Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

Expertise is extended by becoming immersed in cultural practices. We look at an example of mathematical expertise in which immersion in cognitive practices results in the transformation of expert performance.

Ginny Sackett lists many of the universal attributes of the absorbent mind--pattern recognition, order, incarnation, the rules for language, and numeracy. Her essay borders on the metaphysical as it suggests that the mathematical mind is really a non-entity and is responsible for all aspects of knowledge acquisition regardless of the discipline of…

This study investigated the joint effects of online student question-generation and cooperative learning strategies with regard to learning anxiety and student perceptions of the value of the related activity for enhancing self-perceived competence. A 2 (question generation vs non-question generation) × 2 (cooperative learning vs individual…

Background: Personal construct theory (PCT) is a constructivist approach to understanding human thought and action. Preliminary research focusing on applying PCT concepts and methodologies to understanding individuals with high-functioning autism (HFA) has suggested its utility for both research and clinical interventions. The developmental period…

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

Cognitively based views of reading emphasize that proficient readers use both metacognitive and cognitive strategies that facilitate comprehension of text. Metacognitive strategies are self-monitoring and self-regulating behaviors that focus on the processes and products of reading including the reader's awareness of whether or not he or she…

This study investigated the impact of structuring and problematizing scaffolding mechanisms on 240 Iranian English as a foreign language learners' individual and socially shared metacognition in writing skills. The study also sought to find out whether the learners' proficiency level moderated the effect of the scaffolding mechanisms on…

The purpose of this study was to partially replicate the "Historical Problem Solving: A Study of the Cognitive Process Using Historical Evidence" study conducted by Sam Wineburg in 1991. The Historical Problem Solving study conducted by Wineburg (1991) sought to compare the ability of historians and top level students, as they analyzed…

The aim of the study was to investigate differences in cognitive and metacognitive strategy use in the reading comprehension of narrative and expository texts among students with learning disabilities (SLD) and without learning disabilities (SWOLD). A total of 122 fifth and sixth graders took part in the study. Half of them (n = 61) were SLD…

This study examined the effectiveness of an integrated context approach to the instruction of basic compass-and-straightedge construction. The formulation of a perpendicular bisector of a segment was used as a knowledge module to guide students from the pre-attention level to the elaboration level of information processing. The students were…

Objective: College students face a significant number of stressors, increasing risk for internalizing and externalizing psychopathology. The current study examines two promising avenues of intervention aimed to reduce stress and prevent psychopathology in this population: a coping skills group and a cognitive training program. Participants: 62…

Cognitive apprenticeship theory emphasizes the process of making expert thinking "visible" to students and fostering the cognitive and meta-cognitive processes required for expertise. The purpose of this review was to evaluate the use of cognitive apprenticeship theory with the primary aim of understanding how and to what extent the…

All students should be provided with opportunities to develop conceptual understanding prior to procedural fluency. To develop students' conceptual understanding, teachers must learn such skills as how to select, plan, and enact cognitively demanding tasks (CDT) and to evaluate evidence of student learning. Therefore, teachers need opportunities…