Patterns in Education: Linking Theory to Practice Theodore Frick Department of Instructional Systems Technology School of Education Indiana University Bloomington Oct.

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Transcript Patterns in Education: Linking Theory to Practice Theodore Frick Department of Instructional Systems Technology School of Education Indiana University Bloomington Oct. 

Patterns in Education: Linking
Theory to Practice
Theodore Frick
Department of Instructional Systems Technology
School of Education
Indiana University Bloomington
Oct. 13, 2006
Patterns in Education, AECT 2006
1
Overview of APT&C





Analysis of Patterns in Time and
Configuration: APT&C
Fundamental change in perspective for
measurement and analysis
Bridges quantitative and qualitative
paradigms
APT for temporal patterns (both joint and
sequential occurrences of events)
APC for structural patterns (configurations)
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Overview cont’d



APT&C based on mathematical theories
and general systems theory
Value of APT&C is that results can be
directly related to practice
Through APT&C we have new ways of
conducting educational research
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Outline of this presentation


The dilemma: qualitative vs. quantitative
methodologies
Three examples of empirical studies that used
APT&C:



Academic learning time (APT joint occurrences)
Patterns of mode errors in human-computer
interfaces (APT sequential occurrences)
Student autonomy structures in a Montessori
classroom (APC patterns of student choice of work
and guidance of learning)
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Quantitative vs. Qualitative
Paradigms



Research methods in 20th century were largely
quantitative.
Qualitative and mixed methods are gaining more use
in research during past two decades.
Main problems:


Quantitative methods seldom yield significant results that
can be directly linked to educational practice (due to large
within-group variances in experiments or treatments)
Qualitative methods can provide good insights into
practice, but conclusions are often restricted (low
generalizability due to sampling strategy, and may or may
not transfer to similar situations)
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Three Empirical Studies to
Illustrate Value of APT&C

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Academic learning time of mildly
handicapped children (Frick, 1990)
Patterns of mode errors in humancomputer interfaces (An, 2003)
Student autonomy structures in a
Montessori classroom (Koh, 2006)
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Study # 1:
Academic Learning Time Study

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25 systems observed in central and southern Indiana
Tracked 25 target students in academic activities over
several months for 8 -10 hours each
Trained observers coded types of academic learning
contexts, task difficulty and task success
Observers also coded student and instructor
behaviors in math and reading (about 500 time
samples at one-minute intervals for each target
student)
Nearly 15,000 time moments sampled overall.
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What observers coded in math and
reading activities each minute

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Types of student engagement: written, oral,
and covert on-task; off-task behaviors (later
recoded as engagement, EN, and nonengagement, NE)
Types of instructor behaviors: structuring,
explaining, demonstrating, questioning,
feedback (later recoded as direct instruction,
DI), and monitoring academic seatwork (nondirect instruction, ND).
Observer comments to elaborate what was
happening
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Observer coding form
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Codes for target student
moves
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Codes for instructor moves
and focus
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Standard analysis: columns 1 and 2:
independent measures of DI and of EN
were correlated (n = 25)
p(DI)
p(EN)
p(DI & EN)
p(DI & NE)
p(ND & EN)
p(ND & NE)
p(EN|DI)
p(EN|ND)
0.50
0.39
0.27
0.34
0.48
0.40
0.44
0.36
Etc.
Mean
(SD)
0.432
(0.144)
0.80
0.49
0.56
0.69
0.73
0.75
0.84
0.75
Etc.
Mean
(SD)
0.741
(0.101)
0.46
0.37
0.26
0.34
0.47
0.39
0.40
0.33
0.04
0.02
0.01
0.00
0.01
0.01
0.04
0.03
0.34
0.12
0.30
0.35
0.25
0.35
0.44
0.42
0.16
0.49
0.43
0.31
0.26
0.25
0.11
0.22
0.92
0.95
0.97
1.00
0.98
0.98
0.91
0.92
0.67
0.20
0.41
0.53
0.49
0.59
0.80
0.65
Mean
(SD)
0.416
(0.139)
Mean
(SD)
0.015
(0.010)
Mean
(SD)
0.324
(0.114)
Mean
(SD)
0.243
(0.104)
Mean
(SD)
0.967
(0.029)
Mean
(SD)
0.573
(0.142)
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Linear Models Approach

