Core Principles for Instruction in Mathematics

I’ll tell anyone who will listen that I love my job. I get the privilege of teaching mathematics at Regents School of Austin – a distinctively Christian institution not only in its faith commitments but also in its dedication to the development of the Christian mind.

One of the many reasons I love working at Regents is given below. Here you will find the first page of the Math-Science Department Faculty Manual which states the Core Principles for Instruction in Mathematics:

(Much of the credit for this confession goes to Mr. John Mays, a longtime faculty member who you can read more from at Novare Math and Science).

Core Principles for Instruction in Mathematics

Mastery of basic skills and real-world applications is essential to learning mathematics. Instruction in mathematics must constantly focus on these two fundamentals. Basic skills must be practiced to mastery so that they become permanent parts of the students’ analytical toolbox. But abstract skills without application to actual problems are like tools which are purchased but never used to gain experience. The application of basic skills to real-world problems is an ongoing essential for developing experience with using the tools of mathematics.

Mathematics is not “religiously neutral.” It is a fact that mathematical principles are abstractions which reside in the human mind. It is also a fact that mathematical order exists in the objective reality of the natural world. Many mathematicians and scientists have been utterly unable to understand how abstractions in the human mind can have correspondence to the external physical world. This puzzle cannot be understood or comprehended apart from the recognition of the existence of the Creator who has imbedded mathematical order in both the world and the human mind (section 4.1).

The value of mathematics is not merely utilitarian in nature. Through the study of mathematics students sharpen their abilities to think logically. They encounter purely abstract entities (such as perfect circles, higher dimensionalities, and the transcendental numbers pi and e which point to the real existence of nonmaterial universals. Because human beings are made in the image of God, their lives do not consist only in the pursuit of economic and material goals (Matt. 6:25-33), and the study of mathematics affords a rich opportunity to meditate on the miracle of creation and of the status and role of human beings in it.

The history of mathematics as a cultural endeavor is a valuable part of a full education in mathematics. Mathematics has obviously played a profound role in major cultures since ancient times, and continues to do so. Students should understand the cultural role of mathematics throughout the ages, and the cultural context and history of the major mathematicians who have contributed to the development of mathematics. Additionally, students should be taught to avoid thinking of mathematics as something static and given, and should comprehend the dynamic nature of mathematical theory. Mathematics, like every other discipline in God’s creation, is something that human beings continue to explore and develop, and a student who makes mathematics the focus of his life’s work is continuing the great tradition of the cultural mandate, God’s charter to man to develop and explore every aspect of the creation of which we are a part (Gen. 2:15).


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