PHENOMENOGRAPHY AS A
RESEARCH METHODOLOGY
SANDRA HERBERT
SCHOOL OF EDUCATION
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THIS PRESENTATION
• phenomenography
• conceptions of rate as an example
• data collection
• analysis → categories → outcome space
• Discussion
• Other example if time permits
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PHENOMENOGRAPHY
Research method adapted for mapping the
qualitatively different ways in which people
experience, conceptualise, perceive, and
understand various aspects of, and phenomena
in, the world around them
(Marton, 1986, p. 31)
• aims to:
reveal categories of description
delineated by dimensions of variation
emerging from data & hence,
structuring categories into outcome space
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WHY PHENOMENOGRAPHY?
• demonstrated efficacy in a range of educational
research including mathematics.
• focus on ideas expressed by the group of participants.
–attempts to describe phenomenon as seen by participants.
• variation in conceptions is expected.
• identify variation (categories of description).
–diversity of students → range of variation
–structure categories into an outcome space
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OUTCOME SPACE
• structured set of categories of description
• one category likely to display “correct meaning,
correct knowledge or correct understanding” (Webb,
1996)
–as accepted by community of practice
• other categories display less complete understanding
• individual may hold >1 conception.
• outcome space considered to be final result of
phenomenographic investigation (Marton,1988).
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ANALYSIS
• each data source considered several times
• categories of description
–groupings of meaning statements
• dimensions of variation
–themes of expanding awareness
• emerged from data over many iterations
• categories delineated in terms of dimensions
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OVERVIEW OF
PHENOMENOGRAPHIC STUDY
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THIS PHENOMENOGRAPHIC
STUDY
•Investigating conceptions of rate
• Selection of sample:
– aim for maximum variation;
– 20 diverse Year 10 students.
• Conduct interviews:
– phenomenographic video-recorded semi-structured interviews
– based on computer simulations, enabling exploration of constant & variable rate
in multiple representations
• Phenomenographic analysis of responses to reveal students’
conceptions
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DATA COLLECTION
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Consistent
presentation to
ensure attention
to same
phenomenon
PHENOMENOGRAPHIC
ANALYSIS OF THIS STUDY
• immersion in data.
–each video repeatedly viewed.
–gestures used to give insights into meaning of words
• pooling & grouping of meaningful responses from
data into meaning statements.
• grouping of meaning statements into initial
categories.
• formation of initial dimensions
• final dimensions & categories developed over
many iterations.
• categories structured into outcome space.
– based on dimensions
– probably hierarchical.
–some categories more complex & complete.
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EVOLUTION OF
CATEGORIES & DIMENSIONS
• interviews transcribed
–checked against audio & video
• immersion
in data
• interpret gist of participants’ verbal & non-verbal
communications
• set of meaning statements
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Transcript
it goes up three point two meters
every half a meter
Interpretation
• suggests understanding of rate involving constant change in one
variable wrt unit change of another variable.
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Transcript
R: what do you think the graph [of non-rectangle window] might look like? [long
pause]
S: I don’t think it would be a straight line [pause] because this window’s not
square hmm I dunno because its up the top umm curved there [pause] umm a
straight line means its always the same
R: what’s always the same?
S: the umm
Interpretation of Gestures
• identified key differences in rate for the window
• gestures communicate awareness that graph of
curved section not the same rectangular section.
• constant rate results in linear graph
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MEANING STATEMENTS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Students see rate, which may vary, as a quantitative relationship between two
quantities which may vary.
Students see rate, which may vary, as a qualitative relationship between two
quantities which may vary.
Students see rate as a single number measuring a constant relationship between
two quantities which may vary.
Students see rate as a two numbers representing a constant relationship between
two quantities which may vary.
Students see rate as a constant relationship between two quantities.
Students see rate as a comparison between two quantities.
Students see rate as a relationship between two quantities.
Students see rate as something to do with change.
Students see rate as speed.
Students see rate as something to do with time.
Students see rate as something to do with fractions.
Students see rate as an amount.
Students see rate as the result of a formula calculation.
Students see rate as a single number measuring something at a particular stage.
Students see rate as a word they’ve heard eg. birth rate, interest rate
Students see rate as nothing at all.
Students see rate as something to do with maths
Students see rate as something to do with two quantities
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16.
15.
11.
17.
12.
13.
14.
Students see rate as nothing at all.
Students see rate as a word they’ve heard eg. birth rate,
interest rate, council rates.
Students see rate as something to do with fractions.
Students see rate as something to do with maths
8.
Students see rate as an amount.
Students see rate as the result of a formula calculation.
Students see rate as a single number measuring something at a
particular stage.
Students see rate as something to do with change.
9.
10.
Students see rate as speed.
Students see rate as something to do with time.
6.
18.
7.
Students see rate as a comparison between two quantities.
Students see rate as something to do with two quantities
Students see rate as a relationship between two quantities.
5.
Students see rate as a constant relationship between two
quantities.
Students see rate as a two numbers representing a constant
relationship between two quantities which may vary.