Linear models approach (quantitative
method):


Relates independent measures through a
mathematical function
Treats deviation from model as error
variance
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Linear Models Approach cont’d
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Linear models results:

Means and standard deviations

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Mean p(DI) = 0.432 s.d. = 0.144
Mean p(EN) = 0.741 s.d. = 0.101
Regression equation
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
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EN = 0.57 + 0.40DI
R2 = 0.33
DI “explains” 33 percent of the variance in student
engagement; 67 percent unexplained
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Analysis of Patterns in Time


APT measures a relation directly by
counting occurrences of when a
temporal pattern is true or false in
observational data
Probability of joint or sequential
occurrence can be estimated for a
pattern from the counts
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APT Results for same 25 systems:
includes measures of joint and conditional
occurrences
p(DI)
p(EN)
p(DI & EN)
p(DI & NE)
p(ND & EN)
p(ND & NE)
p(EN|DI)
p(EN|ND)
0.50
0.39
0.27
0.34
0.48
0.40
0.44
0.36
Etc.
Mean
(SD)
0.432
(0.144)
0.80
0.49
0.56
0.69
0.73
0.75
0.84
0.75
Etc.
Mean
(SD)
0.741
(0.101)
0.46
0.37
0.26
0.34
0.47
0.39
0.40
0.33
Etc.
Mean
(SD)
0.416
(0.139)
0.04
0.02
0.01
0.00
0.01
0.01
0.04
0.03
Etc.
Mean
(SD)
0.015
(0.010)
0.34
0.12
0.30
0.35
0.25
0.35
0.44
0.42
Etc.
Mean
(SD)
0.324
(0.114)
0.16
0.49
0.43
0.31
0.26
0.25
0.11
0.22
Etc.
Mean
(SD)
0.243
(0.104)
0.92
0.95
0.97
1.00
0.98
0.98
0.91
0.92
Etc.
Mean
(SD)
0.967
(0.029)
0.67
0.20
0.41
0.53
0.49
0.59
0.80
0.65
Etc.
Mean
(SD)
0.573
(0.142)
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APT Results

Means and standard deviations for the relations
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Mean p(EN | DI) = 0.967 s.d. = 0.029
Mean p(EN | ND) = 0.573 s.d. = 0.142
When direct instruction is occurring, students are
highly engaged.
When non-direct instruction is occurring they are less
engaged.
Students were 13 times more likely to be off-task
during non-direct instruction compared with direct
instruction: (1 - 0.573) / (1 – 0.967) = 12.94.
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APT: joint occurrence
calculation example
Time
Instr.
Eng.
1:00
DI
EN
1:01
DI
NE
1:02
DI
EN
1:03
ND
NE
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p(DI) = ¾ = 0.75
p(ND) = ¼ = 0.25
p(EN) = ½ = 0.50
p(NE) = ½ = 0.50
p(DI & EN) = 2/4 = 0.50
p(DI & NE) = ¼ = 0.25
p(ND & EN) = 0/4 = 0.0
p(ND & NE) = ¼ = 0.25
p(EN|DI) = 2/3 = 0.67
p(EN|ND) = 0/1 = 0.00
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LMA vs. APT

Linear models relate the independent
measures by a function for a line:

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e.g., EN = 0.57 + 0.40DI
APT measures the relation in terms of joint,
conditional, or sequential occurrence:

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e.g., p (EN|DI) = 0.967
e.g., p (EN|ND) = 0.573
DI = direct instruction, EN = student engagement,
ND = non-direct instruction
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Study #2:
Patterns of Mode Errors in HCI

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Software mode: when the same action results in two
or more outcomes (Raskin, 2000).
E.g., In one context, pressing the ‘d’ key results in
the letter ‘d’ echoed on the screen
In another context, pressing the ‘d’ key results in
deleting a file.
Mode errors by humans can cause serious problems:
 Destruction of important work
 Decreased productivity
 Not able to complete tasks
Modes occur in almost all modern human-computer
interfaces (e.g., OS 10, Windows XP, Word,
Photoshop, etc.)
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An (2003) study of mode
errors


