IES Grant

Title: | Using Contrasting Examples to Support Procedural Flexibility and Conceptual Understanding in Mathematics | ||

Center: | NCER | Year: | 2005 |

Principal Investigator: | Star, Jon | Awardee: | Harvard University |

Program: | Cognition and Student Learning [Program Details] | ||

Award Period: | 3 years | Award Amount: | $1,014,175 |

Type: | Development and Innovation | Award Number: | R305H050005 |

Description: |
This research team argues that there are times when students have the computational skills to solve specific mathematics problems, but do not understand the underlying mathematical principles or reasons why a specific set of computations results in the correct answer. The investigators hypothesize that structuring lessons so that contrasting examples are used to highlight specific principles will lead to better understanding and better integration of computational skills and conceptual knowledge. The research team will test whether or not the use of contrasting examples will improve students' ability to apply what they have learned and adapt existing procedures to solve novel math problems. Structured Abstract
In this project, the use of contrasting examples is examined both in the context of algebra problem solving and computational estimation. At the conclusion of this project, the research team will have tested whether or not the use of contrasting examples will improve students' ability to apply what they have learned and adapt existing procedures to solve novel math problems.
In Studies 3 and 4, classrooms are randomly assigned to condition, and the manipulation occurs both in partner activities and in whole-class discussions. In Study 5, the classroom intervention will be scaled up to more diverse classrooms in public schools as first steps towards assessing the generalizability of this teaching approach. Studies 1, 3, and 5 will be on linear equation solving with seventh-grade students, and Studies 2 and 4 will be on mental math and computational estimation with fifth-grade students.
Rittle-Johnson, B., and Star, J.R. (2011). The Power of Comparison in Learning and Instruction: Learning Outcomes Supported by Different Types of Comparisons. In J.P. Mestre, and B.H. Ross (Eds.),
Durkin, K., and Rittle-Johnson, B. (2012). The Effectiveness of Using Incorrect Examples to Support Learning About Decimal Magnitude. Rittle-Johnson, B., and Star, J.R. (2007). Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge? An Experimental Study on Learning to Solve Equations. Rittle-Johnson, B., and Star, J.R. (2009). Compared With What? The Effects of Different Comparisons on Conceptual Knowledge and Procedural Flexibility for Equation Solving. Rittle-Johnson, B., Star, J.R., and Durkin, K. (2009). The Importance of Prior Knowledge When Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving. Rittle-Johnson, B., Star, J.R., and Durkin, K. (2012). Developing Procedural Flexibility: Are Novices Prepared to Learn From Comparing Procedures?. Star, J.R., and Rittle-Johnson, B. (2008). Flexibility in Problem Solving: The Case of Equation Solving. Star, J.R., and Rittle-Johnson, B. (2009). It Pays to Compare: An Experimental Study on Computational Estimation. Star, J.R., and Rittle-Johnson, B. (2009). Making Algebra Work: Instructional Strategies That Deepen Student Understanding, Within and Between Algebraic Representations. Star, J.R., Kenyon, M., Joiner, R., and Rittle-Johnson, B. (2010). Comparison Helps Students Learn to be Better Estimators. Star, J.R., Kenyon, M., Joiner, R., and Rittle-Johnson, B. (in press). Comparison Helps Students Learn to Solve Equations.
Star, J.R. (2008). |
||

Back |