Cover, copy, and compare (CCC) is a study strategy in which students cover their notes, attempt to copy them, and then compare for accuracy. We evaluated whether CCC could be used to establish equivalence classes with undergraduate students. A video training package and experimenter feedback were used to teach participants to engage in CCC with…

This study aimed to investigate prospective middle school mathematics teachers' noticing of students' algebraic thinking based on students' correct and incorrect solutions within the context of pattern generalization. Designed as a qualitative case study, three noticing prompts were asked of thirty-two prospective middle school mathematics…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

Technology offers exciting possibilities for instruction with learners with autism spectrum disorder (ASD), but limited research has evaluated the use of web-based applications (apps) as learning tools for this population. We wondered if using apps would function as a precurrent response to solve problems in the form of questions on a worksheet.…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…