This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…

Base-rate neglect refers to the tendency for people to underweight base-rate probabilities in favor of diagnostic information. It is commonly held that base-rate neglect occurs because effortful (Type 2) reasoning is required to process base-rate information, whereas diagnostic information is accessible to fast, intuitive (Type 1) processing…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a…

This performance assessment pilot study was a major research component of the overall National Science Foundation funded Redesigned High Schools for Transformed STEM Learning Project. Secondary Earth/Environmental Science students' abilities to translate cognitive knowledge into demonstrable performance-based proficiencies were specifically…

Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in…

The Encouraging Persistence Maintaining Challenge (EMPC) Project has been working with secondary teachers in Melbourne as they seek to build persistence in students, during work on challenging mathematics tasks. The authors have developed sequences of tasks in various topic areas for Years 7 and 8, which require students to connect different…

Computer-based assessment can provide new insights into behavioral processes of task completion that cannot be uncovered by paper-based instruments. Time presents a major characteristic of the task completion process. Psychologically, time on task has 2 different interpretations, suggesting opposing associations with task outcome: Spending more…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

While it is well recognized that students are prone to difficulties when performing linguistic-to-algebra translations, the nature of students' difficulties remain an issue of contention. Moreover, the literature indicates that these difficulties are not easily remediated by domain-specific instruction. Some have opined that this is the case…

The act of note-taking offloads cognitive pressure and note-taking applications could be used as an important tool for foreign language acquisition. Its use, importance, and efficacy in a foreign language learning context could be justifiably debated. However, existing computer-assisted language learning literature is almost silent on the topic.…

In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

How can geometry teachers design great tasks that allow students to make connections among interrelated concepts and expand their geometric reasoning skills? Many curricular materials provide problems for students to apply a single geometric concept. However, these problems do not always promote reasoning opportunities for students, because…