Math for Goodness Sake

1. Math for Goodness Sake Cultivating Mathematical Affections Joshua B. Wilkerson, Th.M. Regents School of Austin Texas State University www.GodandMath.com 2014 SCL Conference / Austin, TX

2. 2014 SCL Conference / Austin, TX www.GodandMath.com Why do we teach math?

3. 2014 SCL Conference / Austin, TX www.GodandMath.com Why We Teach Math • Regents School of Austin Mission Statement: The mission of Regents School is to provide a classical and Christian education, founded upon and informed by a Christian worldview, that equips students to know, love and practice that which is true, good and beautiful, and challenges them to strive for excellence as they live purposefully and intelligently in the service of God and man.

4. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is… Beautiful! • “The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.” ~ G.H. Hardy, A Mathematician’s Apology • “The mathematical sciences particularly exhibit order, symmetry, and limitation; these are the greatest forms of the beautiful.” ~ Aristotle

5. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is… True! • “To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.” ~Hilda Phoebe Hudson Source: xkcd: Certainty (http://xkcd.com/263/)

6. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is… Good?

7. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is… Good? • Math is… • Confusing • Boring • Stressful • Too abstract • Not applicable to me • The complete opposite of all that is good and holy

8. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is… Good? • The Primary Question: “When am I ever going to use this?” “Why should I value this?” Our perspective needs to be that mathematics is at its core a virtuous activity and its enjoyment is not reserved for the “intellectual elite”

9. 2014 SCL Conference / Austin, TX www.GodandMath.com Math is Good! • Mathematics is at its core a virtuous activity and its enjoyment is not reserved for the “intellectual elite” • Questions to Consider: • Why should mathematics be viewed as an inherently virtuous activity? • How do we as Christian educators instill in students an appreciation for the inherent goodness of math?

10. 2014 SCL Conference / Austin, TX www.GodandMath.com Why is Math Good? • Our God is a God of Order • God is love • God is just • God is order • Order  quality that God portrays • Order = quality that emanates from God’s nature

11. 2014 SCL Conference / Austin, TX www.GodandMath.com Why is Math Good? • “He (Christ) is the image of the invisible God, the firstborn of all creation. For by Himall things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities – all things were created through Him and for Him. And He is before allthings, and in Himall things hold together.” ~ Colossians 1:15-17 (emphasis added)

12. 2014 SCL Conference / Austin, TX www.GodandMath.com Why is Math Good? • “The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.” • “I was merely thinking God’s thoughts after Him. Since we astronomers are priests of the highest God in regard to the book of nature, it benefits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God.” ~ Johannes Kepler

13. 2014 SCL Conference / Austin, TX www.GodandMath.com Why is Math Good? • If we believe that God is a God of order… • Then mathematical results don’t simply correlate with some quality that God displays, rather they can be understood as a manifestation of God’s nature. • Then in a way we are communing with God in our work as mathematicians, gaining deeper insight into His character. • Then we understand order in mathematics as a deeply profound and intimate aspect of Christian faith that should lead us to worship

14. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • By cultivating mathematical affections • What does this mean? • Affections  Emotions • Affections = Aesthetics • Orientation of your life • Mechanism for determining what is worthwhile • Jonathan Edwards, A Treatise Concerning Religious Affections

15. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • James K.A. Smith, Desiring the Kingdom • Thinkers (know) • Believers (still know) • Lovers • Love takes practice

16. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • James K.A. Smith, Desiring the Kingdom • “An education is a constellation of practices, rituals, and routines that inculcates a particular vision of the good life by inscribing or infusing that vision into the heart (the gut) by means of material, embodied practices” (26). • “There are no private practices; thus our hearts are constantly being formed by others, and most often through the cultural institutions that we create” (71).

17. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • David J. Clarke, NCTM Assessment Standards for School Mathematics • “It is through our assessment that we communicate most clearly to students which activities and learning outcomes we value.”

