Geometry and the Homeless

This week I had the pleasure of writing a short note about my Geometry students’ spring project for my school’s newsletter. I thought I would include that below (as well as some pictures that weren’t included in the newsletter). I’ll provide a full write up here upon the completion of the semester.

Regents School of Austin eNewsletter

Regents high school students are partnering with a local ministry to apply their math skills. Please read this inspiring story from Mr. Josh Wilkerson. He is one of our math teachers in the School of Rhetoric.

~ Rod Gilbert, Head of School

1 Peter 4:10 commands us: “Each of you should use whatever gift you have received to serve others, as faithful stewards of God’s grace in its various forms.”

I use this foundational truth as the basis to address that customary question of the high school mathematics classroom: When am I ever going to use these math concepts? God instilled a mathematical gift into every human being, enabling humanity to fulfill the purposes of the Great Commandment (to love our neighbors) and the Great Commission (to take the good news to all people). How might we employ our “math-mindedness” in serving others as the Apostle Peter commands?

Mobile Loaves and Fishes (MLF) ministers to the homeless community here in Austin. They recently purchased a tract of land on which they plan to construct an affordable living community for the chronically homeless called Community First. The acreage includes space for trailers, RVs, micro-homes designed by University of Texas architecture students, a large garden with animals, a workshop, chapel, and a medical facility all in the hopes of being a self-sustaining community. The vision of Community First seeks to overcome the homeless mindset and demonstrate that home is more than a physical structure. Home is relationships and far more than just a roof.

MLF graciously allowed our freshman geometry class to participate with them in this project. They have asked our students to utilize their understanding of geometry by designing an awning for RVs. These awnings provide shade and protection to the roof of the RV but it is also creative and energy efficient. Furthermore, these awnings contribute to the mission of MLF in developing relationships and fostering true community.

This past Monday the students visited the MLF Community First project site so they could see the immediate fruit of their labor. The students spent time hearing directly from MLF representatives about their vision and their heart for the homeless, and also about the very real need they have in their design process that the students can meet. There were many questions asked, many measurements taken, and then more questions asked. The MLF representatives were very accommodating and thrilled to see the excitement that the students of Regents had over this opportunity. At the end of the project, these same MLF representatives will travel to Regents to hear the presentation of each team of students and then select a winning design.

As their teacher, I marvel at these students as they mature to understand that learning has NO meaning unless it produces a sustained and substantial influence not only on the way people think, but also on how they act, feel, worship, and serve. I am excited to see what the remainder of this semester holds.

Josh Wilkerson
SOR Mathematics Appreciation Teacher
Appreciating AP Statistics and Geometry

Additional Pictures Not Included in the Newsletter:

Students hearing a presentation from MLF
Students hearing a presentation from MLF
Discussing layout with Dave Sekel of MLF
Discussing layout with Dave Sekel of MLF
Students analyzing the RV that they will design an awning for
Students analyzing the RV that they will design an awning for
Analyzing EVERY component of the RV
Analyzing EVERY component of the RV

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).

Defining Geometry Christianly

I must again apologize for the delay between posts. I have spent the last few weeks settling in to my new teaching position at Regents School of Austin. I plan on sharing more about Regents later. Throughout my orientation to the school I have been practically overwhelmed by amazingly well stated arguments for understanding mathematics from a Christian perspective and outstanding faculty who live it out in the classroom. I have been doing a lot of mental processing and I hope to share the fruit of that labor soon.

For now, I wanted to share my first day of school lesson for my advanced geometry class. For the first time in my professional career I am in a position to openly teach on the integration of faith and mathematics. I plan on taking full advantage of the opportunity. I’ll share as much as I can here, in hopes that it may be helpful to other teachers, and in hopes that these lessons might get refined through comments and discussions in community.

Euclid in Raphael’s “School of Athens”

What is Geometry?

The prefix Geo means “earth” and the suffix metric means “measurement.” Put them together and you get the idea that to do Geometry means to literally “measure the earth.” Even in its earliest forms, Geometry was used to analyze positions and movements of celestial objects so its reach went beyond the literal “earth.” Perhaps then a better translation for Geometry would be to “measure nature.”

At this point I direct my students to a poster I have mounted above my door:

This phrase is said to have been inscribed on the door of Plato’s academy. It roughly translates to “Let no one ignorant of Geometry enter here.” This translation necessitates clarification for students. Plato was not standing at the door checking transcripts to see who had their Geometry credit. Plato is not interested in his pupils’ ability to do mathematics, rather he is interested in his pupils’ ability to think. In this context, Geometry is a way of thinking; a way of thinking that is logical and consistent, and to be ignorant of it is to be unwilling to accept the value of reasoned study.

With this idea in mind we can broaden our definition of Geometry from “measuring nature” to “thinking logically and consistently about nature” or perhaps more succinctly “thinking rightly about nature,” though this last phrasing is likely to gain little acceptance in a postmodern world where truth (rightness) is relative. Oh well. Truth is objective. I am not going to argue for this point here, but it is crucial to accept if we are going to continue to define geometry Christianly.

The next logical question is, if Geometry is “thinking rightly about nature,” how do we define “rightly”? As Christians, our definition of truth/rightness comes from the nature and revelation of God. God is Truth and He has given us His Word to reveal Himself (truth) to us. His Word appears in a variety of ways and in general we can classify God’s revelation into two broad categories: special revelation and general revelation.

Special revelation is detailed and specific revelation of the nature of God, the nature of creation, and how the creation is to relate to the Creator. This is the Word of God as revealed in the written Word of Scripture and the incarnate Word of Jesus Christ. This revelation is primary. This revelation is salvific.

General revelation is how God has revealed Himself through His creation. Looking at the intricate designs and beauty of nature gives us a sense that there must be a Designer, a Creator, behind them. Creation is the Word of God that was spoken in Genesis 1 that brought forth order from chaos.  This ordered realm in which we live is where we find Geometry, only now we can refine the definition from “thinking rightly about nature” to a more Christian perspective of “thinking rightly about creation” – and by “rightly” we mean with an understanding that special revelation exists and is the primary source of revelation for ordering our lives and our relationship to God.

Putting these ideas together (the ideas of applying Geometry to nature, realizing it is a system of thinking, understanding nature as creation from a Creator, and seeing special revelation as necessary for correctly orienting our thought processes) we begin to see how one may approach the study of Geometry from a Christian perspective:

To do Geometry Christianly is to  order our lives in a right relationship with God, through His Son Jesus Christ and His Holy Word, so that we might be able to think clearly, consistently, and truly about His created order.

The verse that ties this all together is the verse that is used as the theme for this website: Colossians 1:15-17.

He (Christ) is the image of the invisible God, the firstbornover all creation, for all things in heaven and on earth were created by him – all things, whether visible or invisible, whether thrones or dominions,whether principalities or powers – all things were created through him and for him. He himself is before all things and all things are held togetherin him.