Math Matters: a Pedagogy of Remediation

MATH MATTERS:

A PEDAGOGY

OF REMEDIATION

________________________________________

Clement B.G. London, Ed.D.;

Chuka P.B. Ejiofor, Ph.D.;

Pearl C. London, P.D.

Copyright © 2005 by Clement B.G. London, Ed.D.; Chuka P.B.

Ejiofor, Ph.D.; Pearl C. London, P.D.

All rights reserved. No part of this book may be reproduced or transmitted in

any form or by any means, electronic or mechanical, including photocopying,

recording, or by any information storage and retrieval system, without permission

in writing from the copyright owner.

To order additional copies of this book, contact:

Xlibris Corporation

1-888-795-4274

www.Xlibris.com

[email protected]

19779

CONTENTS

Preface

Environmental Factors and

Personality Development

In Formative Years

Does Learning Produce A

Change in Behavior?

Triple Context: Demography,

Diversity, and Democracy

Language: A Basis for

Teaching and Learning Math

Test-Taking Skills:

Guidelines For Curricular And

Instructional Practices

Comments/observations

Works Cited

Notes

About the Authors

Preface

A major question for all teachers is an understanding of the dynamics of developmental procedures for transformative education. Such procedures should always involve democratic, intellectual, and social constructs that, in the final analysis, would aim to emancipate the individual human being and liberate all citizens.

Issues surrounding the beginning of a discourse on mathematics teaching and learning or, for that matter, any of the disciplines, should, of necessity, begin with the formative years of children. The fact of the matter is that the success or failure in the learning and teaching of mathematics seems to have their bases in early environmental factors which contribute to the personality development of individuals during the formative years that lie between the ages one and six.

Based in part on the findings of numerous research studies, it is hypothesized here that understanding the dynamics of the magic years of children and society becomes necessary, especially when dealing with the discipline of mathematics, in the teaching-learning transactions of education. Why is there such a dearth of teachers of mathematics in many public schools, internationally, and an obvious scarcity of students and teachers seriously pursuing the discipline of mathematics with vigor, locally, regionally, or nationally?

This is true in the case of developed countries, which celebrate and honor technology, and are steeped in the by-product of information processing. As such, the problems associated with mathematics teaching are international in scope. The teaching and learning of mathematics continue to be problematic for many, especially educators; and it remains an area that begs further investigation. At issue is the salient question as to how we may address related problems. Do we seek to improve standard operating procedures or, altogether, chart new trails? The issues require careful, refreshing and comprehensive educational procedures; hence the legitimacy of this book!

The contents of this book should interest a wide range of educators, researchers, schools of education, teachers, parents, and community organizations. The book may be used as a primary or secondary source in courses in teacher preparation, staff development, parenting, human relations, early childhood education, as well as deliberations on administrative change processes in schools. Pre-service and in-service specialists will find relevant information in planning as well as the suggestion of teaching and learning strategies of presenting lessons of mathematics in classrooms.

The authors bring together several years of appropriate educational expertise in an honest attempt to address those problems, by using those techniques which are grounded in research, and the teaching and learning of mathematics. We begin the discussion with pertinent information on basic factors of environmental issues, personality development and the criticality of the effects of those developmental factors in relation to teaching and learning, generally and specifically.

The discussion continues with investigation into the question as to whether learning produces any changes in behavior. This is followed by a discussion that takes a critical investigation of the triple contexts that explain the effect of demography, democracy, and diversity on teaching and learning.

Language receives appropriate attention and is examined as a basis for teaching and learning mathematics. The discourseconsiders the implication of the multiplicity of languages in classrooms and the pervasiveness of cultural nuances that are conditioned by immigration and relevant demographic changes. Some dynamics of multicultural education are factored into the discussion, with ample attempts that direct attention to the presence of classroom diversity, within the context of the democratic process at work.

Altogether, efforts remain rooted in the notion that the formative, magic years of early childhood education are honored, as preferred points of initiation. This is accepted, not only because research supports our point of view in this discourse, but also because there is much scholarly conviction that derives its sustenance from the combined teaching experiences of the authors of this book.

At the completion of a mathematics presentation, it becomes necessary to evaluate its success. Such expectation gives authenticity to pedagogical efforts. The topic on test-taking skills and guidelines for curricular practices find their meaningfulness in the success of the teacher or instructor. A class is as successful as its teacher.

We thank those individuals who helped us to prepare this book; above all: those parents, their children and their children’s teachers who inspired us to address the various components of this book.

We also thank our colleagues of elementary, secondary, and tertiary levels of education for their contributions regarding their conceptualizations in this conversation about the teaching and learning of mathematics.

Clement B.G. London

Chuka P. B. Ejiofor

Pearl C. London

"The great object of education should be commensurate

with the object of life."

Ralph Waldo Emerson, 1803-1883.

Environmental Factors and

Personality Development

In Formative Years

It is said that personality develops among children as a result of the constant interactions between and among those persons who are closest to them, as well as how successfully children learn to respond to their environment.

The individuality of children should not be overlooked in child rearing and personality development. There should not be any glittering generalities as to what is good or bad for children, because one child’s capacity, problems, or shortcomings may not necessarily be applicable to another. Each child is endowed with her/his own script.

Since parents are usually the first influential persons or teachers, in the overall development of their children, it is necessary for parents to study the characteristics and needs of their children; and make the necessary accommodations to help them through those earliest and most important years. This is the ideal, but the real may be that such awesome responsibility may be delegated to someone else. In today’s world, that is a factor, as schools andother related institutions in many instances, often assume that function. Each child at birth is custom-made.

Neonates are known to function on the gratification of impulses. However, it is the duty of parents to gradually establish some routines and regulations for their children without creating undue frustration. Parents are expected to be always aware of the fact that among the developmental phases of children, there are certain well-defined issues; and that care-givers must take into consideration what those particular stages are, and also what the capacities and abilities children seem to suggest.

Hence, the act of caring for the neonate, the toddler, and the preschooler will differ considerably on the basis of the differing types of stimuli administered. Also, because of the different types of responses each child is expected to make. During any stage, however, children must be spared of great anxiety-producing situations. If the environment produces excessive anxiety within children, it is possible that they may eventually become neurotic, unstable, hostile or withdrawn.