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• Revision:Early Arithmetic Development and the Work Of Robert Siegler

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Psychology > Early Arithmetic Development and the Work Of Robert Siegler

• Early 1980's Siegler and colleagues produced evidence indicating that children use a variety of different strategies to solve single digit addition problems.
  • Before this, researchers had believed that grade one's used the sum strategy and that grade three's used the retrieval strategy, while grade two's used both - a stage description of development.
  • However, Siegler shows that all young (and even old) people use a variety of strategies throughout their development.
  • In fact, at any given point in their development children will use 5 or 6 different strategies - higher and lower order strategies coexist and compete. Thus, development is not the process of moving from one strategy to the next.

• Development involves the increasingly adaptive use of the available strategies as well as the discovery of more advanced strategies.
  • Development is both a quantitative and qualitative process.
• Indeed, variability is an integral aspect of behaviour and, according to Siegler (1994), is said to occur between children of different ages and children of the same age; within a child when presented with a series of similar problems; within the same child when presented with the same problem on more than one occasion and with the same child on the same problem.
  • Siegler's (1996) overlapping waves model of cognitive development was formulated to better incorporate the notion of cognitive variability.
  • The overlapping waves model proposes that, at any given age, children will resort to a multitude ways of thinking. Instead of a step-like or linear progression, development can be best described as a series of overlapping waves. Each wave represents the frequency of a strategies use over time. Since children resort to numerous strategies at any point in their development, the model is characterised by many overlapping waves.
  • Siegler has emphasised the VARIABILITY of cognitive action and argues that the stage theories (the staircase metaphor of cognitive development) have overlooked the extent of variability that actually occurs.
  • Before Siegler's overlapping waves model, and until relatively recently, Piaget's general theory of cognitive development was the dominant one. In this paradigm, experiments were designed to reduce, if not eliminate, evidence of cognitive variability.
  • It is precisely this variability that has now become important, in a Gestalt-like switch that, according to Kuhn (1970, as cited in Grannott, 1998), often characterises a change in the dominant paradigm.
    • According to the stage approach, children's thinking is determined by their age related level, and their thinking at each level has a certain stability.
    • Piagetian researchers have focused on the way children think about particular topics at particular ages, and this hunt for age related essences has meant that theorists have overlooked the extent of the variation that occurs in the way their subjects think (Siegler, 1996).
    • Cognitive variation, in these stage theories, is limited to the period of transition between the stages. The sudden shift from on level to the next is poorly understood, while untidy evidence of cognitive variability is swept under the carpet by means of labels such as decalage.
• The shift from one level to the next in the stage theories is poorly understood because, according to Siegler, the gulf between the stages does not actually occur.
• Many recent studies have detected competencies earlier than some of the stage-theories predict and later incompetence at ages when people are expected to be operating at a level described by the most advanced stage. Siegler argues that these inconsistencies reflect the extent of the cognitive variation that occurs throughout our development.
• Siegler has adopted an evolutionary understanding of this variability along Darwinian principles. Variation proposes, while selection disposes.
• However, empirical support for both positions or models of development. The strategies are discovered is a sequence of increasing complexity, from simpler to more advanced strategies - a Piagetian principle, even though variability may characterise how they are used.
• Also, children do use multiple strategies at any given point in time support for Siegler
• Maybe both correct - variability occurs around some orderly underlying structural development.

Some Addition Strategies

Retrieval involves retrieving the answer directly from memory.

The sum strategy involves counting each of the addends separately, then counting up to the first addend and continuing to count on by the number indicated by the second addend. This is one of the more basic strategies and often reflects the way children are initially taught.

The shortcut-sum strategy involves counting from one up to the total of the two addends.

The count from first strategy involves counting on from the first addend by the number indicated by the second addend.

The min strategy involves counting on from the larger of the two addends by the number indicated by the smaller of the addends.

Decomposition involves breaking the problem into more manageable parts. Decomposition could be described a class of strategies since there are many different ways in which problems can be decomposed and recombined.

Guessing is different to retrieval in that the child explains that he or she guessed. The child makes no attempt to retrieve an answer from memory, but simply provides any number that comes to mind, which implies that the number is randomly generated. There is evidence, however, that children spontaneously activate the sum of the two numbers, so it seems likely that guessing somehow involves consciously not attempting retrieve an answer.

Finger recognition involves putting up fingers to represent each of the addends and the child recognises the total, which is different to using fingers to assist counting.

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