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The Power of Comparison in Learning & Instruction

The Power of Comparison in Learning & Instruction. Learning Outcomes Supported by Different Types of Comparisons Dr. Jon R. Star, Harvard University Dr. Bethany Rittle-Johnson, Vanderbilt University. Overview of our studies Review of five studies on comparison

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The Power of Comparison in Learning & Instruction

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  1. The Power of Comparison in Learning & Instruction Learning Outcomes Supported by Different Types of Comparisons Dr. Jon R. Star, Harvard University Dr. Bethany Rittle-Johnson, Vanderbilt University

  2. Association for Psychological Science Overview of our studies Review of five studies on comparison Summary of findings across studies Plan for this talk

  3. Association for Psychological Science • How does comparison support learning of school mathematics within a classroom setting? • Redesigned 2 - 3 math lessons on a particular topic (e.g., equation solving, estimation) • Implemented during students’ mathematics classes • Five studies • Effectiveness of comparing correct methods (5 of 5) • Effectiveness of comparing problem types (2 of 5) • Focus on equation solving (4 of 5) • Focus on estimation (1 of 5) Overview of studies (Rittle-Johnson & Star, in press)

  4. Association for Psychological Science Packet of worked examples, prompts for explanation for each condition Students work in pairs Side-by-side comparison, labeled solution steps, some direct instruction Explicit prompts to identify similarities/differences Randomly assigned student pairs to condition within the same classroom Measures of procedural knowledge, conceptual knowledge, and procedural flexibility Characteristics of all five studies

  5. Association for Psychological Science • Procedural knowledge (e.g., equation solving) • Ability to adapt known procedures to novel problems (i.e., transfer) • Conceptual knowledge (e.g., equivalence, like terms, composite variables) • “Is 98 = 21x equivalent to 98 + 2x = 21x + 2x?” • Procedural flexibility • Flexible Use - Use of more efficient solution methods on procedural knowledge assessment (i.e., fewer solution steps) • Flexible Knowledge • Knowledge of multiple methods (e.g., solve each equation in two different ways when prompted) • Ability to evaluate methods (e.g., “Looking at the problem shown above, do you think that this first step is a good way to start this problem?”) Measures

  6. Association for Psychological Science Five Contrasting Cases studies • Study 1: Does comparing solution methods facilitate conceptual and procedural knowledge? (Rittle-Johnson & Star, 2007)

  7. Association for Psychological Science • Research question: Does comparing solution methods improve equation solving knowledge? • Research design • Random assignment to • Compare condition: Students compare and contrast alternative solution methods for equation solving • Sequential condition: Students study same solution methods sequentially • Pretest - Intervention – Posttest • Participants • 70 7th-grade students and their math teacher Study 1 (Rittle-Johnson & Star, 2007)

  8. Association for Psychological Science Equation solving strategies

  9. Association for Psychological Science Study 1: Compare condition (Rittle-Johnson & Star, 2007)

  10. next page next page next page Association for Psychological Science Study 1: Sequential condition (Rittle-Johnson & Star, 2007)

  11. Association for Psychological Science Study 1: Results F(1, 31) =4.49, p < .05 (Rittle-Johnson & Star, 2007)

  12. Association for Psychological Science Study 1: Results Flexible Use of Procedures ~ p = .06; * p < .05 F(1,31) = 7.73, p < .01 (Rittle-Johnson & Star, 2007)

  13. Association for Psychological Science Study 1: Results No Difference (Rittle-Johnson & Star, 2007)

  14. Association for Psychological Science • Students in the compare condition • Showed greater gains in procedural knowledge and flexibility • Were more likely to use more efficient method and somewhat less likely to use the conventional method • Maintained conceptual knowledge Study 1: Results summary (Rittle-Johnson & Star, 2007)

  15. Association for Psychological Science Five Contrasting Cases studies • Study 2: It pays to compare: An experimental study on computational estimation(Star & Rittle-Johnson, 2009)

