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July 1, 2016
Vol. 58
No. 7

Road Tested / Flipping Math to Engage Curiosity

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As a high school mathematics teacher, I often reflect on my own K–12 math education as a way to guide and improve my instruction. Some of my most enriching experiences happened when teachers encouraged my inquisitiveness and challenged me to investigate an idea or problem.
In my own classes, I try to foster a similar environment of exploration, application, and love of mathematics. I continually search for ways to stimulate students' interest in both abstract and applicable algebra, calculus, and geometry concepts. A flipped classroom approach, I have found, piques students' curiosity by freeing class time for exploratory projects and discovery-based learning.

To Video or Not to Video?

In a flipped classroom, students watch instructional videos as homework and then come to class to work on problems and collaborate with peers on applying what they learned in the videos. I don't flip every class: I provide supplementary videos, as needed, for students who would like to revisit the instruction at home—and save the flipped videos for appropriate concepts (for instance, dry topics that require a lot of definitions and notation).
As an example, when introducing functions in a junior-level algebra 2/precalculus course, I assigned a video with an overview of basic parent functions, the relationship between independent and dependent variables, and rates of change. When students came into class, we reviewed the concepts as a warm-up and then dove into a collaborative, discovery-based activity. Students worked with peers to analyze the time it took for a rock climber to make it to the top of a rock wall based on the steepness. They were highly engaged as they analyzed the variables through graphical analysis, tables, and function generating. Some students even pushed themselves to explore exponential versus linear relationships.
Without first introducing the concepts at home, I would not have been able to involve students in such a challenging activity. Usually, when students get stuck on a homework problem, it is hard to move on without help. But if students are assigned a video, they can take notes and come in with questions about their misunderstandings. The struggle then happens in class, where the teacher and other students can offer their guidance and support.
By allowing students to collaboratively solve interesting and difficult problems in the classroom, we awaken their curiosity and intrinsic motivation to learn. For instance, when my students explored logarithms and exponential functions in class, they began to wonder how they could apply logarithms in their future careers or what real-life activities could be modeled by exponential functions. They thought about investing money and used exponential functions to decide which company and bank account would provide the best return. It was amazing how far the students took their learning when they were able to engage deeply.

The Goal

Using videos to lay the groundwork has been simple: I create some of the instructional videos on my own with VoiceThread, iMovie, or QuickTime, and I also use supplementary videos from sources like Khan Academy and YouTube. I post the videos to Google Classroom, along with the required questions or assignment.
Because our district has a one-to-one laptop program, all students have access to a device. To ensure students are connected at home, I survey them during the first week of school, asking them to write down their names, what they want to be when they grow up, and to check off whether they have Internet access outside of school. If they don't have access, I can provide them with a USB flash drive repository of the videos.
My goal is not to have students memorize, but to have them understand. This goal reflects the Common Core State Standards, which recommend applying concepts and ideas rather than just learning procedures and formulas.

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Would you like to write for the next "Road Tested" column? Visit www.ascd.org/educationupdate for submission details.

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