The Text of Mathematics

Which of these is most similar to a math textbook?

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This past summer I was challenged by Jacob Mohler to consider the difference between a ‘text’ and a ‘textbook.’ The text is the original foundation and the textbook is (unsurprisingly as the name suggests) a book about the text. The Bible is a text. A Bible commentary is a textbook.

How would you classify the following? Text or textbook?

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Clearly these would be classified as textbooks. The question then arises: what is the text of mathematics? And perhaps more importantly, how are we engaging students with the text of mathematics?

A Christian cannot fully grow in their walk with the Lord by only ever engaging Bible commentaries – they have to spend time in the text, in the inspired word of God. If all we are ever giving our math students are the equivalent of commentaries, are we doing them a disservice? What is the text of mathematics that students need to engage with?

What the text of mathematics is NOT: I don’t think the answer to the question lies in teaching from original sources in mathematics, for instance using Euclid’s Elements in a geometry course. While Euclid offers a more ancient view of geometry, I’m not sure he offers the original view of geometry – he doesn’t even offer an always correct  view of geometry. I would still consider Euclid’s Elements a textbook. What makes the Bible different from Bible commentaries is not merely its age.

I would argue that there is no written, scriptural equivalent for mathematics. Rather, I believe the text of mathematics is this: the text is the teacher.

If we keep with the Bible versus Bible commentary analogy, I think there are actually two ways people can interact with the Bible. One way is certainly to sit down and read it. Another way people interact with the Bible (the text) is through their interactions with believers who have allowed the text (and in reality the creator and savior God behind the text) to transform their lives.

Preach the Gospel at all times. If necessary, use words. ~ St. Francis of Assisi

This quote from St. Francis speaks to the transformative power of the Gospel on the lives that we lead (not just the acquisition of new knowledge). Jesus says “By this all people will know that you are my disciples, if you have love for one another” (John 13:35). The way we live as Christians matters. It should point people to God. It should reveal to them in our actions what the text says in its words. Jesus was the “Word became flesh” (John 1:14) and that is our calling as Christians as well.

So then how do our math students interact with the text of mathematics? Through their interactions with their teacher.

I’ll often define my job as a “math appreciation teacher” rather than just a math teacher. Content delivery is only part of my job. In fact, as a new department chair I challenged my teachers that they weren’t hired for their ability to deliver content. In our technological age the reality is that students can get content from Khan Academy 9or any similar venue). The real job that my teachers were hired for is cultivating mathematical affections. Interacting with students in such a way that students see a noticeable difference in the affections/attitudes/dispositions of their teacher towards mathematics – that’s the real job.

The Gospel is more than content knowledge. Math is more than content knowledge. The affections (or lack thereof) in teachers play a much larger role in students’ experience of mathematics than I think people tend to credit. I challenge my teachers that they are the text of mathematics.

Teach math at all times. If necessary, explain content.

 

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The definition of a “math person”

It has been awhile since I have posted here. My new responsibilities as the math department chair have taken up quite a bit of my time – but I am certainly relishing the opportunity to put into practice many of the ideas I have espoused here on GodandMath over the years. One of my responsibilities has been hosting a series of math talks for parents. This has been a great way for me to meet more families in our school community and to have a platform to explain our department’s philosophy of math education. This post is a summary of that philosophy that I have been sharing with parents.

Our department’s number one aim is to cultivate the mathematical affections of students – a phrase I have written about numerous times here. Essentially, the aim is to provide students a meaningful experience of mathematics that solidifies their appreciation of the discipline regardless of their future studies or career trajectories. This goal is in contrast to the prevailing attitude of society towards their mathematics education, summed up in the phrase “I’m not a math person.”

I start these parent meetings by asking who in the audience has ever said or thought “I’m not a math person”? I then ask for a few brave volunteers to explain what they mean by that. Without fail (whether in these parents meetings or in any context when someone admits to me that they aren’t a math person – which always seems to happen whenever you tell someone you’re a math teacher) there explanation falls somewhere along the lines of: I couldn’t remember all the rules, I wasn’t good at memorizing multiples, I never completed the problems fast enough, etc. Basically reiterating the prevailing view of society that to be a math person is to be efficient and accurate in computation and factual recall.

My typical response to people is “Yeah, I hate that stuff too. But I’m still a math person. What you’re describing isn’t how I see math. Can I show you how I see math?”

Our goal is to give students a very different impression of mathematics than what society has. We want to take away from students this go-to opt-out phrase of “Well, I’m not getting it, I’m just not a math person.” Mathematics, true mathematics, is inviting and uplifting for everyone.

How we as a department aim to cultivate students’ mathematical affections is through developing problem solvers. Below is a working summary of how our department defines problem solving (written to the student).

Defining Problem Solving: [1]

 Problem solving has been defined as what to do when you don’t know what to do. In some of your math classes, you probably learned about mathematical ideas by first working on an example and then practicing with an exercise. An exercise asks you to repeat a method you learned from a similar example. A problem is usually more complex than an exercise, so it is harder to solve because you don’t have a preconceived notion about how to solve it.

Problem Solving Expectations:

  1. Perseverance: Humility paired with confidence. Grit. In this class you will be asked to solve some tough problems. You will be able to solve most of them by being persistent and by talking with other students. When you come across an especially difficult problem, don’t give up. You may find that sometimes your first approach to a problem doesn’t work. When this happens, don’t be afraid to abandon the approach and try something else. Be persistent. If you get frustrated with a problem, put it aside and come back to it later. But don’t give up on the problem.
  2. Collaboration: You will be expected to talk to your classmates! Your teacher will ask you to get help from one another.
  3. Communication: In addition to working with your classmates, reading the book, and learning from your teacher, you will also be expected to communicate about your work and your mathematical thinking. You will do this by presenting your solutions to the entire class and by writing up complete solutions to problems. You will do presentations and write-ups, because talking and writing allow you to show your thinking. These communication processes will further develop your thinking skills.
  4. Grace: When you work with other students, you are free to make conjectures, ask questions, make mistakes, and express your ideas and opinions. You don’t have to worry about being criticized for your thoughts or your wrong answers.
  5. Service: Your growth in your math educational journey is not just about you. If the big problems of this world (curing disease, ending hunger, ending human trafficking, addressing sustainability, etc.) are going to be solved then mathematics will play a central role in their solution. If you are going to truly become a problem-solver then there has to be action taken.

At this point, after having explain our departmental goals and philosophy, I return to my original question.

“Ok, so you may not be a math person. But do you believe in the value of perseverance? Do you think collaborating in community and communicating ideas well are important skills? Do you believe in showing others grace and receiving grace yourself? I should hope so in our Christian community. Do you believe that we are called to serve others and put their needs before our own? If you said ‘yes’ to any of these, then congratulations, you’re a math person!

 

[1] Adapted from Johnson, K. & Herr, T. Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures, 2nd Ed., Key Curriculum Press, 2001.

 

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: