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Math is ______________

Math is ______________. Josh Wilkerson, Ph.D. Regents School of Austin Mathematics Appreciation Teacher www.GodandMath.com 2017 RSA Classical Christian Development / Austin, TX. Let ’ s talk about Math!.

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Math is ______________

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  1. Math is ______________ Josh Wilkerson, Ph.D. Regents School of Austin Mathematics Appreciation Teacher www.GodandMath.com 2017 RSA Classical Christian Development / Austin, TX

  2. Let’s talk about Math! • I would contend that 100%* of people have a visceral, memorable experience of math class. • The shame to me, being a math teacher, is that I would venture the vast majority of those experiences are negative. * Note that I teach statistics so I don’t throw that number around lightly to just mean “a lot”

  3. Regents 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. Math is ______________ TRUE • I mean, 2 + 2 = 4 every time (amirite?) • “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 • Does God use mathematics because He is a God of order or does math have order because God uses it? • Order is not a characteristic God displays but a quality that He defines by His nature and math gives us a glimpse into that nature.

  5. Math is ______________ BEAUTIFUL

  6. 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

  7. Math is ______________ CONFUSING STRESSFUL TOO ABSTRACT NOT APPLICABLE FOR ME THE EXACT OPPOSITE OF ALL THAT IS GOOD AND HOLY GOOD?

  8. What Students Seek • The Primary Question: “When am I ever going to use this?” “Why should I value this?”

  9. What Students Seek • “Our hearts our restless until they rest in you.” • Augustine, Confessions • That restlessness is what is walking into your math class. • Students want to find value (our curriculum) • Students want to be valued (our pedagogy)

  10. What Teachers Seek

  11. Affirmation in Research • When teachers talk about their mathematics classes, they seem just as likely to mention their students’ enthusiasm or hostility toward mathematics as to report their cognitive achievements. • Similarly, inquiries of students are just as likely to produce affective as cognitive responses, comments about liking (or hating) mathematics are as common as reports of instructional activities. • Affective issues play a central role in mathematics learning and instruction. • Douglas McLeod in Handbook of research on mathematics teaching and learning (1992)

  12. Affirmation in Policy • “Being mathematically literate includes having an appreciation of the value and beauty of mathematics as well as being able and inclined to appraise and use quantitative information.” • NCTM Standards for Teaching Mathematics • “Mathematical proficiency has five strands: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Productive disposition is the habitual inclination to see mathematics as sensible, useful, and worthwhile.” • Adding it Up: Helping Children Learn Mathematics (National Research Council)

  13. As it stands… • As it stands our current methods of teaching mathematics are producing untold numbers of students who see mathematics more about natural ability rather than effort, who are willing to accept poor performance in mathematics, who often openly proclaim their ignorance of math without embarrassment, and who treat their lack of accomplishment in mathematics as permanent state over which they have little control. • McLeod (1992)

  14. Mr. Williams is driving down the road at 70 MPH when he happens upon a tipped cow. Unable to swerve it is fortunate that the prostrate bovine is angled at a perfect 30 degrees from the horizontal. Assuming no wind resistance how long will Mr. Williams be airborne before he hits the ground? Explain your reasoning.

  15. 70 MPH 30o

  16. Different at Regents • So does 2 + 2 = Jesus now?

  17. Different at Regents • “If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea” • Antoine de Saint-Exupery

  18. Cultivating Affections (part 1) • Education is not primarily a heady project concerned with providing information; rather, education is most fundamentally a matter of formation, a task of shaping and creating a certain kind of people. • What makes them a distinctive kind of people is what they love or desire or value. • An education, then, 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. • There is no neutral, nonformative education • James K.A. Smith, Desiring the Kingdom (2009)

  19. Cultivating Affections (part 2) • Mathematics educators who set out to modify existing, strongly-held belief structures of their students are not likely to be successful addressing only the content of their students’ beliefs…it will be important to provide experiences that are sufficiently rich, varied, and powerful in their emotional content. • G.A. Goldin in Beliefs: A hidden variable in mathematics education? (2002)

  20. Cultivating Mathematical Affections • Students want to know your story… • What are the touchstone moments you can recall from a math classroom? • What would you say are the “thick” practices/routines/liturgies of a math classroom? • How has your experience of those practices shaped your perspective of mathematics? • In light of our own experience of mathematics how do we work to shape our students’ experience of mathematics? How do we cultivate their mathematical affections?

  21. Math is ______________ INVITING

  22. Math is ______________ INVITING • Often our invitation into mathematics is already excluding some students • This example is teaching binary numbers but that term is never used • Would rather students understand the underlying concepts and connections than parrot terminology without understanding

  23. The Global Math Project

  24. Math is ______________ ANALOGY FLATLAND: A parable in many dimensions Edwin Abbot 1884

  25. Crucifixion (Corpus Hypercubus) – Salvador Dali

  26. Math is ______________ SERVING

  27. Service-Learning

  28. Service-Learning

  29. Service-Learning

  30. Service-Learning

  31. Service-Learning • Affective learning objective is primary • Cognitive learning objective is still present and operating at a high level • Opportunity to communicate the value of affective learning outcomes through assessment • “It is through our assessment that we communicate most clearly to students which activities and learning outcomes we value.” • David J. Clarke, NCTM Assessment Standards for School Mathematics • Reflection is key • Moves toward inculcating a servant’s heart

  32. WHY Consider Service-Learning? “Yeah, definitely, much more positive. It was hard, don't get me wrong and I'm not saying the ‘I'm no good at math thing’ didn't change, but I do think ... I am sure that I can learn it, because I am sure I can learn it. It just will take longer and when you don't feel so completely discouraged about it ... When you do feel that you do have shot to understand it and learn it, for me at least it really raises my attitude towards it. It doesn't feel like it's this hopeless thing that I just have to suffer through. It is kind-of just a hill you climb, right?”

  33. Math is ______________ UPLIFTING

  34. Regents 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 (inviting) as they live purposefully and intelligently in the service of God and man.

  35. Action Items • Everyone: • Stop gossiping about math and go talk face to face • G.H. Hardy, A Mathematician’s Apology • Paul Lockhart, A Mathematician’s Lament • Francis Su, “The Lesson of Grace in Teaching” and “Math for Human Flourishing” • Math teachers K-12: • Join in the Global Math Project • Share your math story and invite students to share theirs – a math autobiography assignment • Ask them to draw a mathematician and have a conversation about the results • Offer reflective questions in class and on exams • (4th – 8th) let me come talk to your class about math and service!

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