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Mixed methods approach (usability
evaluation, qualitative and quantitative)
16 college students performed eight
computer tasks with three modern GUI
interfaces (word processor, address book,
image editor).
Participants were videotaped, and stimulatedrecall interviews were conducted immediately
afterwards to clarify why certain actions were
taken, when viewing their videos.
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An (2003) study of mode
errors (cont’d)

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Over 280 problematic actions were observed,
and 52 were problems due to mode errors
52/280 = .19, or roughly 1 out of 5 problems
were due to software modes
Three general patterns (conditions) of mode
errors emerged from qualitative analyses:
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Type A: Right action, wrong result
Type B: It isn’t there where I need it
Type C: It isn’t there at all
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An (2003) study of mode
errors (cont’d)

Source of error analysis revealed that mode
errors appeared to result from 8 types of
design incongruity:
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Unaffordance
Invisibility
Misled expectation
Unmet expectation
Mismatched expectation
Inconsistency
Unmemorability
Over-automation
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An (2003) study of mode
errors (cont’d)

Consequences of mode errors:
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Can’t find hidden function
Can’t find unavailable function
False success
Stuck performance
Inhibited performance
Inefficient performance
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APT: analysis of sequential patterns of
mode errors, sources and consequences
Relative
Frequency
Likelihood
(p)
34 out of 52
0.65
AND IF source of mode error IS unaffordance,
THEN consequence IS can’t find hidden function OR false
success?
15 out of 34
0.44
10 out of 15
0.67
b)
AND IF source of mode error IS invisibility,
THEN consequence IS stuck performance?
6 out of 34
5 out of 6
0.18
0.83
c)
AND IF source of mode error IS misled expectation,
THEN consequence IS false success?
7 out of 34
6 out of 7
0.21
0.86
Query
Type A
1
a)
IF type of mode error IS right action, wrong result,
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APT: analysis of sequential patterns of
mode errors, sources and consequences
Relative
Frequency
Likelihood
(p)
8 out of 52
0.15
AND IF source of mode error IS mismatched expectation,
THEN consequence IS can’t find hidden function?
8 out of 8
8 out of 8
1.00
1.00
Query
Relative
Frequency
Likelihood
(p)
10 out of 52
0.19
Query
Type B
2
a)
Type C
3
IF type of mode error IS it isn’t there where I need it,
IF type of mode error IS it isn’t there at all,
a)
AND IF source of mode error IS unmet expectation,
THEN consequence IS can’t find unavailable function?
10 out of 10
10 out of 10
1.00
1.00
b)
AND IF source of mode error IS unaffordance,
THEN IF source of mode error IS unmet expectation,
THEN consequence IS can’t find unavailable
function?
3 out of 10
3 out of 3
3 out of 3
0.30
1.00
1.00
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APT: analysis of sequential patterns of
mode errors, sources and consequences

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APT results have practical implications
E.g., if the mode error is ‘right action, wrong
result’ and if the source of the error is
unaffordance (function not obvious), then 67
percent of the time users could not find a
hidden function or thought they did the task
correctly when in fact they had not (false
success).
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APT Methodology: sequential
occurrence

When one event precedes another, and when
observers code the order in which events
occur:

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APT can estimate the probability of the
consequent following the antecedent event.
APT can estimate likelihoods of sequences longer
than two (unlike Markov chains).
APT can estimate both joint and sequential event
occurrences in complex combinations.
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APT Coding (temporal
configuration)
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
Null
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APT Classifications and
Categories

