APAC 2016: Statistics, Significance, and Service

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

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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.

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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

CAMT 2016: Cultivating Mathematical Affections through Service-Learning

2016_logo

This week I am leading a workshop at the 2016 Conference for the Advancement of Mathematics Teaching in San Antonio, TX 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 written about it numerous times before here on GodandMath.com. 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 projects in which students partner with non-profit organizations. Through these projects, students integrate their conceptual understanding of math with the practical functioning of their local community, ultimately gaining deeper knowledge of content and a deeper appreciation for the role math plays in society. Examples from geometry and statistics will be provided.

PRESENTATION:

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

Screen Shot 2016-06-29 at 12.35.59 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:

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?

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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Screen Shot 2016-06-29 at 1.10.27 PM

From my Geometry project:

Screen Shot 2016-06-29 at 1.08.28 PM Screen Shot 2016-06-29 at 1.08.42 PM

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EXTERNAL RESOURCES:

A Perspective on “Favorite Classes”

Slate.com recently ran a series on “Favorite Classes.” I thought that it would be worth sharing, and briefly commenting on, their perspective on mathematics and statistics.

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First, I love the title on their post about mathematics: You’re Not Actually Bad at Math. Here are some excellent quotes:

The idea that someone can be bad at math is wrong, and it hides several harmful assumptions. It’s an excuse to justify individual failure, rather than a real understanding of mental capabilities. Giving up on math means you don’t believe that careful study can change the way you think. No one is born knowing the axiom of completeness, and even the most accomplished mathematicians had to learn how to learn this stuff. Put another way: Writing is also not something that anyone is “good” at without a lot of practice, but it would be completely unacceptable to think that your composition skills could not improve.

I agree with the author that the phrase “I am not a math person” is used largely as an excuse to help the self esteem of a person who has had difficultly in mathematics. The reality of the situation is that difficulty and struggle are inherent in the process of doing mathematics well. The only reason a person would think that their initial failure to grasp a concept makes them ‘not a math person’ is that they have come to understand the practice of mathematics as solely about obtaining ‘correct’ answers. This leads to a second key quote:

It seems that the origin of math phobia is not the content of math itself; it cannot rest solely on someone’s inability to sit through logic puzzles, because people exercise careful abstract reasoning in every other field without the same sort of fear. Instead, I think the form is largely to blame. All of high school math is basically a one-way linear staircase that leads to calculus. If you fall off at any point, you’re doomed. Calculus prep has infiltrated the curriculum to such a degree that I think people conflate doing algebra with all of math. Students spend so much time memorizing computational tricks that they don’t get to see anything else—that those algorithms have a logical derivation, and that plenty of math isn’t even like that.

In short: the form of teaching matters, not just the content that is taught. I have discussed the form of teaching before. If math is taught purely as algorithmic thinking that leads to a single ‘correct’ solution then it should not be surprising to hear the people who don’t get the ‘correct’ answer to label themselves “not a math person.” As I have discussed before on the topic of the form of teaching, we as math educators need to be mindful of not just the content we teach but also how the manner in which we teach it is shaping student perspectives on mathematics. On this note I encourage you to search for articles on “Productive Struggle” in mathematics. Here is one such article from a colleague at Texas State University that was recently published in the Journal of Mathematics Teacher Education.

See also this article from the Atlantic on “The Myth of ‘I’m Bad at Math.'”

Finally, I believe this last quote speaks directly to the mindset we as math educators should be seeking to instill in our students:

Not every educated person needs to be a mathematician, but no educated person should be afraid of the steps it takes to get there.

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The second article is titled: “What are the Odds? To learn to think critically, take a statistics class.”

If there’s one skill almost everyone agrees schools should be teaching, it’s critical thinking, although what, exactly, critical thinking consists of is conveniently left undefined. For the longest time, I preferred to believe that it meant learning to be skeptical about words, specifically the arguments, exhortations, and beguilements foisted upon the public by politicians, advertisers, corporations, and the dodgier elements of the press. As a former English major, I figured I had this one nailed; if there was anything I mastered in college, it’s the ability to find the hidden and sometimes manipulative meanings in language.

What I, in my complacency, chose to ignore is just how much of the persuasion now aimed at the average citizen comes in the form of numbers, specifically numbers that tell us about the future, about how likely something is to happen (or not happen) based on how much it happened (or didn’t) in the past. These numbers sing to us the siren song of cause and effect, humanity’s favorite tune. Why do we like it so much? Because knowing what causes events and conditions is the first step toward controlling them, and we human beings are all about controlling our environments. That’s how we ended up ruling this planet, and it’s how some of us hope to save it.

…Statistics and the science of probability represent the ultimate in critical thinking, because they teach us how to criticize the ways we habitually think

I have written before on the Myth of Critical Thinking in Mathematics. To “think critically” is by definition “to be critical of thoughts” or in other words “to critique ideas” as they arise rather than accepting or rejecting them blindly. Critical thinking means thinking rationally and reasoning through arguments with care and consideration of the options on the table. This, of course, sounds all well and good until we as educators stop and actually consider the reality of the situation in the math classroom.

A critique can only be meaningful if you already have a standard by which to judge something. I can’t critique an argument as “true” unless I know what it means for something to be “true.” I can’t critique a painting as “beautiful” unless I know hat it means to be “beautiful.” I can’t critique an act of charity as “good” unless I know what it means to be “good.”

There is an underlying standard of judgment that is being instilled in students (whether knowingly or unknowingly) and this is the root of what is occurring in mathematics classrooms. The way in which students implement their “critical thinking skills” upon the completion of their mathematics courses is simply a symptom of a deeper reality that is being formed within them. That reality can be formed from a Christian perspective where it is God who sets the absolute standards for Truth, Beauty and Goodness, or it can be formed by very humanistic standards of relative truth, subjective beauty, and goodness defined by utility.

The humanistic standards that are pervasive in our educaitonal system is what I believe leads to the last part of the quote above: “We human beings are all about controlling our environments. That’s how we ended up ruling this planet, and it’s how some of us hope to save it.” A Christian perspective realizes that we as human beings are indeed all about controlling our environments, but that is as a result of sin and brokenness and not a trait to be admired. We wound up ruling this planet not by innate ability but by God’s granting to us the stewardship of His creation. And we can never save this planet – we can only rest in the promised hope of future redemption in Christ.

I strongly support the claims made by this article on the need for an understanding of statistics, especially in this age of digital media. However I believe we also must always be mindful of the worldview that we bring to the table in understanding statistics.