Soon, John’s affable style coaxes them into an explosion of possibilities, and the board is filled with as many answers as there were pairs of students. Ultimately, they agree on an answer based on the PEMDAS order of operations, different from the main character Milo’s left-to-right approach.

Finding that answer is not the end of the dialogue; in fact, it is the beginning. With John’s encouragement, members of the class question the whole idea of PEMDAS and the arbitrariness of mathematical rules. Before the period ends, John asks his students to come up with different configurations at home and thereby different answers to review the next day. He tells them, “I love these kinds of conversations.”

Graland’s tradition of inquiry is on full display here as John follows two of his “red threads,” which Ritchhart defines as “an apt metaphor for describing the beliefs, passions, values, and goals that tie and unite a teacher’s practice over time and contexts.” One, he commits to the study of mathematics, or truly, the study of thinking, as a “community endeavor,” involving students and teachers exploring together. Two, he skillfully creates what Ritchhart describes as “a playground of ideas.” This playground of ideas depends on a commitment to inquiry, to fully “living the questions.”

In 2021, at my back-to-school welcoming remarks, I told the story of Georgia Nelson writing a letter to be read decades later at the 75th anniversary of the school in 2002, shortly after the class described above took place. The letter explains her philosophy of living the learning. In this epistle, she declares, “It was the goal, and time and again is the reality that this school was created not only to teach children, but to help them live their learning and by doing so, live their lives.” The phrase, “live their learning,” captured my attention, and I expanded her idea based on my own experience at Graland to include three elements: to live the questions, to live your passions, and to live with purpose, all of which capture the deep dedication of Graland educators, educators like John Threlkeld, to infuse the learning experience with joy, engagement, and meaning.

Since I taught ninth grade with John for seven years, I am not at all surprised by the vignette in Ron Ritchhart’s work. John was a teacher who fully embraced his student’s curiosity, provided opportunities for a playful exploration of ideas, and often joined them in that intellectual experience, relishing in it and showing his passion for mathematics and for the intellectual traits math fostered.

This fall, when we unveiled the intellectual attributes of a graduate, we were pleased to honor the tradition of inquiry represented by John Threlkeld and other Graland educators, while emphasizing to our current educators the intellectual traits that students need to thrive in the future: purpose, authenticity, creativity, insight, and perspective. These five attributes compliment the five character traits that we shared in the character and community framework last year and complete the ten attributes of a graduate based on our guiding principles.

In that brief forty-five minutes over a quarter of a century ago, John cultivates those intellectual attributes by encouraging the students to critically assess the problem and gain insight by trying to solve it. They are asked to communicate their answers in front of the entire class and celebrated for leading the collective conversation by adding their authentic thinking. Their creativity in solving the equation is also applauded, and they are directed to continue that innovation by challenging the idea of order of operations itself. Then, they discuss the purpose behind the mathematical rule and question its arbitrariness, the beginning of considering how mathematical expertise applies to the real world. Through it all, John introduces them to the experience of a robust cognitive exploration, an experience that will expand their perspective of a lifelong intellectual journey fueled by playful curiosity.

Over close to a century, Graland has committed itself to the intellectual journey of its students both during their time here and beyond. That journey is essential to us achieving our mission to foster intellectual excellence and strong character in our students so that they become engaged citizens and thoughtful leaders. I feel proud to follow the legacy of instructional leaders like Georgia Nelson and John Threlkeld, who realized that Graland was about more than just teaching; it was about creating an immersive learning experience, “a playground of ideas,” to explore together. These were the red threads of John Threlkeld, and in many ways, the red threads of Graland. We are committed to following in the footsteps of those who came before and continuing the tradition of living the learning so that our students live lives of curiosity, passion, and purpose.