Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy

Here is some information on my talk at the 20th ACMS Conference (2015) at Redeemer University College. More information can be found in my article of the same title in the June 2015 issue of Perspectives of Science and Christian Faith:

Abstract:

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.

PowerPoint:

ACMS Cultivating affections

Outline:

PDF of talking points outline

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.

McLeod, D.B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.

National Council of Teachers of Mathematics. (1991). Standards for teaching mathematics. Reston, VA: NCTM.

National Council of Teachers of Mathematics. (1995). Mathematics Assessment Standards. Reston, VA: NCTM.

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.

Veatch, M. (2001). Mathematics and values. In R. Howell & J. Bradley (Eds.), Mathematics in a Postmodern Age: A Christian Perspective. GrandRapids: Eerdmans, pp.223-249.

Zan, R., Brown, L., Evans, J., & Hannula, M.S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics (Affect in Mathematics Education: Exploring Theoretical Frameworks: A PME Special Issue), 63:2, 113-121.

20th ACMS Conference

May 25, 2015 2 comments

The 20th Association of Christians in the Mathematical Sciences (ACMS) conference began Monday with the first pre-conference session. This is the 3rd time that I have attended the ACMS Conference and I am always refreshed to spend time among mathematicians and educators who care so deeply about living out their faith in the discipline that God has called them to. My goal is to continually update this post throughout the week with insights gained or further thoughts raised during the week’s activities.

Conference Day 2

The day began with another excellent devotional from John Roe (who has graciously contributed his thoughts on GodandMath.com in the past). Personally, I feel blessed after every time I hear John Roe speak – he just has a way about him that seems infused with grace and deep spiritual understanding. John led us through Ephesians 3:14-19 with particular focus on the four dimensional analogy used by Paul:

For this reason I bow my knees before the Father, from whom every family in heaven and on earth is named, that according to the riches of his glory he may grant you to be strengthened with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith—that you, being rooted and grounded in love, may have strength to comprehend with all the saints what is the breadth and length and height and depth, and to know the love of Christ that surpasses knowledge, that you may be filled with all the fullness of God.

Some of John’s points:

  • When thinking of the love of God, don’t think in abstractions. Think of the concrete. Think of the cross.
  • Wideness – if you fold your arms across your chest this is the typical position of religion; inclusive and safe. If you stretch your arms wide open this is the position of Christ on the cross.
  • Longness – (a dimension of time perhaps) God’s patience and love are endless. God’s love wins because it endures more than we do.
  • Highness – The son of Man was lifted up. Christ does not shrink from being on display in that shameful place; He doesn’t hide.
  • Deepness – How deep Christ went – down to earth, down to the grave. How deep in our own hearts are the places that He can reach. He went there and He proclaimed freedom there.

(NOTE: at this point parallel sessions began, so what follows is a recap of the talks I attended)

Annalisa Crannell spoke on “The God of Mathematics,” which is actually the title of an adult Sunday School class she led at her church. The emphasis of her class was not on what math proves about God but rather how math gives a metaphor for better understanding God. Metaphor is inherent in both faith (“you are the light of the world”) and mathematics (“populations is an exponential function of time”). Annalisa was able to get into some really deep and interesting mathematics and all in the context of equipping adults in her local church and drawing them into a deeper relationship with God. How cool is that?

Jim Bradley gave a talk on “Random Numbers and God’s Nature.” This was a snippet of a larger project on randomness and divine providence that Jim has been working on. I encourage you to explore Jim’s work in more detail as there is no way a paragraph summary here can do it justice. The basic idea: what if randomness is a part of God’s nature? DISCLAIMER: Here randomness is NOT defined as chance or fate or indifference. Randomness is this sense is defined in a technical sense as a number that is irreducible, cannot be generate by an algorithm, and is unpredictable. So for instance by this definition π is not random because it is predictable. However a string of 1’s and 0’s where each digit is determined by the flip of a coin (heads for one, tails for zero) would be random. A key math result is that almost all numbers are random – meaning patterns (that we so often as Christian mathematicians treat as being infused into the core of creation) are actually unusual (and therefore why they are so noticeable). If you take and Augustinian perspective of numbers being situated as a part of God’s nature then random numbers existed in the mind of God from eternity. Perhaps this idea might give us some insight in divine infinitude – God cannot be reduced to something finite, no linguistic description will ever be adequate, and God’s mystery is unfathomable. By mystery we don’t mean confusing, but rather infinite depth – it can be understood but never completely understood.

