1. References
Conclusion
Several empirical investigations of instructional
differences among high-performing and low-
performing nations on international assessments
have implicated the amount of cognitive support for
connecting and drawing patterns among ideas in
the classroom as a key contributor to the
international achievement gap (Richland, Zur, &
Holyoak, 2007; Richland, Chan, Morrison, & Au,
2010). This critical ability to discern meaningful
patterns within otherwise unconnected information
is termed relational reasoning (Alexander and the
Disciplined Reading and Learning Research
Laboratory, 2012; Dumas, Alexander, &
Grossnickle, 2013, p. 392). Since the
conceptualization of relational reasoning as a body
of strategies, the differences in strategic processing
between individuals with high relational reasoning
ability and low relational reasoning ability have not
been empirically observed.
Do individuals with high- and low- relational
reasoning ability differ in their strategic processing
when solving problems. More specifically, does the
pattern of strategy use differ between high-ability
individuals and low-ability individuals?
Introduction Methods
Results
.
Differences in Strategic Processing Between Individuals with High and Low
Relational Reasoning Ability: A Case Analysis
Robyn T. Harper, Mentored by Dr, Patricia Alexander, Emily Grossnickle, & Denis Dumas
University of Maryland, College Park
Alexander, P. A., Grossnickle, E. M., Dumas, D., &
Hattan, C., (in press). A retrospective and
prospective examination of cognitive strategies
and academic development: Where have we
come in twenty-five years? In A. O’Donnell (Ed.),
Handbook of educational psychology. Oxford,
UK: Oxford University Press.
Alexander, P. A. and the Disciplined Reading and
Learning Research Laboratory (2012). Reading
into the future: competence for the 21st century.
Educational Psychologist, 47(4), 259–280.
Alexander, P. A., Haensly, P. A., Crimmins-Jeanes,
M., & White, C. S. (1986). Analogy training: A
study of the effects on verbal reasoning. The
Journal of Educational Research, 77–80.
Dumas, D., Alexander, P. A., & Grossnickle, E. M.
(2013). Relational Reasoning and Its
Manifestations in the Educational Context: a
Systematic Review of the Literature. Educational
Psychology Review, 25(3), 391–427.
Richland, L. E., Chan, T.-K., Morrison, R. G., & Au,
T. K.-F. (2010). Young children’s analogical
reasoning across cultures: Similarities and
differences. Journal of Experimental Child
Psychology, 105(1), 146–153.
Richland, L. E., Zur, O., & Holyoak, K. J. (2007).
Cognitive supports for analogies in the
mathematics classroom. Science-New York then
Washington, 316(5828), 1128.
Sternberg, R. J. (1977). Component processes in
analogical reasoning. Psychological Review,
84(4), 353.
The participants were separated into two groups,
high-relational reasoning ability and low-relational
reasoning ability, based on their performance on the
TORR (Alexander et al., in press). The 16 highest
scoring participants were placed in the high-ability
group, while the 16 lowest scoring participants were
placed in the low-ability group. The low-ability
group’s scores on the TORR ranged from 7 to 12,
with an average score of 9.56 (SD=1.59). The high-
ability group’s scores ranged from 22 to 28, with an
average score of 24.31 (SD=1.62).
Of these students, four were selected as case
studies in order to further analyze the strategic
processing of students from each group. One male
and one female participant were chosen both the
low-ability and high-ability groups. They were
chosen based on the clarity of their think-aloud
transcriptions. Each case has been given a
pseudonym and their demographic descriptions
have been provided.
Ashley is a 20 year old,
Caucasian female in her
junior year. She reported
that English is her first
language. She is a
Kinesiology major with a
4.0 GPA. Ashley scored
a 26 on the TORR.
Eric is a 23 year old,
Asian male in his senior
year at the university. He
reported that English is
his first language. He is
a Computer Science
major with a 3.0 GPA.
Eric also scored a 26 on
the TORR.
Kyle is a 22 year old,
Caucasian male in his
senior year. He reported
that English is his first
language. He is a
Criminal Justice major
with a 3.1 GPA. Kyle
scored a 10 on the
TORR.
Lisa is a 22 year old,
Hispanic female in her
senior year at the
university. She reported
that English was not her
first language . She is an
Economics major with a
2.75 GPA. Lisa scored a
9 on the TORR.
Analogy: described as the
effortful detection of relational
similarity between two
seemingly independent
concepts, objects, or situations
(Bostrom, 2008; Hesse, 1959).
Anomaly: The ability to
detect and analyze
exceptions to patterns or
rules has been measured
for decades through
intelligence testing
(Alexander, Grossnickle,
Dumas, & Hattan, in
press).
Antimony: Refers to multiple
principles or statements that
are apparently contradictory
but nonetheless true”
(Mosenthal, 1988; Alexander
and the Disciplined Reading
and Learning Research
Laboratory, 2012, p. 34).
Antithesis: Involves
the recognition of a
directly oppositional
relation between two
propositions,
principles, or
explanations (Heit &
Nicholson, 2010).
Analytical Framework
For the purpose of this study, Sternberg’s
(1977) model of componential theory was used
based on its well-researched nature and potential
to be generalized to other forms of relational
reasoning. According to Sternberg, analogical
reasoning occurs in four steps: encoding, inferring,
mapping, and applying. In the encoding step,
mental representations of the problem are formed
through the acknowledgement of relevant attributes
(Alexander, Haensly, Jeanes, & White, 1986). Then,
lower-order relationships are recognized between
adjacent terms in the problem during the inferring
step (Alexander et al., 1986). The overall pattern
depicted in a problem is determined in the mapping
phase (Alexander et al., 1986). Finally, individuals
apply the information they have gathered by
selecting an answer (Alexander et al. 1986).
ENCODE INFER MAP APPLY
ENCODE INFER MAP APPLY
ENCODE INFER MAP APPLY
GUESS
Low-ability participants tended to encode problems
correctly but gave up on the problems, guessing
incorrectly, before even attempting to make an
inference about the pattern shown.
When low-ability participants chose not to guess,
they inferred incorrectly, leading to an incorrect
answer choice.
High-ability participants either inferred what the pattern
was correctly on the first attempt, and quickly chose the
correct answer, or reviewed previous steps in the
problem solving process until the correct answer was
found.
After an in-depth case analysis, it was found that
individuals with low relational reasoning ability
differed from those with high ability in the typical
patterns of strategies used when engaged in
relational reasoning tasks. Participants with low
relational reasoning ability were more likely to guess
or make incorrect inferences without revisiting the
problem. Participants with high relational reasoning
ability either quickly solved the problem correctly on
the first attempt, or revisited previous steps in the
problem solving process until a correct answer was
found. In future studies, a more quantitative analysis
will be done in order to understand more general
differences between individuals with high-and low-
relational reasoning abilities.