The influence of learner-generated domain representations on learning combinatorics and probability theory.

The aim of the current study was to examine the effects of providing support in the form of tools for constructing representations, and in particular the differential effects of the representational format of these tools (conceptual, arithmetical, or textual) in terms of perceived affordances and learning outcomes. The domain involved was combinatorics and probability theory. A between-subjects pre-test–post-test design was applied with secondary education students randomly distributed over four conditions. Participants completed the same tasks in a simulation-based learning environment. Participants in three experimental conditions were provided with a representational tool that could be used to construct a domain representation. The experimental manipulation concerned the format of the tool (conceptual, arithmetical, or textual). Participants in a control condition did not have access to a representational tool. Data from 127 students were analyzed. It was found that the construction of a domain representation significantly improved learning outcomes. The format in which students constructed a representation did not directly affect learning outcomes or the quality of the created domain representations. The arithmetical format, however, was the least stimulating for students to engage in externalizing their knowledge

The effects of representational format on learning combinatorics from an interactive computer simulation

The current study investigated the effects of different external representational formats on learning combinatorics and probability theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions each using a single external representational format (Diagram, Arithmetic, or Text), and two conditions using multiple representations (Text + Arithmetic or Diagram + Arithmetic). The major finding of the study is that a format that combines text and arithmetics was most beneficial for learning, in particular with regard to procedural knowledge, that is the ability to execute action sequences to solve problems. Diagrams were found to negatively affect learning and to increase cognitive load. Combining diagrams with arithmetical representations reduced cognitive load, but did not improve learning outcomes

Conceptual understanding of electrical circuits in secondary vocational engineering education: combining traditional instruction with inquiry learning in a virtual lab

Background: Traditionally, engineering curricula about electrical circuits use textbook instruction and hands-on lessons, which are effective approaches for teaching terms and definitions, the procedural use of formulas, and how to build circuits. Nonetheless, students often lack conceptual understanding. Purpose (Hypothesis): The aim of this study was to discover how to facilitate the acquisition of conceptual understanding. We hypothesized that adding an instructional approach in the form of inquiry learning in a virtual lab would be more effective than relying on traditional instruction alone. Design/Method: Students in secondary vocational engineering education were randomly assigned to one of two conditions in a quasi-experimental study. In the traditional condition, the curriculum was supplemented with computer-based practice. In the virtual lab condition, the traditional curriculum was supplemented with inquiry learning in a virtual lab. Results: Results showed that students in the virtual lab condition scored significantly higher on conceptual understanding (Cohen's d=0.65) and on procedural skills (d=0.76). In particular, students in this condition scored higher (d=1.19) on solving complex problems. This result occurred for both complex conceptual and procedural problems. Conclusion: Since students in the virtual lab condition acquired better conceptual understanding and also developed better procedural skills than students in the traditional condition, it appears that conceptual understanding and procedural skills develop in an iterative fashion