Variation is good – Math book is bad
Connecting typologies to dichotomous wording
[email protected]
Aim in the whole study
Aim in the paper
To investigate the development
of novice primary school
teachers’ professional identity.
The aim is to investigate this
development as seen from the
perspective of the teachers
themselves.
To connect two parts from this
study, a dichotomy and three
typologies, and show how this
connection offers a multifaceted
meaning of the otherwise
seemingly static statements in
the dichotomy.
To show the need of socially
orientated ethnographic inspired
research.
Disposition
1.
2.
3.
4.
5.
6.
7.
The study
Data collection
Analysis
Theoretical framing
Dichotomy
Typologies
The connection
The study
• A case study of seven novice primary school mathematics
teachers.
• Identity as ”a special kind of person” (Gee, 2000-2001).
• Etnographic approach: Understand the meaning activities
have to individuals and how individuals understand
themselves and others (Arvatson & Ehn, 2009; Aspers,
2007; Hammersley & Atkinsson, 2007).
• Reaching such an understanding requires, according to
Aspers (2007), interaction.
Data Collection
• Observations, Interviews (formal and informal) and selfrecordings.
• The time has been used in a selective, intermittent way,
which means that the time taken for fieldwork, from
starting to stopping, has been long (two years) but with a
flexible frequency regarding the field visits.
• The empirical materials are treated as, named by Aspers
(2007), complete-empiricism, implying all the material
constitutes a whole that the analysis is based on. “Thick
descriptions”
Analysis
•
•
Analysis is not a separate part of ethnography but starts in the pilot study and
continues through the fieldwork and the writing process (Hammersley &
Atkinson, 2007).
The analysis has been conducted using methods inspired by the
constructivists’ grounded theory (Charmaz, 2006) to create categories.
transcribe
initial coding: line by line/incident by incident
focused coding
axial coding
theoretical coding
•
The dichotomy and the typologies are two such created categories.
Theoretical framing
Identity &
Identity Deveopment
•Wenger’s (1998) communities
of practice.
Discover patterns of
participation by being
present. Understand the
meaning activities have to
individuals and how
individuals understand
themselves and others…
The professional part of
professional identity
• Patterns of participation, a shift
from objectified beliefs to
individuals’ patterns of
participation in social practices
(Skott, 2010).
• The same patterns of
participation are valid also as prereified mathematical knowledge
for teaching.
The dichotomy
Innovative mathematics teaching
The teacher
reformative
creative
autonomous
daring
up-to-date
The teaching
reveals different ways of thinking
group work
concrete
student-focused
reality-based
integrated with other subjects
varied
focused on processes and problems
mathematics is hidden
connected components
The outcome of the teaching
cooperating students
active students
many solutions to a problem
motivated students
comfortable students
students having fun
students understanding
mathematics becomes interesting
Traditional mathematics teaching
The teacher
conservative
controlled by the math book
heteronomous
weak
stagnant
The teaching
reveals only one way of thinking
solo work
abstract
student-distanced
reality-distanced
separate from other subjects
repetitive, based on the math book
focused on products
mathematics is visible
separate components
The outcome of the teaching
students working alone
passive students
one solution to a problem
uninterested students
uncomfortable students
students being bored
students not understanding
mathematics becomes uninteresting
Gunilla:
I believe many teachers would like this
[pointing to the left side of the dichotomy].
Helena:
Gunilla:
Nina:
Gunilla:
Nina:
Yes.
But they feel unsure about covering everything.
Mm.
Will we reach our goals working like this? Do I
dare step away from the math book, leaving
this traditional and safe way of working? Or
will I risk my students failing? […]
And above all, this way of working [pointing to
the left side of the dichotomy] takes a lot more
time for the teacher. I feel that.
The typologies
• The coach-orientated mathematics teacher
The main focus of the coach-orientated mathematics teacher is to teach the student how to
organise and take responsibility for their own learning. These teachers, in both talk and action,
foster team spirit in the class and encourage students to help each other and they want their
students to develop strategies for self-help.
• The content-orientated mathematics teacher
The main focus of the content-orientated mathematics teacher is how the content is to be
treated in the teaching and learning. These teachers, in both talk and action, focus on how
different content can be represented and understood.
• The emotion-orientated mathematics teacher
The main focus of the emotion-orientated teacher is the students’ emotions and self esteem.
