This video really made me smile.
A spoof on the the cup song (which I love and learned how do the "cup thing" this summer in Honduras) has caught viral attention. This version of the song even made it on the WGN news. This version of the "new" cup song includes lyrics that highlight fractions, fraction operations, and how math can be fun. Take a few minutes and watch these kids. They are hilarious and awesome!
This song made me smile and even giggle. The kids were so cute and it was edited in a way that is super mathtastic and teacheriffic. Any teacher could share their this with students in their own classes. I am proud the school, the teachers, and the students for taking the time to produce this, share this, and how how math is fun. I just finished teaching a class for preservice elementary teachers at ISU this semester where the main focus of the class was conceptual understandings about number, with a heavy focus on rational number. I thought about my students when I saw this and I thought that maybe I should share this with them.
Then my smile faded...
Although the whole video is sweet and funny, there were a couple things that glared at me. Although this is a funny, cute, and awesome video, the importance of algorithms without conceptual meaning stood out to me as I watched this video. Let me be clear, I am not criticizing this school, these teachers, or these students… or even algorithms. This is just a video, and I don't know what happens in their classrooms. And, again, these teacher provided a creative opportunity for their students that is admirable. However, we are immersed in a society and a mathematical culture, where the right answer is the most important thing and learning the algorithm for efficiency on the next standardized test takes priority. I wonder how others interpret this video. The point of mathematics and using fractions is far deeper than little "tricks" about how to use an algorithm. For example, take a look at 3 minutes 27 seconds of the video. The kids sing, "To multiply fractions you stay in line. But, when you divide you got to flip the second fraction. Then you can multiply just fine." I ask, why? Why can we efficiently flip the second fraction and multiply across? This is something even mathematics majors and mathematically proficient students at universities struggle to explain conceptually. But, if we don't understand why, mathematics just becomes a product and communication of obscure rules and procedures, which are useless when someone hands you a calculator. The conceptual underpinning of fractions need to take the front seat in our instruction. For me, this video highlighted this glaring issue that plagues many of our schools today. I think it is important for students to invent and create their own strategies for learning about number, even when it comes to fraction division.
What do students invent?
Letting students invent their own strategies and building upon these strategies is a way to facilitate conceptual understandings and even build up to self-discovery of the formal algorithms. How do students reason about fractions? I would like to point you to two of my favorite books on rational number instruction (see below). Both of these books highlight student invented strategies and conceptual understandings of rational number. Both books have samples of student work. Both books provide problems to give your students. Both books illustrate that the algorithms in this video aren't the only way to do these problems effectively or efficiently.