Teaching Mathematics Classically

By SHANE ARTRIP

“There is geometry in the humming of the strings, there is music in the spacing of the spheres.” (Pythagoras 582 BC – 497 BC) 

Teaching mathematics in a classical manner encompasses so much more than addition, subtraction, multiplication, and division facts. Recitation of fact families can be heard in many younger grade-level classrooms across the world. However, are these children awakened to the true beauty of the many patterns naturally present in creation? A classical approach to mathematics ignites the natural wonder and imagination of students to recognize and look for patterns. An example of a fascinating numerical property found in nature is known as the Fibonacci Sequence. The sequence follows the form: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,… Note that the third term is the sum of the first two, the fourth the sum of the second and third, and so on. These numbers are found in the spiral arrangements of petals, pine cones, pineapples, and sunflowers as well as in the genealogy of the male bee just to name a few instances. 

As we teach mathematics to our students, we have the opportunity to point out attributes of God. God is limitless and boundless. He is from everlasting to everlasting, without beginning or end. Our real number system incorporates the concept of infinity in both directions. The integers have neither beginning nor end. Even young children can grapple with the concept that counting numbers continue onward indefinitely while considering the parallel of how long eternal life lasts. 

God created this universe in an orderly, precise, and logical manner. The forces that hold our planets within orbit, and the perfect proportions of elements, minerals, and water present on Earth so that life can exist was perfectly designed by Him. Our philosophers, scientists, and scholars did not invent mathematics as a mental exercise for future students. They documented their discoveries of relationships, patterns, and laws already present and applied these principles to learn more about the world around them, to achieve breakthroughs in the fields of various sciences and medicine, and to invent many things we take for granted in our daily lives. 

The three properties of equality shout out the attributes of God to all who will notice. 

1. The Reflexive Property: For any real number, a = a.

(God said to Moses, I AM WHO I AM” Exodus 3:14a)

2. The Symmetric Property: For any two real numbers, if a = b, then b = a. 

(…he that hath seen me hath seen the Father, Believe me that I am in the Father, and the Father in me. John 14:9b, John 14:11a)

3. The Transitive Property: For any three real numbers, if a = b and b = c, then a = c. 

(The triune God – For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one. I John 5:7) 

In what ways can classical teachers facilitate and guide their students toward discovery in the mathematics? First, the teacher must intentionally step back from the content-driven rush for quantity and prepare the lessons with fresh eyes while searching for those attributes of God: absolute Truth, constant, orderly, eternal, etc. that are illustrated in the simple operations and relationships. The teacher must genuinely understand the concepts behind the “tips and tricks” algorithms of the particular process. In doing so, that teacher will better equip their students in the art of critical thinking and problem solving rather than limiting the child to solving just one or two particular problem types. 

When my students solve an algebraic equation, they must apply the algebraic properties and rules in a logical and precise way in order to find the correct solution set. My students have often heard that I am just as interested in the “documentation” of solving the equation as I am in the final answer. This “documentation” demonstrates the thought process that was applied in order to arrive at the proposed solution. No matter the path our students take as they grow into adulthood, whether the university, the military, the business world, or managing a home, they will be problem solvers. Every day presents itself with thousands of thoughts and decisions, many of which require careful, and clear contemplation. Of course, the most important problem that students will ever encounter is that of SELF and their relationship with a Holy God. These beginning algebraic problems serve as a training ground for critical thinking and problem- solving skills. The study of mathematics, when executed properly, exercises the mind, challenges it to reason inductively, equips it to make connections in order to predict outcomes in everyday situations, and ultimately points toward the true solution to our problem of SELF in our Lord Jesus Christ. 

Teachers, challenge yourselves to develop a simple passion for discovery of patterns. These patterns are present in music, history, science, poetry, languages, athletics, and much more. Passion in teachers readily inspires a passion for learning within students. Most students can discern whether a teacher is confident in teaching his or her subject matter. It is our calling to step, and even leap, outside our comfort zone to develop ourselves, to learn something new, and to prepare our lessons as we would a rich banquet for our guests in which to savor and delight. O taste and see that the LORD is good: blessed is the man that trusteth in him. (Psalm 34:8)

Mrs. Shane Artrip teaches Upper School math, science, and grammar Latin. Mrs. Artrip holds a Bachelor’s degree in mathematics from Texas State University and a Master’s degree in mathematics from Marshall University. She has taught for 30 years at varying levels from grammar school through university.  She and her husband, Jim, attend Rock Branch Independent Church where she serves as the choir director and as an assistant in children’s music ministry.  They have three grown children and two grandchildren.  Mrs. Artrip served as Covenant’s Headmaster for 5 years and currently serves as Upper School Academic Advisor.