These teachers, in both talk and action, focus on the students’ emotional experiences of the
teaching and learning and on creating positive attitudes towards mathematics.
The connection
Variation is good – Math book is bad
The coach-orientated
mathematics teacher
The emotion-orientated
mathematics teacher
The content-orientated
mathematics teacher
Variation is good
According to the coach-orientated mathematics teacher, variation implies
organising the learning environment in different ways with the purpose of
making it possible for every student to find their best way of learning.
According to the content-orientated mathematics teacher, variation implies
representing the mathematical content in different ways with the purpose of
giving the students an opportunity to gain a richer understanding.
According to the emotional orientated mathematics teacher, variation implies
doing lots of different things during the mathematics lessons with the purpose
of the students perceiving the teaching, and therefore also mathematics, as fun.
Math book is bad
According to the coach-orientated mathematics teacher, the math book is bad
as it is not the best way for all children to learn.
According to the content-orientated mathematics teacher, the math book is bad
as it represents mathematics in one way only, which works against students
gaining a richer understanding of mathematics.
According to the emotional orientated mathematics teacher, the math book is
bad because it is boring and, working in the math book results in students
thinking of mathematics as boring.
Gunilla:
I believe many teachers would like this [pointing to
the left side of the dichotomy].
Helena:
Gunilla:
Nina:
Gunilla:
Nina:
Yes.
But they feel unsure about covering everything.
Mm.
Will we reach our goals working like this? Do I
dare step away from the math book, leaving
this traditional and safe way of working? Or
will I risk my students failing? […]
And above all, this way of working [pointing to
the left side of the dichotomy] takes a lot more
time for the teacher. I feel that.
”This” … takes a lot more time
For the coach-orientated mathematics teacher and the emotion-orientated
teacher, the extra time would, in general, imply the same use, organising the
learning environment in different ways.
Their reasons for doing this would, however, differ. For the coach-orientated
teacher, the aim would be to offer activities where each student could find their
best way of learning. For the emotion-orientated teacher, the aim would be to
enable the students to have fun.
For the content-orientated mathematics teacher, the time factor regarding
variation would, instead, imply planning and teaching the mathematical content
using different representations. The reason for this would be to give the
students a richer understanding of mathematics.
As such, the coach-orientated mathematics teacher and the content-orientated
teacher have the same reason for variation, students should learn mathematics,
but they would try to achieve this in different ways with different meanings for
the word variation.
The dichotomy
Innovative mathematics teaching
The teacher
reformative
creative
autonomous
daring
up-to-date
The teaching
reveals different ways of thinking
group work
concrete
student-focused
reality-based
integrated with other subjects
varied
focused on processes and problems
mathematics is hidden
connected components
The outcome of the teaching
cooperating students
active students
many solutions to a problem
motivated students
comfortable students
students having fun
students understanding
mathematics becomes interesting
Traditional mathematics teaching
The teacher
conservative
controlled by the math book
heteronomous
weak
stagnant
The teaching
reveals only one way of thinking
solo work
abstract
student-distanced
reality-distanced
separate from other subjects
repetitive, based on the math book
focused on products
mathematics is visible
separate components
The outcome of the teaching
students working alone
passive students
one solution to a problem
uninterested students
uncomfortable students
students being bored
students not understanding
mathematics becomes uninteresting
References
Arvastson, G. & Ehn, B. (2009) Etnografiska observationer. [Ethnographic
observations] Studentlitteratur AB
Aspers, P. (2007) Etnografiska metoder. [Ethnographic methods] Liber AB
Charmaz, K. (2006). Constructing Grounded Theory. A Practical Guide
Through Qualitative Analysis. London: SAGE Publications Ltd.
Gee, J.P. (2000-2001) Identity as an analytic lens for research in education.
Review of Research in Education. 25, 99-125
Hammersley, M. & Atkinson, P. (2007) Ethnography. Principles in practice.
Third edition. Routledge
Skott, J. (2010) Shifting the Direction of Belief Research: From Beliefs to
Patterns of Participation. In: Pinto, M.F. & Kawasaki, T.F. (Eds) Proceedings
of the 34th Conference of the International Group for the Psychology of
Mathematics Education. (Vol. 4, pp. 193-200). Belo Horizonte, Brazil: PME
Wenger, E. (1998) Communities of Practice. Learning, Meaning and, Identity.
Cambridge: Cambridge University Press.