Transcript Context is important - Welcome to Department of Mathematics

Context is important!
Contextual Learning
Let’s get it started!
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Opening activity
Shoppers and grocery store math
Dairy farm example
Theoretical history
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Jean Piaget
Children construct knowledge through the
differentiation and integration of repeated activities
performed through the context of play
Saw play as a necessary and important part of
child’s cognitive development
His work influenced American education to develop a
more child-centered approach4
Theoretical history
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Lev Vygotsky
Contemporary of Piaget
Beginning of social learning theory
Believed development of cognitive skills is
fundamentally related to social interactions,
particularly with important adults in child’s life
Knowledge acquired from social interactions of
children with adults included gaining knowledge of
the shared culture of the people (internalization)
Vygotsky cont.
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“Every function in the child's cultural development
appears twice: first, on the social level, and later, on
the individual level; first, between people
(interpsychological) and then inside the child
(intrapsychological). This applies equally to
voluntary attention, to logical memory, and to the
formation of concepts. All the higher functions
originate as actual relationships between
individuals.“1
Situated cognition theory
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Jean Lave and others
Social anthropologist, UC Berkeley
“…argues that learning as it normally occurs
is a function of the activity, context, and
culture in which it occurs (i.e. it is situated).”2
Social interaction is a necessary part of
situated learning
Situated cognition theory
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“In order to understand cognitive development, it is
necessary to consider the everyday contexts in
which children are provided guidance by adults in
approaching and solving novel problems.
Illustrations of mother-child instruction support the
idea that adults assist children with new problems by
guiding the transfer of knowledge and skills from
more familiar contexts, thereby guiding the child and
making connections.” (Rogoff & Gardner, 115)
Situated cognition theory
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For traditional school structures, learning and
doing are separate
Concepts taught abstractly (separated from
context) are not easily generalized to real-life
applications
Students should learn in context and in
relation to real-world contexts/situations
Situated cognitive learning
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“Both the learner and the teacher are actively
involved in such instruction. The child
participates in problem solving with the adult,
rather than listening to explicit explanation or
watching demonstration by the adult.”
(Rogoff & Gardner, 116)
Opportunities for situated learning
activities
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Kitchens
Gardens/greenhouses
Field trips
Study aboard programs
Sports, music practices
Situated learning for teachers
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“Without the creation of a context of interaction
which is intelligible, given his or her current
knowledge and skills, the dyad cannot communicate,
and the teacher will not be able to lead the learner
toward an understanding of the new information.”
(Rogoff & Gardner, 98)
“Effective instruction may require the teacher to lead
the learner through the process, with both involved in
the activity.” (101)
Culture cognition relations
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Geoffrey B. Saxe
Mathematics education professor, UC Berkeley
Several studies on acquisition of mathematics skills
through participation in culture practices
Documented difference between processes of
school mathematics and processes of out-of-school
mathematics
Saxe cont.
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Fundamental questions: How do people
develop mathematics for real-life activities
and is there transfer of the knowledge that
aids in understanding school mathematics?
Interdependence between real-life
mathematics skills and cultural context of
situation
An Example of Saxe’s Work
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Saxe Article
Other researchers
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T. Nunes, Educational Studies, U. of Oxford
D. Carraher, Psychology, City University of New York
Research on school mathematics (particularly
arithmetic) and street mathematics
Found that children performed better at street
mathematics than non-contextualized school
mathematics
Other researchers
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Elaine Johnson
Educational consultant
Considered to be an “authority”3 on contextual
teaching and learning
Authored book Contextual Teaching and Learning:
What it is and why it’s here to stay (2002)
Book reflects belief that teaching academic subjects
in the context of students’ own lives and experiences
helps all young people to achieve academically
Elaine Johnson cont.
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Components to be included in CTL
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Making connections to find meaning
Self-regulated learning
Collaborating
Critical and creative thinking
High standards
Using authentic assessments
Activity
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Within your group, write a definition for
contextual learning.
Begin the sentence “Contextual learning
is…”
Some definitions emerge
http://www.ncrel.org/sdrs/areas/issues/envrnmn
t/stw/sw1lk3.htm
Alternate definitions
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“Contextual teaching and learning enables students
to connect the content of academic subjects with the
immediate context of their daily lives to discover
meaning.” (Johnson, 2002, p. 24)
“… an educational process that aims to help
students see meaning in the academic material they
are studying by connecting academic subjects …with
the context of their personal, social, and cultural
circumstances.” (Johnson, 2002, p. 25)
Our Take: The Ultimate Goal
(Implications for Practical Teaching)
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Meet students at their frame of reference
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Instruct in many frames of reference
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Accessing their prior knowledge & context
Teacher and student involved in process
Application of knowledge in any frame of
reference (transfer)
Ultimate goal!
http://www.cord.org/the-react-strategy/
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Center for Occupational Research and
Development (CORD)
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Contextual teaching strategies
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Relating: Learning in context
Experiencing: Learning by doing
Applying: Learning by concepts in action
Cooperating: Learning in groups with others
Transferring: Using knowledge in new
context/situation
Disadvantages and Difficulties
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Must teach using multiple contexts to
promote transfer (application of skill across
different contexts)
Potentially time consuming
Balancing this approach with state standards
Activity
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What opportunities have you had to
implement contextual learning?
In your Assessment Plan group, choose one
objective or assessment task and develop a
context for teaching the objective/task.
Question to ponder…
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Is all of mathematics contextual?
Bibliography
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Carraher, T.N. & Schielmann, A.D. (1985). Computation routines prescribed by schools: help or hindrance? Journal for
Research in Mathematics Education, 16(1), 37-44.
Crawford, M. (2001). Teaching contextually: Research, rationale, and techniques for improving student motivation and
achievement in mathematics and science. CORD. Waco, TX: CCI Publishing, Inc.
Johnson, E. B. (2002). Contextual teaching and learning: what it is and why it’s here to stay. Thousand Oakes, CA: Corwin
Press, Inc.
Lave J., Murtaugh, M., & de la Rocha, O. (1984). The Dialectic of Arithmetic in Grocery Shopping. In B. Rogoff & J. Lave (Eds.),
Everyday Cognition: Its Development in Social Context (pp. 67-94). Cambridge, MA: Harvard University Press.
Rogoff, B. & Gardner, W. (1984). Adult Guidance of Cognitive Development. In B. Rogoff & J. Lave (Eds.), Everyday Cognition:
Its Development in Social Context (pp. 95-116). Cambridge, MA: Harvard University Press.
Saxe, G.B. (1988). Candy selling and math learning. Educational Researcher, 17(6), 14 – 21.
Saxe, G.B. (1989). Transfer of learning across cultural practices. Cognition and instruction, 6(4), 325-330.
Saxe, G. B. (1999). Cognition, development, and cultural practices. In E. Turiel (Ed.), Culture and Development . New Directions
in Child Psychology. SF: Jossey-Bass.
Scribner, S. (1984). Studying Working Intelligence. In B. Rogoff & J. Lave (Eds.), Everyday Cognition: Its Development in Social
Context (pp. 9-40). Cambridge, MA: Harvard University Press.
1http://en.wikipedia.org/wiki/Lev_Vygotsky
2http://tip.psychology.org/lave.html
3http://corwinpressspeakers.com/Speaker.aspx?id=522330 (Elaine Johnson website)
4http://en.wikipedia.org/wiki/Jean_Piaget
http://www.nae.edu/nae/naetech.nsf/weblinks/kgrg-582sq2?opendocument (Dan Hull website)