Math Justice League Blog

Dear Math Justice League, 

I am someone who in education communities self-identifies as a lover of fractions. Yet, each time I broach this subject, I’m met with a familiar expression of skepticism, often accompanied by a sigh of exasperation, “Ugh, fractions! They’re the worst!” And you know what? I can't resist the urge to try and win over at least one person in the group. But let's face it, changing people's minds about fractions, especially when they've been taught poorly, isn't easy. So, here I am, trying to reach a wider audience. If you've made it this far and are even considering reading the rest of this ode to fractions, I'll take it as a small win.

Reflecting on my mathematical journey, my experiences with fractions as a student were relatively neutral, with no strong emotions either way. I was generally eager to please and remembered most of the “rules” my teachers taught me. Things like, when adding or subtracting fractions, “multiply the numerator and denominator by the opposite denominator,” or when dividing fractions, using the “keep, change, flip” method. I memorized these “rules” about fractions and used them to get (mostly) correct answers on assessments. 

After navigating my schooling with these rules, which served me well enough, I returned to the classroom as a teacher, ready to do the same for my third-grade students. However, my conviction wavered when students posed simple yet profound questions like: "Why do we multiply the numerator and denominator by the opposite denominator?" and “Why do we need common denominators?” I was stumped, and I knew that the response “Because that’s what my teacher taught me” was not going to cut it. My understanding of fractions was built on shaky ground. That day marked the beginning of my quest to unravel the mysteries of fractions, to provide my students with more meaningful exploration and explanation of this misunderstood math concept. 

In this resource, I offer explanations rooted in conceptual understanding to common questions kids (and adults) have about fractions. While I don't claim to be a fraction expert, nor will you become one after reading this, I encourage you to view this as a stepping stone toward deeper understanding. Emphasizing the importance of comprehending the “why” behind the established “rules,” I hope this serves as a catalyst for further exploration.

Mathematics is a language and the purpose of teaching mathematics is to empower students to be fluent and elegant within it. Not allowing students a proper understanding of fractions would be akin to teaching nothing but prose to our students and expecting them to write beautiful poetry. It’s not going to happen. 

There are many resources online and YouTube videos to support with fraction understanding. However, I suggest being a skeptical consumer of materials you come across. If you see nothing but steps on how to find the right answer, you should look elsewhere.

With a deeper understanding of fractions and a clearer grasp of the “whys,” perhaps we can cultivate a generation of fraction enthusiasts who perceive fractions not as objects of dread but as the intriguing mathematical constructs they truly are.

In Crew, 

Warren Corazzini

EL Education Coach, Math Specialist