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
Each column is a classification
Classifications co-exist in time
Categories of events within a classification
cannot co-exist in time (since they are
mutually exclusive, by definition)
An observer codes event changes within each
classification in the order that they occur.
Date/time is always a classification and is
recorded whenever there is an event change.
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Example of sequential coding
with three classifications
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
Null
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APT Query: IF target student IS Mona?
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
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Null
33
APT Query and Results
Query
IF target student IS Mona?
Results
Cumulative duration = (9:13 – 9:01) = 12 minutes
Cumulative frequency = 1 event
Likelihood = 1 out of 1 relevant event changes =
1.00
Proportion time = 12 minutes out of 12 = 1.00
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APT Query: IF target student is
Mona AND instruction is direct?
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
Null
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APT Query Results
Query
IF target student IS Mona
AND instruction IS direct?
Results
Cumulative duration = (9:08 – 9:01) = 7 minutes
Cumulative frequency = 1 event
Likelihood = 1 out of 2 relevant event changes =
0.50
Proportion time = 7 minutes out of 12 = 0.583
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APT Query: IF target student IS Mona AND
instruction IS direct, THEN student engagement
IS on-task?
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
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Null
37
APT Query Results
Query
IF target student IS Mona
AND instruction IS direct,
THEN student engagement IS on-task?
Results
Cumulative duration = (9:06 – 9:03) + (9:08 – 9:07)
= 4 minutes
Cumulative frequency = 2
Likelihood = 2 out of 4 = 0.50
Proportion time = 4 minutes out of 6 = 0.667
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APT Query Syntax
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APT Syntax (cont’d)
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APT Syntax (cont’d)
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APT Query Syntax

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
Thus, simple to very complex temporal
patterns can be specified within APT
queries.
Joint and/or sequential occurrences of
events can be specified.
Results include frequency counts,
likelihood estimates, durations and
proportions of total time.
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Theoretical Foundations
of APT

Mathematical theory



Information theory



Set theory
Probability theory
Classifications (more than one, non-exclusive)
Categories within each classification must be
mutually exclusive and exhaustive
General systems theory

SIGGS Theory Model
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Advantages of APT



APT brings theoretical rigor to pattern
identification in qualitative research.
APT measures relations not possible in
quantitative methods such as the linear
models approach.
APT requires a different kind of conceptual
framework for measurement and analysis
than those for qualitative and quantitative
approaches.
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APC: Analysis of Patterns in
Configuration


Thompson (2005) realized that APT
could be extended to measure and
analyze structure of systems.
Structure pertains to relationships
among parts.
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45
Familiar Patterns: Structural

Geographical relation:



Bloomington is located in southern Indiana on the
North American continent.
Bloomington is south of Indianapolis.
Organizational relation:

Gerardo Gonzalez is University Dean of the School
of Education who directs and supervises:


Oct. 13, 2006
Peter Kloosterman, Executive Associate Dean, SoE, IUB
campus
Khaula Murtahda, Executive Associate Dean, SoE, IUPUI
campus
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46
Familiar Patterns: Structural

Familial relation:



Philip and Irma Frick are the parents of Theodore
Frick
William and Helen Brophy are the parents of
Kathleen Brophy
Instructional relation:

During fall semester, 2005,T. Frick was the R690
instructor of:

Oct. 13, 2006
Andrew, Omer, Shyamasri, Nichole, Jamison, Sunnie,
Emmanuel, Uvsh, Chris, Theano
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A pattern is a relation

General form of a relation:
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Temporal & Structural Patterns &
Logical Relations

Temporal Patterns



Structural Patterns or Configurations


A precedes B
A co-occurs with B
A affect relation B
Logical Relations


A implies B
A is equivalent to B
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Affect relation: guides
research of
Faculty Person 2
Faculty Person 1
Student 3
Student 1
Student 2
Student 4
Student 5
Old IST Ph.D. structure
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Affect relation: guides
research of
Faculty Person 2
Faculty Person 1
Student 3
Student 1
Student 2
Student 4
Student 5
New IST Ph.D. structure
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APC allows us to measure
structural properties of di-graphs
Property
Count Value
Active Dependence
1.00 paths
5.97
Centrality
4.00 paths
23.89
Compactness
9.00 paths
53.76
Complete Connectedness 0.00 paths
0.00
Complexness
5.00 paths
5.00
Etc.
Etc.
Etc.
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52
Study #3: Autonomy structures in a
Montessori classroom (Koh, 2006)



Case study to explore Montessori
classroom structures that support
student autonomy
Observed on 10 occasions for about an
hour at different times of morning
session (1 head teacher, 2 assistant
teachers, 28 students ages 10-12)
Ethnographic approach initially
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53
Koh (2006) study cont’d

Class activities were built around two
different activity structures:



