The Narrative of Mathematics Teachers: Elementary School Mathematics Teachers' Features of Education, Knowledge, Teaching and Personality

131 Pages·2018·3.445 MB·English

by  Dorit Patkin, Avikam Gazit

The Narrative of Mathematics Teachers
The Narrative of
Mathematics Teachers
Elementary School Mathematics Teachers’ Features of
Education, Knowledge, Teaching and Personality
Edited by
Dorit Patkin
Avikam Gazit
leiden | boston
Cover illustration: Photograph by Sara Gazit
All chapters in this book have undergone peer review.
The Library of Congress Cataloging-in-Publication Data is available online at http://catalog.loc.gov
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isbn 978-90-04-38400-2 (paperback)
isbn 978-90-04-38401-9 (hardback)
isbn 978-90-04-38406-4 (e-book)
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Contents
Preface vii
Acknowledgements xi
Notes on Contributors xii
PART 1
Teachers’ Education and Teachers’ Knowledge
1 What Should We Expect from Somebody Who Teaches
Mathematics in Elementary School? 3
Shlomo Vinner
2 Pre-Service Mathematics Teachers’ Attitudes toward
Integration of Humor in Mathematics Lessons 16
Avikam Gazit
3 Geometric Thinking Levels of Pre-Service and In-Service
Mathematics Teachers at Various Stages of Their Education 30
Dorit Patkin and Ruthi Barkai
PART 2
Teaching and Teachers’ Personality
4 A Multicultural View of Mathematics Male-Teachers at Israeli
Elementary Schools 51
Eti Gilad and Shosh Millet
5 Do “Those Who Understand” Teach? Mathematics Teachers’
Professional Image 70
Dorit Patkin and Avikam Gazit
6 Elementary School Mathematics Pre-Service Teachers’
Perception of Their Professional Image 92
Nili Mendelson
vi Contents
Root Canal 119
Avikam Gazit
Epilog 120
Dorit Patkin and Avikam Gazit
Preface
The teaching profession is not perceived as prestigious and it is commonly
believed that some teachers are forced to engage in this profession or choose it
due to lack of other alternatives. Shulman (1986) presents a cynical quotation
of Bernard Shaw: “Those who can – do and those who can’t – teach”. He slightly
changed it into the slogan of “Tomorrow’s Teachers” reform in the United States:
“Those who can – do and those who understand – teach”. Shulman emphasized
three types of knowledge that teachers need: Professional knowledge,
pedagogical knowledge and didactic-curricular knowledge (Shulman, 1987).
Teaching is not a profession which is suitable for anyone. In education,
there is a continuing challenge which aims to directly link teachers’ properties
and characteristics to an effective education and teaching. This link is very
important especially when it concerns the education of young children in
elementary school (Thomason & La Paro, 2013).
The question to be asked then is what about teachers’ personality? Studies
which have examined the factors that affect students’ attainments, illustrate
that teachers’ quality has a significant impact. Hattie (2003) conducted a
meta-analytic study of factors that affect students’ academic attainments and
found that the differences between teachers accounted for 30% of the variance
in their students’ scores. A longitudinal study of Rockoff (2004) involved
monitoring teachers for 10 years. The study found that the differences between
those teachers accounted for 23% of the variance in their students’ attainments.
There is a an educational and somewhat philosophical discussion about
teachers’ centrality and the components of the teaching profession, according
for example to Shulman’s (1987) approach. However, there is no validated
scientific platform for answering who is the good, ideal or appropriate teacher.
Wilson and Young (2005) offer three approaches to the determination of
good teachers: scholar teachers, professional teachers and moral teachers.
Scholar teachers are well educated, intellectual and apply a rich language.
Professional teachers possess subject matter knowledge and are versed in
a variety of teaching and learning methods. Moral teachers embrace caring
values, believing that their students have emotional and intellectual skills. The
third approach of caring teachers has become a leading approach in recent
years due to the caring ideas of Noddings (2012).
Many changes were introduced to teacher education during the last two
decades (Beach & Bagley, 2013). The significant change in teachers’ education
is not the acquisition of knowledge. Rather, it implies turning them into
active partners to the knowledge processing and adaptation to the students.
The implementation of ICT technology in the classroom and new methods of
viii Preface
students’ assessment have changed the interaction between teachers, students
and learning material. These changes have probably affected mathematics
teaching and mathematics teacher education programs.
The National Council of Teachers of Mathematics (NCTM, 2000) emphasizes
six principles which address overarching themes:
– Equity. Excellence in mathematics education requires equity – high
expectations and strong support for all students.
– Curriculum. A curriculum is more than a collection of activities: it must be
