Cultivating Mathematical Affections

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

• The Primary Question
• When am I ever
• going to use this?

Why should I value this?
3
What Teachers Seek
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com
4
Affirmation in Research
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

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

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

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

• 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
How did we get here?
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
How did we get here?
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
How did we get here?
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
A Secular Solution
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• The affective domain is not simply based on
  subjective emotions (though emotion may play a
  small part in affective learning), rather its
  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
An Explicitly Christian Solution
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• A Treatise Concerning Religious Affections
• Affections ? Emotions
• Affections Aesthetics
• Orientation of Your Life
• Mechanism for Determining what is
  Worthwhile

Jonathan Edwards (1703 1758)
13
An Explicitly Christian Solution
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
Agreement of Approaches
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
  beliefsit 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
The Mathematical Experience Cultivating
Mathematical Affections
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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
Service-Learning
20th ACMS Conference / Redeemer University
College / 2015
www.GodandMath.com

• 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 servants heart