In this paper I intend to illustrate Vygotsky's Zone of Proximal Development (ZPD) and then extend the discussion to scaffolding and its relationship with the ZPD. This is then followed by some concerns raised in literature regarding scaffolding as a concept and as a metaphor which involves analysing the arguments for regarding the role of…

Conversations in collaborative problem-solving activities can be used to probe the collaboration skills of the team members. Annotating the conversations into different collaboration skills by human raters is laborious and time consuming. In this report, we report our work on developing an automated annotation system, CPS-rater, for conversational…

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

Organizations are faced with solving increasingly complex problems. Addressing these issues requires effective leadership that can facilitate a collaborative problem solving approach where multiple perspectives are leveraged. In this conceptual paper, we critique the effectiveness of earlier leadership models in tackling complex organizational…

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

The paper discusses some interesting, mainly philosophical paradigms of the modeling and control areas, which are still partly unsolved and/or only partially studied. First the possible introduction of a prejudice free control--similar to the term for the modeling introduced by Rudi Kalman--is investigated. Next the real constraints in real…

Many physical education curriculum frameworks include statements about the inclusion of critical inquiry processes and the development of creativity and problem-solving skills. The learning environment created by physical education can encourage or limit the application and development of the learners' cognitive resources for critical and creative…

Individuals with an aptitude for interpreting spatial information (high mental rotation ability: HMRA) typically master anatomy with more ease, and more quickly, than those with low mental rotation ability (LMRA). This article explores how visual attention differs with time limits on spatial reasoning tests. Participants were assorted to two…

Thinking and learning are corresponding and interdependent processes in every classroom. To improve learning, teachers must be open to new ideas, particularly ideas that locate conditions for maximum learning. This paper presents four overlooked but critical ideas that identify a common area, a GAP experience within which maximum learning is…

Correctional educators have discovered common thinking and behavioral errors which impede pro-social adjustment. In order for the inmate student to hope to experience societal reintegration, these errors must be detected and corrected. The program described herein--a consequential thinking seminar called ABLE MINDS--has as its goals: 1) The…

Considering the role of mathematics-focused professional development programs in improving teachers' content knowledge and quality of teaching, we provided teachers opportunities for dealing with mathematics problems and positioning themselves as students in a large-scale long-term professional development (PD) project. In this proposal, we aimed…

Word problems are an integral part of any secondary mathematics curriculum and one purpose has been to prepare students for the real-world--for everyday events as well as workplace problem-solving. Prior literature suggests that word problems have not met this objective, in part, because the textbook problems do not mirror the kinds of problems…

Developing critical thinking is an important factor in education. In this study, the author defines critical thinking as the set of skills and dispositions which enable one to solve problems logically and to attempt to reflect autonomously by means of metacognitive regulation of one's own problem-solving processes. To identify the validity and…

State policy plays a critical role in determining whether and how well local education improvement strategies can be implemented. As states rework their education policies under the Every Student Succeeds Act (ESSA), state and local leaders need a way to assess their current policy environment and identify the changes needed to encourage local…