Structured Abstract
Setting
The research studies take place in a private school in an urban center in the southern United States, and in public suburban and rural middle schools in both the southern United States, and in the Midwest.
Sample
A total of approximately 825 grade 5 and 7 students are participating in this research. The majority of the children participating are White, and approximately 10 percent are African American. Approximately 25 percent of the participating children qualify for free and reduced-price lunch.
Materials are being developed to support both students and teachers in the use of contrasting examples. In each experiment, students are presented with worked-out examples of mathematics problems and are asked to answer questions about the examples. Students using contrasting examples are shown a pair of worked examples illustrating different solutions to the same problem and are asked to compare and contrast the solution procedures.
Research design and methods
The researchers are comparing learning from contrasting examples to learning from sequentially presented examples (a more common educational approach) in five studies.
In studies 1 and 2, pairs of students are randomly assigned to condition, and the manipulation occurs while each pair studies worked examples and solves practice problems in their mathematics classrooms.
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.
Control condition
Students in the control condition are presented the same worked examples as the treatment students but are shown each worked example separately and are asked to think about the individual solutions.
Key measures
Students are completing experimenter-developed tests that measure their ability to perform the linear equation solving or computational estimation that they are currently being taught.
Data analytic strategy
For the studies where pairs of students are assigned to condition, multivariate analysis of variance (MANOVA) techniques are used to compare performance of students in the two conditions. For studies where classrooms are assigned to condition, hierarchical linear modeling techniques are used.
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
Publications:
ERIC Citations: Find available citations in ERIC for this award here.
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Book chapters
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.), The Psychology of Learning and Motivation, Volume 55 (pp. 199-226). San Diego: Elsevier.
Journal articles
Durkin, K., and Rittle-Johnson, B. (2012). The Effectiveness of Using Incorrect Examples to Support Learning About Decimal Magnitude. Learning and Instruction, 22(3): 206-214.
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. Journal of Educational Psychology, 99(3): 561-574.
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. Journal of Educational Psychology, 101(3): 529-544.
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. Journal of Educational Psychology, 3(4): 836-852.
Rittle-Johnson, B., Star, J.R., and Durkin, K. (2012). Developing Procedural Flexibility: Are Novices Prepared to Learn From Comparing Procedures?. British Journal of Educational Psychology, 82(3): 436-455.
Star, J.R., and Rittle-Johnson, B. (2008). Flexibility in Problem Solving: The Case of Equation Solving. Learning and Instruction, 18(6): 565-579.
Star, J.R., and Rittle-Johnson, B. (2009). It Pays to Compare: An Experimental Study on Computational Estimation. Journal of Experimental Child Psychology, 102(4): 408-426.
Star, J.R., and Rittle-Johnson, B. (2009). Making Algebra Work: Instructional Strategies That Deepen Student Understanding, Within and Between Algebraic Representations. ERS Spectrum, 27(2): 11-18.
Star, J.R., Kenyon, M., Joiner, R., and Rittle-Johnson, B. (2010). Comparison Helps Students Learn to be Better Estimators. Teaching Children Mathematics, 16(9): 557-563.
Star, J.R., Kenyon, M., Joiner, R., and Rittle-Johnson, B. (in press). Comparison Helps Students Learn to Solve Equations. Mathematics Teacher. Star, J.R., Rittle-Johnson, B., Lynch, K., and Perova, N. (2009).
The Role of Prior Knowledge and Comparison in the Development of Strategy Flexibility: The Case of Computational Estimation. ZDM-The International Journal on Mathematics Education, 41(5): 569-579.
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