Jeremy case offered an excellent review of the book Mathematics without Apologies: Portrait of a Problematic Vocation. The ACMS produced a book called Mathematics in a Postmodern Age, and Jeremy suggested this book could be thought of as “A Postmodern Age in Mathematics.” This book (also written as a response to Hardy’s A Mathematician’s Apology) argues that mathematicians should seek more than the good, the true, and beautiful in mathematics – namely application. From a Christian perspective many of the arguments in the book are untenable. But as Jeremy astutely pointed out: the arguments are very strong for those not grounded in Christ, so this needs to be a work we pay attention to and a conversation that we engage in. We need more than application to be fruitful as mathematicians – we need to consider how we are not just apply mathematics but serving (both God and neighbor)  through that process.

Conference Day 1

The official opening of the ACMS conference was led by ACMS President Troy Riggs. Troy gave some brief remarks before the opening keynote address, but the remarks were powerful reminders nonetheless. Troy challenged our western conception of truth and encouraged a more biblical view of truth: that truth is not something that we possess but it is something (someone) we follow.

In mathematics, as in faith, there is the reality of the tension between immanence and transcendence; and these are not necessarily two opposite ends of a spectrum. For instance π seems so straightforward and immanent: the ratio of the circumference of a circle to its diameter. But π has such surprising depth, being classified as a transcendental number and even popping up in places like equations for normal distributions in statistics. From the opposite perspective, something like a 4D hypercube seems initially so abstract and transcendent. Yet one can quickly come to see the pattern of properties as they extend from 2D to 3D to 4D and we find that a 4D hypercube is quite easy to work with mathematically (very immanent).

This is why the ACMS logo draws heavily on Dali’s Corpus Hypercubus. Dali saw the unfolding of a 4D hypercube into 3D space as the perfect representation for communicating the mystery of the transcendent God coming down to be immanently present in creation at the cross.

The opening keynote address was given by Matthew Dickerson on “Can Computers Reason.” I must admit that I was so wrapped up in his presentation that I did not take nearly enough notes to even paraphrase his talk here. But he was speaking on many ideas set forth in his book The Mind and the Machine which I would highly recommend exploring. Here is a brief summary from Amazon:

What does it mean to be human? Some naturalists believe that the human mind can be reduced to brain biology, suggesting that we are no more than complex biochemical machines. Computer scientist Matthew Dickerson critiques a physicalist/naturalist view of human persons and defends theistic accounts of human nature. He responds to the widespread assertion that human consciousness is nothing more than “software” that can one day be downloaded into supercomputers. Drawing on C. S. Lewis and J. R. R. Tolkien, Dickerson gets at the heart of human nature itself, highlighting a far richer vision of personhood, creativity, and love. This thought-provoking book on a timely topic will appeal to those interested in science and religion, philosophy, and technology; readers of the materialist New Atheists; and anyone who simply cares what it means to be human.

Pre-Conference Day 3

The day began with the morning devotional by Matt DeLong. As with yesterday’s devotional, the words seemed to speak truth and aptly apply to every conversation had throughout the day. Matt took us to John 1:35-38 where we see perhaps the first question asked by Jesus during his adult ministry: “what do you want?” This is not asked in an offensive way as is typical today, but He is genuinely leading eager disciples to examine their heart if they are to follow Him.

