The contribution of external representations in pre-school mathematical problem solving

Abstract

Could problem solving be the object of teaching in early education? Could appropriate teaching interventions develop to scaffold children's efforts to solve problems? These were the central questions of this article. The sample consisted of 18 children attending public pre-school in Cyprus. The problem they were asked to solve was to find all solutions of the pentomino. The children's problem solving was supported by graphically representing their solutions on squared paper. The findings show that children responded positively to the problem and were successful in finding all solutions for the specific problem. The graphical representation of the solutions and the forms of teacherÁchildren and childrenÁ children interactions played an important role in the positive outcome of the activity.

International perspectives on early years practice

“…During circle time, the children discussed the task with the teacher and generated several possible solutions. Shiakalli and Zacharos's (2012) observations revealed that children as young as four and five and half years of age are capable of producing graphical representations which successfully solve a range of mathematical problems.…”

“…By way of example, the first paper by the Greek academics Shiakalli and Zacharos (2012) is focused on the development of mathematical problem solving in preschool children. As the authors note, mathematical thinking and problem solving is one of the most basic aims of mathematical problem solving.…”

A systematic information problem-solving process

“…McKinsey & Company had illustrated pyramid principle (so-called "Pyramid Structure") in 2010 [18]. The method was based on hard-headed thinking to find the layers and relationship between disperse events and problems.…”

The Employment of Verbal and Visual Information for 3rd Grade Deaf Students in Arithmetic Story Problem Solving

“…Vaikai linkę nustoti spręsti, kai tik randa sprendimą. O reikėtų skatinti ieškoti dar kitų sprendimo būdų (Shiakalli ir Zacharos, 2012).…”

“…Schemos pavidalo instrukcija padeda geriau suprasti įvairiapusiškus tekstiniame uždavinyje aprašomus santykius (Polotskaia et al, 2015). Todėl grafinis vaizdavimas, konstruojant simbolinius vaizdus, susijusius su kasdieniu vaiko ugdymu, yra ypač naudingas mokantis matematikos (Shiakalli ir Zacharos, 2012). Vaizdinės priemonės (skaičių tiesė, dešimtainės sandaros blokai, geometrinės figūros…) leidžia mokiniams išbandyti ir tokiu būdu pajausti abstrakčią matematiką naudojantis konkrečiu modeliu (Way, 2006).…”