The purpose of this study was to examine children''s mathematical word problem solving abilities and processes according to the affecting variables on them. This study also investigated children''s mathematical word problem solving cases observed in educational environments. For these purposes, the following research questions were established.
1. What are the relationships between children''s mathematical word problem solving abilities and the affecting variables?
1-1. how are children''s mathematical word problem solving abilities different according to the affecting variables (gender, age, language abilities, and computation abilities)?
1-2. what are the relationships between children''s mathematical word problem solving abilities and the affecting variable, and what is the relative influence of variables on children''s mathematical word problem solving abilities?
2. What are the relationships between children''s mathematical word problem solving processes and the affecting variables?
2-1. how are children''s mathematical word problem solving strategies and error types different according to the affecting variables (gender, age, language abilities, and computation abilities)?
2-2. how are the patterns of children''s mathematical word problem solving processes by decision trees?
3. How are the cases of children''s mathematical word problem solving experiences in their educational environments?
The participants of this study were 346 children aged four through six, enrolling day-care centers or kindergartens in D or G cities.
To find out the relationships between children''s mathematical word problem solving abilities and processes and the affecting variables, this study employed six different measurement tools. For the assessment of children''s mathematical word problem solving abilities, So-yon Kim and Su-young Kim(2015)''s measurement tool of children''s mathematical word problem solving abilities was used. In terms of children''s language abilities, modified version of Peabody Picture Vocabulary Test Revised(PPT-R) by Young-tae Kim, Hae-song Chang, Sun-sook Lim and Hyun-jung Bae(1995) was used in assessing children''s vocabulary abilities, while modified version of Test of Language Development-2, Primary(TOLD-2) by So-yeong Pae, Sun-sook Lim, Ji-hee Lee and Hae-song Chang(2004) in assessing children''s language understanding abilities. To assess children''s computation ability, Hye-jin Choi and Hae-ik Hwang(2007)''s children''s picture-mathematical ability test was used. For the analysis of problem solving strategies and error types, children''s mathematical word problem solving strategies and errors found in the problem solving processes were observed, documented and then classified.
The study results were as follows.
First, children''s mathematical word problem solving abilities did not statistically differ according to gender, but showed significant differences according to age. Statistical differences of children''s mathematical word problem solving abilities were also found according to both children''s language abilities and computation abilities. Specifically, children''s mathematical word problem solving abilities showed positive co-relations with children''s ages. Among the affecting variables, children''s language abilities were found the most influential variable on children''s mathematical word problem solving abilities.
Second, children''s mathematical word problem solving strategies used in solving combined questions showed significant differences according to gender. Male children used a direct-retrieval strategy most, while female children used counting all strategy most. In addition, significant differences were observed in children''s mathematical word problem solving strategies according to age and as were in all types of addition and subtraction questions. Children of higher ages were more likely to use direct-retrieval strategy than their lower aged counterparts. In terms of error types, significant differences according to gender were found only in solving subtraction questions, and female children used a no-response strategy more often than their male counterparts. Significant differences in error types according to age were observed in both addition and subtraction questions. In terms of addition, children aged four years and six months through five years and five months used a no-response strategy most, while children aged five years and six months through six years and six months a computation error most. In terms of subtraction, children of all levels of age employed a no-response strategy most, but the frequency of no-response strategy tended to decrease according to the age increase of the children.
Third, children’s mathematical word problem solving strategies were significant different according to both their language abilities and computation abilities. In solving addition, children with higher levels of language and computation abilities used a direct-retrieval strategy most, while children with lower levels of language and computation abilities a counting-all strategy most. In solving subtraction, children with higher levels of language and computation abilities used a direct-retrieval strategy most, while children with lower levels of language and computation abilities a separating-from strategy most. In terms of error types, significant differences were found in all types of addition and subtraction questions. Children with higher levels of language and computation abilities employed a computation error most, while children with lower levels of language and computation abilities a no-response strategy most.
Forth, children’s mathematical word problem solving process by decision-trees varied according to their mathematical word problem solving abilities. In terms of the addition, both male and female children - aged six years through six years and six months, with high level of word problem solving abilities and language abilities - answered the questions correctly by using a direct-retrieval strategy. In contrast, male and female children - aged four years and six months through four years and 11 months, with both low level of word problem solving abilities and language abilities - reached correct answers by using a counting all strategy. In terms of the subtraction, among the children with high level of language and computation abilities, aged six years through six years and six months, male children solved the problems successfully by using a direct-retrieval strategy, while female children by a direct-retrieval and separate from strategy. Among the children with low level of language and computation abilities, aged four years through four years and 11 months, both male and female children failed to solve the problems by using a no response strategy.
Findings of this study showed the critical relationships among children''s mathematical word problem solving abilities, processes and the affecting variables. The study findings also demonstrated children''s mathematical word problem solving strategies and error types according to the affecting variables. In addition, the case study provided good examples of young children''s mathematical experiences in day-care centers and kindergartens. Study findings and the case study suggested that directors and teachers in young childhood educations should provide good educational environments, in which young children could have a variety of mathematical experiences and therefore they could naturally improve and expand their mathematical abilities and solving strategies through the experiences.