Updated on February 17, 2005

Span Theory

Span theory (Bachelder, 1970/1971; Bachelder & Denny, 1977a, b) is a theory of intelligence which got its start in the late 1960s in a program (Denny, 1966) which aimed to develop improved ways to teach people with moderate to severe mental retardation. From the beginning, the goal of span theory has been to understand individual differences in intelligence and learning in a way which will lead to more effective teaching and training.

According to span theory, each of us has a measureable span ability which is measured reasonably well by the digit span tests which have been part of IQ tests since the very first IQ test in the late 19th century. It also has the TASL process, the method of task analysis which links span ability with the ability to perform in specific tasks. The concept of span ability overlaps somewhat with the concept of working memory, the basis of new additions to the latest Wechsler Intelligence Scale for Children (WISC-IV, 2003).

Span theory has fundamental similarities with mainstream theoretical approaches to intelligence including working memory theory and the several neoPiagetian theories of intelligence such as those of Juan Pascual-Leone (1970) and Robbie Case (1992). One of the critical differences between span theory and these cognitive and cognitive science theories, is that the emphasis of span theory from the very beginning has been to solve practical problems teaching and training people with mental retardation. The other approaches have been oriented largely toward laboratory research and to the development of theories of normal intelligence.


Bachelder, B. L. (1970/1971). The memory span paradigm: Its use for the analysis of mental retardation. (Doctoral Dissertation, Michigan State University, 1970). Dissertation Abstracts International, 32(1), 576B-577B.

Bachelder, B. L., & Denny, M. R. (1977). A theory of intelligence: I. Span and the complexity of stimulus control. Intelligence, 1, 127-150.

Bachelder, B. L., & Denny, M. R. (1977). A theory of intelligence: II. The role of span in a variety of intellectual tasks. Intelligence, 1, 237- 256.

Case, R. (1992). The mind's staircase: Exploring the conceptual underpinnings of children's thought and knowledge. Hillsdale, NJ: Erlbaum.

Denny, M. R. (1966). A theoretical analysis and its application to training the mentally retarded. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 2). (pp. 1-27). New York: Academic Press.

Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget's developmental states. Acta Psychologica, 32, 301-345.