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Content Matters: Towards a Symbiosis of General and DomainSpecific Theories of Learning and Instruct

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The derivation of general principles for design from the theory. The translation of the principles into concrete designs in specific domains ... – PowerPoint PPT presentation

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Title: Content Matters: Towards a Symbiosis of General and DomainSpecific Theories of Learning and Instruct


1
Content Matters Towards a Symbiosis of General
and Domain-Specific Theories of Learning and
Instruction
  • Paul Cobb
  • Vanderbilt University
  • Nashville, USA

2
Top Down Relation Between Theory and Practice
  • The development of domain independent theory
  • The derivation of general principles for design
    from the theory
  • The translation of the principles into concrete
    designs in specific domains
  • The assessment of the concrete designs to test
    whether they work as anticipated

3
Bottom Up Relation Methodological Orientation
  • Classroom design experiments
  • Responsible for a group of students learning
  • Teacher a member of the research team
  • From several weeks to a year or more in duration

4
Bottom Up Relation Methodological Orientation
  • Sequences of instructional activities and
    associated tools
  • Analyses of the process of the students
    mathematical learning and the specific means by
    which that learning is supported and organized

5
Bottom Up Relation Methodological Orientation
  • Means of support
  • Instructional tasks
  • Tools and resources
  • Organization of classroom activities
  • Classroom norms and discourse

6
Design Research Cycle
7
Instructional Design
  • Delineation of significant mathematical ideas
    within a domain -- problematize the content
  • Conjectured learning route or trajectory for
    students learning that culminates with these
    significant mathematical ideas
  • Conjectured means of organizing learning along
    the envisioned trajectory

8
Instructional Design
  • The conjectured learning route depends on the
    means by which learning is supported and
    organized
  • Attempting to engineer students development of
    particular forms of mathematical reasoning

9
Resources and Constraints for Design
  • General theories of learning and instruction
  • Students prior knowledge
  • Historical development of ideas and processes in
    the particular mathematical domain

10
Resources and Constraints for Design
  • Analyses of sequences of cognitive levels and of
    student misconceptions
  • Do not problematize the domain
  • Document the consequences of typical school
    instruction
  • Analyses of the process of students learning in
    innovative instructional environments

11
Overall Purpose
  • Not to demonstrate that the instructional design
    works
  • Not even to test whether the design works
  • Test, revise, and improve the conjectures
    inherent in the design

12
Domain Specific Instructional Theory
  • Substantiated learning trajectory that culminates
    with significant mathematical ideas
  • Demonstrated means of supporting and organizing
    learning along that trajectory

13
Design Heuristics
  • Abstract design heuristics from a number of
    domain specific instructional theories
  • Empirically grounded in a range concrete designs
  • Feeds forward to guide the development of other
    domain specific instructional theories
  • Open to continual refinement and improvement

14
Bottom Up Relation Between Theory and Practice
  • Instructional design serves as the context for
    the development of theory
  • If you want to understand something, try to
    change it
  • If you want to change something, try to
    understand it
  • Symbiotic relationship between psychology of
    mathematical learning and instructional design

15
Top Down Relation Between Theory and Practice
  • The development of domain independent theory
  • The derivation of principles for design from the
    theory
  • The translation of the principles into concrete
    designs
  • The assessment of the concrete designs to test
    whether they work as anticipated

16
Top Down Relation Between Theory and Practice
  • Rarely if ever occurs in practice
  • One-way chain of reasoning implied in research
    reports
  • Alive and well in the discourse of educational
    research

17
Top Down Relation Between Theory and Practice
  • Purpose Test whether the design works
  • Experimental or quasi-experimental designs
  • Focus is typically on learning outcomes rather
    than learning processes
  • Limited guidance for improvement of designs

18
Top Down Relation Between Theory and Practice
  • Ill-suited for testing and revising theory
  • Weak feedback loop from design to theory
  • Failure of concrete designs rarely leads to
    revision of general theory
  • Attempt to demonstrate practical relevance of
    theory

