A Math Catechism

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.

SCL 2017: Cultivating Mathematical Affections through Service-Learning

This week I am giving a presentation at the 2017 Society for Classical Learning (SCL) conference on “Cultivating Mathematical Affections through Service-Learning.” The talk is on integrating service-learning projects into mathematics curriculum, specifically with the goal of impacting students on an affective level. Since this is my dissertation topic, I’ve presented on it numerous times before – and now that my dissertation is done (!), I hope to finally be able to devote more time to building out resources on this site. In addition to the resources that you will find below, feel free to check out some of the prior posts on service learning:

AUDIO:

https://societyforclassicallearning.org/resources/cultivating-mathematical-affections-through-service-learning/

ABSTRACT:

This session will examine the benefits of service-learning projects in mathematics. Service-learning projects engage students in integrating their conceptual understanding of math with the practical functioning of their local community. Ultimately students gain deeper content knowledge and a deeper appreciation for the role math plays in society.

PRESENTATION:

You can click the image below to find the PowerPoint that accompanied my presentation.

Screen Shot 2017-06-18 at 8.53.29 PM

For many of the service-learning projects that my students have completed I am indebted to the willing partnership of Mobile Loaves and Fishes. Here is some introductory information on this great ministry:

How a Food Truck, Faith and Community Welcomes the Homeless, from the Huffington Post.

https://player.vimeo.com/video/220569713

“Teaser” for Inferno Films latest feature documentary. from layton blaylock on Vimeo.

10 THINGS TO CONSIDER BEFORE IMPLEMENTING A SERVICE-LEARNING PROJECT:

The following are the foundational questions that you as an instructor should consider and reflect upon prior to implementing a service-learning project. This list is not meant to be chronological though some aspects will naturally precede others. Start by considering the course learning objectives and your method of assessing those objectives and then go from there.

1.What are the major learning objectives/big ideas/enduring understandings for your course?

2. What are real-world situations where students can apply the concepts studied in your course?

3. List some potential community partners along with some basic descriptors that may impact how your students work with each partner (ex: What is the size of the organization? What issues does the organization address? Is the organization non-profit, governmental, religiously affiliated? Etc.) In lieu of a partner organization you can also consider a general community need for students to address. List some general descriptors of the project involved in addressing this community need.

4. Look for potential matches between organizations on your list from question 3 and your responses to questions 1 and 2. If there are multiple potential matches then consider the pros/cons of each and list them. Be sure to recognize how your matching affects the organization of the project (large scale as a class v. small scale as groups), which in turn may affect your response to question 5 below.

5. Once you have begun narrowing potential community partners that offer opportunities for students to interact with course content, consider how will you assess students? What will be the final product? What expectations will you have for students throughout the project and how will you communicate that to the students?

6. How will students be organized to meet the objectives that they will be assessed on? Will students work as individuals, teams, as a whole class?

7. How will students be equipped to complete the project successfully? What will they have gained from the course up to the point of assigning the project that will aid them? What additional tools/skills/knowledge will students need as the project proceeds?

8. What will be the timeframe for the project? How will students be held accountable to the timeframe? At what points will students receive feedback on their progress?

9. Why should students care about the project? What will you do as an instructor to get student buy-in on the project?

10. How will students reflect throughout the project? What opportunities will you provide for students to pause and consider the work they have done?

HANDOUTS:

From my AP Statistics Project:

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From my Geometry project:

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EXTERNAL RESOURCES:

APAC 2016: Statistics, Significance, and Service

I’ve started a new site for service-learning resources in mathematics: SLmath.com.

home

This week I am leading a workshop at the 2016 AP Annual Conference on “Statistics, Significance, and Service” in Anaheim, CA. The talk is on integrating service-learning projects into AP Statistics curriculum, specifically with the goal of impacting students on an affective level. In addition to the resources that you will find below, feel free to check out some of the prior posts on service learning:

ABSTRACT:

This session will equip participants to design, implement, and evaluate service-learning based statistics projects in which students partner with non-profit organizations in their local community. These projects synthesize the major concepts of experimental design, data analysis, and statistical inference in the real-world context of community service, ultimately cultivating in students a deeper appreciation for the discipline of statistics. In this session participants will evaluate successful examples of such projects, critically analyze the benefits of the innovative assessment methods involved, and engage in discussion assessing the feasibility and logistics of implementing service projects in their own curriculum.

(This session will expand on the session “Serving the Community through Statistics” from the 2015 AP Annual Conference by including results of my completed dissertation research on cultivating a productive disposition in statistics students through service learning)

PRESENTATION:

You can click the image below to find the PowerPoint that accompanied my presentation.

