Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.

By Bethany Rittle-Johnson, Jon Star. 2007

593 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1591c94ea47a603ca35cae9e01e656305931cb88

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Citations in the corpus

The influence of framing on transfer: initial evidence from a tutoring experiment (2011, background): “Researchers emphasize the importance of students fully learning the content they are supposed to transfer (Bransford et al. 1999), being provided with enough examples of that content (Gick and Holyoak 1983; Mestre 2003), comparing examples to form generalizations at the right level of abstraction (G”
Conceptual knowledge of fraction arithmetic. (2015, background): “…of the procedures – implicit or explicit knowledge of how the procedures work, why they make sense, and how they are related to other procedures and concepts in the domain (Byrnes & Wasik, 1991; Hiebert & LeFevre, 1986; RittleJohnson & Schneider, in press; Rittle-Johnson & Star, 2007).”
Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. (2011, background): “Rittle-Johnson and Star (2007, 2009), for example, found that students developed more procedural flexibility in algebraic manipulations if they compared alternative solutions side by side than if they saw them sequentially.”
Analogical Reasoning in the Classroom: Insights from Cognitive Science. (2015, background): “Similarly, studies have suggested that analogical reasoning is enhanced when images of the source and target are displayed simultaneously versus sequentially (Christie & Gentner, 2010; Rittle-Johnson & Star, 2007).”
Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword. (2016, methodology): “These results could have been driven by the types of solution strategies that students used (Rittle-Johnson & Star, 2007, 2009), particularly subtraction (a common misconception).”
Comparing Four Instructional Techniques for Promoting Robust Knowledge (2015, methodology): “2001; Novick and Holyoak 1991), the amount of variety in a learner’s solution procedures (Rittle-Johnson and Star 2007), and mapping errors between problems (Ross and Kilbane 1997).”
Improving Seventh Grade Students' Learning of Ratio and Proportion: The Role of Schema-Based Instruction. (2009, result): “Third, instruction explicitly focused on a comparison of strategies, including identification of which strategies were easier to implement on which problems (and why), consistent with the recommendations of prior research in this area (Rittle-Johnson & Star, 2007; Star & Rittle-Johnson, 2009).”
Teaching the Conceptual Structure of Mathematics (2012, methodology): “Our team is using controlled videotaped presentation of varied instruction, whereas other research groups are designing tools that aid teachers in leading instruction by comparisons as well as studying comparisons made by peers (see Rittle-Johnson & Star, 2007 , 2009 ; Star & Rittle-Johnson, 2009”
Step Tutor: Supporting Students through Step-by-Step Example-Based Feedback (2020, background): “We want to encourage learning the step through comparison, because prior work in programming education suggests that comparison is a powerful way for a student to learn from examples and generalize domain principles [17, 35, 40].”
Understanding the Development of Flexibility in Struggling Algebra Students (2010, methodology): “The current study builds on prior work by using techniques that have shown to be effective in promoting and assessing flexibility (Rittle-Johnson & Star, 2007; Star & Rittle-Johnson, 2008).”
Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment (2013, background): “Further, recent studies by Rittle-Johnson and colleagues (e.g., Rittle-Johnson & Star, 2007) provide empirical evidence for improving student learning when instruction emphasizes and supports comparing and contrasting multiple solution methods.”
Learning Through Case Comparisons: A Meta-Analytic Review (2013, background): “Codes for the process variables were entered as follows: The type of instructions was coded as either prompted or D ow nl oa de d by [ U ni ve rs ity O f Pi tts bu rg h] a t 0 8: 32 2 2 A pr il 20 13 TABLE 1 Sample Included in the Meta-Analysis of Case Comparisons Learning Tasks Experiment Year CC n”