What is 2/3 divided by 1/2? Easy…keep, change, flip. 2/3 x 2 equals 4/3. I did this in my head in about three seconds. I sat in Dr. Juli Dixon’s class feeling like I had a pretty good handle on elementary math content. Dr. Dixon then asked us to solve the equation without using an algorithm. Um, what? I tried to draw a model and failed. I tried to relate it to other division problems. If I have 2/3 of a cake and share it with 1/2 a person…that didn’t really help either. I tried to force my model to show 4/3 but I found myself becoming more confused.I honestly felt stupid and tried to hide my paper from my peers and Dr. Dixon. It was then I realized this may be how my students are feeling and that I may have been failing them all along by teaching tricks and procedures without any true understanding.
Dr. Dixon went on facilitate an activity in which we explored dividing fractions. I think for the first time in my life, I finally understood where the procedure came from. From then on, I was motivated to learn the why to every algorithm, procedure, or strategy I taught my students. I also began to make kids do more of the sense-making versus me modeling all the time, began valuing a kids exploration of a topic rather than a correct answer, and fostered a safe environment for my students to make mistakes. I saw a definite change in the attitudes of my students in mathematics and I began to truly love to teach math.
The research agrees on many of the best practices for teaching mathematics. Students need conceptual before procedural, to have conversations about math, and be in an environment which values mistakes and allows for the time to make them. However, change can be hard for teachers. Time, resources, professional development opportunities, family obligations, fear, administrative support, and the list goes on, can all impact how or even if a teacher grows professionally.
If you’re looking for a starting place on how to start transitioning your math teaching, you’re in the right place. If you’re here to question why your old school methods won’t suffice anymore, that’s a conversation for a different day. I’m always going to suggest to start small. A great activity to start implementing is “Which One Doesn’t Belong?” Students are presented with four different pictures and asked to identify the outlier. There are many different answers to these and allow students at any level to access the math. You will begin to learn a great deal about your students’ understanding in math and see the value in math conversations in the classroom. If you’re looking for one step further, try a 3-Act task. These are longer, and often take a whole math period but boy are they worth it. I also suggest looking at NCTM’s website in which you can look at the research behind best practices and get additional strategies to try with your students.
No matter where you are at in your journey, I implore you to start anywhere and give yourself patience and understanding. I also encourage you to find at least one other person at your school to talk to about your own professional growth. Math coaches are great person to reach out to (I may be biased). I know there is an endless amount of items on a teacher’s to-do list, however trust me when I say once you begin this journey in teaching mathematics differently, you’ll be hooked.
