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PHENOMENOGRAPHY AS A RESEARCH METHODOLOGY
SANDRA HERBERTSCHOOL 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 descriptiondelineated by dimensions of variationemerging 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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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
Consistent presentation to ensure attention to same phenomenon
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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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Interpretation•suggests understanding of rate involving constant change in one variable wrt unit change of another variable.
Transcript
it goes up three point two meters
every half a meter
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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
TranscriptR: 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
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MEANING STATEMENTS1. Students see rate, which may vary, as a quantitative relationship between
two quantities which may vary. 2. Students see rate, which may vary, as a qualitative relationship between two
quantities which may vary. 3. Students see rate as a single number measuring a constant relationship
between two quantities which may vary. 4. Students see rate as a two numbers representing a constant relationship
between two quantities which may vary. 5. Students see rate as a constant relationship between two quantities.6. Students see rate as a comparison between two quantities. 7. Students see rate as a relationship between two quantities.8. Students see rate as something to do with change. 9. Students see rate as speed. 10. Students see rate as something to do with time.11. Students see rate as something to do with fractions. 12. Students see rate as an amount. 13. Students see rate as the result of a formula calculation. 14. Students see rate as a single number measuring something at a particular
stage. 15. Students see rate as a word they’ve heard eg. birth rate, interest rate16. Students see rate as nothing at all.17. Students see rate as something to do with maths18. Students see rate as something to do with two quantities
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GROUPING OF MEANING STATEMENTS
CATEGORIES
16. Students see rate as nothing at all.15. Students see rate as a word they’ve heard eg. birth rate,
interest rate, council rates.11. Students see rate as something to do with fractions. 17. Students see rate as something to do with maths
12. Students see rate as an amount. 13. Students see rate as the result of a formula calculation. 14. Students see rate as a single number measuring something at
a particular stage. 8. Students see rate as something to do with change.
9. Students see rate as speed. 10. Students see rate as something to do with time.
6. Students see rate as a comparison between two quantities. 18. Students see rate as something to do with two quantities7. Students see rate as a relationship between two quantities.
5. Students see rate as a constant relationship between two quantities.
4. Students see rate as a two numbers representing a constant relationship between two quantities which may vary.
3. Students see rate as a single number measuring a constant relationship between two quantities which may vary.
2. Students see rate, which may vary, as a qualitative relationship between two quantities which may vary.
1. Students see rate, which may vary, as a quantitative relationship between two quantities which may vary.
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VERSION 1
•5 categories & 3 dimensions
•categories of description1. Rate is seen as abstract concept that can be applied to variety of contexts
( with sub- categories or >1 category?)2. Rate is seen as something to do with motion.3. Rate is seen as something to do with time but not motion OR is this motion
but not time?4. Rate is seen as a mathematical concept, but not even understood in
application to motion5. Rate is not seen
•dimensions of variation
1. Type of Rate: with attributes ‘constant’ & ‘variable’
2. Context: with attributes ‘speed’ & ‘not-speed’
3. 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’, ‘2-changing’
•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’, ‘quantitative-constant’& ‘quantitative-variable’
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VERSION 5
1. Rate is experienced as a word2. Rate is experienced as the result of a formula
calculation3. Rate is experienced as a change in a quality4. Rate is experienced as a change in a single
quantity5. Rate is experienced as the relationship between
two changing quantities6. Rate is experienced as the relationship between
two changing quantities of distance and time i.e. speed
7. Rate is experienced as an unchanging numeric relationship between two changing quantities
8. Rate is experienced as a numeric relationship between two changing quantities
Categories
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VERSION 9Dimensions of Variation 1. Focus on word ‘rate’2. Focus on variables3. Focus on relationship between variables4. Focus on nature of related variables
Categories Rate is experienced as :-
A. a word rating a qualityB. a word associated with a numeric valueC. 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 OUTCOME SPACE
Rate experienced as a word associated with something numeric
Rate experienced as constant numeric relationship b/w 2
changing quantities
Rate experienced as a single quantity
Rate experienced as numeric relationship b/w any 2 changing
quantities
Rate experienced as rating of a quality
Rate experienced as qualitative relationship b/w 2 changing
quantities
Rate experienced as speed
Rate experienced as formula calculation
EVENTUALLY!!
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Categories of Description
Dimension Attribute A B C D E F G H
Word ‘rate’ Quality
Quantity
Variables One - fixed
One - changing
Two - changing
Relationship Qualitative
Quantitative constant
Quantitative variable
Nature of Distance & time
variables Any pair
STRUCTURED BY DIMENSIONS
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Sandra [email protected]
ARTICLES UTILISING PHENOMENOGRAPHYHerbert, 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
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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
expressing ideasdescribing actions giving reasons for actions justifying actionsprovingdiscriminating between choices - selectioncommunication to oneself - self talkevaluation of an argumentnot relevant to younger yearsmaking connectionsapplication of prior knowledgeabout learning curriculum contentsolving word problemsan indicator of mathematical abilityan important part of mathematics which needs improvementa series of logical steps
Teachers see mathematical reasoning as:
solving open-ended problemsneeding less structured lessonsjustifying to another person.part of every mathematics lessonmetacognitionlanguage necessary to reason withinference from evidencesimilar to reasoning in other curriculum areasdiscussing with another persondifferent from contentthinkinglooking for patternsgeneralising
Grouping of Meaning Statements Initial Categories
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CATEGORIES AND OUTCOME SPACE BASED ON DIMENSIONS
Audience Purpose Presentation Type of reasoningSelf Recount Verbal Adaptive
Others Compare/ Contrast Symbolic Inductive Make choices Diagram/Written Deductive Explain Gesture (action) Inferential Argue step-by-step Articulate reasons Justify Hypothesise Generalise Prove Evaluate Connect
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Structure of outcome space Categories of Description
Dimension Attribute/Value A B C D E F G
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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OUTCOME SPACE OF PRIMARY TEACHERS' PERCEPTIONS OF MATHEMATICAL REASONING
Category Perception of mathematical reasoning
Category A Reasoning is perceived to be thinking.
Category B Reasoning is perceived to be communicating thinking
Category C Reasoning is perceived to be problem solving
Category D Reasoning is perceived to be validating thinking Category E Reasoning is perceived to be forming conjectures
Category F 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 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)
Classroom animals
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DIMENSIONSCurriculum Social/emotional Cost Connections
science responding to disadvantage
inconvenience wider community
humane ethical financial home
other personal development
space out of class
motivation emotional cross curricula
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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.
Category B Classroom animals are perceived to be valuable for humane education.
Category C Classroom animals are perceived as an opportunity for cross curriculum learning
Category D Classroom animals are perceived to be an added burden in the classroom
Category E Classroom animals are perceived to provide opportunities for links to outside the classroom
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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
Ordering of categories from least to most complexLearning – moving from a category to higher category
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
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EXAMPLE: COPE (2002) A STUDY OF IT STUDENTS’ CONCEPTIONS OF INFORMATION SYSTEMSOUTCOME 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 informationsource
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SIMULATIONS WITH GSP
•enable exploration of constant & variable rate in multiple representations