  16. Association for Psychological Science • Research question: Does comparing solution methods improve knowledge of computational estimation? • Research design • Random assignment to • Compare condition: Students compare two solution methods for estimating multi-digit multiplication problems • Sequential condition: Students reflect on same solution methods one at a time • Pretest - Intervention – Posttest – Retention test • Participants • 157 fifth and sixth graders from urban, private school or small, rural school • Moderate to low prior knowledge of strategies for estimation Study 2 (Star & Rittle-Johnson, 2009)

  17. Association for Psychological Science Study 2: Strategies for estimation (Star & Rittle-Johnson, 2009)

  18. Association for Psychological Science Study 2: Compare condition (Star & Rittle-Johnson, 2009)

  19. next page next page next page Association for Psychological Science Study 2: Sequential condition (Star & Rittle-Johnson, 2009)

  20. Association for Psychological Science Study 2: Results No Difference (Star & Rittle-Johnson, 2009)

  21. Association for Psychological Science Study 2: Results F(1, 150) = 14.058, p < .001, η2 = .086 (Star & Rittle-Johnson, 2009)

  22. Association for Psychological Science Effect of condition depended on prior knowledge Study 2 Results F(1, 150) = 14.069, p<.001, η2 = .089 (Star & Rittle-Johnson, 2009)

  23. Association for Psychological Science Students in the compare condition became more flexible estimators Comparing methods aided retention of conceptual knowledge if students had above average knowledge of estimation at pretest Study 2: Results summary (Star & Rittle-Johnson, 2009)

  24. Association for Psychological Science Five Contrasting Cases studies • Study 3: The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving (Rittle-Johnson, Star, & Durkin, 2009)

  25. Association for Psychological Science • Research question: Do children with different levels of prior knowledge benefit equally from comparing solution methods? • Research design • Random assignment to • Compare solution methods • Compare problem types • Study sequentially (no comparison) • Identified whether students used algebra at pretest • 40% did not attempt algebra • 60% attempted algebra • 20% of students accurately used algebra • Participants: 236 7th & 8th-grade students in classes with limited algebra instruction Study 3 (Rittle-Johnson, Star, & Durkin, 2009)

  26. Association for Psychological Science Study 3: Compare conditions (Rittle-Johnson, Star, & Durkin, 2009)

  27. next page next page next page Association for Psychological Science Study 3: Sequential condition (Rittle-Johnson, Star, & Durkin, 2009)

  28. Association for Psychological Science Study 3: Results F(2, 213)= 8.466, p< .001

  29. Association for Psychological Science Study 3: Results F(2, 210)= 7.292, p <.001 F(2, 224)= 2.548, p= .080

  30. Association for Psychological Science Study 3: Results F(2, 226) =2.497, p <.085

  31. Association for Psychological Science • Prior knowledge matters! • Students with little prior knowledge may not benefit from comparing solution methods • For Students without prior knowledge of algebra • Sequential study of examples or comparing problem types was best for procedural and conceptual knowledge, and flexibility • Sequential study produced fewer signs of confusion • For students who had attempted algebra, comparing solution methods tended to be most effective Study 3: Results summary (Rittle-Johnson, Star, & Durkin, 2009)

  32. Association for Psychological Science Study 4: Developing procedural flexibility: When should multiple solution methods be introduced? (Rittle-Johnson, Star, & Durkin, in press) Five Contrasting Cases studies

  33. Association for Psychological Science • Research questions • What is the impact of early introduction to multiple procedures in equation solving? • How can comparison support learning of these procedures? • Research design • Random assignment to • Immediate compare [Immediate CP] • Delay – compare [Delay CP] • No compare [No CP] • Slower lesson pace, longer intervention time • Pretest - Intervention – Posttest – One-month-Retention Test • Participants: 198 8th grade students in TN classes with limited algebra instruction (i.e., novices) Study 4 (Rittle-Johnson, Star, & Durkin, in press)