coherent, focused on important mathematics, and well-articulated across
the grades.
– Teaching. Effective mathematics teaching requires understanding what
students know and need to learn and then challenging and supporting them
in learning it well.
– Learning. Students must learn mathematics with understanding, actively
building new knowledge from experience and prior knowledge.
– Assessment.  Assessment should support the learning of important
mathematics and provide useful information to both teachers and students.
– Technology. Technology is essential in teaching and learning mathematics;
it impacts the mathematics that is taught and enhances students’ learning.
These themes entail three main dilemmas in the professional education of
mathematics teachers:
1. The gap between content knowledge of mathematics subject matter
and pedagogical knowledge needed to teach heterogeneous student
population generally (Jasmine & Singer-Gabella, 2011).
2. The gap between the goals of mathematics instruction, whereby stu-
dents should view mathematics knowledge as challenging and inter-
esting, and the teachers’ feelings and beliefs, which do not transcend
this purpose and mission level (Vinner, 2011).
3. The gap between the real nature of mathematics and common per-
ceptions about mathematics esoteric and alienated body of knowl-
edge that only a privileged few are able to cope with its requirements
( Dudley, 2010).
Elementary school mathematics teacher education is designed with an
emphasis on the elements of knowledge, personality and teaching methods.
Unfortunately, not always there is a balance between these elements, and as a
result both teachers and students lose out.
This book aims to present chapters written by prominent scholars of
mathematics education, referring to the following components of teachers’
image: education, knowledge, teaching and personality.
Part 1 of the book deals with teachers’ education and knowledge components.
The first chapter, written by Shlomo Vinner, discusses the realistic expectations
Preface ix
from elementary school mathematics teachers. Vinner recommends that
teacher education programs refrain from dealing with complex and unnecessary
mathematics issues which Vygotsky (1986) argues are beyond teachers’ zone
of proximal development (ZPD). Vinner suggests that in addition to the
mathematics discipline, attention should be paid to other aspects of elementary
school mathematics teaching. Chapter 2, written by Avikam Gazit, presents
a study which explored the attitudes of elementary school mathematics pre-
service female teachers towards the integration of humor in class. Humor plays
an important role in reducing anxiety and improving cognitive capabilities.
Most of the participants concurred there is room for humor in class and
expressed their willingness to introduce it in their lessons. Chapter 3, written
by Dorit Patkin and Ruthi Barkai, presents a study of van Hiele geometric
thinking levels of mathematics in-service and pre-service elementary school
teachers. The study illustrates that many of the participants are versed in the
topic of triangles and quadrilaterals on the highest thinking level. Conversely,
the percentage of those versed in the topic of circles on the third level is lower.
All the participants manifested a lack of mastery on the two highest levels as far
as solids were concerned.
Part 2 of the book deals with teachers’ components of teaching and
personality. The first chapter in this part (Chapter 4), written by Eti Gilad and
Shosh Millet, compares the motives and role perception of elementary school
mathematics male-teachers who belong to different cultures: Israeli-born,
Ethiopian immigrants, former USSA immigrants and Bedouins. The Israeli-
born and former USSR immigrant teachers choose to engage in mathematics
teaching on the basis of internal motives, such as sense of vocation, ambition
to nurture the future generation or a wish to continue in a known state of
learning. On the other hand, the internal motives of Ethiopian immigrants
and Bedouins are integrated with external motives, such as wages, working
conditions and social rewards. Chapter 5, by Dorit Patkin & Avikam Gazit,
describes a study which examines the professional and personal self-image of
elementary school mathematics teachers. According to the research findings,
teachers maintain they embody most of the ideal properties while rejecting
characteristics which are considered as unsuitable for teaching. The study found
almost no significant differences between experienced and novice teachers.
The last chapter (Chapter 6) is written by Nili Mendelson. It discusses a study
which investigates the professional image of elementary school mathematics
pre-service teachers in comparison with teachers of other disciplines’ image.
The professional image was examined by means of a picture/metaphor series.
The two figures with whom the participants identified to the greatest extent
were the conductor and the animal keeper. At the same time, there was a
sweeping rejection of the judge and animal trainer figures.
x Preface
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