Conceptual Framework and
Perspectives Evidenced in Research
Two Articles Perspectives
From:
Carpenter, T.
P., & Moser, J. M. (1984). The acquisition of addition and subtraction
concepts in grades one through three. Journal for Research in Mathematics
Education, 15, 179202.
Anderson, L. M., Brophy, J. E., & Evertson, C. M. (1979). An experimental study of effective
teaching in firstgrade reading groups. The Elementary School Journal,
79(4), 193223.
To begin with the Carpenter
and Moser article, The Acquisition of Addition and Subtraction Concepts
in Grades One Through Three, I believe that this article is grounded in
a cognitivist perspective on learning.
This research involved a 3year longitudinal study of the conceptual development of children’s skills and knowledge with regard to solving addition and subtraction problems. The primary goal, as set out by the authors, was to illustrate the key stages in the development of these skills, and to test the assumptions of other proposed models of the knowledge and procedures children use in solving simple problems. (Carpenter & Moser, pg. 179) Inherent in this fundamental basis for the study is a clear indication of cognitive theory on learning, in the sense that there is a focus on developmental stages of learning and models of knowledge and procedures concerning how children learn math. The article details previous research findings on children’s solution strategies for problems, and discusses the tendency to model what is depicted in a problem. Through this discussion of addition and subtraction methods, the authors describe a progression of strategies from basic to more advanced, which suggests a developmental model of learning. According to Greeno, Collins & Resnick (1996), an important tradition in the cognitive school of learning initiated by Piaget, emphasizes the cognitive growth of a learner, particularly in terms of cognitive understanding and construction of knowledge. “Learning is understood as a constructive process of conceptual growth…and growth in general cognitive abilities such as problemsolving strategies and metacognitive processes.” (Greeno, Colllins & Resnick, 1996, pg. 16) This is directly in line with the object of study of the Carpenter and Moser article. The processes described by the authors do not focus on accumulating discreet facts or acquiring skill sets through learned behaviors, as in a behaviorist perspective. They do not place an emphasis on social context or environmental settings as in situative perspective. What they do concentrate on is the progression of natural problem solving processes utilized by children in the course of learning development. One of the implications of their findings is that current math instruction could be improved if it capitalized on the rich informal mathematics that children bring to the table. (Carpenter & Moser, 1984, pg. 200) This application of learnedconstructed knowledge and processes is a significant aspect of the cognitive school of thinking. As noted in Greeno, Collins and Resnick, the cognitive perspective stresses that “children’s learning must be viewed as transforming significant understanding that they already have, rather than as simple acquisitions written on blank slates.” (Greeno et al., 1996, pg. 18) The research findings of Carpenter and Moser correspond well to this view of original knowledge constructed in a sequence of natural learning and development. The results of the study show some variability in the ways that children use problem solving strategies, and demonstrate a need for some revision of the current model of the learning sequence in mathematical problem solving (e.g. the use of and instruction on word problems does not need to be deferred until computational skills are mastered). A critical component of the authors’ argument is that children’s solution strategies change over time and instruction should move them through successive stages in this development. Overall, Carpenter and Moser have clearly defined their perspective on learning and stayed well within the conceptual framework of cognitivist thought for studying the processes for problem solving and mathematical reasoning skills and structures for children. The next article by Anderson, Brophy and Evertson, An Experimental Study of Effective Teaching in Firstgrade Reading Groups, is clearly grounded in the behaviorist school of thought. With regard to the key aspects of this study, behaviorism rang out as the overarching perspective from which the authors’ framed their ideas and conclusions. The very first initial discussion of the background describes the purpose of defining relationships between what teachers do (behaviors and processes) and what occurs with students (outcomes behaviors or products). This focus on process and product, or behavioroutcome, and stimulusresponse, if you will, is integral to the foundation of behaviorism. In the behaviorist view described by Greeno, Collins and Resnick, “learning is the process in which associations and skills are acquired, and transfer occurs to the extent that behaviors learned in one situation are utilized in another situation.” (Greeno, et al., 1996, pg. 16) The research reported by Anderson, Brophy and Evertson describes a First Grade Reading Study Group, which endeavored to translate research findings to classroom practice and indicated the influence of teacher behavior on student outcomes. Teachers in the treatment group were asked to follow certain principles of instruction (implementing certain behaviors), with the student outcome being reading behaviors over several months. An essential criterion for behaviorism is observable behavior and measurable outcomes, and therefore the line of research pursued in this article fits well here. To give an example of the concrete measurability of these treatments, just a few examples of the 22 applied behaviors included:
It’s also important to note
that in a learning setting behaviorism tends to place a great deal more
responsibility on the instructor than on the student. The learner
receives information and knowledge built through the instruction and processes
applied by the teacher, who has the more active role in judging the best
way to condition and guide the students to learn. This instructional
model used in the First Grade Reading Groups did just that as evidenced
by the authors’ the “teacher’s role in implementing the model was an active
and important one, and this aspect of the study was emphasized” (Anderson,
et al., 1979) Behaviorism is employed here as teachers were required
to draw on their knowledge of the needs of students as learners.
The measures taken of student
performance were quite specific examples of standardized testing used to
quantify student readiness and reading achievement. With observable
outcomes as the hallmark of behaviorist theory, both the treatment behaviors
and the performance measures of outcome used by Anderson, et al. seem to
fit nicely into this perspective.
In consideration of the results
of the study, which found a significant difference in achievement based
on application of the teacher behaviors prescribed, the authors were able
to conclude that many components of the proposed instructional model were
related to desirable behaviors, or high reading achievement. In this
instructional model designed to give the teacher a controlling and leading
role in directing the students, the application of behaviorism in practice
is consistently applied.
Greeno, J. G., Collins, A. M., & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner & R.
Calfee (Eds.), Handbook of educational psychology (pp. 1546). New York:
Macmillan.
Carpenter, T. P., & Moser,
J. M. (1984). The acquisition of addition and
subtraction concepts in grades
one through three. Journal for Research in Mathematics Education, 15, 179202.
Anderson, L. M., Brophy, J.
E., & Evertson, C. M. (1979). An experimental
study of effective teaching
in firstgrade reading groups. The Elementary School Journal, 79(4), 193223.
