A Christian Constructivist The impact of worldview on learning theories and the mathematics educatio

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A Christian Constructivist? The impact of
worldview on learning theories and the
mathematics education research communityACMS
Biennial ConferenceJune 3, 2005

• Jeffrey Barrett, Illinois State University
• jbarrett_at_ilstu.edu
• Dave Klanderman, Trinity Christian College
• Dave.Klanderman_at_trnty.edu

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Outline of Presentation

• Tensions between Christians and the Academy
• Valid and true conclusions from diverse starting
  points
• The struggle for coherency and consistency in
  building a learning theory
• University in Diversity Using a Christian
  Worldview to search for a grand theory
• Our responsibilities as Christian scholars
• Next Steps

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Tension between Christians and the Academy

• Schaeffer, Kuyper, and Guinness A mandate for
  Christians to engage actively in all aspects of
  culture
• Marsdens Outrageous Idea of Christian
  Scholarship The Utopian Problem
• Vignettes from graduate school
• SUNY Buffalo (1994)
• Northern Illinois University (1996)

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Valid and true conclusions from diverse starting
points

• Piaget Stages of development and levels of
  understanding
• Exemplar Understanding the function concept
• Level 1 Lack of coordination of variables
• Level 2 Coordination of variables in local
  cases
• Level 3 Sequential coordination of variables
• Level 4 Generalized coordination of variables
• Genetic Epistemology

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Valid and true conclusions from diverse starting
points

• Vygotsky Zone of proximal development
• Marxism/Sociocultural dominance
• Confrey Splitting conjecture and imbeddedness
  of units
• Radical Constructivist/Secular Humanist
• Cobb Connecting mathematical tasks and the
  learning environment
• Social Constructivist/Pragmatist

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Valid and true conclusions from diverse starting
points

• Different responses to Gods existence and
  relating to scholarship
• Atheism
• Agnosticism
• Dualism
• Christian Worldview
• Other Worldviews

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The struggle for coherency and consistency in
building a learning theory

• What does taken as shared mean?
• Some terminology (as defined in the mathematics
  education community)
• Radical Constructivism
• Sociocultural Constructivism
• Other versions of Constructivism

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The struggle for coherency and consistency in
building a learning theory

• Cobb (1995) Complementary nature of
  sociocultural and (radical) constructivist
  perspectives
• E.g. Interpreting a hundreds chart
• Lehrman (1996) Intersubjectivity and
  limitations of radical constructivism
• E.g. Is 1 an even number?

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The struggle for coherency and consistency in
building a learning theory

• Cobb and Thompson (1998) Trying to avoid the
  split brain syndrome making psychological and
  sociocultural perspectives compatible
• One literally does not exist without the other
• Cobb and Brown (1999) Underpinnings of
  cognitive and situated learning theories
• Schaeffers notion of philosophical despair

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University in Diversity Using a Christian
Worldview to search for a grand theory

• Cobbs attempt to avoid the lure of cosmology
  argues instead for his own voice
• Cobbs definition of coherent and consistent
  theory wants positive change, improvement,
  workability, etc.

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University in Diversity Using a Christian
Worldview to search for a grand theory

• As Christians, we respond to Cobbs yearning for
  explanation by praising our Creator God
• Implications of a well-ordered Creation and
  people as Gods image bearers
• E.g. Language and thought are distinct yet
  inherently connected

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University in Diversity Using a Christian
Worldview to search for a grand theory

• Analogy to the paradox of the Trinity
• Distinctiveness with specified roles
• Unity and integrity
• Meaning-making
• Psychocognitively and in sociocultural contexts

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Our responsibilities as Christian scholars

• Motivation to reach the individual
• Listen with mercy
• Identify attempts to avoid/rationalize
• Offer competing integrative theory with boldness
  and humility
• Motivation to reach the broader (sociocultural)
  community
• Start with review of common tension in current
  research

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Next Steps

• Continue collaborative scholarship in the math
  education research community
• E.g. Barrett, Clements, Klanderman, Pennisi, and
  Polaki (in press). Students coordination of
  geometric reasoning and measuring strategies on a
  fixed perimeter task Developing mathematical
  understanding of linear measurement. Journal
  for Research in Mathematics Education.
• Conduct a review of recent research where
  tensions between individual and community are
  most evident.
• Offer an attempt to resolve this tension.