Proportional reasoning is both complex and layered, making it challenging to define. Lamon (1999) identified characteristics of proportional thinkers, such as being able to understand covariance of quantities; distinguish between proportional and nonproportional relationships; use a variety of strategies flexibly, most of which are nonalgorithmic,…

Brainstorming is a creativity technique in which a group of people (or an individual person) spontaneously generates a set of ideas to find the solution to a particular problem. This paper describes an innovative approach called "brainstorming with yo-yos," which was implemented in an outreach to high school event to increase high school…

The purpose of this study is to identify the effect of using metacognitive strategies for problem solving in "geometry" on fifth grade students' achievement, metacognitive skills and attitude. Experimental method was used with a pretest/posttest control group design. Firstly, both groups were subject to a pretest that was comprised of…

This article describes the steps incorporated to teach an engineering design process in a fifth-grade science classroom. The engineering design-based activity was an existing scientific inquiry activity using UV light--detecting beads and purposefully creating a series of engineering design-based challenges around the investigation. The…

Developmental mathematics is one of the most serious barriers to educational and economic achievement. Over 60 percent of all students entering community colleges in the United States are required to complete remedial/developmental courses as a first step towards earning associate's or bachelor's degrees. Then, to earn a degree,…

Every community has individuals or groups who manage to find better solutions to problems than their peers, although everyone has access to the same resources and challenges. Those are the positive deviants.

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

In many domains, problem solving involves the application of general domain principles to specific problem representations. In 3 classroom studies with an intelligent tutoring system, we examined the impact of (learner-generated) interactions and (tutor-provided) visual cues designed to facilitate rule-diagram mapping (where students connect…

In higher education the main subjects build on the knowledge acquired in high school. Research shows that students entering universities have acquired basic knowledge to different extents. It is very important to be able to apply mathematical knowledge directly. Students often treat practical knowledge separately from theoretical knowledge. They…

This article describes a method for the assessment of professional student outcomes (performance-type outcomes or soft skills). The method is based upon group activities, research on modern electrical engineering topics by individual students, classroom presentations on chosen research topics, final presentations, and technical report writing.…

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when…

We present a new method for analyzing a student's learning over time for a specific skill: analysis of the graph of the student's moment-by-moment learning over time. Moment-by-moment learning is calculated using a data-mined model that assesses the probability that a student learned a skill or concept at a specific time during learning (Baker,…

Students in the United States demonstrate low proficiency in their math skills. One promising intervention, computer-assisted instruction, may be used for remediation. There is growing support that computer-assisted instruction is effective for increasing addition and multiplication accuracy and fluency, but more research is necessary in order to…

This study takes an experimental approach to "lingua receptiva" (LaRa), a communication mode in which interlocutors each use their own--different--native language. In contrast to previous work on LaRa, this study investigates the phenomenon in genetically unrelated languages. Native speakers of Estonian and Russian were engaged in a…

The focus of the present study is on the developmental antecedents of domain-general experimentation skills. We hypothesized that false-belief understanding would predict the ability to distinguish a conclusive from an inconclusive experiment. We conducted a longitudinal study with two assessment points (t1 and t2) to investigate this hypothesis.…