Thinking Strategies for Solving Problems

Copyright © 2016 by Mailoo Selvaratnam.

ISBN:   Softcover         978-1-4828-6276-8

              eBook              978-1-4828-6277-5

All rights reserved. No part of this book may be used or reproduced by any means, graphic, electronic, or mechanical, including photocopying, recording, taping or by any information storage retrieval system without the written permission of the author except in the case of brief quotations embodied in critical articles and reviews.

Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them.

Toll Free 0800 990 914 (South Africa)

+44 20 3014 3997 (outside South Africa)

www.partridgepublishing.com/africa

Contents

PREFACE

CHAPTER 1

INTRODUCTION

CHAPTER 2

CLARIFICATION AND CLEAR PRESENTATION OF PROBLEMS

CHAPTER 3

IDENTIFICATION AND FOCUSING ON THE GOAL

CHAPTER 4

IDENTIFICATION OF PRINCIPLES NEEDED FOR SOLUTIONS

CHAPTER 5

USE OF EQUATIONS FOR CALCULATIONS AND DEDUCTIONS

CHAPTER 6

PROCEEDING STEP - BY – STEP WITH THE SOLUTION

PREFACE

This monograph is intended primarily for lecturers/ instructors of high school and first year university science courses, and for motivated science students at universities, tertiary institutions and high schools. Parts of the book may also be used by persons without a science background because many problems in the monograph do not need science concepts for their solutions. The non-science problems (examples and exercises) are given first in each chapter, before the science problems, to assist readers without a science background.

The monograph discusses cognitive strategies (thinking strategies) that are fundamentally important for solving problems encountered in physical science courses. Many of these strategies are also important for solving problems encountered in our daily lives. The emphasis throughout the monograph is on the strategies one should use for solving problems efficiently, on how one should set-about solving a problem, and not just on obtaining the solution.

Cognitive strategies and skills are important because they are the tools for all types of learning and problem solving. They are also an important factor that affects our intelligence (Intelligence Quotient, IQ) and self-confidence. An important objective of all academic courses should therefore be the training of students in cognitive skills and strategies

A large amount of research evidence suggests that the learning difficulties of many students are due to their not being sufficiently competent in cognitive strategies and skills. This may be one of the important reasons for rote-learning by many students.

The Examples and Exercises in this monograph are intended to be used by teachers to train students. Training in cognitive strategies and skills is best done by integrating them, at the appropriate places, with the teaching of subject-content knowledge. Repeated training throughout a course will be needed to ensure that students become competent in them. The use of these strategies should become a habit of the mind.

I am particularly grateful to the following who contributed significantly to the improvement of the monograph: Mr. Placid Fernandez, St. Michaels High School, Mafikeng; Ms. Millicent Mongale, North-West University, Mafikeng Campus; Prof. Sebastian Canagaratna, Ohio Northern University, USA. Others whom I should thank for helping me in the preparation of the monograph are: Prof. Helen Drummond and Ms. Mathola Kefilwe from North-West University, my wife Hema, my daughter in law Wathsala Dissanayake and Mr. Thayendran Naidoo.

CHAPTER 1

INTRODUCTION

An important objective of academic courses should be the improvement of the cognitive abilities (thinking abilities) of students because they are the tools for all types of learning, decision-making and problem-solving. Competence in cognitive abilities is hence essential if students are to learn efficiently and also solve problems they encounter, not only in their academic courses but also throughout their lives.

Increased competence in cognitive abilities can also be expected to increase students’ self-confidence and develop their intelligence. Research suggests that intelligence (Intelligence Quotient, IQ) depends not only on genetic inheritance but also on ones level of competence in cognitive abilities (particularly cognitive strategies).

Intelligence can be improved by providing explicit

training in cognitive strategies and skills.

There are many types of cognitive abilities and they have been classified in different ways and at different depths of detail. A broad classification is as cognitive skills (thinking skills) and cognitive strategies (thinking strategies).

Cognitive skills are the basic building-blocks of all mental activities. Some of them are of general applicability (e.g. skills associated with reading, writing and dealing with numbers) while others are specialized. Specialized skills are often needed for the effective learning of science and this includes mathematical skills, organization skills, information-processing skills, three-dimensional visualization skills and various types of reasoning skills (e.g. deductive reasoning, inductive reasoning, and analogical reasoning).

Cognitive strategies are plans of action for guiding, controlling and executing mental tasks associated with learning and use of knowledge. They determine how we set-about learning a topic or approach the solution of a problem. Cognitive strategies are generally linked with cognitive skills and the execution of a strategy often needs competence in some cognitive skills. Unlike a cognitive skill, which is often narrow and specific to subject-content, a cognitive strategy is broad and is generally applicable to a variety of situations and contexts. Just a few cognitive strategies are needed for effective learning and problem solving, in contrast to cognitive skills where many are often needed.

Extensive research has shown that many students do not have sufficient competence in the cognitive strategies and skills needed for effective learning and problem solving. This lack of competence will seriously handicap effective learning and problem solving, and may be an important reason for rote-learning (memorization without much understanding) by many students.

The main