Psalm 37:4 states: “Delight yourself in the Lordand he will give you the desires of your heart.” Often we have a tendency to read this as God will give us what we want if we follow Him. Perhaps a better way of thinking of it: God will shape the desires of your heart – He will give you the right desires to have in life in you first delight in Him. 

Matt then quoted from Dorothy Sayers “Why Work?”:

Work is not, primarily, a thing one does to live, but the thing one lives to do. It is, or it should be, the full expression of the worker’s faculties, the thing in which he finds spiritual, mental and bodily satisfaction, and the medium in which he offers himself to God.

Ephesians 2:10 (from the Message paraphrase):

Now God has us where he wants us, with all the time in this world and the next to shower grace and kindness upon us in Christ Jesus. Saving is all his idea, and all his work. All we do is trust him enough to let him do it. It’s God’s gift from start to finish! We don’t play the major role. If we did, we’d probably go around bragging that we’d done the whole thing! No, we neither make nor save ourselves. God does both the making and saving. He creates each of us by Christ Jesus to join him in the work he does, the good work he has gotten ready for us to do, work we had better be doing.

Matt then closed with an excellent prayer for vocation from Garber’s Visions of Vocation cited on Day 1 (I’m going to have to go read this book now).

There was then an excellent small group session that I was a part of with other gradate students receiving advice from those who had gone before us.

  • Excellent reminder that the job of teaching is infinite, but we are only finite. Here it would be appropriate to read/listen to Francis Su’s talk “The Lesson of Grace in Teaching.”
  • Reminder that it is ok to identify yourself as Christian in a secular university – especially to be clear to students how this impacts them: that you see every student as important and having inherent worth apart from grades.
  • Teaching in a Christian or public school may just changes the ways in which your faith is emphasized in those contexts. At a Christian school you are called more to discipleship. At a public school you are called more to being missional. (Though both discipleship and mission happen in both contexts).

Pre-Conference Day 2

(Disclaimer: there was a ton of great information shared today. A TON. What is below is just a brief rundown and doesn’t do the day’s presentations and conversations justice. Perhaps at a later date, after some mental processing, I will give a fuller treatment.)

The day began with a devotional led by Anthony Tongen. The focus was on Ephesians 4:1-6:

I therefore, a prisoner for the Lord, urge you to walk in a manner worthy of the calling to which you have been called, with all humility and gentleness, with patience, bearing with one another in love, eager to maintain the unity of the Spirit in the bond of peace. There is one body and one Spirit—just as you were called to the one hope that belongs to your call—one Lord, one faith, zone baptism, one God and Father of all, who is over all and through all and in all.

I had always read this passage and considered the “calling” that Paul was speaking of a purely spiritual calling – describing the life we are meant to lead as Christ followers. This is undoubtedly true, but it is also so much more than that. Seeing this as only a spiritual calling falls into the error of dualism as mentioned on day 1; the error of thinking that the spiritual life and our vocational life are separate things. Paul is urging us to walk worthily of God’s holistic calling on our life. Teaching is one profession outside of ministry that commonly is referred to as a calling. So what does it look like to be God-honoring in or vocation as mathematics teachers? To teach with humility, gentleness, patience, love, etc. God is sovereign over all of life and He calls us to walk worthily at every moment of that life.

Matt DeLong expanded on this more during a session on family life and faculty life. In Garber’s Vision of Vocation, cited on Day 1, he defines vocation as what you are called to be as a human being before the face of God. It is not just a job. As Paul would say, it is a calling. (Side note: the school where I teach has the school motto of Coram Deo which is Latin for “Before the face of God” – I love my school. A lot.)

