Lessons

A Philosophy of Teaching Math from a Christian Perspective

joshwilkersonLeave a comment

In my last post I shared our school’s math catechism. It struck me that for those interested in the topic of a catechism, you might also find our math department’s philosophy statement useful as well as it could also be used as a catechism.

One thing to note: as a K-12 math department we constantly revisit our departmental philosophy, so aspects of this could change in the future. What is below is where we are at right now.

Regents School of Austin Department of Mathematics

Departmental Philosophy

Mission Statement (WHY?):

The study of mathematics at Regents School of Austin is a Christ-centered discipleship process in which we cultivate the affections of students to pursue that which is True, Good, and Beautiful in the science and art of quantitative and critical reasoning.

Portrait of a Graduate (Students, WHAT?):

We are educating problem-solvers to become winsome servant-leaders who value active engagement in meaningful struggle as the means of growth academically, personally, relationally, and spiritually.

Mathematical Practices at Regents (Characteristics of professional excellence, HOW?):

Sense-making: Meaning. Before a problem can be solved it must be understood within the context of prior knowledge. Critical thinking is by definition the critique of ideas. Critique requires a prior standard against which new knowledge can be measured. All problems must be gauged through a Christian lens that sees God as the foundation of truth, beauty, and goodness.

Perseverance: Confidence paired with humility. Grit. There is no opting out. Engaging in the process of working towards a solution is more formative than achieving the solution itself. Perseverance is forged through shepherded periods of struggle.

Collaboration: Teamwork. Math is not meant to be done in isolation and neither the teacher nor the textbook is the ultimate authority. Students should be able engage well with their classmates, learning to both listen and lead.  

Communication: Students are expected to communicate reasoning in verbal, visual, and written form to both classmates as well as their teacher. Communication necessarily happens in community, with a diversity of thoughts and abilities. To communicate well is to be prepared to engage the thoughts of others and to be willing to have one’s own thoughts refined in return.

Grace: Mistakes will be made. They must be made in order to learn. Students must feel free to make conjectures, ask questions, make mistakes, and express ideas and opinions without fear of criticism. Students are expected to show grace to both their classmates and their teacher. And students can expect to receive grace from both their classmates and their teacher.

Service: A real problem is never truly solved without some sacrifice made on the part of the problem-solver (a giving of talent, time, or treasure). A true problem-solver operates in a constant mindset of serving others. Math education is not ultimately about self-promotion, rather it is about equipping students to love and serve others well.

Affection: An innate wonderment at the realities of mathematics, the applications of mathematics, and the connection between them. Embracing the imbued curiosity of humanness and exploring imaginative, creative, beautiful, and powerful notions introduced through the study of mathematics.

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A Math Catechism (UPDATED)

joshwilkerson2 Comments

Previously I shared a proposed Catechism for Mathematics. If you are wondering why it might be wise to consider a catechism in mathematics or what a catechism even is, I encourage you to check out that previous post.

At the start of this school year I met with my math faculty K-12 to refine the language of the catechism and make it into something that we could do K-12, with age appropriate responses. Below is what we came up with. We are getting close to being a month into our semester and the early returns are positive. I love being able to ask any student on campus “what is mathematics?” or “how is a Christian to understand mathematics?” and get a thoughtful response in return.

[Update: I’ve recently been made aware of Joshua Gibbs collection of math and science catechisms over on his Circe Institute blog. I encourage you to check those out as well. Gibbs also has a great book that argues for the power of catechism in the classroom that is also well worth reading.]

Defining terms (since I teach at a classical Christian school that uses language they might not be familiar to all readers):

  • School of Rhetoric (SOR) = High School, grades 9-12
  • School of Logic (SOL) = Middle School, grades 7-8

Regents School of Austin Mathematics Catechism

What is mathematics?

