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Development is not a single path

This post is the fifth in a periodic series exploring common misconceptions around how students learn. We first touched on these misconceptions in our September 2015 report, The Science of Learning, and will be exploring them in more depth over the next few months.

Today’s post from Dr. Bradley J. Morris and Dr. Clarissa A. Thompson explores the myth that cognitive development proceeds via a fixed progression of age-related stages. Though there is scant evidence in support of this myth, it is pervasive, particularly in education. Morris is a developmental cognitive scientist and is Associate Professor of Educational Psychology and Co-director of the Science of Learning and Education (SOLE) center at Kent State University, while Thompson is an Assistant Professor in Kent State’s Department of Psychological Sciences.

One of the most persistent myths in child development is that development unfolds in a predictable series of stages that build upon previous gains (e.g., Piaget, 1977); however, there is little support for this pattern of change despite decades of research on development (Newcombe, 2013).

Yet despite lack of evidence, the assumption of stage-like development is pervasive, particularly in education, and is often used to inform educational practice. The idea of stages meshes with our intuitions that children learn more effectively when instruction does not wildly exceed their current understanding, but is development best explained by stage-like change or by other factors like knowledge and working memory capacity? In this post, we will focus on two implications of stage-like development based on Piaget’s influential theory: earlier knowledge is replaced by more advanced knowledge, and thinking progresses from concrete content to being abstract.

Age (and stage) is a poor predictor of performance
The idea of a stage often matches our intuitions about development progressing in an orderly, predictable fashion analogous to a staircase on which one must walk up each step to reach the top (rather than skipping to the fifth step). Yet stages do not provide an accurate description of, or the best explanation for, development. Knowledge is not “transformed” in development. New knowledge is added to – and often competes with – old knowledge.

A fascinating study by Shtulman and Valcarcel (2012) investigated this by measuring how quickly adults could verify simple scientific “facts.” Their results showed that people took longer to verify “facts” if they had an earlier misconception related to that knowledge (e.g., the sun revolves around the earth) than if the “facts” weren’t associated with earlier misconceptions (e.g., the moon revolves around the earth). This suggests that new knowledge co-exists with and may interfere with older information.

Another piece of evidence against stages is that children (and adults) show considerable variability in how they approach problem solving. One influential model, overlapping waves (Siegler, 2012), provides an elegant, evolutionary explanation for how knowledge competes with its “rivals”. For example, when children learn to add two numbers they often begin by representing numbers on each hand (e.g., three fingers plus two fingers) and then counting all the fingers. Later they discover short cuts like counting up from the larger number. After sufficient practice, they can simply retrieve the correct answer. Siegler’s work demonstrated considerable variability in the paths that children take to reach a similar outcome (e.g., remembering that 2 + 3 = 5). For educators, this work demonstrates that (a) knowledge remains and may interfere with new information being learned, and (b) there is considerable variation in how children learn even simple knowledge.

Development is not a single path
A second aspect of the myth is that development proceeds from concrete to abstract thinking. Piaget’s concrete operational stage suggested that children can think logically but only when provided with concrete (not abstract) materials. This suggests that children are capable of thinking about mathematical operations but only when they are working with real-world situations. For example, children of a certain age can think about quantities using examples like “cats” but not when using abstract symbols like numbers.

Although Piaget’s stage theory states that children are limited to concrete thought until early adolescence, recent evidence suggests that young children (Rhodes, Gelman, & Karuza, 2014) and even infants can think abstractly (Dewar & Xu, 2010). Rather than being an index of one’s current developmental trajectory, abstract thought (and other capacities like memory) emerges from having a sufficient knowledge base. A classic study by Chi (1978) demonstrated that adults with nominally larger working memory capacities were less accurate at remembering the positions of chess pieces than children with smaller capacities who were chess players. Even adults have difficulty thinking abstractly about something with which they are unfamiliar. If an adult had trouble seeing the similarity between the electrical system of a car and the nervous system of the body, we wouldn’t say he is not in the right stage to understand the concept. Similarly, it is more helpful to think of young children as novices, who need more knowledge (see Alan Lesgold’s post on novices-experts), rather than being limited by stage.

Implications for selecting and implementing instructional materials
As described above, concrete refers to a “stage;” however, it also describes instructional materials that are intended to maximize learning during this stage. For example, when teaching first graders to add the number of people in two classrooms, a teacher might use photographs of actual people or stick figures. The photographs are concrete, whereas stick figures are abstract. Concrete materials have been favored because they connect to the real world, which activates relevant background knowledge, making the materials beneficial for learning. Unfortunately, concrete examples have at least two limitations for learning. One, they provide irrelevant information (e.g., the funny hat one person is wearing) that draws children’s attention away from what is important. Two, concrete examples often limit children’s ability to transfer that knowledge to other tasks.

Both limitations were demonstrated in a recent paper in which elementary school children interpreted bar graphs (Kaminski & Sloutsky, 2013). Children who were given graphs with irrelevant information (e.g., pictures of shoes in the bars on a graph that represented the number of shoes lost/found) produced more errors and often acquired suboptimal strategies like counting the items within the graphs.

That said, however, concrete materials are not “bad”; like any instructional tool their effectiveness is related to being used properly. A technique known as concreteness fading can improve learning outcomes by combining the strengths of different types of materials in instruction (Fyfe, McNeil, Son, & Goldstone, 2014). Concreteness fading begins with using concrete materials, but gradually moves instruction towards the use of abstract materials. In addition, this technique includes comparisons between materials, which helps students notice relevant and irrelevant features.

Although we have only scratched the surface of this issue, this evidence provides helpful information for educators. First, age (and stage) is a poor predictor of performance and matters much less than true individual differences (e.g., the knowledge a child has when she enters your classroom). Second, development is not a single path, but is instead highly variable both between and within children. Finally, educators should use care in selecting and implementing instructional materials because some aid whereas others hinder learning.

 

References

Chi, M. T. H. (1978). Knowledge structures and memory development. In R. Siegler (Ed.), Children’s thinking: What develops? (pp. 73-96). Hillsdale, NJ: Lawrence Erlbaum Associates.

Dewar, K. M., & Xu, F. (2010). Induction, overhypothesis, and the origin of abstract knowledge evidence from 9-month-old infants. Psychological Science, 21(12), 1871-1877.

Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review26(1), 9-25.

Kaminski, J. A., & Sloutsky, V. M. (2013). Extraneous perceptual information interferes with children’s acquisition of mathematical knowledge. Journal of Educational Psychology105(2), 351-363.

Newcombe, N.S. (2013). Cognitive development: Changing views of cognitive change. WIREs in Cognitive Science, 4, 479-491.

Piaget, J. (1977). The development of thought: Equilibration of cognitive structures (Trans A. Rosin). Viking.

Rhodes, M., Gelman, S. A., & Karuza, J. C. (2014). Preschool ontology: The role of beliefs about category boundaries in early categorization. Journal of Cognition and Development15(1), 78-93.

Shtulman, A., & Valcarcel, J. (2012). Scientific knowledge suppresses but does not supplant earlier intuitions. Cognition124(2), 209-215.

Siegler, R. S. (2016). Magnitude knowledge: the common core of numerical development. Developmental Science, 19(3), 341–361.


Bradley J. Morris and Clarissa Thompson


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