ACMS 2017: Cultivating Mathematical Affections through Engagement in Service-Learning

Here is some information on my talk at the 21st ACMS Conference (2017) at Charleston Southern University.

Abstract:

Why should students value mathematics? While extensive research exists on developing the cognitive ability of students, very little research has examined how to cultivate the affections of students for mathematics. The phrase “mathematical affections” is a play on the affective domain of learning as well as on the general notion of care towards something. Mathematical affections are more than a respect for the utility of the subject; the term is much broader and includes aesthetic features as well as habits of mind and attitude.

This paper will analyze the findings from a research project exploring the impact of service-learning on the cultivation of mathematical affections in students. This was a qualitative case study of high school students who recently completed a service-learning project in their mathematics course. Data was 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 (2001) as well as the concept of formative “cultural liturgies” offered by the philosopher James K.A. Smith (2009).

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.

PowerPoint:

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References:

Goldin, G.A. (2002). Affect, meta-affect, and mathematical belief structures. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.),  Beliefs: a hidden variable in mathematics education? Netherlands: Kluwer Academic Publishers, pp. 59-72.

Hadlock, C. R. (2005). Mathematics in service to the community: Concepts and models for service-learning in the mathematical sciences (No. 66). Mathematical Association of America.

Krathwohl, D.R., Bloom, B.S., & Masia, B.B. (1964). Taxonomy of educational objectives: Handbook II. Affective Domain. New York: Longman.

National Research Council (2001). Adding it up: Helping children learn mathematics. Washington D.C.: National Academy Press.

Smith, J.K.A. (2009). Desiring the kingdom: Worship, worldview, and cultural formation. Grand Rapids, MI: Baker Academic.

Wilkerson, J. (2015). Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy. In Perspectives on Science and Christian Faith, 67(2), 111-123.

Using Math to Fight Homelessness

(From Arches, a magazine published by Regents School of Austin)

AP Statistics student Vanessa Aguirre shares how their class harnessed the power of surveying, statistics and service to help the Mobile Loaves & Fishes ministry in their efforts to combat homelessness in Austin.

On a rainy Tuesday morning, the thirty-six AP Statistics students walked through the Community First! Village of Mobile Loaves and Fishes, a local Austin non-profit focusing on the needs and betterment of the homeless community. The community village this organization founded is a beautiful, solitary sanctuary, with mini-homes right out of a housekeeping magazine and gardens dotting the landscape. Weaving through the clusters of houses and RVs, the high school students knocked on doors and waited with baited breaths, holding copies of a survey they helped design for the residents of the village.

“I was pretty nervous,” senior Lydia Strickland said.

Over the course of the morning, the students went from door to door, talking to the residents and sharing their stories, working to fill the survey as their school project that would help Mobile Loaves and Fishes (also known as MLF) in its aim to fight homelessness. The math students worked in tandem with MLF to, ultimately, answer the question: Does a lack of community cause homelessness? The high school students used ideas and concepts learned throughout the year to edit, carry out, and analyze a survey given to the residents living in the community village the non-profit has made.

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This question is largely based on Bruce K. Alexander’s “Rat Park” study, where Alexander and other scientists set up a study administering drugs to rats not in isolated cages, but in communities with a positive environment, and found that the drug intake of rats went down dramatically. This shows that environment and community play a significant role in drug use—and leads others to wonder if more than just drug use can be improved. The AP statistics and MLF worked together to explore this train of thought, and to reaffirm MLF’s community-based program.

Homelessness is, after all, a very real problem. According to the National Alliance to End Homelessness, there were 564,708 homeless people in the United States in January of 2015, 15% of which were considered chronically homeless. More pragmatically, each homeless person costs taxpayers around $14,480 a year. When you do the math, that amounts to homelessness costing more than eight billion annually.

Not only does homelessness affect those directly involved, but it impacts society as well. Efforts to curb homelessness will have a positive impact on everyone. As a large and established homeless outreach ministry based in Austin, Mobile Loaves and Fishes attempts to do just that—curb, and ideally eventually end, homelessness and the factors behind it. In partnering with the AP Statistics students of Regents School of Austin, MLF hoped to gain more data on the effectiveness of their Community First! Village and the philosophy that poor environment and lack of community are the root problems of homelessness.

“We believe what we’re seeing anecdotally on the property is being verified through the statistical analysis, so we love this [the AP Statistics project,]” Alan Graham, Mobile Loaves and Fishes co-founder and director, said. “It confirms our model at Community First, that the only model that’s going to move the needle in a significant way is a kingdom-based model that’s all about community. So we need that data.”

Not only has the AP Stats project helped as a service, but it’s also helped as learning tool for the students, giving them a deeper appreciation of the concepts they learned in class.

“I liked the real-world application,” junior Emily Raeder said. “That was great.”

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This service-learning model is meant to lead students into developing higher-order critical thinking, in a real-world environment, where service to the community (such as alleviating homelessness) is presented as crucial to the course objectives and larger applications of education. Dr. Wilkerson, the Regents AP Statistics and Calculus teacher, sees service-learning as a valuable tool in math education.

“I think it helps because you get to use statistics in a real-life situation that’s meaningful in an immediate context,” he said. “Students realize that what you learn in math class aren’t things you would just have to do down the road, in the distant foggy future. Students learn the connection between helping people and using statistics, and they learn it on a deeper level.”

The project showed that math and making a difference in the world can go hand in hand. In order to help Mobile Loaves and Fishes and its residents, the AP Statistics students at Regents had to learn exploratory data analysis, data collection, probability, and statistical inference. On top of all this, students also got to practice their speaking skills. Students presented the results to representatives from MLF, the culmination of the class’s hard work.

The high schoolers also got a better appreciation of how even the little things can affect the world around them.

“I talked to this one man who talked about what a difference people who give out bags with goodies at stoplights made, that it made his day,” one junior said. “He said those things made a big difference. But we don’t put much thought into it.”

These math students may just be proof that math really can accomplish anything.

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Summer Institute 2017: Service-Learning in Mathematics

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Regents School of Austin, where I teach, will be hosting a summer institute for teachers and I’ll be leading a workshop on implementing service-learning in math courses. The target audience is math teachers at any level K-16 or pre-service math teachers.

Here are the details:

This workshop will assist you in developing successful service-learning projects in mathematics. Service-learning projects engage students in integrating their conceptual understanding of mathematics 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.

Several examples of service-learning projects will be presented in detail from geometry and statistics, as well implementable ideas for other math courses. You will have the opportunity to brainstorm and work in conjunction with other educators to analyze the key components of a successful project, engage in discussion assessing the feasibility and logistics of implementing service projects in your own curriculum, critique project evaluation rubrics, and begin the design of your own service-learning project.

You will leave this workshop equipped to:

  • Determine the keys to a rewarding service-learning experience (after hearing personal testimony from students and community partners)

  • Modify and implement sample materials from past Regents projects (including project descriptions, calendars, and grading rubrics)

  • Connect the enduring understandings of your course with a community need

  • Evaluate student learning outcomes in keeping with your curriculum

  • Engage students with meaningful applications of math in the personal context of their local community

If you are interested, here is the link to registration page (that contains further details). 

Feel free to contact me if you have any questions and please share with colleagues that you think might be interested.