Head problems
Morning work period
Koh was interested in two kinds of
affect relations:


s chooses work y
y guides learning of s
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Koh (2006) study cont’d


Digraphs were drawn for affect relation
structures during Head Problems and
during Morning Work Period
APC software was used to calculate
structure measures of these digraphs
(Frick & Thompson, 2006)
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55
Koh (2006) study cont’d

Structures measured:






Active dependence
Centrality
Complexity
Independence
Interdependence
Complete connectivity
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Active Dependence: definition
and measure
Active dependent-component partition, ADS, =df a partition, Y = (VGO,RGA), characterized by
initiating component affect-relations.
S =df Y | vi,vjY(V )rd(I)(e)Y(R)[e = (vi,vj)  rd(I)(e) = 1]
AD
M : Active dependent-component partition measure, M (ADS), =df a measure of initiating
affect-relations.
M (ADS) =df [(i=1,…,n[j=1,…,mdI(j)(v)  log2|Ai|])  n] 100
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APC Results from
Koh (2006) study
Morning Work
Period
Head Problems
Property
Value
60
50
40
30
20
10
0
Active
dependence
Centrality
Complexity
Independence
Interdependence
Complete
connectivity
Structural Property
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APC Results from
Koh (2006) study (cont’d)




Active dependence higher in Head
Problems vs. Morning Work Period
Centrality higher in Head Problems vs.
Morning Work Period
Interdependence lower in Head
Problems vs. Morning Work Period
Complexity lower in Head Problems vs.
Morning Work Period
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APC Results from
Koh (2006) study (cont’d)


The structure of the Morning Work
Period supported student autonomy
During the Morning Work period there
was:




Less active dependence
No centrality
Greater complexity
Greater interdependence
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APC Results from
Koh (2006) study (cont’d)


The 3 teachers’ responses to the Problems in
Schools Questionnaire (SDT, 2006) showed
them to be “highly autonomy supportive”.
Student responses to the Academic SelfRegulation Questionnaire (SDT, 2006)
indicated a greater tendency to undertake
learning activities because they perceived
some personal value and identification with
the learning goals, rather than because they
felt compelled by external factors.
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APC Results from
Koh (2006) study (cont’d)



The structural configuration of the Morning Work
Period, where students chose learning activities and
worked at their own pace is characteristic of
Montessori classrooms.
The structural configuration of the Head Problems
activity chosen by the head teacher with all students
working on the same problems, is more typical of
traditional K-12 classrooms in the U.S.
APC allowed analysis and comparison of structural
properties of those two configurations of affect
relations.
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Summary

APT allows measurement and analysis
of temporal properties



Joint occurrences
Sequential occurrences
Combinations of joint and sequential
occurrences
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APT: joint occurrence
example
Oct. 13, 2006
Time
Instr.
Eng.
1:00
DI
EN
1:01
DI
NE
1:02
DI
EN
1:03
ND
NE
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APT joint and sequential occurrence
example
Clock
Time
9:01
9:02
9:03
9:04
9:05
9:06
9:07
9:08
9:09
9:10
9:11
9:12
9:13
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Target
Student
Mona
Instruction
Direct
Student
Engagement
Off-task
On-task
Off-task
On-task
Non-Direct
Off-task
Null
Null
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Null
65
Summary

APC allows measurement and analysis
of structural properties
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APC allows measures of structural
properties of an affect relation (e.g.,
guides research of)
Faculty Person 2
Faculty Person 1
Student 3
Student 1
Student 2
Student 4
Student 5
New IST Ph.D. structure
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APC property measures and
values
Property
Count Value
Active Dependence
1.00 paths
5.97
Centrality
4.00 paths
23.89
Compactness
9.00 paths
53.76
Complete Connectedness 0.00 paths
0.00
Complexness
5.00 paths
5.00
Etc.
Etc.
Etc.
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Summary: APT&C




Analysis of Patterns in Time and
Configuration permits measurement and
analysis of human learning and work
environments.
The value of APT&C methodology was
illustrated by clear results from three
empirical studies.
These results have direct implications for
practice. APT&C is a way to link theory to
practice.
Software is under development to do APT&C.
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Questions
For more information on APT&C:
http://www.indiana.edu/~aptfrick
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