Screen Shot 2016-07-12 at 1.04.09 PM

10 THINGS TO CONSIDER BEFORE IMPLEMENTING A SERVICE-LEARNING PROJECT:

The following are the foundational questions that you as an instructor should consider and reflect upon prior to implementing a service-learning project. This list is not meant to be chronological though some aspects will naturally precede others. Start by considering the course learning objectives and your method of assessing those objectives and then go from there.

1.What are the major learning objectives/big ideas/enduring understandings for your course?

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:

  • Exploring Data: Describing patterns and departures from patterns
  • Sampling and Experimentation: Planning and conducting a study
  • Anticipating Patterns: Exploring random phenomena using probability and simulation
  • Statistical Inference: Estimating population parameters and testing hypotheses

2. What are real-world situations where students can apply the concepts studied in your course?

  • Identifying a non-profit service agency which requires survey research (program evaluation, client needs assessment, etc.)
  • Students develop a survey instrument, conduct survey, compile and code data, analyze data, present results

3. List some potential community partners along with some basic descriptors that may impact how your students work with each partner (ex: What is the size of the organization? What issues does the organization address? Is the organization non-profit, governmental, religiously affiliated? Etc.) In lieu of a partner organization you can also consider a general community need for students to address. List some general descriptors of the project involved in addressing this community need.

4. Look for potential matches between organizations on your list from question 3 and your responses to questions 1 and 2. If there are multiple potential matches then consider the pros/cons of each and list them. Be sure to recognize how your matching affects the organization of the project (large scale as a class v. small scale as groups), which in turn may affect your response to question 5 below.

5. Once you have begun narrowing potential community partners that offer opportunities for students to interact with course content, consider how will you assess students? What will be the final product? What expectations will you have for students throughout the project and how will you communicate that to the students?

6. How will students be organized to meet the objectives that they will be assessed on? Will students work as individuals, teams, as a whole class?

7. How will students be equipped to complete the project successfully? What will they have gained from the course up to the point of assigning the project that will aid them? What additional tools/skills/knowledge will students need as the project proceeds?

8. What will be the timeframe for the project? How will students be held accountable to the timeframe? At what points will students receive feedback on their progress?

9. Why should students care about the project? What will you do as an instructor to get student buy-in on the project?

10. How will students reflect throughout the project? What opportunities will you provide for students to pause and consider the work they have done?

HANDOUTS:

From my 2015-16 AP Statistics Project (Organized as an entire class project over the full year):

From my 2014-15 AP Statistics Project (Organized as small group projects in the spring semester):

*NOTE: some documents above were also used in this project, either in the form in which they are posted above or in a slightly modified version

ADDITIONAL RESOURCES:

Hadlock, C.R. (2005). Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

            Chapter 3: Service-Learning in Statistics

Reed, G. (2005). “Perspectives on statistics projects in a service-learning framework.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

Root, R., Thorme, T., & Gray, C. (2005). “Making meaning, applying statistics.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

Sungur, E.A., Anderson, J.E., & Winchester, B.S. (2005). “Integration of service-learning into statistics education.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

Hydorn, D.L. (2005). “Community service projects in a first statistics course.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

Massey, M. (2005). “Service-learning projects in data interpretation.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

Chapter 6: Getting Down to Work

Webster, J. & Vinsonhaler, C. (2005). “Getting down to work – a ‘how-to’ guide for designing and teaching a service-learning course.” In C.R. Hadlock (Ed.), Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences. Washington, DC: Mathematical Association of America.

“Service-Learning and Mathematics” webpage:

Bailey, B. & Sinn, R. (2011). “Real Data & Service Learning Projects in Statistics.” Service-learning in collegiate mathematics, MAA contributed paper session, 2011 Joint Mathematics Meetings, New Orleans, LA.

Hydorn, D. (2011). “Community Service-Learning in Mathematics: Models for Course Design.” Service-learning in collegiate mathematics, MAA contributed paper session, 2011 Joint Mathematics Meetings, New Orleans, LA.

PRIMUS, Vol. 23 (6)

Hadlock, C.R. (2013). “Service-learning in the mathematical sciences.” PRIMUS, Vol. 23 (6), pp. 500-506.

Other

Lynn Adsit’s blog on implementing a service-learning project in AP Stats

Harry, A. & Troisi, J. (2014). “Service-Oriented Statistics.” 

Hampton, M.C. (1995). Syllabus for Intro to Statistics. University of Utah. 

Duke, J.I. (1999). “Service-Learning: taking mathematics into the real world.” The Mathematics Teacher, 92 (9), pp. 794-796, 799.

Leong, J. (2006). High school students’ attitudes and beliefs regarding statistics in a service-learning-based statistics course. Unpublished doctoral dissertation. Georgia State University.

For many of the service-learning projects that my students have completed I am indebted to the willing partnership of Mobile Loaves and Fishes. Here is some introductory information on this great ministry:

Community First! Village Goes Beyond Housing for Austin Homeless, from the Austinot