
INTERNATIONAL RESEARCH GROUP MEASURING DEVELOPMENT
AERA 1997, CHICAGO
Symposium
Modeling Development: Solving Methodological Problems with Rasch
Analysis
 Organizer, Theo L. Dawson, Graduate School of Education, University
of California at Berkeley
 Chair, Trevor Bond, James Cook University, Townsville,
Australia
Discussant, Mark Wilson, Graduate School of Education, University of
California at Berkeley
 Identifying Learner Characteristics Relevant
to Children's Understanding of Area Concepts
Trevor Bond & Kellie Parkinson, School of Education James Cook
University,
Townsville, Australia
 Reasoning About "Good Education":
A Developmental Analysis
Theo Linda Dawson, Graduate School of Education, University of California
at Berkeley
 A Rasch Analysis of a Set of
PiagetianBased
Written Problems Representing Different Forms of Thought and Different Logical
Operations
William Gray, Educational Psychology, University of Toledo, Ohio
 Beyond Rasch in the Measurement of Stagelike
Development
Karen Draney, Graduate School of Education, University of California
at Berkeley
Abstracts
Identifying Learner Characteristics Relevant to Children's
Understanding
of Area Concepts
Trevor G Bond & Kellie Parkinson, School of Education,
James Cook University Australia
A representative sample of fortytwo students (age from 5 years; 3 months
to 13 years; 1 month.) were randomly selected from a total student population
of 142 students at a small private primary school in northern Australia.
Those children's understandings of area concepts taught during the primary
school years were assessed by their performance in two testing situations:
The first consisted of a written test of ability to solve 'area' problems
with items drawn from school texts, school examinations and other relevant
curriculum documents. The second was an individual interview for each child
where four 'area' tasks such as the 'Meadows and Farmhouse Experiment' taken
from Chapter 11 of The Child's Conception of Geometry (Piaget, Inhelder
and Szeminska, 1960, pp. 261 301) were administered.
Rasch analysis based on the Partial Credit Model provided a finely detailed
quantitative description of the developmental and learning progressions
revealed in the ensuing data. It is evident that the mathematics curriculum
does not satisfactorily match the learner's developmental sequence at some
key points. Moreover, the children's ability to conserve area on the Piagetian
tasks, rather than other learner characteristics, such as age and school
grade seems to be a prerequisite for complete success on the mathematical
test of area. The discussion focuses on the assessment of developmental
(and other) characteristics of schoolaged learners and suggests how curriculum
and school organization might better capitalize on such information in the
design and sequencing of learning experiences.
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Reasoning About "Good Education": A Developmental
Analysis
Theo Linda Dawson, Graduate School of Education, University
of California at Berkeley
 To assess the development of reasoning about the nature of a "good
education," 116 semistructured clinical interviews were conducted
with a largely middle and upper middleclass group of participants ranging
in age from 5 to 85. Most of the participants took part in Armon's (1984)
lifespan longitudinal study of moral reasoning and reasoning about the
good, but were previously unscored. All interviews were conducted as specified
by Armon (1984). The stage of each scorable response was determined using
Common's General Stage Model (Commons, 1984), which identifies (in developmental
sequence) primary, concrete, abstract, formal, systematic, and metasystematic
stages of performance. Using criteria from the General Stage Scoring Manual,
all scorable statements from each of the interviews were identified, randomly
ordered, and scored blindly.
 The scores were submitted to a Rasch analysis, the results of which
(1) support the sequence of development proposed in the General Stage Model,
(2) indicate that individuals reasoned relatively uniformly throughout their
interviews, and (3) provide evidence of 'gappiness' that supports the concept
of a steplike progression from stage to stage.
 The Good Education scores of participants from Armon's study (N=77)
were then added to the data from a previous Rasch analysis of her results.
In the earlier analysis, it was found that Kohlberg's Moral Reasoning measure
and Armon's Good Life, Good Work, Good Friendship, and Good Person measures
appeared to be tapping the same underlying dimension of reasoning. Reanalysis
of the data, including the Good Education scores, reveals that the General
Stage Scoring System also appears to tap this single dimension. The theoretical
and practical implications of this finding will be discussed.
