Perspectives on School Learning

Selected Writings of John B. Carroll

L. W. Anderson

• Publisher: Routledge
• Year: 2014
• ISBN:
  9781135876616
• Edition: 1
• Topic: Bildung
• Subtopic: Bildung Allgemein

First Published in 1985. This volume offers a collection of John B. Carroll's works on the mastery of learning and related topics. Including discussions and information around his "Model of School Learning" and a biographical background.

I

School Learning

Introduction to Part I, School Learning

Lorin W. Anderson

Few ideas have had a more profound influence on educational research and practice as those embedded in John Carroll’s model of school learning. One of the largest, most successful studies of classroom instruction and school learning —the Beginning Teacher Evaluation Study —was designed primarily around the model of school learning. Virtually every approach to adaptive education, that is, instruction that attempts to adapt to, or accommodate, a variety of individual differences in learners, is based on assumptions and premises inherent in the model of school learning. Proponents of two such approaches, Mastery Learning and Individually Prescribed Instruction, have openly admitted their indebtedness to Carroll and his ideas (Bloom, 1968; Wang & Lindvall, 1970).

Yet, despite these positive influences, the model has been subject to a variety of misinterpretations and misunderstandings. As Carroll writes in The Model of School Learning: Progress of an Idea, “(t)hose who criticize the theory underlying the model are, I fear, often guilty of misunderstanding it” (p. 99).

In this introduction I begin with a brief discussion of the model of school learning. Then I present some of the misunderstandings and misinterpretations that have resulted from a less than careful reading of Carroll.

The Model of School Learning

Rather than begin with a description of the model —its variables and hypothesized interrelations — let me begin with a discussion of the purpose of the model, that is, a consideration of why Carroll developed the model in the first place. The model of school learning grew out of Carroll’s work in, and study of, second language learning. Specifically, Carroll initially was interested in developing a predictive model of success in learning a second language. The first paper in this section, A Model for Studying the Prediction of Success in Complex Learning Tasks, is a part of a longer paper, one entitled The Prediction of Success in Intensive Foreign Language Training.

Overall, the best predictors of success in studies conducted by Carroll (using his Modern Language Aptitude Test) or reviewed by Carroll turned out to be measures of aptitudes. At the same time, however, Carroll noticed that the relationship of these aptitudes with achievement (success) was much stronger in certain studies than in others. Carroll sought to find out why this was so. In essence, then, the model of school learning was developed in an attempt to explain the differential predictive validity of aptitude measures in different studies, conditions, or situations. As a consequence, the model contains aptitude and achievement as two of the major variables and includes four additional major variables; variables believed to help explain the different strengths of the aptitude-achievement relationship in different studies. These latter four variables are the ability to understand instruction, perseverance, the quality of instruction, and the opportunity to learn, and when combined with aptitude, form the five major independent variables of the model.

These five variables can be grouped in several ways. In A Model for Studying the Prediction of Success in Complex Learning Tasks, for example, they are grouped fairly traditionally. Quality of instruction and opportunity to learn are called “Instructional Variables.” Aptitude, ability to understand instruction, and perseverance are classified as “Individual Difference Variables.”

In A Model of School Learning, however, the variables are grouped quite differently. They are grouped on the basis of whether they influence (1) the amount of time the learner needs to spend in order to learn well, or (2) the amount of time the learner actually spends in the process of learning. Aptitude, ability to understand instruction, and quality of instruction are hypothesized to primarily influence time needed to learn. Opportunity to learn and perseverance are hypothesized to influence time spent in learning. And, finally, the degree of learning is hypothesized to be some function of the extent to which the learner actually spends the amount of time he or she needs to learn.

On the surface the model does appear quite simple. In reality, it’s quite complex. Part of the complexity comes from the interactions among the variables; part, interestingly enough, comes from the use of time as a metric. The interactional complexity will be discussed at this time; the time issue is discussed in the next section.

In order to understand something of the nature of the hypothesized interactions let us first consider time needed to learn. The primary influence on time needed to learn is the learner’s aptitude. However, ability to understand instruction and quality of instruction also influence time needed to learn, but they do so in an interesting, indirect manner.

First, ability to understand instruction interacts with the quality of instruction. That is, the better the quality of instruction, the less the need for ability to understand instruction, and conversely. In A Model for Studying the Prediction of Success in Complex Learning Tasks, Carroll includes a variable which he labels LL and which refers to the extent to which the learner understands the instruction as presented. This actual understanding of instruction, LL, is thought to be some function of the learner’s ability to understand instruction, g; (general intelligence), and the quality of the instruction, (the way in which the instruction is presented).

