My Publications and Presentations

Dissertation

“Cultivating Mathematical Affections: Developing a Productive Disposition through Engagement in Service-Learning.” (unpublished as of yet, Texas State University, 2017).

Articles

“Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy,” Perspectives on Science and Christian Faith, Volume 67 Number 2 (June 2015).

“Beyond Practicality: George Berkeley and the Need for Philosophical Integration in Mathematics,” Journal of the Association of Christians in the Mathematical Sciences.

Book Reviews

“Review of J. Bradley and R. Howell, Mathematics Through the Eyes of Faith,Perspectives on Science and Christian Faith, Volume 63 Number 4 (December 2011).

“Critical Review of C. Hitchens, god is not Great: How Religion Poisons Everything,Kindred Spirit (Fall, 2008).

Presentations

“Serving the Community through Statistics: A Capstone Project,” Workshop for the AP Annual Conference, Austin, TX, July 2015.

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. 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 statistics plays in the organization and evaluation of service societies. In this session participants will witness several successful examples of such projects, identify the key components of a successful project, engage in discussion assessing the feasibility and logistics of implementing service projects in their own curriculum, and critique project evaluation rubrics.

“Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy,” The 20th Association of Christians in the Mathematical Sciences Conference, Redeemer University College, May 2015.

The goal of this paper is to make the case that Christian faith has an opportunity to impact the discussion on best practices in mathematics not primarily through the cognitive discussion on objectives and standards, but through the affective discussion on the formation of values, the cultivation of mathematical affections – not merely knowing, but also loving, and practicing the truth, beauty, and goodness inherent in mathematics. First I will outline the work being done on affect in mathematics education, examining what values are actually endorsed by the community of mathematics educators. After summarizing this work on affect it will be clear that, even in the words of leading researchers, the field is lacking any cohesive, formal approach to analyzing and assessing the affective domain of learning. In part two of this paper I will argue the thesis that Christian faith offers solutions to the frustrations and shortcomings admitted by researchers on affect in mathematics education. Christian faith offers insight into how mathematical affections might actually be shaped. Here I will draw heavily on the work of philosopher James K.A. Smith and make explicit connection between his work and the mathematics classroom. Finally, I will conclude with a call to action discussing how we as Christian educators might begin to have fruitful contributions to and dialogue with the current research being done in mathematics education.

“Cultivating Mathematical Affections: Re-Imagining Research on Affect in Mathematics Education,” Mathematical Association of America Session on Mathematics Education at the Joint Mathematics Meetings, San Antonio, TX, January 2015.

This presentation will outline the design, implementation, and evaluation of 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. 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 statistics plays in the organization and evaluation of service societies. Successful examples and practical resources will be provided.

“From the Classroom to the Community (and Back Again): Stories of Statistics, Significance, and Service,” Mathematical Association of America Session on Best Practices for Introductory Statistics at the Joint Mathematics Meetings, San Antonio, TX, January 2015.

“When am I ever going to use this?” is a common question in mathematics. It is also more typically presented as a statement. It is a statement of frustration. It is the culmination of confusion and stress and typically serves as an exclamation by the student of their withdrawal from the mental activity at hand. I argue that the real question being raised by students is “Why should I value this?” We as math educators must do a better job of addressing this non-cognitive question. We need to do a better job of cultivating what I term as mathematical affections.

Affective language permeates national policy documents on the teaching of mathematics as an ideal we should strive to inculcate into students, but there is little discussion on how to go about doing this. This talk will examine the specific passages of the policy documents in question, discuss the shortcomings in the current body of research that exists on affect in math education, and outline a new framework (based on recent work in cognitive psychology and contemporary philosophy) for understanding how we might cultivate mathematical affections. Practical classroom resources and exercises will be offered.

“Math for Goodness Sake: Cultivating Mathematical Affections,” Society for Classical Learning Conference, Austin, TX, June 2014

The mission of Regents School of Austin (and undoubtedly any classical Christian education) is to equip students to know, love and practice that which is true, good and beautiful. How does the teaching of mathematics fit into this mission? There are numerous resources that address the beauty and truth of mathematics, but how do we instill in students an appreciation for the inherent goodness of math (especially since many students experience mathematics as confusing, stressful and generally contrary to anything considered good)?

Mathematics is at its core a good and virtuous activity and its enjoyment is not reserved for the “intellectual elite.” This talk will examine how the goodness of mathematics is actually rooted in a proper understanding of the ordered nature of God. When viewed through this lens we can see mathematics as a missional activity that increases our versatility as worshipers of Christ. Several practical methods for developing what I term “mathematical affections” will be presented for consideration and classroom use.

“Serving the Community through Statistics: A Capstone Project for an AP or College Introductory Statistics Course,” AP Statistics Reading Best Practices Presentation, Kansas City, MO, June 2014.

This presentation will outline the design, implementation, and evaluation of 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. 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 statistics plays in the organization and evaluation of service societies. Successful examples and practical resources will be provided.

