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Learning Outside Of The Box: Teaching Math Using Socratic Seminar

Jamille Hernandez has been bringing her passion for mathematics into the classroom for decades. Along with introducing her students to the behavior of exponential, logarithmic, and trigonometric functions, she has been introducing them to behaviors they can use to solve complex, novel problems—and not just math problems—through a technique known as Socratic Seminar.

"Jamille Hernandez"If you’re surprised to hear about a Socratic approach being used to teach mathematics, then you’re not alone. Most of us only heard the name Socrates in our history and philosophy classes or maybe in law school. Socratic Seminar is not a commonly used technique for teaching mathematics. After all, the ideas and questions of mathematics simply cannot be addressed in the same manner as the ideas and questions of the humanities, can they? Looking back throughout history, many philosophers considered questions of mathematics alongside other big questions about the nature of the world and our role in it. We can use the same approach to consider ideas from any discipline in today’s classrooms, right? According to Jamille Hernandez’s decades of experience, the answer is of course we can! She claims Socratic Seminar as “one of the strongest instructional learning techniques that I own to date.”

In her 13 years of teaching AP Calculus in CTD’s Summer Program, Hernandez has seen students participate wholeheartedly and reap the benefits of Socratic Seminar. During discussion time, Hernandez facilitates rather than instructs. There is no one in charge. Student groups respond to a question that requires them to apply what they have learned in class to a problem they have never seen before. Hernandez often uses AP® Free Response Questions (FRQs).

Socratic Seminar allows Hernandez to differentiate for her students through the careful composition of discussion groups and the level of complexity of problems she assigns. A group that has not yet mastered a concept will be given a more basic problem, while a group who has a better grasp of the concept will be challenged with a complex problem. Through their debrief, students see how other groups applied the same concept to solve their problems.

After their discussions, Hernandez reviews with her students where they excelled at identifying relevant concepts and expressing their ideas effectively--how they were brilliant, as she puts it. She also reviews the areas where they need reinforcement. Students then write a brief self-reflection about what they learned, how they grew and what they need to work on.

For CTD’s high math performers who think they know what to expect in a math class, Socratic Seminar may be a bit unsettling. It requires participants “to think out loud and to make mistakes out loud.” And making mistakes is important. As Emanuel Lasker, one of history’s philosopher/mathematicians put it, “Without errors, there can be no brilliance.” The one-subject-all-day format of CTD’s Summer Program means that a classroom community can come together very quickly. In Hernandez’s AP® Calc classes, students are learning how to correct a peer’s misconception or offer an insight gently, and with kindness. It’s about moving the conversation forward to better understanding, not winning points.

In a class with other students who have a passion and a talent for math, CTD students can find a new reference point for themselves. It can be humbling for students accustomed to being the top performers in their home schools. They have to adjust to the bigger fish in their new pond. But Socratic Seminar calls for adjustments by everyone. Hernandez calls them “recalibrations.” Students who typically wouldn’t speak up, learn to express their thinking in discussion. Students who are eager to raise their hand with the answer, learn to ask a question to benefit the group instead. Hernandez’s goal is to empower every one of her students by providing a learning space where they can be successful and see how meaningful their own contributions are.

Hernandez sees it as her job to inspire and nurture her students’ love for math. “I think mathematics is wow. It’s just absolutely wow. I’m in awe of how the pieces all come together.” She brings that awe to her classroom and encourages her students to lean into their own interest in math. Through Socratic Seminar, they reveal ideas to one another, complementing her instruction. Peer-to-peer sharing can make concepts more accessible and deepen students’ passion for the subject.

We may not think of the math classroom as a place where leadership skills are the focus, but the speaking and listening skills students use in Socratic Seminar are foundational leadership skills. Hernandez sees how students develop these skills at the same time they are developing their understanding of the mathematics. She hears from her former CTD students from time to time, and their stories have convinced her that their Socratic Seminar experience at CTD allowed them to move forward with greater self-confidence.

Hernandez’s expert use of Socratic Seminar within CTD’s Summer Program has given her and her many students what she calls “a platform for growth.” “There really isn’t a better feeling as a professional than to see that you’re empowering others to be the best that they can be and, in turn, allowing them to inspire you to be better.”

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