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 Plan for this talk Overview of our studies Review of five studies on comparison Summary of findings across studies 5/27/ Association for Psychological Science Overview of studies How does comparison support learning of school mathematics within a classroom setting? Redesigned 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) 5/27/ Association for Psychological Science (Rittle-Johnson & Star, in press) Characteristics of all five studies 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 5/27/ Association for Psychological Science Measures 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 x = 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?) 6 5/27/2011 Association for Psychological Science Study 1 (Rittle-Johnson & Star, 2007) Study 2 (Star & Rittle- Johnson, 2009) Study 3 (Rittle-Johnson, Star, & Durkin, 2009) Study 4 (Rittle-Johnson, Star, & Durkin, in press) Study 5 (Rittle-Johnson & Star, 2009) Five Contrasting Cases studies 5/27/ Association for Psychological Science Study 1: Does comparing solution methods facilitate conceptual and procedural knowledge? (Rittle-Johnson & Star, 2007) Study 1 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 8 5/27/2011 Association for Psychological Science (Rittle-Johnson & Star, 2007) Equation solving strategies 9 5/27/2011 Association for Psychological Science Study 1: Compare condition 10 5/27/2011 Association for Psychological Science (Rittle-Johnson & Star, 2007) Study 1: Sequential condition 11 5/27/2011 Association for Psychological Science next page (Rittle-Johnson & Star, 2007) Study 1: Results 12 5/27/2011 Association for Psychological Science (Rittle-Johnson & Star, 2007) F(1, 31) =4.49, p