Students see rate as a single number measuring a constant
relationship between two quantities which may vary.
4.
3.
2.
1.
Students see rate, which may vary, as a qualitative relationship
between two quantities which may vary.
Students see rate, which may vary, as a quantitative relationship
between two quantities which may vary.
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GROUPING
OF MEANING
STATEMENTS

CATEGORIES
VERSION 1
• 5 categories & 3 dimensions
• categories of description
1.
2.
3.
4.
5.
Rate is seen as abstract concept that can be applied to variety of contexts ( with subcategories or >1 category?)
Rate is seen as something to do with motion.
Rate is seen as something to do with time but not motion OR is this motion but not
time?
Rate is seen as a mathematical concept, but not even understood in application to
motion
Rate is not seen
• dimensions of variation
1.
2.
3.
Type of Rate: with attributes ‘constant’ & ‘variable’
Context: with attributes ‘speed’ & ‘not-speed’
Relationship: with attributes ‘qualitative’ & ‘quantitative’
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ITERATIVE PROCESS
• consideration of structure of outcome space
–least to most complex
• some categories more complex & complete than
others
–include aspects of awareness of earlier categories
• more detail in descriptions of categories
–return to data
–focus on how rate was experienced with less emphasis
on what the participants did or said
–ask “Can these be grouped?” “Are there examples of
things that students say/do which illustrate this
category?”
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VERSION 5
• Dimensions of Variation
• another 2 dimensions added
– Property attributed to rate: with attributes ‘quality’ & ‘quantity’
– Characteristics of property: with attributes ‘1-fixed’, ‘1-changing’, ‘2changing’
• labels & attributes of other dimensions changed
– Context became Related variables: with attributes ‘distance&time’ &
‘any pair’
– Type of rate & Relationship were combined in ‘nature of
relationship’ with attributes with attributes ‘qualitative’, ‘quantitativeconstant’& ‘quantitative-variable’
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VERSION 5
Categories
1.
2.
3.
4.
5.
6.
7.
8.
Rate is experienced as a word
Rate is experienced as the result of a formula
calculation
Rate is experienced as a change in a quality
Rate is experienced as a change in a single quantity
Rate is experienced as the relationship between two
changing quantities
Rate is experienced as the relationship between two
changing quantities of distance and time i.e. speed
Rate is experienced as an unchanging numeric
relationship between two changing quantities
Rate is experienced as a numeric relationship between
two changing quantities
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VERSION 9
Dimensions of Variation
1.
2.
3.
4.
Focus on word ‘rate’
Focus on variables
Focus on relationship between variables
Focus on nature of related variables
Categories
Rate is experienced as :A. a word rating a quality
B. a word associated with a numeric value
C. the result of a formula calculation with little meaning
D. a single quantity
E. a relationship between two changing quantities
F. a constant numeric relationship between two changing quantities
G. a numeric relationship between two changing quantities of distance and time
i.e. speed
H. a numeric relationship between any two changing quantities
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Rate experienced as a word
associated with something numeric
Rate experienced as formula
calculation
Rate experienced as a single
quantity
EVENTUALLY!!
Rate experienced as rating of a
quality
Rate experienced as qualitative
relationship b/w 2 changing
quantities
Rate experienced as constant
numeric relationship b/w 2
changing quantities
Rate experienced as speed
Rate experienced as numeric
relationship b/w any 2 changing
quantities
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RATE OUTCOME
SPACE
STRUCTURED BY DIMENSIONS
Categories of Description
Dimension
Attribute
Word ‘rate’
Quality
Quantity
Variables
One - fixed
One - changing
Two - changing
Relationship Qualitative
Quantitative constant
Quantitative variable
Nature of
Distance & time
variables
Any pair
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A
B
C
D
E
F
G
H
ARTICLES UTILISING
PHENOMENOGRAPHY
Herbert, S. & Pierce, R. (2013). Gesture as data for a phenomenographic analysis of mathematical
conceptions. International Journal of Educational Research, 60, 1 - 10.
Herbert, S. & Pierce, R. (2012). Revealing educationally critical aspects of rate. Educational
Studies in Mathematics. 81 (1), 85-101
Herbert, S. , Vale, C., Loong, E., Bragg, L. & Widjaja, W. (submitted). Developing a framework for
primary teachers’ perceptions of Mathematical Reasoning. Educational Studies in Mathematics
Herbert, S. & Lynch, J. (in progress). Teachers’ Perceptions of Classroom Animals: A
Phenomenographic Study
Sandra Herbert
sandra.herbert@deakin.edu.au
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OTHER EXAMPLES
•Teachers’ perceptions of mathematical
reasoning - ESM
•Teachers’ perceptions of classroom animals
– forthcoming
•Teachers’ responses to AC:Science –
collecting data
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MEANING STATEMENTS
Teachers see mathematical reasoning as:
expressing ideas
describing actions
giving reasons for actions
justifying actions
proving
discriminating between choices - selection
communication to oneself - self talk
evaluation of an argument
not relevant to younger years
making connections
application of prior knowledge
about learning curriculum content
solving word problems
an indicator of mathematical ability
an important part of mathematics which
needs improvement
a series of logical steps
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solving open-ended problems
needing less structured lessons
justifying to another person.
