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Cultivating Mathematical Affections

Cultivating Mathematical Affections. The Influence of Christian Faith on Mathematics Pedagogy. Joshua B. Wilkerson Texas State University www.GodandMath.com 20 th ACMS Conference / Redeemer University College.

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Cultivating Mathematical Affections

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  1. Cultivating Mathematical Affections The Influence of Christian Faith on Mathematics Pedagogy Joshua B. Wilkerson Texas State University www.GodandMath.com 20th ACMS Conference / Redeemer University College

  2. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com What Students Seek • The Primary Question: “When am I ever going to use this?” “Why should I value this?”

  3. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com What Teachers Seek

  4. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com 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)

  5. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com 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

  6. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com Affirmation in Policy • “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)

  7. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com Results? • 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)

  8. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com How did we get here? • Not talking about affections. • There is a prevalent attitude that one learns what is good mathematics by seeing and doing it, not by discussing values. The knowledge needed by the person entering the field will rub off on her. The classroom clearly reflects this attitude. • Michael Veatch on “Mathematics and Values” (2001)

  9. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com How did we get here? • Not understanding affections. • Affect has generally been seen as ‘other’ than mathematical thinking, as just not part of it. Indeed, throughout modern history, reasoning has normally seems to require the suppression, or the control of, emotion. • Rosetta Zan in Educational Studies in Mathematics (2006)

  10. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com How did we get here? • Setting the wrong ‘corrective’ course. • Although affect is a central concern of students and teachers, research on affect in mathematics education continues to reside on the periphery of the field … All research in mathematics education can be strengthened if researchers will integrate affective issues into studies of cognition and instruction. • McLeod (1992)

  11. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com A Secular Solution: • The affective domain is not simply based on subjective emotions (though emotion may play a small part in affective learning), rather it’s about demonstrated behavior, attitude, and characteristics of the learner. • D.R. Krathwohl, Taxonomy of educational objectives: Handbook II. Affective Domain (1964) • “Being mathematically literate includes having an appreciation of the value and beauty of mathematics” • “Productive disposition is the habitual inclination to see mathematics as sensible, useful, and worthwhile.”

  12. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com An Explicitly Christian Solution: • A Treatise Concerning Religious Affections • Affections  Emotions • Affections = Aesthetics • Orientation of Your Life • Mechanism for Determining what is Worthwhile Jonathan Edwards (1703 – 1758)

  13. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com An Explicitly Christian Solution: • 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)

  14. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com Agreement of Approaches • 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 to foster students’ construction of new meta-affect. • G.A. Goldin in Beliefs: A hidden variable in mathematics education? (2002)

  15. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com The Mathematical Experience: Cultivating Mathematical Affections • Mathematical Affections: Not only to know, but to also love and practice that which is true, good, and beautiful. • We need to recognize the opportunity that we have as Christian educators to speak to a fundamental question in the field of mathematics education. • Potentially fruitful areas to explore in this regard: • Use of technology in the classroom • Assessment strategies • Service-Learning

  16. 20th ACMS Conference / Redeemer University College / 2015 www.GodandMath.com 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

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