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Cultivating Mathematical Affections

Explore the role of emotions in math learning, shifting focus to creating positive attitudes and values towards mathematics.

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Cultivating Mathematical Affections

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  1. Cultivating Mathematical Affections Re-Imagining Research on Affect in Math Education Joshua B. Wilkerson Texas State University www.GodandMath.com 2015 Joint Mathematics Meetings / San Antonio, TX

  2. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com The Ideal Lesson/Classroom

  3. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Learning • 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)

  4. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Objectives in Mathematics • “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

  5. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Objectives in 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)

  6. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Learning • 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) • 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)

  7. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Learning • 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) • Affections  Emotions • Affections = Aesthetics • Orientation of your life • Mechanism for determining what is worthwhile

  8. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Learning • 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)

  9. What if…?

  10. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Affective Learning • 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)

  11. 2015 Joint Mathematics Meetings / San Antonio, TX www.GodandMath.com Mathematical Affections • 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) • Technology • Assessment

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