Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to…

For developmental education students, rates of developmental math course completion and persistence into required college-level math courses are particularly low. This literature review examines the evidence base on one potential means for improving the course completion and learning outcomes of developmental mathematics students: reforming…

According to industry representatives, computer science education needs to emphasize the processes involved in solving computing problems rather than their solutions. Most of the current assessment tools used by universities and computer science departments analyze student answers to problems rather than investigating the processes involved in…

In 2006, the authors began a project to understand what happens in middle school technology education classrooms in order to document the goals that technology education teachers pursue, the instructional strategies they use to teach children to meet these outcomes, the measures they use to assess achievement of these goals, and the learning…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

Purpose: The Rapid Assessment of Problem Solving test (RAPS) is a clinical measure of problem solving based on the 20 Questions Test. This article updates clinicians on the RAPS, addresses questions raised about the test in an earlier article (R. C. Marshall, C. M. Karow, C. Morelli, K. Iden, & J. Dixon, 2003a), and discusses the clinical…

In this paper it is proposed that the prefrontal lobe participates in two closely related but different executive function abilities: (1) "metacognitive executive functions": problem solving, planning, concept formation, strategy development and implementation, controlling attention, working memory, and the like; that is, executive functions as…

Six experiments examined children's ability to make inferences using temporal order information. Children completed versions of a task involving a toy zoo; one version required reasoning about past events (search task) and the other required reasoning about future events (planning task). Children younger than 5 years failed both the search and the…

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students' conviction based only on…

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

Students learned a strategy for planning, writing, and evaluating compare-contrast essays. Instruction followed the principles of self-regulated strategy development, which aims to improve knowledge about writing, strategic writing processes, self-regulation, and motivation. Six adolescent students, 3 with learning disabilities in writing and 3…

In the past, if a question is asked of a student, and that student needed a few minutes to think, that student's thinking would be interrupted by somebody else who'd be shouting out. Now, teachers at St. Johnsbury School in Vermont are really focusing on think time for students and really working with other students in the classroom to be…

This study investigated possible factors that might influence the degree of student participation in asynchronous online discussion forums. Degree of participation refers to the number of messages posted by the students. Data were collected from 41 forums, students' reflection logs, and students' interviews. Of these 41 forums, the top third…

The purpose of this technical report is to describe a research study exploring students' cognitive processing while solving problems related to division of fractions. Four students were interviewed using verbal protocol techniques with the intention of better understanding their cognitive processing when dividing fractions. Information gained from…

We have developed a process model that learns in multiple ways while finding faults in a simple control panel device. The model predicts human participants' learning through its own learning. The model's performance was systematically compared to human learning data, including the time course and specific sequence of learned behaviors. These…