Solving Arithmetic Problems

And then our fourth term, our fourth term is negative three.

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Although many researchers stress the importance of metacognitive processes in regulated strategy selection, there is also ample evidence that strategies can be selected without involving consciousness (see for instance Verschaffel et al.

it, since it may rather be that students notice an (adaptive) approach based on aspects of the numbers and their relations in the problems instead of selecting it from a number of possible strategies before starting the solution (Threlfall ).

Furthermore, the problems were designed to maximally elicit shortcut strategies.

Finally, the use of shortcut strategies was stimulated by an explicit instruction to look for a clever strategy.

The following general patterns of factors impacting shortcut strategy use emerge.

The first factor is the instructional setting: generally speaking, students following a more reform-based investigative or problem-solving program focusing on a diversity of strategies were more likely to use shortcut strategies than children in a more traditional skills-oriented program focusing on the acquisition and mastery of standard strategies (Blöte et al. The second factor is problem characteristics: besides the impact of number characteristics, the presentation format has also been found to have an effect, with word problems eliciting more shortcut strategies than symbolically presented problems (De Smedt et al. Fourth and finally, characteristics of the task or task instructions were important.

Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies.

An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems.

Finally, the use of shortcut strategies did not yield higher performance than using standard strategies.

All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.): the ability to apply meaningfully learned procedures flexibly and creatively.