This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

We examined, on a trial-by-trial basis, fraction magnitude comparison strategies of adults with more and less mathematical knowledge. College students with high mathematical proficiency used a large variety of strategies that were well tailored to the characteristics of the problems and that were guaranteed to yield correct performance if executed…

Definitions of related concepts (e.g., "genotype-phenotype") are prevalent in introductory classes. Consequently, it is important that educators and students know which strategy(s) work best for learning them. This study showed that a new comparative elaboration strategy, called differential-associative processing, was better for learning…

Electronic marking tools that incorporate statement banks have become increasingly prevalent within higher education. In an experiment, printed and emailed feedback was returned to 243 first-year students on a credit-bearing laboratory report assessment. A transmission approach was used, students being provided with comments on their work, but no…

Intelligent tutoring systems (ITS) support students in learning a complex problem-solving skill. One feature that makes an ITS architecturally complex, and hard to build, is support for strategy freedom, that is, the ability to let students pursue multiple solution strategies within a given problem. But does greater freedom mean that students…

Concept maps have been widely employed for helping students organise their knowledge as well as evaluating their knowledge structures in a wide range of subject matters. Although researchers have recognised concept maps as being an important educational tool, past experiences have also revealed the difficulty of evaluating the correctness of a…

Learning with instructional animations may overstretch limited working memory resources due to intense processing demands associated with transient information. The authors investigated whether explicit instructional advice coupled with a task-specific learner control mechanism (such as a timeline scrollbar) could facilitate the successful…

Based on current theories of multimedia learning, we propose a strategy for learning from animations. Two different experimental studies were conducted in order to evaluate the strategy. In the first study, 22 sixth graders learned from an animation without the strategy while 21 students were encouraged to make use of the proposed strategy during…

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…