“The Mission of Mathematics,” Faculty Inservice Training, Regents School of Austin, August 2013.

The mission of mathematics, as informed by a Christian worldview, is to: increase our versatility in worship by (1) Refining our sinfully broken minds through a contemplation of the creation God called ‘good’, (2) Engaging us in the difficult yet worthwhile pursuit of the ideal by which critical thought may be judged, and (3) Instilling within us a sense of awe in communing with the Creator.

“Mathematical Affections: Assessing Values in the Math Classroom,” The 19th Association of Christians in the Mathematical Sciences Conference, Bethel University, May 2013.

When am I ever going to use this? As a math teacher, this is the number one question that I hear from students. It is also a wrong question; it isn’t the question the student truly intended to ask. The question they are really asking is “Why should I value this?” and they express their inquiry in terms of practicality because that is the language in which their culture has conditioned them to speak. While the utility of mathematical concepts are certainly important, we as educators need to utilize the mathematics classroom to address the more fundamental issue of fostering a proper sense of values. Learning has little meaning unless it produces a sustained and substantial influence on the way people think, act, feel, and ultimately worship. According to the NCTM standards it is through assessment that we most clearly communicate to students what aspects of mathematics are to be valued. This talk will address two essential questions:

1) Why is it necessary to develop assessments that equip students to not only know and practice but also love that which is true, good and beautiful?

2) How do we design worthwhile mathematical assessments that synthesize something seemingly non-objective like personal values with something seemingly non-subjective like mathematics?

The title of this talk is in homage to Jonathan Edwards’ Treatise on Religious Affections. Edwards’ goal was to discern the true nature of religion and in so doing dissuade his congregation from merely participating in a Christian culture (a mimicked outward expression) and motivate them to long for true Christian conversion (an inward reality of authentic Christian character). The purpose of this talk is to engage ACMS members in discerning the true nature of mathematical assessment and how we use it in the classroom: does it simply mimic the modern culture of utility by requiring outward demonstrations of knowledge retention and application, or does it aim deeper at analyzing true inward character formation? In closing, examples of affective mathematical assessments will be presented as resources for consideration and classroom use.

Service-Learning Panel, The 19th Association of Christians in the Mathematical Sciences Conference, Bethel University, May 2013.

Abstract by Panel Organizer Dr. Karl-Dieter Crisman: Many of us have wanted to incorporate service experiences in courses, or are being asked by our institutions to do so. Service-learning is a way of looking at service as being a partner with and leading to learning for our students. But in math, there are not a lot of resources to use! Our panelists will present classroom-tested ideas from several different levels of courses, and we will end with a short time for more brainstorming among all participants.

Stewards of the Created Order: A Case for Christian Influence in the Field of Mathematics,” Evangelical Theological Society Southwest Regional Meeting, Dallas, TX, March, 2013.

Mathematics gives a glimpse (albeit an imperfect one) into the mind of God and the language of His creation. Mathematical thinking is then one way in which humanity fulfills its role as Divine imagers and stewards of God’s created order. As God’s stewards we are under obligation to cultivate not only the ground but our minds, embrace the reasoning ability that God has instilled within us and develop a distinctly Christian perspective of mathematics. This paper will argue the case for the influence of Christianity on the field of mathematics in three parts: the influence of faith on the acceptation (understanding) of mathematics, on the appreciation (value) of mathematics, and on the application (work) of mathematics.

“Serving through Statistics,” Conference for the Advancement of Mathematics Teaching, Houston, TX, July 2012.

In this presentation I discuss the keys to designing and successfully implementing a service learning project for AP Statistics students that provides valuable real-world experience in experimental design, collaboration with community officials, data gathering, statistical analysis and the publication their results, all within the context of community service.

Beyond Practicality: George Berkeley and the Need for Philosophical Integration in Mathematics,” Mathematical Association of America Session on Philosophy of Mathematics and Mathematical Practice at the Joint Mathematics Meetings, Boston, MA, January 2012.

In this paper I demonstrate the need for a philosophical reflection in mathematics, as opposed to purely practical motivations, because it actually leads to more practical applications of mathematics. This is historically evidenced in the work of George Berkeley.

“Integrating Faith and Mathematics: What We Can Learn From Process Theology,” The 18th Association of Christians in the Mathematical Sciences Conference, Westmont College, June 2011.

In this paper I present Process Theology as a clear historical example of how theological foundations have significant impact on the practice mathematics. The tenets of process theology are examined and shown to radically depart from Christian orthodoxy. Therefore its proposal for integrating orthodox Christian faith and mathematics cannot be accepted. Yet the process perspective still has something to offer for the construction of a framework within which a distinctly Christian perspective of mathematics might be developed.

“Finding Beauty in Mathematics,” Dallas Theological Seminary Admissions Department Promotional Video, (August, 2010).

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