 References
 Armon, C. (1984b). Ideals of the good life: Evaluative reasoning in
children and adults. Unpublished Doctoral dissertation, Harvard, Boston.
Commons, M. L., Richards, F. A., with Ruf, F. J., ArmstrongRoche, M., &
Bretzius, S. (1984). A general model of stage theory. In M. Commons, F.
A. Richards, & C. Armon (Eds.), Beyond Formal Operations (pp.
120140). New York: Praeger.
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A Rasch Analysis of a Set of PiagetianBased Written Problems Representing
Different Forms of Thought
and Different Logical Operations
William M. Gray & Christine Fox, Educational Psychology,
University of Toledo
This is an analysis of a data set of 553 participants who answered 24
items from How Is Your Logic?. Mean age was 16.66 (SD = 4.97), ranging from
10.95 to 48.46. Males were 55.3% of the sample. Within a two week period,
participants solved 24 written problems that represent different formal
operations and different concrete operations. Each problem required a
constructed
response and answers were classified according to the form of thought required
for a correct answer and the form of thought produced by participants on
the problems.
Rasch analysis provided support for the construction of the problems as
congruent with the meaning of the underlying dimension of operational thought.
Problem placements clearly separated the concrete problems and the formal
problems with no concrete problem being more difficult than a formal problem
and no formal problem being easier than a concrete problem.
Within the concrete problems, the seriation problems were the easiest and
the multiplication of classes problems were more difficult. Within the formal
problems, the combination problems were easier than, and separated from,
the remaining formal problems. Making correct inclusions, proportional
reasoning,
and one permutation problem were the next easiest, although that permutation
problem was not in its expected position. Denying incorrect inclusions problems
were the most difficult along with the proportional reasoning explanation
problems. All explanation problems were more difficult that their corresponding
judgment problems. These results support recent suggestions that Rasch analysis
is appropriate when analyzing data generated from a good developmental theory.
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Beyond Rasch in the Measurement of Stagelike Development
Mark Wilson & Karen Draney, Graduate School of Education,
University of California, Berkeley
One of the assumptions inherent in a Rasch model approach to development
is that the patterns of the item difficulty estimates are sufficient to
validly describe the student responses. This is the usual assumption in
standardized tests, where the growth of students from lower achievement
to higher achievement is usually conceived of as "smooth". This
is distinctly not the case with stagelike development in general, and
especially
not so in the case of Piagetian and NeoPiagetian theories, where the
achievement
of new equilibria at successive stages would seem to imply that the students'
understandings of items would change from stage to stage, and hence, that
the item parameters may well be rearranged as the students move from stage
to stage. There is a general class of item response models, described by
Mislevy and Verhelst (1990), designed to model the situation where different
subjects employ different solution strategies: we assume that the strategies
are not observed, but that the differential relationship between the strategies
and certain classes of items is known a priori. This general approach has
been applied to the case of stagelike development by a number of authors
under the title of the "Saltus" model (Mislevy & Wilson, 1995;
Wilson, 1989; Wilson & Draney, 1995). In this presentation, we will
introduce the Saltus model as an extension of the Rasch model, then briefly
describe its application to the three data sets presented in the previous
three papers. A discussion of future prospects for this approach concludes
the presentation.
References
Mislevy, R. J., & Verhelst, N. (1990). Modeling item responses when
different subjects employ different solution strategies. Psychometrika
55, 195215.
Mislevy, R. J., & Wilson, M. (1995). Marginal maximum likelihood estimation
for a psychometric model of discontinuous development. Psychometrika.
Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive
development. Psychological Bulletin, 105, 276289.
Wilson, M. & Draney, K. (1995, April). Partial credit in a developmental
context: A mixture model approach. Paper presented at the annual meeting
of the National Council for Measurement in Education, San Franscisco.
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