Choosing between the Existing Backup Strategies

AND OTHERS

3.5 Choosing between the Existing Backup Strategies

SINGLE DIGIT ADDITION

PROBLEM

SELECT BACKUP STRATEGY

YES

YES NO

ATTEMPT RETRIEVAL'...f---<PROBLEMFAMILlARITY>----Jl~~1 EXCEEDS

THRESHOLD

L - - - - I

NO

- - j

STATE THE ANSWER EXECUTE BACK-UP

STRATEGY

Figure 3-B.Flow diagram depicting Schunn et al. 's (1997) retrieval/compute decision process.

The various retrieval models do, to an extent, explain how a child might choose between retrieving an answer or calculating it. However, they do not describe how one selects from the various competing backup strategies after deciding not to retrieve. This is the focus of the next section.

The first generation of models that were developed to account for strategy selection were the metacognitive models that proposed that the child's cognitive knowledge was used to govern their cognitive processes (Siegler, 1996). The term

metacognitive has been used in different ways in

the cognitive science literature. Siegler reserves the term for knowledge and processes that are explicit, rational, flexible, responsive to problem-solving goals and conscious (Crowley, Shrager,

&

Siegler, 1997; Siegler, 1996). The metacognitive mechanisms are potentially verbalisable and open to the process of reflection. They can be adapted to fit novel situations but the cost is that they are slow and require a great deal of the working memory resources. These early metacognitive models assert that the child is able to judge her intellectual capacity, the various strategies that she is able to choose from, and the demands ofthe task (Siegler, 1996). A rational selection is then made based on these three considerations. While some studies do indicate that explicit cognitive knowled!.:e is related to performance (for example, Baroody

&

Gannon, 1994;

Cowen & Renton, 1996; Canobi, Reeve, & Pattison, 1999), children appear to often make adaptive strategy choices without the explicit knowledge that these metacognitive models require (Siegler, 1996)..

Associative mechanisms, on the other hand, refer to the part ofhuman cognition that is " implicit,

fast and responsive to nuances in the environment" (Crowley et aI., 1997, p. 463). Strategy

selection involves the learned correlations between the tasks, actions and their outcomes (Crowley

et al.). Associative systems operate without the need ofreflective awareness and thus do not place

excessive demands on the working memory system. These processes become automised and are

not conscious. The down side is that they require a great deal of problem solving experience to

make the associative connections. Also, they are not easily adapted to novel situations.

It

is worth

noting that these two types of mechanisms (associative and metacognitive) seem to have

complimentary strengths and weaknesses.

The Siegler strategy choice model (1987; 1989a; Siegler and Jenkins, 1989) offers a description of how children choose between the competing backup strategies in the event that they did not retrieve an answer. Successful use of any particular backup strategy, in terms of speed and accuracy (or other possible variables), results in an increased strength of the strategy. The probability of choosing any particular strategy is proportional to its strength relative to the other competing strategies. New strategies have, according to Siegler, novelty points, which increases their likelihood of being used, but the points decrease over time. Novelty points ensure that new strategies are selected even though they have not yet established strength relative to the existing ones. Also, experience with different problems will result in a closer fit between the strategies and individual problems. Therefore strategy choice involves selecting the best strategy in terms ofthe problem presented.

The flow diagram illustrates some of the limitations ofthis model. The model suggests that one strategy will be used continuously on any given problem until it fails to generate an answer with sufficient speed·and accuracy. However, this inflexibility is not a feature of children's addition (Siegler, 1996). Similarly, the model cannot account for the generalisation of strategies to new situations.

NO

Figure3-C.Flow diagram depicting Siegler's (1987; 1989a) strategy choice model

Siegler and Shipley (1995) developed the Adaptive Strategy Choice Model (ASCM) as a modification of the earlier associative models. According to the ASCM, strategies operate on a problem to produce not only the answer, but also information regarding the effectiveness of the operation. This information is then retained in a data base under four headings: Global data refers to the history of the strategies effectiveness on all of the problems that it has been used, for example, all simple addition problems. Feature data refers to the effectivenessOl)specific classes of problems, such as simple addition problems with a large difference between the size of the addends. Problem-specific data refers to the strategy effectiveness on specific individual problems.

Novelty data refers to the novelty points discussed earlier that allow new strategies to be competitive with old ones. As these new strategies are used their novelty points are gradually lost.

This loss, however, is compensated by an increase in the strength associated with the different categories retained in the database. The database becomes a more accurate reflection of the effectiveness of the various strategies.

The Adaptive Strategy Choice Model differs from earlier associative models by explaining how successful use of a strategy in one situation is generalised to new situations. When a strategy is used on a problem that has not been solved using this particular strategy before, the selection would have been made according to the global and feature data associated with the strategy. If the strategy had never been used on the class ofproblem, then the decision would be made on the global data only. This model has been used to explain the selection of strategies in other domains (for example, Piaget's number conservation task in Siegler, 1995).

The Adaptive Strategy Choice Model assumes that strategy choice decisions are based on speed and accuracy only (although other variables could easily be incorporated into the model's decision making process). Other variables of strategy effectiveness could include the effort required to provide an answer (although effort is probably reflected by speed) or the ability to solve the problem under conditions of cognitive stress. Children may select their strategy on its aesthetic value. Also, ASCM offers a rational account of strategy selection and it is not clear how the model accounts for the variability that appears to characterise action.

While the various models encountered so far may, to a degree, explain how one chooses from existing strategies none of (hem explain how children develop these strategies in the first place.

Itis important to note the distinction between two types of strategy discovery. The first occurs when the difference between old and new methods has to do with the answers that they generate.

This occurs when the child is motivated to discover new strategies because the existing ones are flawed. The advantages ofgenerating new problem solving methods are obvious. The second type of discovery occurs when the difference between old and new is not in the answers that they generate but possibly in their efficiency or aesthetic value (Siegler& Jenkins, 1989). Siegler and Jenkins present evidence that indicates that children do not generate flawed simple addition

strategies, so strategy discovery in this domain is ofthe second type. (According to Siegler (2000) if children construct flawed strategies, then this would indicate that they do not have an appropriate conceptual understanding of the domain.)