Gál-Szabó Zsófia Gabriella: Preparation for measuring the strategies used in solving enumerative combinatorial problems
With regard to measuring enumerative combinatorial problems, we can define two dimensions (based on Csapó, 2003). The quantitative dimension shows the correctness of the solution, while the qualitative one represents the strategy of thinking. Several national surveys have dealt with the first dimension, however in connection with the qualitative dimension, in other words, the combinatoric strategies, only international studies are known. Therefore, the aim of this literature review is to be prepared for our further investigation on combinatoric strategy usage. The paper overviews the main international and national studies related to combinatorial reasoning, as well as research-es in combinatoric strategies. Based on Piaget’s theory (see eg. Inhelder & Piaget, 1967), each developmental stage is characterised by different task solving strategies from trial-and-error proce-dure to systematic solution search. In this context, English (1991, 1993) observed six different strat-egies from the random item selection to the systematic item selection. People who use the most effective “odometer” strategies hold an item fixed and search for all the options systematically. These most effective strategies are necessary to enumerate the all possible solutions without mistakes in case of a complicated task (see Adey & Csapó, 2012). To examine combinatoric strategies, manipulative, paper-based and computer-based tasks are all appropriate. During testing, observations, video analyses, eye-tracking methods, think aloud methods and log file analyses could help to understand students’ way of thinking. Based on the paper, we plan to use a technology-based testing procedure and log file analysis in our investigations. A preliminary examination is necessary beforehand to study students’ task solving behavior with eye-tracking method.
Keywords: combinatorial reasoning, enumerative combinatorial problems, thinking strategies, combinatorics strategiesDownload...