Second, the actual understanding of instruction interacts with learner aptitude to determine the amount of time needed to learn. Put simply, the better the understanding of the instruction as presented, the more the time needed to learn depends solely on the learner’s aptitude. Conversely, the poorer the understanding of instruction as presented, the more the time needed to learn will be increased beyond that which can be predicted from the learner’s aptitude.

These two sets of interactions can be represented algebraically as follows:

1. U_ij = f(g_i, p_j);
2. A^′_ij = A_ij./U_ij.
   Where A^′_ij is the time actually needed to learn, and
   A_ij is the time needed to learn as predicted from the learner’s aptitude.

Since U_ij is scaled from 0 to 1, Equation (2) implies that time actually needed to learn increases from A_ij to infinity as a function of the value of LL. Students not understanding the instruction at all, for example, will need an infinite amount of time to learn (i.e., they will never learn).

Time spent in learning also is determined by the interaction among variables. In fact, time spent in learning involves an interaction among all five major independent variables. Carroll states that time spent in learning “will be equal to the smallest of the following three quantities: (1) opportunity— the time allowed for learning, (2) perseverance —the amount of time the learner is willing to engage actively in learning, and (3) aptitude —the amount of time needed to learn, increased by whatever amount necessary in view of poor quality of instruction and lack of ability to understand less than optimal instruction” (A Model of School Learning, p. 28). It should be noted the quantity 3 is identical with A^′_ij as defined above. As such this last quantity involves the interaction of aptitude, ability to understand instruction, and quality of instruction.

Carroll gives us a rationale for defining time spent in learning as the smallest of the three quantities. “(I)t is assumed that the individual will stop work as soon as he either (1) learns the task to the specified criterion of mastery (that is, spends the time needed), (2) spends an amount of time denoted by M_ij (perseverance), or (3) is precluded from completing his learning because of the expiration of time as denoted by O. [opportunity to learn], whichever of these events occurs earliest” (A Model for Studying the Prediction of Success in Complex Learning Tasks, p. 12).

As can be seen in this analysis of the model, it is much more complex than it appears on the surface. Given such underlying complexity it is small wonder that people fail to understand the model completely upon first or even second reading. Similarly, it is understandable that other people attempt to simplify the model by selecting particular variables for study or use. Let us now turn to other issues involved in misreading Carroll’s writings on the topic.

Misreading Carroll

The failure to understand two concepts leads to most of the misunderstanding and misinterpretation of the Carroll model. These concepts are task and time.

The concept of task (or more specifically learning task) defines the “scope of the model” (A Model of School Learning, p. 20). A learning task is defined as the activity of “going from ignorance of some specified fact or concept to knowledge or understanding of it, or of proceeding from incapability of performing some specified act to capability of performing it” (A Model of School Learning, p. 20). Carroll’s model of school learning only applies to the learning of specified learning tasks! This focus on learning tasks is not a theoretical limitation since, “most, but not all, goals can be expressed in the form of learning tasks or a series of learning tasks” (A Model of School Learning, p. 20), but may be a practical limitation since “(i)n actual school practice, the various tasks to be learned are not necessarily treated as separate and distinct” (A Model of School Learning, p. 20). Furthermore, “the process of teaching is often organized (whether rightly so or not) so that learning will take place ‘incidentally’ and in the course of other activities” (A Model of School Learning, p. 20, emphasis mine). In other words, one reason the model may not apply to school learning is because teachers do not teach directly for student learning of clearly specified, distinct learning tasks.

The model will apply to learning tasks that have already been acquired either partially or totally, but only if a “correction factor” is included to account for the degree of learning already possessed by the learner. “It may be useful … to conceive that a learner’s estimated needed time, a_t, for a given task, t, may be written as a mathematical function of a series of basic aptitudes, symbolized with Greek letters and subscripts, minus the amount of time, S_t, saved by virtue of prior learnings relevant to the task. Thus: a_t = f(α₁, α₂, …, α_n) – S_t.”...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Editor’s Preface
• Author’s Introduction
• Part I: School Learning
• Part II: Individual Differences and School Learning
• Part III: Instruction and School Learning
• Part IV: Research and School Learning
• Appendix
• Author Index
• Subject Index