A Math Catechism (UPDATED)

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!

Seeing God and His Beauty in Math

I recently came across a podcast episode of “Think Biblically: Conversations on Faith and Culture,” from BIOLA University, that at this point is about a year old. The topic is seeing God and His beauty in math and the podcast guest is Jason Wilson, associate professor of mathematics at BIOLA.

I met Jason at the first conference for the Association of Christians in the Mathematical Sciences (ACMS) that I attended in 2011. I have always found Jason to be extremely thoughtful in integrating his faith with his understanding of mathematics. I hope you enjoy this podcast.

https://www.biola.edu/blogs/think-biblically/2019/seeing-god-and-his-beauty-in-math

PRIMUS: Cultivating a Productive Disposition Toward Mathematics by Engaging in Service-Learning

I have had the good fortune of being recently published in the journal PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies).

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The article stems from my dissertation research and the examples of service-learning that I have shared on this site. I hope it presents a convincing case for the benefits of implementing service-learning in your classes.

If you don’t have access to PRIMUS and would like a free copy of the article, please feel free to email me at jwilkerson<at>regentsaustin<dot>org.

ABSTRACT:

This research explores the positive impact of service-learning on the disposition of students in mathematics. This was a qualitative case study of high school AP Statistics students who completed a service-learning project. Data were gathered from student interviews, reflection journals, and field observations. The framework for the analysis follows the definition of “productive disposition” offered by the National Research Council and that remains foundational to the Common Core Standards for Mathematical Practice. The major themes that emerge from the data indicate that through service-learning, students see math as sensible, useful, and worthwhile. This supports the potential of service-learning as a pedagogical tool that can be utilized to develop a productive disposition in students; addressing at a practical level how the affective objectives of national policy documents can be achieved.