White, P' 1996' Conceptual knowledge in introductory calculus'

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Class Presentation by Melina Day based
on Conceptual Knowledge in Introductory Calculus
White, P. (1996). Conceptual knowledge in
introductory calculus. Journal for
Research in Mathematics Education. 27 (1).
Retrieved February 14, 2006 from
http//links.jstor.sici?sici0021182512819
96013A13C793C793ACKIIC3E2.0.CO3B2-6
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• I chose this article because I
• have become very interested in
• the conceptual part of learning
• versus procedural learning and
• I am also planning on taking a
• calculus course this summer.

My Rationale for Reading Article

• changes have brought up the
• question about the role of
• calculus courses
• technology
• qualifications of teachers
• math competence of
• students

Changes for Calculus Courses?
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• skill-based calculus
• why rote, manipulative
• learning with computers and
• calculators that can perform
• procedures
• can explore concepts
• applications more
• abstract concepts that are
• difficult for students to
• understand
• what other concepts are needed
• to apply calculus knowledge

Things to Consider
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• instrumental understanding or
• procedural knowledge that is
• not supported
• knowing the rules without
• knowing why they work
• means no conceptual knowledge
• students are not able to solve
• application problems

Problem
leads to
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• design concept-based calculus
• instruction
• so students can solve
• application problems

Solution?
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STUDY

• 40 first-year college students
• previously had calculus in high
• school
• identifying appropriate
• derivative
• rates of change
• maximization
• 4 tests (4 questions per test)
• 4 groups of 10
• 4 students per group were
• interviewed to learn about
• student reasoning

What Kind of Design?
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• teaching was a positive factor
• areas that held back success
• underdeveloped concept of
• a variable
• limited to algebraic symbols
• abstract-apart ideas (use
• symbolic context with no
• connection)
• abstract-general concepts
• (formation of links among
• different contexts)

What Were the Results?
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Conclusion
Studies found
an abstract-general concept of a variable is
needed for successful study of calculus a
concept-oriented calculus course is more likely
to be successful with this foundation