Danah Henriksen
CEP 900
September 15, 2003
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, 179-202.

Anderson, L. M., Brophy, J. E., & Evertson, C. M. (1979). An experimental 

study of effective teaching in first-grade reading groups. The Elementary School Journal, 79(4), 193-223.

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 3-year 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 problem-solving 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 learned-constructed 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 First-grade 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 behavior-outcome, and stimulus-response, 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:

  • Teachers should use a standard and predictable signal to get the children’s attention.
  • The teacher should have the children repeat new words or sounds until they are said satisfactorily.
  • Calling on volunteers should be restricted chiefly to parts of the lesson in which children are contributing personal experiences or opinions.
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. 15-46). 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, 179-202.
Anderson, L. M., Brophy, J. E., & Evertson, C. M. (1979). An experimental
study of effective teaching in first-grade reading groups. The Elementary School Journal, 79(4), 193-223.