part of every mathematics lesson
metacognition
language necessary to reason with
inference from evidence
similar to reasoning in other curriculum
areas
discussing with another person
different from content
thinking
looking for patterns
generalising
Grouping of Meaning
Statements  Initial
Categories
CATEGORIES AND OUTCOME
SPACE BASED ON DIMENSIONS
Audience
Self
Others
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Purpose
Recount
Compare/ Contrast
Make choices
Explain
Argue step-by-step
Articulate reasons
Justify
Hypothesise
Generalise
Prove
Evaluate
Connect
Presentation
Verbal
Symbolic
Diagram/Written
Gesture (action)
Type of reasoning
Adaptive
Inductive
Deductive
Inferential
Structure of outcome space
Dimension
Attribute/Value
Audience
Self
Others
Purpose
Recount
Compare/Contrast
Make choices
Explain
Argue step-by-step
Articulate reasons
Justify
Hypothesise
Generalise
Prove
Evaluate
Connect
Presentation
Verbal
Symbolic
Diagram/written
Gesture (action)
Type of
Adaptive
Reasoning
Inductive
Deductive
Inferential
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Categories of Description
A
B
C
D
E
F
G
OUTCOME SPACE OF PRIMARY
TEACHERS' PERCEPTIONS OF
MATHEMATICAL REASONING
Category
Category A
Category B
Category C
Category D
Category E
Category F
Perception of mathematical reasoning
Reasoning is perceived to be thinking.
Reasoning is perceived to be communicating thinking
Reasoning is perceived to be problem solving
Reasoning is perceived to be validating thinking
Reasoning is perceived to be forming conjectures
Reasoning is perceived to be using logical arguments for
validating conjectures
Category G Reasoning is perceived to be connecting aspects of
mathematics
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MEANING STATEMENTS
Classroom animals
•
•
•
•
•
•
•
•
•
•
•
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Classroom animals are seen to be an opportunity for science education
Classroom animals are seen to be an opportunity for humane education
Classroom animals are seen to be an opportunity for addressing inequity
Classroom animals are seen to be an inconvenience
Classroom animals are seen to be an ethical dilemma
Classroom animals are seen to be a media opportunity
Benefits of classroom animals are seen to be dependent on the type of
animal
Benefits of classroom animals are seen to be dependent on the teacher
Classroom animals are seen to involve a cost (emotional cost, time cost,
financial cost, space costs)
Classroom animals are seen as an opportunity for student social-emotional
development
Classroom animals are seen an opportunity for cross-curricular learning and
enquiry learning
Classroom animals are seen an opportunity for connections (between home
and school; in-class and out-of-class; and classroom and yard/other physical
spaces/locations)
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DIMENSIONS
Curriculum
Social/emotional
Cost
Connections
science
responding to
disadvantage
ethical
inconvenience
financial
wider
community
home
personal
development
motivation
space
out of class
emotional
cross curricula
humane
other
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OUTCOME SPACE OF PRIMARY
TEACHERS' PERCEPTIONS OF
CLASSROOM ANIMALS
Category
Perception of classroom animals
Category A
Classroom animals are perceived to be valuable for science
education.
Classroom animals are perceived to be valuable for humane
education.
Classroom animals are perceived as an opportunity for cross
curriculum learning
Classroom animals are perceived to be an added burden in the
classroom
Classroom animals are perceived to provide opportunities for
links to outside the classroom
Category B
Category C
Category D
Category E
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Example: Lee and Gerber (1999) a study of Hong Kong school
students’ perceptions of graphs, charts and maps
Outcome space consists of a set of 5 categories of description
Category 1
Graphics are seen as ordinary drawings
Category 2
Graphics are seen as partially interpreted
macro representations
Category 3
Graphics are seen as portraying localised
patterns
Category 4
Graphics are seen as representing spatial
relationships
Category 5
Graphics are seen as providing the basis for
reflection, extrapolation and prediction
Ordering of categories from least to most complex
Learning – moving from a category to higher category
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EXAMPLE: COPE (2002) A STUDY OF IT STUDENTS’ CONCEPTIONS OF
INFORMATION SYSTEMS
OUTCOME SPACE CONSISTS OF A SET OF 6 CATEGORIES OF DESCRIPTION
ORDERED FROM MOST TO LEAST COMPLEX
Category 6
A number of communicating information systems within a
single organisation
Category 5
A computerised data manipulation system and all the people
and the data-related procedures they perform to support a
single organisational function.
Category 4
A computerised data manipulation system supporting many
people within a single organisational function.
Category 3
A data manipulation system supporting an individual within a
single organisational function.
Category 2
A simple information retrieval system.
Category 1
A personal search of a static information
source
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SIMULATIONS WITH GSP
• enable exploration of constant & variable rate in
multiple representations
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GEOMETERS’ SKETCHPAD
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SIMULATIONS WITH JMW
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