Matt also pointed us to some sage advice on work/life balance from Drexel University:

  • You have only one life.  Nobody gets a “work life” and a “home life” – don’t expect to separate the two.  The best you can get is one life that is somewhat balanced, at any given time, between competing needs and desires.
  • What one person considers success may not be success for you.  Try not to get caught up in other people’s goals – what’s right for you is what is consistent with your values and priorities.  Get your values clear first – then think about how to get where you want to go.
  • Men and women in academics tend to be highly motivated, and the same thing that makes them want to do an excellent job academically makes them want to do an excellent job in all areas of their life, including rearing children.  Excellence in everything is impossible– do as good a job as possible with what you have, recognizing that perfection in all things, all the time, is impossible.

The best from that list in my opinion: there is no “work life” and “home life.” If the passage from Ephesians makes anyting clear it is that God has called us to ONE life.

Maria Zack then led an excellent session examining the four areas of scholarship offered under the Boyer model, as explained in Faith and Learning cited on Day 1. This is helpful for academic faculty in terms of narrowing a definition of how faith impacts their scholarship.

  • Scholarship of Discovery
    • Narrowing focus to one isolated part of reality to examine its complexity
    • What one would normally associate with typical research
  • Scholarship of Integration
    • How multiple aspects of reality work together
    • This is where the faith integration conversation happens
  • Scholarship of Application
    • Takes seriously the mandate of creation’s interconnectedness
    • works to close the gap between the academy and the real world
    • also referred to as the scholarship of engagement (side note: I love this way of discussing service-learning for my students; not just some side project, but the scholarship of engaging with the discipline and the community)
  • Scholarship of Teaching
    • Focus on the means/ways of handing down knowledge, faith, wisdom, and wonder (I love that wonder is included in this description) across the fragile bonds of connection that link different cultures and successive generations to each other.

Other nuggets of wisdom from today:

When working with students in research, you don’t have to know all of the answers. You just bring more experience to the table in planning to solve the problems.

Derek Schuurman encouraged us in exploring perspectival research (i.e. Christian perspective on mathematics…hey, someone should start a website on that). Why everyone doesn’t pursue this route of research is that we feel inadequate – no one can be both a theologian and philosopher and mathematician and whatever else you want to add (this reference reminded me a lot of Bob Brabenec’s paper on the founding of ACMS which frames my Background page). Derek made the observation that all perspectival research is by nature amateur, but God has called us to it. So how do we achieve it? See the Ephesians passage the opened the day – this turned into a nice passage that really framed all of the discussion from Day 2.

Maria Zack: Being a scholar earns you a voice. However, we as Christians view our voice in the academy very differently that others might. We should be reminded of the quote from St. Francis of Assisi: “Preach the Gospel always. When necessary, use words.” That is the voice we are to have as Christian scholars.

Derek Schuurman citing Donald Knuth: we are users, not developers of theology. Use theology to engage the guild. Perhaps not citing Christ explicitly, but challenging the guild to consider the major questions of the discipline. (Side Note: this is the main idea behind my upcoming article in Perspectives on Science and Christian Faith entitled “Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy.” It is a call for Christian math educators to engage the discussion in math education on how we shape/form student character and affections through our teaching of mathematics.)

Pre-Conference Day 1

Opening session on faith integration led by Derek Schuurman.

Tertullian once asked “What does Athens have to do with Jerusalem?” This is a succinct way of asking what all of us who are interested in doing mathematics and education Christianly are always wondering – what does our faith have to do with our vocation? There is not a quick and easy answer to this. In fact, I believe God desires for us to wrestle with this question constantly for our entire lives, and as we do we begin to gain some insights…which then lead to more questions…which lead to more insights….which lead to you get the idea. I believe that our growth in faith in our profession within the academy is a vital component of our spiritual sanctification; it is God’s refining process in our lives leading us more and more to His perspective. Derek did a great job of touching on this as well as just setting the stage for how we even go about having the the conversation on integrating faith with learning.

