Providing worked examples for learning multiple principles

Abstract

Summary Worked examples support learning. However, if they introduce easy‐to‐confuse concepts or principles, specific ways of providing worked examples may influence their effectiveness. Multiple worked examples can be introduced blocked (i.e., several for the same principle) or interleaved (i.e., switching between principles), and can be sequentially or simultaneously presented. Crossing these two factors provides four ways of presenting worked examples: blocked/sequential, interleaved/sequential, blocked/simultaneous, and interleaved/simultaneous. In an experiment with university students (N = 174), we investigated how these two factors influence the acquisition of procedural and conceptual knowledge about different, but closely related (thus, easy‐to‐confuse) stochastic principles. Additionally, we assessed the ability of students to discriminate between principles with verification tasks. Simultaneous presentation benefitted procedural knowledge whereas, interleaved presentation benefitted conceptual knowledge. No significant differences were found for verification tasks. The results suggest that it is worthwhile to adapt the presentation of the worked examples to the learning goals.

Embracing complexity in research on learning from examples and from problem solving

“…Second, while intra‐example features are not addressed in this special issue, inter‐examples features are; again, by‐and‐large the findings reported in this special issue align very well with was found earlier. For instance, Lu, Kalyuga, and Sweller (2020) as well as Schalk et al (2020) further validate the recommendation to use variable example sequences and to facilitate comparisons between them. One may wonder then how the papers reported in this special issue advance our understanding in learning from examples.…”

Changes in Students’ Understanding of and Visual Attention on Digitally Represented Graphs Across Two Domains in Higher Education: A Postreplication Study

“…In particular, dynamic representations of graphs or the use of graph creation software could promote graph understanding ( Stern et al, 2003 ; Gustafsson and Ryve, 2016 ; Opfermann et al, 2017 ). For example, the dynamic hatching of an “area under a curve” with a parallel indication of the calculated values and a formula display could facilitate understanding in the sense of “learning by examples” ( Schalk et al, 2020 ). However, the extent to which this can have a positive effect on the understanding of certain concepts like “slope” and “area” still needs to be investigated.…”

Advances in designing instruction based on examples

“…This is the issue of sequencing summarized in line 7 of Table 2. Schalk et al (2020) found a small effect size favoring simultaneous presentation for college students' learning of how to solve probability problems. This is consistent with previous work on the benefits of presenting example statistics problems that have different cover stories but the same underlying solution procedure (Quilici & Mayer, 1996).…”

“…The eighth line of Table 2 summarizes this issue of interleaving. Schalk et al (2020) found a small effect favoring interleaving examples in college students learning to analyze probability problems. In a somewhat analogous situation, interleaving of study activities (rather than blocking study activities) has been found to improve learning outcomes (Brown, Roediger III, & McDaniel, 2014; Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013).…”