Using research to shape placement and influence instruction
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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

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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

    • R1Use proportional reasoning

    • R2View a function as a process

    • R3Reason 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


Using research to shape placement and influence instruction

  • 28.30%

  • 13.67%

  • 20.19%

  • 21.62%

  • 15.58%

Point biserial 0.29

Discrimination index 0.47


Using research to shape placement and influence instruction

  • 5.89%

  • 48.01%

  • 27.34%

  • 3.50%

  • 14.63%

Point biserial 0.26

Discrimination index 0.39


Using research to shape placement and influence instruction

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


Using research to shape placement and influence instruction

Graphical reasoning item:


Using research to shape placement and influence instruction

Functional notation and definitions:


Using research to shape placement and influence instruction

Covariational reasoning item:


Using research to shape placement and influence instruction

Quantitative, functional, representations, modeling


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