Preschool children’s views on unsolvable math problems

Olgan, Refika
Cengizoğlu, Seçil
Solmaz, Gizem
Introduction Early childhood mathematics education immerses young children into many kinds of reasoning through seeing, listening and talking, touching and moving that reveal how mathematics associates with the real world. In this array, mathematics education in the early years provides many opportunities for children to handle everyday tasks and inspires them about a way of thinking with interesting and challenging problems (Sperry-Smith, 2006). One of the aims of mathematics education in the early years is to bring children the skill of composition and decomposition of numbers. In traditional view, composition and decomposition of numbers can be learned simply through rote learning and there is no need for children to experience any cognitively embedded process. It is also believed that composition of numbers is a kind of mechanic procedure in which young children are not capable to do it (Baroody, Lai and Mix, 2005). On the other hand, more contemporary approaches in mathematics education argue that the relation among the numbers and composition and decomposition skills can be accomplished by young children through easily realizing the patterns and the relations among the numbers. According to INMPC (2008), children ages between 4 to 6 years begin to develop composition and decomposition skills. In this point, decomposition and composition process make children realize that there could be more than one strategy to solve a problem (Tirosh, Tsamir, Levenson, Tabach and Barkai, 2015). The National Council for the teachers of Mathematics (NCTM, 1989) proposed that developing the skills of composition and decomposition of numbers is important step for problem solving that should be in the center of learning activities in a daily routines of preschools and daily activities should be designed specifically for promoting problem solving skills (Baroody, 2006). In the related literature, there are studies that aimed to reveal young children’s mathematical problem solving skills. In these studies, problems set in a real-life context and also have a solution. In the current study, however, the children received a decomposition problem that has no mathematical solution. Therefore, the aim was to reveal strategies the children use for problem solving when they engage with unsolvable mathematical problems. Methodology The current research is a kind of replication study which was originally conducted by Tirosh, Tsamir, Levenson, Tabach, and Barkai (2015). The participants were 60-72 month-old preschool children (N=50) attending three different preschools in Ankara, Turkey. The convenient sampling method was utilized. Before conducting the study, required ethical measures and consents were gained from University Ethical Council, administrators of the school, and parents of the participant children, as well. The verbatim transcripts were analyzed through multiple coders in order to reach an agreement on codes and categories to ensure the reliability. In the data collection procedure, the children were proposed a birthday party task which is very common a daily life experience for children. For this task, four empty plates and eight cards (on which different amount of candies were seen) placed on a table. One of the eight cards was a blank card that has no candy picture on it. The problem that has no solution since twenty-seven is not divisible by four and seven candies cannot be placed on each of the four plates was introduced to each child as “You have a birthday party and four children are coming. You want to give each child seven candies on their plate. 26. Uluslararası Eğitim Bilimleri Kongresi, 20-23 Nisan 2017 Özetler Kitabı 2488 Can you arrange it so that there are seven candies on each plate? You can arrange the candies however you wish, but there have to be seven candies on each plate” While each child was working out on a task, the researcher sometimes puts remarks if needed to remind children that they can place more than one card on a plate. When the child finished the task, the researcher asked “So, does every child get seven candies?” The researchers followed the same procedure with each child on the same task. Findings There were two salient findings of the current study. The first one is that counting was the most common strategy that the children employed to decompose the candies into the plates equally. The children tried to count the number of candies through touching them and tried to place seven candies into each plates. While decomposition of the 27 candies, children tried to recall the numbers in each plate, thus they made simply subitizing. Moreover, most of the children did not recognize that this problem is an unsolvable but they tried to put forward their own strategies. One of the interesting sides of the problem is the blank card. Even though the blank card represents the zero, children who were 60 month-old (n=18) preferred to place the blank card in one of the plate. They also proposed some solutions including drawing a candy on the blank card. On the other hand, the children who were 72 month-old (n=15) did not use the blank card, but only two of them asserted that this problem is an unsolvable problem. There is only one child in the group of 72 month-old children tried out several strategies and then he decided that blank card is meaningless and the problem is an unsolvable problem. In conclusion, counting the number of the candies was the most frequently used strategy. Moreover, the older children (72 month-old) were more successful than the younger ones (60 month-old) in estimating and subitizing the candies. All of the children did not give up and tried to develop their own strategies to solve the problem that has no solution.
Citation Formats
R. Olgan, S. Cengizoğlu, and G. Solmaz, “Preschool children’s views on unsolvable math problems,” 2017, p. 2487, Accessed: 00, 2021. [Online]. Available: