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:

Screen Shot 2017-06-01 at 10.21.51 PM

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.

21st Biennial ACMS Conference: Call for Papers

The Twenty First Biennial ACMS conference will be held at Charleston Southern University in Charleston, South Carolina May 31-June 3, 2017. The featured speakers are Sloan Despeaux, Dominic Klyve and Derek Schuurman. In the coming months, conference details will be posted at http://acmsonline.org/2017-acms-conference/

At this time proposals are being accepted for talks. The submitted proposals need to include the presenter’s name, presentation title, and an abstract of 250 words or less. Please provide your abstract in Word or TeX/LaTeX. Most presentations are expected to last 15 minutes plus a 5 minute transition time between speakers. A selection of the presentations will last for 25 minutes with a 5 minute transition. Please indicate if you would like to be considered for a longer presentation. There will also be a poster session, especially for students. You will be notified at a later date whether your submission has been selected for the conference.

ACMS is looking for presentations in the following general categories:

 Computer Science

 Computer Science Education

 Mathematics

 Mathematics Education

 Statistics

 Statistics Education

 Interaction of Faith and Discipline

Proposals should be sent to ddawson (at) csuniv.edu by February 15, 2017. Please put “ACMS proposal” in the subject line. Any proposal received after February 15 will be considered if space remains.

Refereed Proceedings:

Please note that this year’s ACMS Proceedings will be refereed. To allow authors time to incorporate audience feedback into their papers, all submissions to the Proceedings will be due September 15, 2017. Submissions for the Proceedings should be in TeX or LaTeX (this type setting software can be obtained for free). If you are not familiar with this software, Tom Price will be offering a workshop in using LaTeX as part of the pre-conference.

God: One and Infinite

by Dr. Daniel Kiteck, Indiana Wesleyan University

The following is from a talk given by Dr. Kiteck at the ACMS Conference this past May. It is with his gracious permission that I am sharing it here. 

Abstract

The ontology of mathematical objects has been of interest for millennia. I focus on the ontology of the number one in relationship to the ontology of God.

1. Introduction

Let ONE represent “the essence of what ‘the number one’ is.” I focus on the cardinal nature of the number one as opposed to its ordinal nature. The primary question is “What is ONE?” First, consider:

“There is no physical entity that is the number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.” [Fraleigh and Beauregard, Introduction]

Why would mathematicians be in wonder over the number one?

2. ONE in Mathematics

ONE is foundational to counting, which is foundational to much of mathematics. This is nicely shown by Doron Zeilberger in his Fundamental Theorem of Enumeration: [Gowers et al., 2010, p. 550]

number one

With some philosophical hand waving (which I admit deserves more attention, but that will be suppressed for now), ONE can be seen as foundational to much of the mathematical spaces that mathematicians work within. Just starting with ONE, we immediately have a unit {1}. From this we can imagine the existence of the unit and the non-existence of the unit: {0, 1}. But, imagining ONE twice, ONE three times, and so on brings us to N. Bringing in the concept of symmetry of an anti-ONE, an anti-ONE twice, etc., gives us Z. But then considering the set of all integers over non-zero integers, Q, and the set of all Dedekind cuts, R, (recalling that each Dedekind cut is an infinite set of rational numbers), we quickly imagine ordered pairs, triples, etc. to then have R 2 , R 3 , etc. So ONE is important to mathematics. But, is ONE important to Jesus?

3. ONE in Theology

3.1 Mark 12

In Mark chapter 12, someone asks Jesus “Of all the commandments, which is the most important?” Jesus famously responds with loving God and loving neighbor. But, the first part of Jesus’ response in verse 29 is

“The most important one,” answered Jesus, “is this: ‘Hear, O Israel The Lord our God, the Lord is one.’ ”

Jesus is quoting one of the most important pieces of scripture for the Jews, from Deuteronomy 6:4. My understanding is that this is commonly not seen as God being numerically one, so differing from ONE, but I still see it as reasonable to ask about how “One God” is related to ONE. But, first, where else in the Bible is it common to use the word “one?”

3.2 More than One?

In Genesis 2 we have two (husband and wife) becoming “one flesh.” But then in Ephesians 5 Paul informs us that this is a mystery actually referring to Christ and the Church. In traditional Christian Theology we have God as trinity [1] : “Three in One.” How are these connected to ONE?

4 The Ontology of ONE

4.1 Trinity

Does the concept of the trinity lead us to ONE and THREE as eternal concepts? Or does it lead us to conclude that we must leave the relationship between God and numbers a mystery? [2]

4.2 One God

Was there one God before God created the number one? I like asking this question to my students. Here are some responses attempting to honor God’s sovereignty: ONE is…

  • part of a “continuous creation,” so distinct from God [Howell and Bradley, 2001, p.71]
  • uncreated, so part of the nature of God in a mysterious way [Boyer and Huddell III, Spring 2015]
  • not “real” in a Platonic sense [Bradley and Howell, 2011, p. 230-235]
  • …wait!…Is “one” the same in “one God” and “number one?” [Ibid.]

Let’s explore this last question.

4.3 Necessity

Is ONE necessary in any universe God may create? I claim “yes” since one universe would be recognized by God.

But what if God had chosen not to create anything? Is ONE necessary then? [3] Perhaps another way to put it is: Must God’s eternal unique existence correspond to ONE? In light of the trinity, I am not confident in making a claim either way. And, in fact, in light of the oneness of Christ and the church, there seems to be some things concerning ONE that may be beyond our understanding. Or perhaps ONE should be seen as a rather distinct idea from many other ideas that are represented by the word “one.”

5 Conclusion

ONE is important to mathematics. “One God” is important to Jesus, but we must be careful with how this relates to ONE, especially in light of the trinity and the sovereignty of God. May our questions concerning ONE, and with mathematics in general, increase our wonder of the ultimate one, God.

I give a special thanks to my wife Karen for helping me sort my thoughts.

Bibliography

Steven D. Boyer and Walter B. Huddell III. Mathematical knowledge and divine mystery: Augustine and his contemporary challengers. Christian Scholar’s Review, XLIV(3):207–235, Spring 2015.

W James Bradley and Russell W Howell. Mathematics through the eyes of faith. HarperCollins Publishers, 2011.

J Fraleigh and R Beauregard. Linear algebra. 1990.

Timothy Gowers, June Barrow-Green, and Imre Leader. The Princeton companion to mathematics. Princeton University Press, 2010.

Russell W Howell and W James Bradley. Mathematics in a postmodern age: A Christian perspective. Wm. B. Eerdmans Publishing Co., 2001.

References

[1] I thank William Lindsey for pointing out the importance of including the trinity in this presentation

[2] I thank Kevin Vander Meulen for this question.

[3] A conversation with Jim Bradley sparked this question. Thank you Jim Bradley for the opportunity!