19
Top Down Relation Between Theory and Practice
  • Assessed with respect to my concerns and
    interests as a mathematics educator
  • Development of general theories typically
    motivated by different sets of concerns and
    interests
  • Cognitive psychology
  • Developmental psychology
  • Sociocultural theory

20
Top Down Relation Between Theory and Practice
  • Emerged historically in response to different
    types of problems
  • Theories as conceptual tools developed for
    particular purposes
  • Ask different types of questions, attempt to gain
    insight into different types of phenomena,
    produce different forms of knowledge

21
Top Down Relation Between Theory and Practice
  • For what purposes are particular types of
    theories useful?
  • For who are particular types of theories useful?
  • General, domain independent theories are
    potentially useful to educational administrators

22
Design Research Cycle
23
Classroom-Based Analyses
  • Classrooms are complex and messy
  • Need interpretive frameworks that enable us to
    see pattern and order in seemingly ill-structured
    events
  • Key criterion Should result in analyses that
    feed back to inform the improvement of
    instructional designs

24
Interpretive Frameworks
25
Social Norms
  • Students are obliged to
  • Explain and justify their solutions
  • Make sense of others explanations
  • Indicate understanding and non-understanding
  • Ask clarifying questions or challenge
    alternatives when differences in interpretations
    have become apparent

26
Sociomathematical Norms
  • What counts as
  • A different mathematical solution
  • A sophisticated mathematical solution
  • An efficient mathematical solution
  • An acceptable mathematical explanation

27
Classroom Mathematical Practices
  • Specific to particular mathematical ideas
  • Counting by one versus conceptualizing numbers as
    composed of tens and ones
  • How mathematical content is actually realized in
    the classroom

28
Analyses and Design
  • Accounts of the process of students mathematical
    learning that are tied to the means by which that
    learning was supported and organized
  • Develop testable conjectures about how the design
    might be improved

29
Classroom Learning Environment
  • Organization of classroom activities
  • Instructional tasks
  • Tools and resources
  • Classroom norms and discourse
  • Social norms
  • Sociomathematical norms
  • Classroom mathematical practices

30
Classroom Learning Environment
  • Instructional tasks as realized in the classroom
    are influenced by
  • Organization of classroom activities
  • Tools and resources
  • Norms and discourse

31
Classroom Activity System
  • The teacher and students jointly constitute the
    classroom learning environment in the course of
    their ongoing interactions
  • Instructional tasks
  • Tools and resources
  • Organization of classroom activities
  • Norms and discourse

32
Top Down Perspective
  • Classroom learning environment composed of
    independent variables
  • Exists independently of teachers and students
    collective activity
  • Under the researchers control -- manipulable
    from the outside the classroom
  • Types of tasks
  • Types of tools
  • Social arrangements
  • Instructional strategies

33
Top Down Perspective
  • Investigate into how variations in the learning
    environment affect aggregate student performance
  • Design x works better or worse than design y
  • Conditions under which x works better or worse
    than y
  • Types of students for whom x works better or
    worse than y

34
Top Down Perspective
  • Limited value in improving designs
  • Teachers and domain specialists
  • Useful to educational administrators
  • Limited expertise in domain-specific processes of
    learning and teaching
  • Have to make a defend decisions that impact a
    large number of classrooms

35
Top Down Perspective
  • New cadre of educational administrators
  • Separate professional concerns from those of
    teachers
  • Both maintain a distance from and manage
    classroom instructional processes
  • Learning environment composed of manipulable
    variables

36
Top Down Perspective
  • Scientific research as the basis for the
    rationalization of educational systems
  • Folk beliefs about science rather than the
    reality of scientific practices
  • Quantification, experimentation, search for
    universal principles and laws

37
Domain Specific and General Theories
  • Hypothesis generating and hypothesis testing
  • Produce different forms of knowledge
  • Contrasting characterizations of learning
    environments
  • Contrasting characterizations of students
  • Useful to different groups of people

38
Division of Labor
  • Domain independent theories and experimental
    studies
  • Administrative perspective
  • Contribute to public policy discourse about
    education

39
Division of Labor
  • Domain specific theories and design experiments
  • Classroom perspective
  • Contribute to instructional design and teaching
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