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.

AP with WE Service Learning Summit

AP and the College Board have partnered with WE to bring WE’s internationally recognized service-based learning framework and resources to AP courses, so students can use what they’re learning to tackle real-life social issues and challenges.service-learning to the AP classroom. Microsoft hosted the inaugural AP with WE Service Teacher Summit at their headquarters in Redmond, WA, March 4-5, 2019.

This event was an opportunity for teachers to meet fellow AP teachers, strengthen their implementation of AP with WE Service, learn best practices, and hear from Microsoft staff. A total of 50 teachers were selected to attend.

What follows below is the outline of the presentation I was asked to give at the summit on cultivating student affections through service-learning. I hope to be able to share the video of the presentation soon.

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My name is Josh Wilkerson and I teach AP Statistics. I also teach other math courses and as a math teacher there is one big question that I am often asked. You are probably asked it to in your other disciplines, but it is especially prevalent in math. The question usually is accompanied by the student having his kind of expression…

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Help me out, what is the big question? (Audience: when am I ever going to use this?)

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When am I ever going to use this (said in an exasperated way). It is never “When? When I am going to get to use this!?” (said in an excited way). Rather it is a dismissive question. Since we are at a conference on service-learning you might think you know where this is going. However, I hope to lead you in a slightly different direction. If we are honest with ourselves, how we respond to the student varies based on our mood at the time. In the best of scenarios we can give them a meaningful future application. In other scenarios we respond with how they will need the information for their next course, or more immediately, they’ll need it for the test next Tuesday.

I would like to pose to you that none of those answers are sufficient because, if we are being even more honest with ourselves, we know that the student isn’t really asking a question. The student is making a statement – a statement that they feel validates their disengagement from the lesson. I would also like to pose to you that if you were to translate their statement to an actual question it would be this…

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Why should I value this? I would argue that this is the most fundamental question to address in any classroom, even (or especially) mathematics. If we respond to the student’s surface level application question with cognitive information we will always have a disconnect. The student is actually longing for affective formation – however you want to parse that, into motivation or engagement or attitude or something else. The main thing is it is more than just being about what they know.

This is not only true for students. Close your eyes for a minute and imagine a great moment in your teaching career – something where everything was clicking and you were thinking “this is why I got into teaching.” Give me a word or short phrase to describe the mental image you came up with (solicit audience responses).

Notice that none of you told me “pythagorean theorem,” or “Great Gatsby,” or “mitosis.” None of you gave me content. Now, to be sure, the content was still there and was still operating on a high cognitive level I’m sure. My point is to not to dismiss content, but to perhaps reorient us on the primary objective of a classroom.

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These aren’t just our feelings. The importance of affect in education has been documented in research.

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Not only in research, but also in positional standards. I have here a few in mathematics but I’m sure that you can find something similar for any discipline. So with all this agreement and support, how are we doing?

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(Read slide). This quote is from 1992 but it is not dated. I know that it is not dated because, as I mentioned at the beginning, I’m a math teacher. Whenever I introduce myself to anyone and the topic of what I do for a living comes up, these are the number one responses I receive. Math teachers may be second only to priests in the number of confessions they take.

This is what keeps me up at night. This is what I want my classroom to address. How do we do that?

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We don’t do it by changing content or even focusing on student beliefs – we do it through rich experiences. The experience of the math classroom needs to change.

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THIS is where I think service-learning is powerful. Not as an answer to application, but as an answer to offering rich and meaningful experiences in the math classroom.

How are the affections of the student impacted when we change the experience of math class from this…

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To this.

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For the past three years my stats students have partnered with a local homeless ministry in Austin for survey research. Here is how they responded to a survey I gave them at the end of the year.

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Transition through graphs – point to growth in content knowledge but then also appreciation.

Yes service learning is application – but it is so much more than that. Through service learning we can shift student postures to ones of self-service (when will use this?) to the service of others. Ultimately their education is not just about them.

Let me close with some words from a student who began the year with a very negative attitude towards mathematics and that improved over the course of the service-learning project. I asked him about it and this is what he said.

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(After first bullet) I like this quote because I’m also a realist – I’m not setting out to make everyone always enthusiastic about math. But there are steps we can take and I think this student took them.

(Read rest of slide)

Why should I value this? Because it will benefit me and it will benefit others.

Thank you.

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APAC 2018: Service-Learning and Statistics

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This week I am leading a workshop at the 2018 AP Annual Conference on “Statistics and Service-Learning” in Houston, TX. 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 AP Statistics service-learning projects in which students partner with nonprofit 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. Through these projects students integrate their conceptual understanding of statistics with the practical functioning of their local community, ultimately gaining a deeper appreciation for the role of statistics in the organization and evaluation of service societies.

PRESENTATION:

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

 

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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

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 AP Statistics Project 2018:

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(Clicking the image above will take you to the students’ final presentation)

From my AP Statistics Project 2016-17:

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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

EXTERNAL RESOURCES: