Students' Verification Strategies for Combinatorial Problems

Seizing the Opportunity to Create Uncertainty in Learning Mathematics

“…This type of uncertainty is particularly common to some specific domains of mathematics, such as the areas of probability and combinatorics. In the case of combinatorial tasks uncertainty is associated with the difficulty to verify the result and to estimate the number of cases under question (Fischbein and Grossman, 1997;Mashiach-Eizenberg and Zaslavsky, 2004). Although there are ways to verify solutions to combinatorial problems, seldom are they readily available to the problem solver.…”

Cooperative problem solving in combinatorics: the inter-relations between control processes and successful solutions

“…However, since no special design was employed to facilitate collaboration (opposed, for example, to the methods suggested by Leikin & Zaslavsky, 1997, 1999, except for the request to solve the problems together, we speculate that this collaboration was fostered by the specific content domain, namely, combinatorics. This domain elicits much uncertainty regarding the solution with hardly any useful and readily accessible ways to verify it (Mashiach Eizenberg & Zaslavsky, 2003). Thus, it creates a natural need to interact and get mutual support and feedback for the ongoing suggestions that come up, as indicated by the excerpts that were presented earlier.…”

“…These difficulties include the lack of well-established and reliable verification strategies (Mashiach Eizenberg & Zaslavsky, 2003). This in turn often decreases the level of confidence in one's solution (Mashiach Eizenberg, 2001).…”

“…By metacognition we refer to "one's knowledge concerning one's own cognitive processes and products or anything related to them" (Flavell, 1976). With respect to combinatorial problem solving, Mashiach Eizenberg and Zaslavsky (2003) found that verification of the solution contributed to the success in solving combinatorial problems. Verification is just one aspect of metacognitive control skills.…”

Felsoroló kombinatív feladatok megértésének vizsgálata az elemszám, az ismétlődés és a felcserélhetőség kritériumok alapján

“…Azonban több kutatás (pl. Mashiach-Eizenberg & Zaslavsky, 2004;Melusova & Vidermanova, 2015;Szitányi & Csíkos, 2015) is felhívja a figyelmet a terület nehézségére és kihívásaira, aminek fényében érthető Lockwood (2015) megállapítása, miszerint szükség van további, a kombinatív gondolkodással kapcsolatos kutatásokra, hiszen bőven tanulhatunk még a témáról. A kapcsolódó kutatások relevanciáját mutatja az is, hogy a kombinatorika tanítása, a kombinatív gondolkodás fejlesztése más területekre is pozitív hatással lehet.…”