  • SOR: Mathematics is the science of patterns and the art of engaging the meaning of those patterns. (Francis Su)
  • SOL: Mathematics is the science of patterns and the art of engaging the meaning of those patterns. (Francis Su)
  • 3rd – 6th : Mathematics is examining patterns to find their meaning. 
  • K – 2: Mathematics is playing with patterns.

What does it mean to be a mathematician?

  • SOR: A mathematician appreciates the value and beauty of mathematics and is able to assess the validity of quantitative arguments. 
  • SOL: A mathematician appreciates the value and beauty of mathematics and is able to assess the validity of quantitative arguments. 
  • 3rd – 6th: A mathematician values the usefulness of numbers to describe the ordered and beautiful patterns we find in this world. 
  • K – 2: A mathematician sees order and beauty in patterns.

Who can be a mathematician? (To whom is mathematics accessible?)

  • SOR:  To anyone who is curious and not stubborn, God has made plaine the order and truth of numbers to everyone who uses reason. (Paraphrase from Augustine)
  • SOL: Since God has given everyone the ability to reason, God has made everyone a mathematician. 
  • 3rd – 6th: Since God has given everyone the ability to reason, God has made everyone a mathematician. 
  • K – 2: Everyone!

If everyone can be a mathematician, what are mathematicians supposed to do?

  • SOR: The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics. (Johannes Kepler)
  • SOL: The chief aim of all investigations of the world should be to discover patterns created by God and revealed to us in the language of mathematics.
  • 3rd – 6th: We study the world looking for the patterns God created by using the language of mathematics. 
  • K – 2: We discover the patterns that God created.

How did God create the patterns we see?

  • SOR: Through Christ, the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15-17)
  • SOL: Through Christ, the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15-17)
  • 3rd – 6th: Through Christ, the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15-17)
  • 1 – 2: Through Christ, the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15-17)-
  • K: Through Christ, the image of the invisible God, the firstborn of all creation. (Colossians 1:15)

What does it mean to do math as a Christian?

  • SOR: In exploring mathematics one is exploring the nature of God’s rule over the universe; in other words, one is exploring the nature of God himself. (Vern Poythress)
  • SOL: In exploring mathematics one is exploring the nature of God’s rule over the universe; in other words, one is exploring the nature of God himself. (Vern Poythress)
  • 3rd – 6th: God made and rules over everything. When we are exploring patterns we are exploring God’s handiwork.
  • K – 2: We are exploring God’s handiwork.

Mathematicians, what are YOU going to do?

  • SOR:  I will always try, ask questions, be creative, be kind, be helpful, not give up and enjoy exploring. I commit to cultivating my mathematical affections. 
  • SOL:   I will always try, ask questions, be creative, be kind, be helpful, not give up and enjoy exploring.
  • 3rd – 6th: I will always try, ask questions, be creative, be kind, be helpful, not give up and enjoy exploring. 
  • K – 2: I will always try, ask questions, not give up, be kind, and have fun!

A Math Catechism

joshwilkerson10 Comments

A catechism ( /ˈkætəˌkɪzəm/; from Ancient Greek: κατηχέω, “to teach orally”) is a summary or exposition of doctrine and serves as a learning introduction to the Sacraments traditionally used in catechesis, or Christian religious teaching of children and adult converts.

For those unfamiliar with the practice of reciting a catechism, think of reciting the Lord’s Prayer, the Apostle’s Creed, or a secular catechism like reciting the Pledge of Allegiance. It is essentially a practice of oral recitation, the repetition of which aids to commit what is recited to memory.

Over the past year I’ve been thinking about what a math catechism might look like.

Teaching at a Christian school requires a deep and meaningful integration of faith with learning. Mathematics is the most foundational concept to integrate with Christian faith (at least in my mind). Math reveals the order that God used in creation and has imbued us with to create as well. Math gives us insight into what it means for something to be true or beautiful. These connections don’t easily lend themselves to particular math lessons. No math teacher should ever saying like “…and that’s how we derive the quadratic formula. You know, this reminds of that verse in Luke….” Math doesn’t integrate with faith in bite-size pieces. Rather it is the whole of mathematics that connects to our faith.