  34. Association for Psychological Science Conditions: Days 1 & 2 Day 1 Day 1 Day 1 Day 2 Day 2 Day 2

  35. Association for Psychological Science Study 4: Results (Rittle-Johnson, Star, & Durkin, in press)

  36. Association for Psychological Science Study 4: Results (Rittle-Johnson, Star, & Durkin, in press)

  37. Association for Psychological Science • Immediate comparison of multiple procedures supports attention to and adaption of efficient procedures, which benefits flexibility • Regardless of prior knowledge, students in the no-delay – compare condition… • Had greater procedural flexibility than students in the other conditions • Even novices gain learn from comparing methods if given adequate instructional support. Study 4: Results summary (Rittle-Johnson, Star, & Durkin, in press)

  38. Association for Psychological Science Five Contrasting Cases studies • Study 5: Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. (Rittle-Johnson & Star, 2009)

  39. Association for Psychological Science • Research question: Is it best to compare solution methods or are other types of comparison also effective? • Research design • Pretest - Intervention– Posttest – Retention Test • Random assignment to • Compare equivalent problems • Compare problem types • Compare solution methods • Intervention • In addition to partner work, solved practiced problems on own • Participants: 162 7th & 8th grade students from 3 schools Study 5 (Rittle-Johnson & Star, 2009)

  40. Association for Psychological Science Study 5: Compare conditions (Rittle-Johnson & Star, 2009)

  41. Association for Psychological Science Study 5: Comparison conditions (Rittle-Johnson & Star, 2009)

  42. Association for Psychological Science Study 5: Results No Differences F (2, 153) = 5.76, p = .004, η2 = .07

  43. Association for Psychological Science Study 5: Results F (2, 153) = 4.96, p = .008, η2 = .06 F (2, 153) = 5.01, p = .008, η2 = .07

  44. Association for Psychological Science • Comparing Solution Methods supported the largest gains in conceptual knowledge and procedural flexibility • Supported attention to multiple methods and their relative efficiency, which both predicted learning • Comparing problem types supported students’ conceptual knowledge and procedural flexibility to a lesser extent Study 5: Results summary (Rittle-Johnson & Star, 2009)

  45. Association for Psychological Science • Learning through comparison works! • Supported by all five studies • Rittle-Johnson, B., & Star, J. R. (2007) • Rittle-Johnson, B., & Star, J. R. (2009) • Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009) • Rittle-Johnson, B., Star, J., & Durkin, K. (in press). • Star, J. R., & Rittle-Johnson, B. (2009) • The power of comparison varies by • What is compared • Who compares • When comparison occurs Summary of findings across studies

  46. Association for Psychological Science Summary of findings across studies

  47. Association for Psychological Science Summary of findings across studies

  48. Association for Psychological Science Summary of findings across studies

  49. Association for Psychological Science Dr. Jon R. Star, Harvard University jon_star@harvard.edu Dr. Bethany Rittle-Johnson, Vanderbilt University b.rittle-johnson@vanderbilt.edu Thanks! Questions? Acknowledgements: Thanks to Kelley Durkin, Courtney Pollack, Katie Lynch, Natasha Perova, and many other research assistants at Vanderbilt, Michigan State, and Harvard This research is supported by a grant from the U.S. Department of Education, Institute for Education Sciences

  50. Association for Psychological Science Rittle-Johnson, B., & Star, J. R. (in press). The power of comparison in learning and instruction: Learning outcomes supported by different types of comparisons. In J. P. Mestre & B.H. Ross (Eds.), Psychology of Learning and Motivation: Cognition in Education (Vol. 55). Rittle-Johnson, B., & 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., & 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., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836-852. Rittle-Johnson, B., Star, J., & Durkin, K. (in press). Developing procedural flexibility: When do novices learn from comparing procedures? British Journal of Educational Psychology. Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102, 408 – 426. References

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