Backwards or forwards? Direction of working and success in problem solving

2019 ◽  
pp. 71-89
Author(s):  
Thomas Gawlick ◽  
Gerrit Welzel
Keyword(s):  
Problem Solving ◽  
Solution Path ◽  
Natural Hypothesis ◽  
Surprising Observation ◽  
Working Backwards

We pose ourselves the question: What can one infer from the direction of working when solvers work on the same task for a second time? This is discussed on the basis of 44 problem solving processes of the TIMSS task K10. A natural hypothesis is that working forwards can be taken as evidence that the task is recognized and a solution path is recalled. This can be confirmed by our analysis. A surprising observation is that when working backwards, pivotal for success is (in case of K10) to change to working forwards soon after reaching the barrier.

Thinking through a Lesson: Successfully Implementing High-Level Tasks

2008 ◽  
Vol 14 (3) ◽  
pp. 132-138 ◽  
Author(s):  
Margaret S. Smith ◽  
Victoria Bill ◽  
Elizabeth K. Hughes
Keyword(s):  
Problem Solving ◽  
Point Of View ◽  
Mathematical Tasks ◽  
Solution Path ◽  
Challenging Tasks ◽  
Reasoning Skills ◽  
Bag Of Marbles ◽  
High Level

Mathematical tasks that give students the opportunity to use reasoning skills while thinking are the most difficult for teachers to implement well. Research by Stein and colleagues (Henningsen and Stein 1997; Stein and Lane 1996; Stein, Grover, and Henningsen 1996) makes the case resoundingly that cognitively challenging tasks that promote thinking, reasoning, and problem solving often decline during implementation as a result of various classroom factors. When this occurs, students must apply previously learned rules and procedures with no connection to meaning or understanding, and the opportunities for thinking and reasoning are lost. Why are such tasks so difficult to implement in ways that maintain the rigor of the activity? Stein and Kim (2006, p. 11) contend that lessons based on high-level (i.e., cognitively challenging) tasks “are less intellectually ‘controllable’ from the teacher's point of view.” They argue that since procedures for solving high-level tasks are often not specified in advance, students must draw on their relevant knowledge and experiences to find a solution path. Take, for example, the Bag of Marbles task shown in figure 1.

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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