This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

Refutation texts have been shown to be effective at promoting knowledge revision. It has been suggested that refutation texts are most effective when the misconception and the correct information are co-activated and integrated with causal networks that support the correct information. We explored two augmentations to a refutation text that might…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes…

An argument map visually represents the structure of an argument, outlining its informal logical connections and informing judgments as to its worthiness. Argument mapping can be augmented with dedicated software that aids the mapping process. Empirical evidence suggests that semester-length subjects using argument mapping along with dedicated…

Examines relationships between critical thinking and writing. Compares a pencil-and-paper and computer-assisted versions of a process/model program to a traditional composition program. Reports experimental groups showed greater argumentative powers. Extends approach to poetry and technical writing. Suggests collaborative learning potential.…