The Cupcake Dilemma (What do you know about fractions?)

Growing up, I learned math by memorizing procedures and facts and completing countless pages of problems. For most of my teaching career, I taught my students the same way. But as fact would have it, I was blessed with seven children of my own. I watched their struggles with math homework. Two of them struggled for years trying to memorize the multiplication facts. Another was lost when she got to algebra, and another suggested that math was easy because all you have to do is memorize the formulas and plug in the numbers. My own kids opened up my eyes to why we need to teach math differently.

Even with the common core in place now for three years, teaching for understanding is not the norm in most classrooms. Just this weekend, my daughter, who was trying to bake cupcakes, called me with this dilemma.

"The recipe says that I need 1/3 cup of oil, but the measuring cup only has a marking for 1/2. What should I do?"

As a seventh grader, she's had years of practice with fractions, but does she really understand fractions? Can she apply what she's learned about fractions in real life situations?

Once I explained how she could estimate 1/3 cup using 1/2 as a reference, she was fine. The cupcakes were delicious. But I'm not convinced that she'll be able to apply that knowledge in the next situation because she doesn't really understand fractions. Memorizing procedures and facts don't always work in real life.

Reflection: How have my math lessons changed to help students develop a deep understanding of mathematics?