Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Loyola University Chicago's Teaching, Learning, and Leading With Schools and Communities (TLLSC) program is an ambitious break from traditional university-based teacher preparation models. This clinically based initial teacher preparation program, fully embedded in local schools and community organizations, takes an ecological perspective on the…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

Although the human mind resists confusion, this feeling of disequilibrium nurtures learning. Newkirk, the author quotes, says intelligence is not a matter of being smart--it is the capacity to view difficulty as an opportunity to stop, reassess, and employ strategies for making sense of problems. These same habits of mind define reflection, a…

This paper examines the development of students' metacognitive skills in a data-rich environment. The study involves the development and use of a Metacognitive Inventory, which evaluates students' awareness of their cognitive processes as they approach and solve problems. This 26-item inventory is based on the Problem Solving Inventory and State…

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

The use of science classroom discourse analysis as a way to gain a better understanding of various student cognitive outcomes has a rich history in Science Education in general and Physics Education Research (PER) in particular. When students talk to each other in a collaborative peer instruction environment, such as in the CLASP classes…

This study investigates problem-solving difficulties of novices in a classroom setting, using a German instructional tool, the Fischertechnik kit of approximately 400 parts. In order to analyse the students' thinking processes as they solved the problems, verbal protocol analysis (VPA) was used to record the students'' thinking processes and…

Solving new problems can be made easier if one can build on experiences with other problems one has already successfully solved. The ability to exploit earlier problem-solving experiences in solving new problems seems to require several cognitive sub-abilities. Minimally, one needs to be able to retrieve relevant knowledge of earlier solved…

This article reports on the results of research, the objective of which was to document and analyze the manner in which students relate different representations when solving problems. A total of 20 students attending their first year of university studies took part in the study. In order to design the problem, the underlying information in each…

The ability to successfully discriminate between multiple potentially relevant source analogs when solving new problems is crucial to proficiency in a mathematics domain. Experimental findings in two different mathematical contexts demonstrate that providing cues to support comparative reasoning during an initial instructional analogy, relative to…

When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g-structures), arithmetic (a-structures), fractal-type (f-structures), and density-type (d-structures). Students select different problem-solving strategies depending on the structure they recognize within the problem domain. They…

Background: Historically, significant advances in scientific understanding have followed advances in measurement and observation. As the resolving power of an instrument increased, so have gains in the understanding of the phenomena being observed. Modern interactive systems are potentially the new "microscopes" when they are…

Recursion is an important concept for any computer science student to master. Many first year students develop the viable "copies" mental model of recursion and can successfully trace the execution of a simple recursive function. This article discusses a study focused on determining whether the ability to successfully trace a recursive…

Alzheimer's disease (AD) can impair metacognition in addition to more basic cognitive functions like memory. However, while global metacognitive inaccuracies are well documented (i.e., low deficit awareness, or anosognosia), the evidence is mixed regarding the effects of AD on local or task-based metacognitive judgments. Here we investigated local…