Developmental Aspects of Children's Ability to Understand Mathematical Proof

1975 ◽  
Vol 6 (1) ◽  
pp. 14-25
Author(s):  
Frank K. Lester
Keyword(s):  
Problem Solving ◽  
Reading Ability ◽  
Mathematical Proof ◽  
Complex Problem ◽  
Upper Elementary ◽  
Future Research ◽  
Elementary Grades ◽  
Problem Solving Strategies ◽  
Measures Of Performance ◽  
Problem Solving Task

Simple elements of mathematical proof were analyzed by considering the making of a proof as a complex problem-solving task. Quantitative measures of performance on certain problem-solving tasks were obtained in order to determine the relation between problem-solving ability and chronological age (6-18). A consideration of all variables suggested that, even though problem-solving ability does increase with age, certain aspects of problem solving that approximate mathematical proof can be dealt with successfully in the upper elementary grades. An analysis of problem-solving strategies is recommended as a further step in the investigation of problem solving. IQ, reading ability, and mathematical aptitude are suggested as possible covariates or blocking variables in future research.

scholarly journals Applying Metacognitive Strategies in Comprehending English Reading Texts

2019 ◽  
Vol 19 (1) ◽  
pp. 138
Author(s):  
Zulfadli A. Aziz ◽  
Chairina Nasir ◽  
Ramazani Ramazani
Keyword(s):  
Problem Solving ◽  
Reading Strategies ◽  
Reading Ability ◽  
High Performance ◽  
Metacognitive Strategies ◽  
Support Strategies ◽  
Problem Solving Strategies ◽  
Low Performance ◽  
Metacognitive Reading Strategies ◽  
Global Strategies

Comprehending English text is still regarded as hard for students. Metacognitive strategies have been considered effective in overcoming reading difficulties by many researchers. The objective of this study is to describe the application of three types of metacognitive reading strategies (global strategies, problem solving strategies, and support strategies) used by the students of Senior High School (SMAN) 1 Ingin Jaya, Aceh Besar. It is a descriptive qualitative study. Metacognitive Awareness of Reading Strategies Inventory (MARSI) questionnaire suggested by Mokhtari and Reichard (2002) was used to collect the data. The result of the study revealed that the students generally showed moderate awareness of all strategies and held a preference of using Problem Solving Strategies, followed by Support Strategies and Global Strategies respectively. The study also showed that high performance students used the strategies more frequently than low performance students. It can be concluded that the more students aware of using metacognitive reading strategies, the better their performance is in reading skill. Therefore, teaching the students to use metacognitive strategies can be a solution in enhancing students’ reading ability.

Problem Solving: Help in the Right Direction for LD Students

1982 ◽  
Vol 29 (6) ◽  
pp. 26-41
Author(s):  
Carol A. Thornton ◽  
Nancy S. Bley
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Upper Elementary ◽  
Elementary Grades ◽  
Basic Facts ◽  
The Right

Until recently problem solving was stressed primarily in the middle and upper elementary grades. The focus in the lower grades was on memorizing basic facts and developing specific computational skills. When children reached the middle elementary grades it was often assumed that because they could compute they also would know when to apply the different operations in problem-solving contexts. Unfortunately this is not always the case. Problem solving involves more than incorporating computational skills. It primarily requires a great deal of decision making.

scholarly journals Studying science denial with a complex problem-solving task

2021 ◽  
Author(s):  
Justin Sulik ◽  
Ryan McKay
Keyword(s):  
Problem Solving ◽  
Cognitive Style ◽  
Political Ideology ◽  
Data Gathering ◽  
Complex Problem ◽  
Complex Problem Solving ◽  
Multi Stage ◽  
Individual Cognition ◽  
Problem Solving Task ◽  
Hypothesis Evaluation

Explanations of science denial rooted in individual cognition tend to focus on general trait-like factors such as cognitive style, conspiracist ideation or delusional ideation. However, we argue that this focus typically glosses over the concrete, mechanistic elements of belief formation, such as hypothesis generation, data gathering, or hypothesis evaluation. We show, empirically, that such elements predict variance in science denial not accounted for by cognitive style, even after accounting for social factors such as political ideology. We conclude that a cognitive account of science denial would benefit from the study of complex (i.e., open-ended, multi-stage) problem solving that incorporates these mechanistic elements.

scholarly journals Tolerance for Uncertainty and Patterns of Decision-Making in Complex Problem-Solving Strategies

2020 ◽  
Vol 4 (3) ◽  
pp. 58
Author(s):  
Vitalii Epishin ◽  
Nataliya Bogacheva
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Negative Attitude ◽  
Decisional Conflict ◽  
Complex Problem ◽  
Complex Problem Solving ◽  
Decision Making Factors ◽  
Problem Solving Strategies ◽  
Risk Intelligence

