Sixth grade math teacher Kevin Randazzo wants his students to do more than memorize math concepts–he wants them to understand why and how they work. Through engaging projects, weekly puzzles and real-world examples, Kevin’s students are learning to become both independent and collaborative problem solvers that can not only do the math at hand, but can articulate their thought processes and see how math lives in the world around them.
Having taught at Calhoun for seven years, Kevin has refined his curriculum to ensure that each student is reaching their greatest potential.
We work with fractions for much of the second trimester because they're so prevalent in math, and there are different things that a fraction can represent. We go into a unit with geometry and then we finish the year with the pre-algebra unit. Pre-algebra is a big buzzword for sixth graders, but we sneak it into everything that we do throughout the first two trimesters. By the time we get there, they realize they’ve been doing it all year. Then we can really sink our teeth into things like graphing, looking at tables and equations, and moving between those three things. [For example], we might make a table from an equation and then a graph that expresses that content in an equivalent manner.
When we do multi-day projects in class I give a thorough set-up of expectations and provide enough information to help the students get started. The first day [of my class] is all struggle, then I come in on the second day and go over what strategies did and did not work. We also talk about taking a problem and breaking it down. We've planned cities in the past for geometry projects. We’ve made our own currencies and exchange rates in class. When I'm making projects I make sure that I would enjoy it if I were a student in my class.
Uniquely Challenging Each Student:
I start every class with a seemingly random math problem, something different and fun to get my students warmed up and ready for the rigor that we will have later on in class. The key is that [students] are feeling supported, challenged and pushed and that every student feels like they're getting something from the class. The cool thing about math is that you can differentiate it pretty quickly. There's always more that you can get out of high-flying students. They may be faster, but might not necessarily have a stronger grasp of the concept compared to a student that is taking their time and going slower. I’ll ask them why they solved a problem the way they did and [they will] have to analyze and articulate their process. That's when it gets really engaging for those students.
One day of the cycle is “station day,” during which students rotate through multiple work areas with different activities. One of these is always to work with a digital learning platform called IXL. With this tool, [students solve] a series of problems that will grow in difficulty as students get closer to mastering a subject, and will plateau in difficulty when students start showing that they're struggling. I'm looking at the growth and the problems that they're answering. Every mistake that they make is much more valuable to me than the right answers that I see. It helps me to assign things that are more specific and more tailored for that student. It also allows me to really be specific with my feedback and observations.
Building Skills and Flexibility:
If I had to sum up the school year [in my class] in one math concept, I would choose “equivalency:” being able to find an equivalent decimal to a fraction, or find an equivalent fraction to another fraction. Working with number sense you can represent your thoughts in a number of different ways using different strategies. Students can't do everything that we learned on their phones or with a calculator. In this class, I value reasoning and flexibility of thinking over robotic skill regurgitation. I want learners who can fail, and absorb strategies, and try something new, students who can sit in their struggle and learn from it rather than wallowing in some initial confusion. These skills are applicable far outside the confines of a math classroom and are ones that can't be downloaded in the app store.
It's one thing to memorize your times tables, [it’s another] to be more flexible with the way you work with numbers. It’s about being comfortable with not knowing everything in a given problem, but having enough wherewithal to work towards the solution, making a hypothesis and working with your operations and numbers to get to that conclusion.
Sixth grade math is awesome because there are so many real-world applications. If you want to pay a bill and figure out tip, you've got to know how to work with percentages. Last year we used the first-ever picture of a black hole as a way to talk about exponents, but also to talk about the women on that team of scientists who made this possible, to show that math has a vibrant and diverse community. Part of tying math to the real world is being able to use real examples, but also seeing the opportunities that are open to anybody in my classes if they want to pursue a life in a [math related] field.
Teacher Talks is a series spotlighting the educators of Calhoun and their approach to progressive education.