scholarly journals Analytical Reasoning and Problem-Solving in Diophantus’s Arithmetica : Two Different Styles of Reasoning in Greek Mathematics

2021 ◽  
pp. 103-130
Author(s):  
Jean Christianidis
Keyword(s):  
Problem Solving ◽  
Analytical Reasoning ◽  
Greek Mathematics ◽  
Styles Of Reasoning

scholarly journals SETP: A New Powerful Tool for Improving Problem Solving, Decision Making and Creativity in Teenagers.

2015 ◽  
Vol 2 (3) ◽  
Author(s):  
Dr. Arvinder Singh ◽  
Dr. Ajay K. Chaudhary
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Cognitive Abilities ◽  
Decisive Factor ◽  
School Students ◽  
Analytical Reasoning ◽  
Solid Foundation

Our decisions decide our destiny. Problem solving, decision-making, analytical reasoning and creativity are important abilities not only for studies but also for every sphere of life. SETP (Seven Effective Thinking Patterns) tool developed by Dr. Arvinder Singh was applied on teenagers to study the effect on their cognitive abilities. The study was done on 50 convent school students. Important parameters like Innovative Thoughts, Decisive Factors, Pros- Cons Analysis and Broader Perspectives were studied on the scale of 1 to 5. Scoring was done for Pre-training and Post-training sessions. For innovative thoughts pre-training score was 2.10±0.678, while for post training it was 3.34±0.717. Decisive factor‟s pre-training score was 1.68±0.653, while for post training it was 3.52±0.735. Pros-cons analysis pre-training score was 1.66±0.557 and post training score was 3.32±0.768. Broader perspective pre-training score was 1.86±0.700, while for post training it was 3.52±0.931.For language pre-training score was 2.70±0.763, while for post training it was 2.76±0.847. For expression pre-training score was 2.68±0.768 and for post training it was 2.88±1.256. The above findings suggest that SETP tool was effective and showed significant improvement in 4 out of 6 parameters. The tool was not effective for language and expression parameters. Important point is that by SETP tool, we were able to enhance the cognitive abilities of school going children, which will make solid foundation for their future.

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

2016 ◽  
Vol 29 (2) ◽  
pp. 129-150 ◽  
Author(s):  
Michalis Sialaros ◽  
Jean Christianidis
Keyword(s):  
Comparative Analysis ◽  
Problem Solving ◽  
Theorem Proving ◽  
Algebraic Reasoning ◽  
Numerical Problem ◽  
Controversial Topic ◽  
Methodological Approaches ◽  
Greek Mathematics ◽  
Geometrical Algebra

ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

An application of the Patient-Oriented Problem-Solving (POPS) System

1991 ◽  
Vol 55 (5) ◽  
pp. 327-331 ◽  
Author(s):  
GT Chiodo ◽  
WW Bullock ◽  
HR Creamer ◽  
DI Rosenstein
Keyword(s):  
Problem Solving

Applying a Self-Regulating Private Speech Model to Classroom Settings

1982 ◽  
Vol 13 (2) ◽  
pp. 129-133
Author(s):  
A. D. Pellegrini
Keyword(s):  
Problem Solving ◽  
Private Speech ◽  
Speech Model

The paper explores the processes by which children use private speech to regulate their behaviors. The first part of the paper explores the ontological development of self-regulating private speech. The theories of Vygotsky and Luria are used to explain this development. The second part of the paper applies these theories to pedagogical settings. The process by which children are exposed to dialogue strategies that help them solve problems is outlined. The strategy has children posing and answering four questions: What is the problem? How will I solve it? Am I using the plan? How did it work? It is argued that this model helps children systematically mediate their problem solving processes.

Creative Problem Solving in Public School Supervision

1989 ◽  
Vol 20 (3) ◽  
pp. 320-332 ◽  
Author(s):  
David A. Shapiro ◽  
Nelson Moses
Keyword(s):  
Public School ◽  
Problem Solving ◽  
School Environment ◽  
Professional Growth ◽  
Cognitive Learning ◽  
School Personnel ◽  
Collaborative Problem Solving ◽  
The Public ◽  
School Supervision ◽  
Team Functioning

This article presents a practical and collegial model of problem solving that is based upon the literature in supervision and cognitive learning theory. The model and the procedures it generates are applied directly to supervisory interactions in the public school environment. Specific principles of supervision and related recommendations for collaborative problem solving are discussed. Implications for public school supervision are addressed in terms of continued professional growth of both supervisees and supervisors, interdisciplinary team functioning, and renewal and retention of public school personnel.

Teaching Language Rules as Solutions to Language Problems

1987 ◽  
Vol 18 (3) ◽  
pp. 194-205 ◽  
Author(s):  
Phil J. Connell
Keyword(s):  
Problem Solving ◽  
Language Teaching ◽  
Teaching Language ◽  
Language Problem ◽  
Language Problems ◽  
Simple Language ◽  
Approach To Teaching

The teaching procedures that are commonly used with language-disordered children do not entirely match the goals that they are intended to achieve. By using a problem-solving approach to teaching language rules, the procedures and goals of language teaching become more harmonious. Such procedures allow a child to create a rule to solve a simple language problem created for the child by a clinician who understands the conditions that control the operation of a rule.

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