초등수학 교과서에 제시된 문장제의 구문론·의미론 분석

오늘날 학교수학에서는 실생활 가운데 적용 가능한 수학이 강조됨에 따라 문장제(word problem)의 역할과 중요성이 부각되고 있으며, 이러한 흐름은 초등수학 교과서에서 다양한 유형의 문장제를 제시하는 것으로 나타나고 있다. 본 연구에서는 초등수학 교과서에 제시된 문장제 가운데 '문자와 식' 영역의 문장제를 중심으로 하여 그 유형을 분석하고자 하였다. 문장제는 구문론, 의미론, 소재, 문제해결 전략의 4가지 분석틀에 맞추어 유형 분석이 이루어졌다. 구문론 분석의 경우 하위 분석 요소로 문제의 길이, 자료 제시와 계산 순서, 불필요하거나 불충분한 수치 정보의 포함, 개방형 여부, 연산의 종류, 연산의 유형을 중심으로 하여 분석이 이루어졌다. 소재는 실생활과 관련된 소재와 순수 수학적 소재로 구분되었으며, 문제해결 전략의 경우는 Lenchner가 제시한 12가지 문제 해결 전략에 따랐으며, 이러한 분석의 틀에 따라 초등수학 교과서의 문장제 유형에 대한 분석이 이루어졌다.

Today importance of word problems in school mathematics increase as mathematics which is applicable to real life is emphasized. Therefore elementary mathematics textbooks include various word problems. In this paper, we restrict to word problems in letters and expressions’ domains of elementary mathematics textbooks and analyse word problems types. Firstly we make the analysis frame composed of syntax, semantics, material, and problem solving strategy. On syntax aspects，number of sentences in word problem, identification between order of data presentation and order of operation, inclusion of unnecessary or insufficient data, open sentence questions，Yngve index (degree of grammatic complexity of word problems) etc. are included. On semantics aspects, existence of operations, steps of problems, kinds and types of operations are investigated. Analysis of materials in word problems are separated into real-life and mathematics material and problem solving strategy is analysed as Lenchners twelve strategies.

As a result of this analysis, there is as followings. Firstly on syntax aspects, average number of sentences in word problem is 2.6(43.1%)， percentage of disagreement between order of data presentation and order of operation is 30%. Decree of inclusion of unnecessary or insufficient data is comparatively low, but in 6th-grade is about 20%, Also Yngve index is increasing from 1st grade(2.22) to 6th grade(2.83). In this way variety and complexity in syntax aspects increase as grades goes. Next on semantics, operation structured word problem is far more than non-operation structured word problem(93.1%;6.9%), In the steps of operations, ratio of 2-step problems is high(33.1%). In kinds of operations, addition is most presented(33.9%), Results of semantic analysis is similar on syntax characteristics, namely general tendency is complex and needs high level thinking as grades goes. Analysis of materials shows that real-life materials is mainly used in word problems. On the other hand, the connection of other subject is nearly handled. In the case of strategies, 'trial-and-error' is most appeared(20%).

Based on these analysis, we concluded as followings. ： degree of difficulty which students is confronted with word problems in elementary mathematics textbooks is gradually high as syntactic and semantic conditions are complicated. Finally we proposed that connection between low-grades(1~3 grades) and high-grades(4~6 grades) is developed and relation between kinds of word problems and student’s problem solving ability is analysed in succeed studies.