Learning by analogy: Discriminating between potential analogs

Learning Through Case Comparisons: A Meta-Analytic Review

“…The domain of math included studies that ranged from solving multistep mathematics problems and solving algebraic equations that were set within the fields of biology, chemistry, and political science (Rittle- Star, 2007, andGerjets et al, 2008, Experiment 2, respectively) to sorting cases by their statistical/algebraic content and understanding the proper use of the linearity assumption (Cummins, 1992, Experiments 1-3; Schuh, 2004, andMcDonough, 2010, Experiment 2, respectively). The example studies from Gadgil, Gerjets, and their colleagues highlight that when coding for domain, what was to be learned was the focus.…”

“…Analogies can also help students acquire a more abstract understanding of the to-be-learned content. Through analogical comparison, students can extract the features that are in common, and the resulting representation can then facilitate transfer to new examples and situations that share the same underlying structure but differ in the specific features (Chen & Daehler, 1989;Gentner et al, 2003;Gerjets, Scheiter, & Schuh, 2008;Gick & Holyoak, 1980, 1983Richland & McDonough, 2010;Schuh, Gerjets, & Scheiter, 2005).…”

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

“…We speculate that presenting two different types of representations in rapid succession, repeated several times, is taxing on students' cognitive load and inhibits their ability to notice structural commonalities between the two representations. Richland and McDonough (2010) [32] came to the same conclusion when they found that arranging the solutions to permutation and combination problems side by side (as opposed to sequentially) reduced the strain on participants' working memory, thereby encouraging them to compare each pair of solutions and notice what was structurally common to both. Similarly, Rittle-Johnson and Star (2007) [48] found that placing worked examples of algebra problems next to each other, with prompts to compare the two different solution methods, was more effective for procedural knowledge gain and for the generation of multiple solutions than when the problems were placed one after the other on separate pages.…”

“…Students benefit from instructional guidance on noticing structural similarities between analogous problems or representations (Alfieri et al, 2014;Richland & McDonough, 2010) [12,32]. In their cross-cultural comparison of mathematics teaching, Richland, Zur and Holyoak (2007) [33] found that teachers from high-performing countries use analogous examples often, but also use specific techniques to encourage structural mapping, such as hand gestures between representations and spatial layouts to make any similarities apparent.…”

Neurodevelopment of relational reasoning: Implications for mathematical pedagogy

“…In a study of videotaped classroom discussions, Richland and colleagues [12] noted that many teachers use analogies, such as that of a balance scale in working with complex equations, but they tend to vary in procedural or conceptual emphasis based on their assessment of students' immediate cognitive needs. Procedural supports help in the moment, but laboratory research on analogy shows that this may come at the cost of long-term understanding, if those students miss the chance to consider the conceptual relationships [52]. The disparity between laboratory and classroom analogy use warrants additional research into what types of analogies are most useful to students.…”