This brought me to the catechism. What if rather than just hoping my students see the deep connections between math and faith, they actually recite those connections every day? Even if the recitation isn’t meaningful in the beginning, the words are being committed to memory. As a child, I learned the Pledge of Allegiance even if I didn’t fully understand it’s implications until I was an adult. Wouldn’t it be amazing if my students could quickly give an answer to “how is a Christian to understand mathematics?” because that questions triggers a specific response that is lodged in their memory?

The thought of constructing something like this was planted in my brain by Joshua Gibbs in an Society for Classical Learning conference talk “How a Catechism can Transform Your Classroom.” I strongly encourage you to check it out.

What follows below is my first attempt at a math catechism. I have not yet decided how I will utilize this – if it is only for older students, or if younger students could learn it piece by piece over the years. I welcome any feedback and advice that you might have. Enjoy.

Regents School of Austin Mathematics Catechism

What is mathematics?

Mathematics is the science of patterns and the art of engaging the meaning of those patterns. (Francis Su)

What does it mean to be a mathematician – that is, to be mathematically literate?

Being mathematically literate includes having an appreciation of the value and beauty of mathematics as well as being able and inclined to appraise quantitative information. (National Council of Teachers of Mathematics)

To whom is mathematics accessible? Who can be a mathematician?

For those enquirers to whom God has given the ability, whose judgment is not clouded by stubbornness… The order and truth of numbers has nothing to do with the senses of the body, but it does exist, complete and immutable, and can be seen in common by everyone who uses reason. (Augustine)

 If math is accessible to all and all are capable of being a mathematician, what is the calling or the chief aim of the mathematician?

The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics. (Johannes Kepler)

How has God authored this order and harmony? How has God imbued meaning, value, and beauty in the patterns of creation?

Through Christ, the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15-17)

How then is the Christian to understand mathematics?

In the total expanse of human life there is not a single square inch of which the Christ, who alone is sovereign, does not declare, ’That is mine!’ (Abraham Kuyper)

In exploring mathematics one is exploring the nature of God’s rule over the universe; in other words, one is exploring the nature of God himself. (Vern Poythress)

How does a Christian understanding of God, creation, and humanity lend insight into grasping the effectiveness of mathematics?

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. (Eugene Wigner)

God created humanity in his own image, giving humans the ability to imagine things in mathematical terms.

Creation has been endowed with beautiful and fruitful properties by the creator. Creation possesses order and structure that can be characterized mathematically.

Humans apply their natural curiosity and their ability to formulate mathematical descriptions to the world they inhabit.

Humanity responds to God by exploring, describing, and wisely stewarding God’s creation. (John Mays)

The goal of the Regents mathematics program is to cultivate problem-solvers. What are the pillars of problem-solving?

Perseverance. Confidence paired with humility. Grit. There is no opting out. Even if a solution isn’t reached there is still much to be gained from being engaged in the process.

Communication and collaboration. Math is not meant to be done in isolation and neither the teacher nor the textbook is the ultimate authority. I am expected to engage with my classmates and communicate my reasoning in verbal, visual, and written form. I am expected to talk to my classmates! These communication processes will further develop my thinking skills.

Grace. Mistakes will be made. They must be made in order to learn. I must feel free to make conjectures, ask questions, make mistakes, and express my ideas and opinions without fear of criticism. I am expected to show grace to my classmates and my teacher. And I can expect to receive grace from my classmates and my teacher.

Service. A problem is never truly solved without a mindset of serving others. My math education is not ultimately about self-promotion, rather it is about equipping me to love and serve others well.

As a student studying mathematics through a Christian lens, you are called to not only learn content but to cultivate virtue. Mathematician, what do you commit cultivate?

 I commit to cultivating: my imagination, my determination, my curiosity, my creativity, my generosity, my charity. I commit to cultivating my mathematical affections.