In a PBL environment, learning results from learners engaging in cognitive processes pivotal in the understanding or resolution of the problem. Using Tan's cognitive function disc, this study examines the learner's perceived cognitive functions at each stage of PBL, as facilitated by the PBL schema. The results suggest that these learners…

I examined the impact of a self-diagnosis activity on students' conceptual understanding and achievements in physics. This activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify and explain their errors--and self-score them--that is, assign scores to their solutions--aided by…

To help middle school students make better sense of decimals and fraction, the author and an eighth-grade math teacher worked on a 90-minute lesson that focused on representing repeating decimals as fractions. They embedded experimentations and explorations using technology and calculators to help promote students' intuitive and conceptual…

For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a…

Success in math is important to all students; it provides them with college and career options in the fields of science, technology, engineering, and mathematics. In the middle grades, students build upon the critical skills taught in elementary school and prepare for entry into algebra, which is considered a gateway to later achievement in school…

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…

There is a long-standing tradition in mathematics education to look to history to inform instruction. An historical analysis of the genesis of a mathematical idea offers insight into: (i) the contexts that give rise to a need for a mathematical construct; (ii) the ways in which available tools might shape the development of that mathematical idea;…

This study aimed to investigate how the semantic structures of problems posed by sixth-grade middle school students for the addition of fractions affect their problem-posing performance. The students were presented with symbolic operations involving the addition of fractions and asked to pose two different problems related to daily-life situations…

Researchers have identified challenges students face when modeling dynamic situations. This report discusses the results of semi-structured clinical interviews with ten prospective secondary mathematics teachers who were provided with a dynamic image of a growing and shrinking cone. We asked the students to graph the relationship between the…

The study reported in this paper is part of a larger study on the roles of examples in learning to prove. We focus here on manifestations of students' productive use of examples for proving in the course of exploring conjectures and proving or disproving them. In this context, we define productive use of examples for proving as students'…

Unfortunately, many students learn about the concept of systems of linear equations in a procedural way. The lessons are taught as three discrete methods. Connections between the methods, in many cases, are not made. As a result, the students' overall understanding of the concept is very limited. By the time the teacher reaches the end of the…

In previous publications the authors of this paper identified specific relations between comprehension and convincement. On the basis of Grounded Theory, this research analyzes the changes that arise in said relations as a response to changing conditions. For their study, the authors analyze an interaction, at a distance, between a tutor and a…

Spatial visualization is an essential prerequisite for understanding geological features at all scales, such as the atomic structures of minerals, the geometry of a complex fault system, or the architecture of sedimentary deposits. Undergraduate geoscience majors bring a range of spatial skill levels to upper-level courses. Fortunately, spatial…

In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

How can physics teachers help students develop consistent problem solving techniques for both simple and complicated physics problems, such as those that encompass objects undergoing multiple forces (mechanical or electrical) as individually portrayed in free-body diagrams and/or phenomenon involving multiple objects, such as Doppler effect…