Derek outlined five approaches to Christian Scholarship:

  1. Dualism: Jerusalem has nothing to do with Athens
  2. Christian Education = Christians Educating
  3. Christianizing the discipline (i.e. throwing in a Bible verse here and there)
  4. Biblicism – seeing the Bible as an authoritative text on mathematics and science
  5. Holistic Christian Scholarship (probably not hard to guess that this is what we are aiming for)

On #3 vs. #5 an apt quote from Luther: “The Christian shoemaker does his duty not by putting little crosses on the shoes, but by making good shoes, because God is interested in good craftsmanship.”

There is a tension between what Derek referred to as structure and direction. Structure is what God built into the universe, the results of the “let there be”‘s. Direction is how we as humans are directing those structures that God has given us stewardship over. We have to always consider if we are directing them towards God or away from Him? Are we exploring mathematics and creating technology in a way that is honoring to God or in a way that is opposed to His will and lifts up the created above the Creator?

Mathematics a discipline is the study of the numerical and spatial aspects of creation. Mathematics can also be seen as culture making (nod to Andy Crouch). It is a tool for stewardship. It offers beauty and delight. It is inseparable from the concept of naming that holds such great Biblical significance.

A Biblical perspective of mathematics: apply biblical themes to guide us with mathematics. How mathematics fits in the grand narrative of creation, fall, redemption and restoration.

Recommended Books:

Faith and Learning: A Practical Guide for Faculty, by Patrick Allen and Kenneth Badley

Called to the Life of the Mind: Some Advice for Evangelical Scholars, by Richard Mouw

The Idea of a Christian College: A Reexamination for Today’s University, by Todd Ream and Perry Glanzer

The Courage to Teach: Exploring the Inner Landscape of a Teacher’s Life, by Parker Palmer

Visions of Vocation: Common Grace for the Common Good, by Steven Garber

Gordon Spykman’s lecture on “Scripture, Faith, and Science.” (info on Spykman by GodandMath contributor Steve Bishop)

Parting quote from Spykman: Nothing matters but the kingdom, but because of the kingdom, everything matters.

Mathematics: Building Community

A while back I wrote a post on “Geometry and the Homeless.” That post was after my first year if partnering with Mobile Loaves and Fishes Community First on a service-learning project for my advanced geometry students. I have now been blessed to have worked with MLF on service-learning projects for the past three years.

Here is a video on MLF’s heart for the Community First project:

I have worked with geometry students on designing RV covers, gazebos, bike racks, and spiral herb gardens. Below is a picture of last year’s winning gazebo design and the current building progress:

photo (1)IMG_2246

I am beginning my dissertation this summer. It will focus on the benefits of service-learning projects in mathematics and it will specifically examine the partnership between my students and MLF. So needless to say, you can expect a lot of future posts on this topic. Ultimately I believe that service-learning is an incredible way to impact a student’s appreciation of mathematics. To use terminology that I’ve written on before: service-learning is an excellent tool for cultivating mathematical affections.

While you can expect much more on this topic here, I wanted to share a recent video that I came across of other institutions partnering with MLF through the process of service-learning. The institution in the video below just so happens to be my alma mater of Texas A&M (Whoop!): Aggies design, build ‘tiny homes’ for homeless as part of curriculum – The Eagle: Local News.

Tiny House Video from TAMU College of Architecture on Vimeo.

Here are a few quotes from the local article that accompanied the video that speak to the impact of this type of project on the learning outcomes the students experienced:

Construction science senior Laura Malek said working on a project that was going to help a “great cause” was a huge motivator during the process. The project also mimicked a real-life work environment, she said, by bringing together students who wouldn’t normally work together.

“Today was so much fun,” she said. “It was amazing to actually see our work in place and actually get some outside feedback. It felt a little surreal to finally see it there today finished and painted. It meant a lot. People seemed to really enjoy the space and that felt really great after our hard work.”

An interesting side note is that the student quoted in the story is the sister of one of the students that was a part of the first ever service-learning project I initiated (see: Serving through Statistics).

Like I said, there will be a lot more to come on this.

Always feel free to contact me if you have any questions about implementing service-learning into your math class.

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