Aims

Across a number of studies, Renkl and his colleagues (e.g., Renkl & Atkinson, 2003) examined the effectiveness of employing a fading approach to support learners transitioning from studying examples to problem solving. With the fading approach, (a) a complete example is presented, (b) followed by an example in which one single solution step is omitted, and (c) then the number of blanks is increased step-by step until the item is a practice problem. Renkl et al. demonstrated that the fading procedure produced reliable effects on near transfer, but not on far transfer. To address this issue, Atkinson, Renkl, and Merrill (2003) combined fading with the introduction of prompts designed to encourage learners to identify the underlying principle illustrated in each worked-out solution step. These straightforward principle-based prompts were designed to permit the learners to tailor their self-explanation according to their own mental model of the situation at hand. Across two experiments, they found that the combination of fading and prompting fostered both near and far transfer performance.

Although Atkinson et al. (2003) demonstrated the efficacy of combining fading and prompting, this effect has only been demonstrated in computer-based environments. Thus, one goal of this study was to explore whether this combination can be successfully implemented in a book-based environment. Another goal was to explore whether the use of matrices can facilitate learning from example-based instruction by making the subgoal structure of worked-out examples and practice problems more salient. Matrices have several strengths including the capability of communicating to learners information about each element through spatial proximity. Thus, learners can process elements adjacent to each other simultaneously, which supports efficient indexing of the elements. Matrices also help to distill information through a two-dimensional grid that makes hierarchical and coordinate relationships among central concepts more explicit, helping learners draw inferences by making connections/comparisons more apparent.

Method

Participants and design. A total of 97 undergraduate students in the US were randomly assigned in roughly equal proportions to the cells of a 2 x 2 between-subjects factorial design where the first factor was self-explanation prompts (present or absent) and the second factor was matrices (present or absent). Thus, this experiment consisted of four conditions: (a) prompting + matrix (n = 25), (b) prompting-only, (n = 25), (c) matrix-only (n = 24) and (d) no prompting, no matrix control (n = 23).

            Pencil-paper materials. The participants were provided a set of pencil-paper materials consisting of a demographic questionnaire, a nine-item pretest measuring prior knowledge on probability, a five-page overview of the fundamental principles of probability, an 18-page instructional packet, and a posttest containing six near- and six far-transfer problems.

The instructional packet consisted of two sets of probability tasks (each set consisted of four tasks). All four conditions shared the same underlying structure, that is, the backward fading approach where in each set, (a) a complete example was presented first, (b) followed by an example in which one single solution step was omitted (the last one), and (c) then the number of omitted steps was increased step-by step until the item was a practice problem. Each task consisted of three steps. When learners encountered an omitted step, they were required to anticipate this step on their own by writing down the solution in the space provided. After providing the anticipated answer, learners were able to check the accuracy of their anticipation on the next page.

While all four conditions relied on the fading approach, they differed in terms of the presence of prompts and use of matrices. In the prompting conditions, learner was encouraged to self-explain each solved worked-out solution step by first examining the step and then identifying which principle of probability the step exemplified. To encourage this process, the learner was prompted to select the probability principle—the same principles covered in the introductory material covered in the handout appeared to the right of the solved solution step. The learners were encouraged to select a principle before turning to the next page to check their accuracy. In the matrix conditions, each set of four tasks with the same solution rationale where displayed in a matrix where the rows represented the problem text and three subgoals while the columns contained the four tasks. The contents of the matrix were filled in over successive pages as each new task appeared in its own new column, allowing learners to make inter-example comparisons.

Procedure. The participants (a) completed the demographic questionnaire, (b) completed the pretest, (c) studied the probability overview, (d) studied the instructional packet, and (e) completed the posttest in a single session.

Results

On both problem-solving measures, we found statistically significant interactions. Simple main effects analysis revealed the same pattern for both measures. Across both measures, the participants assigned to the prompting-only produced more conceptually accurate solutions to transfer problems than their counterparts in the control condition, which consisted of fading only. Moreover, the participants provided with the matrix-only instructional material outperformed their peers in the matrix + prompting condition on both near and far transfer. Interestingly, there was a main effect for prompting (presence or absence) and matrices (presence or absence) on instructional time. When prompts or matrices were present, the participants spent significantly more time studying the instructional material.

Implications

This study offers several implications. First, it provides clear evidence that self-explanation prompts implemented by Atkinson et al. (2003) can be effectively implemented in a book-based learning environment. The participants provided with self-explanation prompts in combination with the faded approach demonstrated better transfer performance then their counterparts studying the same faded material without the prompts. Thus, we recommend that instructional designers consider the use of prompts that encourage the learners to figure out the principle that underlies a solution steps in worked-out examples. However, since the presence of the prompts was detrimental to learners provided with matrices, we recommend that instructional designers should be cautions about employing prompts in combination with matrices in support of example-based learning.