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Using Research to Shape Placement and Influence Instruction. Bernard L. Madison Director, MAA Placement Testing Program (PTP) University of Arkansas. PTP materials available from MAA/Maplesoft Placement Testing Suite Dissemination of CCR and new APCR development supported by NSF (DUE-1122965).

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using research to shape placement and influence instruction

Using Research to Shape Placement and Influence Instruction

Bernard L. Madison

Director, MAA Placement Testing Program (PTP)

University of Arkansas

PTP materials available from MAA/Maplesoft Placement Testing Suite

Dissemination of CCR and new APCR development supported by NSF (DUE-1122965)

theses
Theses
  • Precalculus courses are not achieving their potential in conveying conceptual understand of fundamental functional ideas.
  • Calculus courses are not achieving their potential in conveying conceptual understand of fundamental functional ideas.
developments based on research results
Developments based on Research Results
  • The Precalculus Concept Assessment (PCA): A Tool for Assessing Students’ Reasoning Abilities and Understandings by M. Carlson, M. Oehrtman, and N. Engelke, Cognition and Instruction, 28(2), 113–145, 2010
  • Calculus Concept Readiness (CCR) 2010 Paper by M. Carlson, R. West & BLM. . To appear International Journal for Research in Undergraduate Mathematics Education, Projected Vol. 1, Issue 2, 2015.
  • Algebra and Precalculus Concept Readiness (APCR) 201213
alignment with ccssm
Alignment with CCSSM
  • Algebraic thinking Grades 1-12
    • Computing with unknowns
  • Functions from grade 8
    • Process view of a function
  • Conceptual understanding emphasized
    • Standards of mathematical practice
  • Modeling in many contexts
calculus concept readiness ccr taxonomy
Calculus Concept Readiness (CCR)Taxonomy
  • Reasoning abilities
    • R1 Use proportional reasoning
    • R2 View a function as a process
    • R3 Reason about and represent how two quantities change together (covariational reasoning)
understand and use the following concepts or ideas
Understand and use the following concepts or ideas
  • Quantity
  • Variable
  • Slope/Constant rate of change
  • Average rate of change
  • Function composition
  • Function inverse
  • Function translations (horizontal and vertical shifts)
understand represent and interpret function growth patterns
Understand, represent and interpret function growth patterns
  • Linear
  • Exponential
  • Non-linear polynomial
  • Rational
  • Periodic
understand central ideas of trigonometry
Understand central ideas of trigonometry
  • Angle measure
  • Radian as a unit of measure
  • Sine and cosine functions as covariation
  • Sine and cosine functions in right triangles
  • Reduction from any circle to a unit circle.
other abilities
Other abilities
  • Solve equations
  • Represent and interpret inequalities
  • Represent and interpret absolute value inequalities
  • Use and solve systems of equations
  • Understand and use function notation to express one quantity in terms of another
slide13

28.30%

  • 13.67%
  • 20.19%
  • 21.62%
  • 15.58%

Point biserial 0.29

Discrimination index 0.47

slide14

5.89%

  • 48.01%
  • 27.34%
  • 3.50%
  • 14.63%

Point biserial 0.26

Discrimination index 0.39

slide15

a) 24.96% b) 8.27% c) 19.40% d) 20.19% e) 21.14%

Point biserial 0.05

Discrimination index 0.14

algebra and precalculus concept readiness apcr draft taxonomy
Algebra and Precalculus Concept Readiness (APCR) Draft Taxonomy
  • Reasoning Abilities
    • Quantitative Reasoning
    • Reasoning with Representations
    • Functional Reasoning
    • Covariational Reasoning
    • Proportional Reasoning
    • Variable Reasoning
notations conventions and definitions
Notations, Conventions and Definitions
  • Modeling
  • Measurement
  • Rate of change
  • Function concepts
  • Solving equations
  • Inequalities
  • Properties of real numbers
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