Aligning the Structural Components across Learning Tasks of Case Comparisons
Author: Alfieri, Louis
Date: 2011-00-00
Type: Reports - Research
Subjects: Constructivism (Learning),Instructional Design,Experiential Learning,Meta Analysis,Effect Size,Teaching Methods,Outcomes of Education,Predictor Variables,Research Methodology,Learning Activities,Thinking Skills,Age Differences,Mathematics Instruction,Science Instruction,Logical Thinking,Abstract Reasoning,Learning Processes,Educational Experiments,Classroom Research,Research Reports,Elementary School Students,Secondary School Students,College Students,Literature Reviews

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to support it has rocketed humanity to the top of the natural hierarchy. As a way of appropriating this informal, experiential learning that is at least partly driven by analogous thinking (e.g., categorization; Gentner & Holyoak, 1997), numerous formal learning situations have been designed with case comparisons to teach more traditional subject matter within classrooms (e.g., Gadgil & Nokes, 2009; Gentner, Loewenstein, Thompson, & Forbus, 2009; Mason, 2004; Michael, Klee, Bransford, & Warren, 1993; Nagarajan & Hmelo-Silver, 2006; Rittle-Johnson & Star, in press; Schwartz & Bransford, 1998; etc.). Analogous thinking in the form of learning tasks requiring case comparisons is arguably a form of scaffolded constructivism that is more than merely active (Chi, 2009) because it demands from the learner a level of engagement that goes beyond the learning materials in order to notice the underlying connections between them. The appreciation of those underlying connections potentially leads to learning (Gentner, 2010). In terms of the learning environments outlined by Chi, a learning task of case comparisons is not only active but also constructive (e.g., structural alignment, role-based relational processing, etc.; Gentner, 2010; Holyoak, in press, respectively) because it provides learners with two instances and asks them to construct their own understanding that serves to bridge the cases in the most consistent way. Within the case comparisons literature, there is a great variety in the ways in which cases are instantiated and tested both in laboratory and classroom settings. Some of these variables can be considered process variables because they are related to the learners' processions through learning tasks. Process variables include the following: the qualities of cases, the types of instructions that introduce learners to the tasks, the scaffolds in place to assist learners, etc. Other variables can be considered generalizability variables: the domain of the subject matter (e.g., math, science, etc.), the age and experience levels of participants, etc. Thus, when considering the efficacy of case comparisons and the variety of methodologies that have previously investigated them, a meta-analysis seemed appropriate to get a better of sense of where the field is, how well the authors' model of this learning process fits the patterns observed, and how future investigations could be designed best to answer remaining questions. This current meta-analysis focuses on the following three questions: (1) Overall, are case comparisons a method of instruction that leads to outcomes that are superior to other forms of instruction? (2) To what extent are such findings generalizable to all learners in all domains and situations? (3) What characterizes better case comparisons learning tasks and which conditions of the authors' process variables fall short? Furthermore, the current study presents a new methodology for investigating potential moderators through meta-analytic techniques by investigating to what extent general trends are maintained across levels of other correlated variables. The sample includes studies of learners of all ages and experience-levels and both age and experience were included as potential moderators. Analyses indicated that the effects are largely generalizable. Although few studies investigated adolescent-aged learners, within this sample case comparisons seems beneficial to learners of all ages and of all levels of experience. The marginal difference found between the effect sizes in math and science do not hold up under all circumstances. In studies published in second-tier journals, effect sizes in math and science are functionally equivalent. Effect sizes in the math, science, and other domain are all equivalent when the instructional design is brief and when learners are familiar with the subject matter. Effects also seem consistent in both laboratory and classroom settings but the former tend to be brief in duration and the latter tend to be long (i.e., strongly correlated with duration). When the authors consider the findings for their process variables, several features of case comparisons tasks stand out. Learners benefit most when they are asked only to find the similarities between cases, when they are provided with the features of at least one of the two cases, and when the principle is provided after the case comparisons task. Finding only the similarities helps learners to align the cases (Gentner, 2010) potentially because doing so is the most focused form of case comparisons. Learners can easily be distracted by differences and not have the same amount of study time to appreciate fully the shared common system. Moreover, having the features of at least one case provided, potentially acts as scaffolding for the learner who might otherwise be uncertain as to how to align the two cases. Presenting the principle after the task helps to confirm the learner's potentially tentative understanding (Holyoak, in press). In a related pattern, the more immediate the testing, the better performances are but it is not only the forgetting curve at work (Ebbinghaus, 1913). It seems that the tentative nature of learners' abstractions also factor in because there is no effect of the lag in testing when the authors only analyzed the tasks that included the presentation of the principle after. Such findings support claims made within the preparation-for-future learning (PFL; Bransford & Schwartz 1999; Schwartz & Bransford, 1998) literature. Overall, case comparisons tasks seem to be a promising way to get learners to be constructive and consequently, to learn. (Contains 5 tables, 1 figure and 2 footnotes.)