Earlier this week, one of my AP Calculus AB students paid me a great compliment saying, “I learn more vocabulary in this class than I do in AP English;” he was not speaking of mathematics vocabulary, or academic language. The comment and the discussion that followed made my day.
In speaking freely, fully in the moment, the student recognized my effort to expand my students’ knowledge, not just of calculus, mathematics, standardized tests, or of doing school, but, more broadly, in a Renaissance sense. Fortunately, my studies in the humanities, as well as math, science, and engineering, along with business administration and education, and my lifelong love of reading, offer a trove of vocabulary and experiences for me to share. Doing so is intellectually stimulating for me and, with my comedic leanings, entertaining for many students.
I do not limit this approach to my advanced students; I follow a similar act with my algebra 1 students, just scaling it back to help them bridge from where most of them are at the moment. I also differentiate delivery within the class by varying word complexity to span from my most advanced students to those far below basic, from gifted and talented (GATE) to resource specialist program (RSP) supported, from English-only (EO) to English Learner (EL).
All students benefit since I take the time to diagram etymologic roots for select words helping them see their origin, evolution, and application in what many consider a boring subject: algebra. I recently promoted this approach with a colleague explaining how mathematics instruction from primary school through algebra, geometry, trigonometry, precalculus, calculus, and beyond must support students making connections among these seemingly disparate courses using common vocabulary and their root words. As an example, the connections possible between the concept of ratio and other mathematical concepts are many. Consider rational and irrational numbers as learned in primary school to rational expressions learned in algebra to ratio used in geometry to explain similar triangles or geometric means to the use of the quotient rule in calculus with rational functions. A later post will explore this example in more detail.
If I felt students did not benefit from my linguistic leanings, they would not occupy precious instructional time. However, enriching the instructional discourse this way keeps my students engaged, more so than a narrow discussion limited to subject-specific vocabulary, academic language, or content could do. While “professional knowledge base” in the following quote is vague, I take the liberty to use the reference as one justification for my approach. For my purpose, I consider professional knowledge base as my accumulated knowledge and learnings in my life to anchor my efforts to be the most effective teacher possible.The California Standards for the Teaching Profession (CSTP) state that “effective teaching requires the ability to successfully integrate elements of the professional knowledge base in the service of learning, growth, and development of diverse students across varying contexts.”