Current studies of complex problem-solving do not commonly evaluate the regulatory role of such personality-based variables as tolerance for uncertainty, risk-readiness, and patterns for coping with decisional conflict. This research aims to establish the contribution of those traits into individual parameters of complex problem-solving strategies. The study was conducted on 53 healthy individuals 17 to 29 years old (M = 20.42; SD = 2.34). Our own computerized complex problem task “The Anthill” was developed for this research. We identified five measurable parameters of the participants’ problem-solving strategies: preferred orientational level (POL); orientational level variability (OLV); class quotas‘ range (R); mean and median quotas shift (MS and MeS); and abrupt changes of strategy (AC). Psychodiagnostic methods included: new questionnaire of tolerance/intolerance for uncertainty; personal decision-making factors questionnaire; Melbourne Decision Making Questionnaire; Subjective Risk Intelligence Scale; Eysencks’ Impulsiveness Scale. The study showed the role of tolerance for uncertainty, risk-readiness, negative attitude toward uncertainty, and decision-making styles in the regulation of complex problem-solving strategies. Specifically, procrastination, tolerance for uncertainty, and risk-readiness were significant predictors of individual strategy indicators, such as POL, OLV, and MeS. Thus, personality traits were shown to regulate resource allocation strategies and the required level of orientation in a complex problem.

scholarly journals The effect of conceptual complexity on information search in a complex problem-solving task

1967 ◽  
Vol 7 (4) ◽  
pp. 137-138 ◽  
Author(s):  
Marvin Karlins ◽  
Thomas Coffman ◽  
Helmut Lamm ◽  
Harold Schroder
Keyword(s):  
Problem Solving ◽  
Information Search ◽  
Complex Problem ◽  
Complex Problem Solving ◽  
Problem Solving Task

scholarly journals Comparison of Traditional and ADRI Based Teaching Approaches in an Introductory Programming Course

10.28945/3793 ◽  
2017 ◽  
Vol 16 ◽  
pp. 267-283 ◽  
Author(s):  
Sohail Iqbal Malik ◽  
Jo Coldwell-Neilson
Keyword(s):  
Problem Solving ◽  
Focus Group ◽  
Teaching And Learning ◽  
Science Studies ◽  
Future Research ◽  
Learning Approach ◽  
Final Exam ◽  
Introductory Programming ◽  
Problem Solving Strategies ◽  
Programming Knowledge

Aim/Purpose: This study introduced a new teaching and learning approach based on an ADRI (Approach, Deployment, Result, Improvement) model in an introductory programming (IP) course. The effectiveness of the new teaching and learning process was determined by collecting feedback from the IP instructors and by analyzing the final exam grades of the course. Background: Learning to program is considered a difficult and challenging task for a considerable number of novice programmers. As a result, high failure and dropout rates are often reported in IP courses. Different studies have been conducted to investigate the issue. One of the reasons for this challenge is the multiple skills that students have to master in order to be able to build programs. These skills include programming knowledge and problem-solving strategies and being able to pay equal attention to these required skills in the IP course. Methodology: A focus group was conducted to obtain feedback from the IP instructors about the ADRI approach. The performance of the students who had completed the IP course before ADRI was compared with those who used the ADRI approach by undertaking a comparative analysis of their final exam grades. Contribution: The study demonstrates that the new teaching and learning approach based on the ADRI model encourages students to pay equal attention to programming knowledge and problem-solving strategies, discouraging programming shortcuts and reducing high attrition rates (failure and dropout) in the IP course. Findings: The results of the focus group show that the instructors preferred the ADRI approach compared to the traditional approach. The final exam grades show that the students performed better in semesters which offered the ADRI approach as compared to those semesters without this approach. Future Research: Future research will explore the ADRI approach in other fields of computer science studies, such as database and data structure, to determine if its impact has a wider application than just teaching introductory programming.

Training to Reduce the Disruptive Effects of Interruptions

1994 ◽  
Vol 38 (18) ◽  
pp. 1173-1177 ◽  
Author(s):  
Stephen M. Hess ◽  
Mark C. Detweiler
Keyword(s):  
Problem Solving ◽  
Complex Problem ◽  
Main Task ◽  
Complex Problem Solving ◽  
Excellent Performance ◽  
The Third ◽  
Processing Demands ◽  
Problem Solving Task

Two multi-session experiments are described in which a complex problem-solving task was interrupted at different stages of practice. In Experiment 1, subjects practiced the main problem-solving task for three sessions, with intermittent interruptions during each session. By the end of Session 3, interruptions which were similar to the main task, in terms of type of material processed and processing demands, no longer disrupted performance as they had in Sessions 1 and 2. In Experiment 2, subjects practiced the same problem-solving task for two sessions without interruptions. The same types of interruptions used in Experiment 1 were introduced in Session 3. Although the main task was well learned by the third session, the interruptions disrupted subjects' main-task accuracies dramatically. These results suggest that training tasks under uninterrupted conditions can lead to excellent performance, but may not allow subjects to develop the kinds of strategies needed to flexibly recover from interruptions when they occur.

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