18. 2014 SCL Conference / Austin, TX www.GodandMath.com The Need for Affective Assessment Bloom’s Taxonomy (Revised) Chart Courtesy of CL Jorgensen

19. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • When students ask “When am I ever going to use this?” and really mean “Why should I value this?”… • Offer them embodiment over application • Math is more than calculations • Christianity is more than thinking

20. 2014 SCL Conference / Austin, TX www.GodandMath.com How do We Teach Math as Good? • Excellent Vehicles for Affective Assessment: • Math Journals • Reflection Assignments • Personal Interviews • Class Discussion/Debate • Oral Presentations • Open-Ended Group Problems • Historical Reading and Response • Service-Learning Projects

21. 2014 SCL Conference / Austin, TX www.GodandMath.com Cultivating Mathematical Affections • Example service objective from a Statistics course: • Valuing: TSW support the mission of a local non-profit organization through the design of a statistical study done on the organization’s behalf. • Affective Verb • Cognitive Verb • Method of Assessment • Assessment should require student to defend the worthiness of the cause motivating the project and not simply report valid data analysis.

22. 2014 SCL Conference / Austin, TX www.GodandMath.com Cultivating Mathematical Affections • Students are actually doingreal mathematics.  • There is something about the physical practice of getting outside the classroom to collect and analyze data that implants an appreciation for the processes of mathematics into students. • Students are actually doing real mathematics in an unfamiliar/uncomfortable (read: human) way. • In service-learning there is interaction with actual human beings. The data on the paper now has a face and the analysis becomes a little messier and less clinical. • Shifts focus from individualistic outcomes (such as a grade) to more altruistic aims of education. • Students are actually doing real mathematics in an unfamiliar/uncomfortable (read: human) way and they (as well as the community) are experiencing firsthand the fruits of their labor.

23. 2014 SCL Conference / Austin, TX www.GodandMath.com Cultivating Mathematical Affections

24. 2014 SCL Conference / Austin, TX www.GodandMath.com Cultivating Mathematical Affections • “The service-based aspect of the project made it more engaging because we met new people and we had the mindset that we could actually help someone by completing this project.” • Student Response to Service Project • “Whoever wishes to become great among you shall be your servant, and whoever wishes to be first among you shall be your slave; just as the Son of Man did not come to be served, but to serve, and to give His life a ransom for many.” • Matthew 20:26-28

25. 2014 SCL Conference / Austin, TX www.GodandMath.com Cultivating Mathematical Affections • Know, love, and practice that which is true, good, and beautiful • Embodiment over application • Math is more than calculations • Christianity is more than thinking • Math is Good!

26. 2014 SCL Conference / Austin, TX www.GodandMath.com Questions?

27. Resources • www.GodandMath.com • Mathematics through the Eyes of Faith, Russell Howell & James Bradley (eds) • www.WhatifLearning.com • Kuyers Institute for Christian Teaching and Learning

28. 19th ACMS Conference / Bethel University / 2013 www.GodandMath.com Cultivating Mathematical Affections • Examples from a Statistics course: • Receiving: The student will (TSW) differentiate between valid and fallacious statistical arguments and argue their reasons in a written response. • Affective Verb • Cognitive Verb • Method of Assessment • Assessment should account for the initial discernment between truth and falsehood in addition to the correctness of the argument.

29. 19th ACMS Conference / Bethel University / 2013 www.GodandMath.com Cultivating Mathematical Affections • Examples from a Statistics course: • Responding: TSW engage in class discussion comparing and contrasting religious and statistical knowledge. • Affective Verb • Cognitive Verbs • Method of Assessment • Assessment should account for the level of engagement in addition to the determination of proper similarities and differences.

30. Cultivating Mathematical Affections • Examples from a Statistics course: • Organizing: TSW definethe limitations of statistical inference procedures and accordingly make recommendations to the acting agency in an oral presentation. • Affective Verb Phrase • Cognitive Verb Phrase • Method of Assessment • Assessment should account for recognition of shortcomings (humility) in the oral presentation.

31. 19th ACMS Conference / Bethel University / 2013 www.GodandMath.com Cultivating Mathematical Affections • Examples from a Statistics course: • Characterizing: TSW be evaluated in their intellectual integrity and rated positively by their peers through a written reflection survey. • Affective Verb Phrase • Cognitive Verb • Method of Assessment • Assessment allows for students to communicate their personal reflection and evaluation of others.