never realized it until I observed my young son learning to multiply and divide large numbers. To truly understand these operations his teacher started with place value. For example, he learned to multiply 75*15 as a matrix with 70x10 + 5*10 + 70*5 + 5*5 and he can now connect that to the traditional methods. The problem is that sometimes place value is taught without making the connection to things like multiplication. Similarly, with fractions, the minute you see a strip with 5 segments and an identical strip with only three segments, the issue calculating 3/5 + 1/3 becomes clear (as does the need for a common denominator). There needs to be a strategy for articulating the underlying principles before routines become set in and the meaning becomes lost in the routine. These connections take time to make and it is important to make them at a young age. He still says "1 out of 3" instead of "one third" because that is the meaning that was taught to him.