• Communications of Mathematical Education
• /
• v.23 no.3
• /
• pp.599-624
• /
• 2009

The purpose of this study was to investigate the relationship between error types and Polya's problem solving process. For doing this, we selected 106 sophomore students in a middle school and gave them algebra word problem test. With this test, we analyzed the students' error types in solving algebra word problems. First, We analyzed students' errors in solving algebra word problems into the following six error types. The result showed that the rate of student's errors in each type is as follows: "misinterpreted language"(39.7%), "distorted theorem or solution"(38.2%), "technical error"(11.8%), "unverified solution"(7.4%), "misused data"(2.9%) and "logically invalid inference"(0%). Therefore, we found that the most of student's errors occur in "misinterpreted language" and "distorted theorem or solution" types. According to the analysis of the relationship between students' error types and Polya's problem-solving process, we found that students who made errors of "misinterpreted language" and "distorted theorem or solution" types had some problems in the stage of "understanding", "planning" and "looking back". Also those who made errors of "unverified solution" type showed some problems in "planing" and "looking back" steps. Finally, errors of "misused data" and "technical error" types were related in "carrying out" and "looking back" steps, respectively.

• Communications of Mathematical Education
• /
• v.6
• /
• pp.317-335
• /
• 1997

• Journal of the Korean School Mathematics Society
• /
• v.16 no.1
• /
• pp.113-139
• /
• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2021.05a
• /
• pp.362-365
• /
• 2021

이 논문에서는 자연어로 구성된 수학 문장제 문제를 자동으로 풀이하기 위한 Transformer 기반의 생성 모델인 KoEPT를 제안한다. 수학 문장제 문제는 일상 상황을 수학적 형식으로 표현한 자연어 문제로, 문장제 문제 풀이 기술은 실생활에 응용 가능성이 많아 국내외에서 다양하게 연구된 바 있다. 한국어의 경우 지금까지의 연구는 문제를 유형으로 분류하여 풀이하는 기법들이 주로 시도되었으나, 이러한 기법은 다양한 수식을 포괄하여 분류 난도가 높은 데이터셋에 적용하기 어렵다는 한계가 있다. 본 논문은 이를 해결하기 위해 우선 현존하는 한국어 수학 문장제 문제 데이터셋인 CC, IL, ALG514의 분류 난도를 측정한 후 5겹 교차 검증 기법을 사용하여 KoEPT의 성능을 평가하였다. 평가에 사용된 한국어 데이터셋들에 대하여, KoEPT는 CC에서는 기존 최고 성능과 대등한 99.1%, IL과 ALG514에서 각각 89.3%, 80.5%로 새로운 최고 성능을 얻었다. 뿐만 아니라 평가 결과 KoEPT는 분류 난도가 높은 데이터셋에 대해 상대적으로 개선된 성능을 보였다.

• Communications of Mathematical Education
• /
• v.38 no.1
• /
• pp.49-67
• /
• 2024

Recent interest in the diverse applications of artificial intelligence (AI) language models has highlighted the need to explore didactical uses in mathematics education. AI language models, capable of natural language processing, show promise in solving mathematical word problems. This study tested the capability of ChatGPT, an AI language model, to solve word problems from elementary school textbooks, and analyzed both the solutions and errors made. The results showed that the AI language model achieved an accuracy rate of 81.08%, with errors in problem comprehension, equation formulation, and calculation. Based on this analysis of solution processes and error types, the study suggests implications for the didactical application of AI language models in education.

• Education of Primary School Mathematics
• /
• v.25 no.4
• /
• pp.395-410
• /
• 2022

Nominalization is one of the grammatical metaphors, and it is the representation of verbal meaning through noun equivalent phrases. In mathematical word problems, texts using nominalization have both the advantage of clarifying the object to be noted in the mathematization stage, and the disadvantage of complicating sentence structure, making it difficult to understand the sentences and hindering the experience of the full steps in mathematical modelling. The purpose of this study is to analyze word problems in the textbooks from the perspective of nominalization, a linguistic element, and to derive implications in relation to students' difficulties during solving the word problems. To this end, the types of nominalization of 341 word problems from the content domain of 'Numbers and Operations' of elementary math textbooks according to the 2015 revised national curriculum were analyzed in four aspects: grade-band group, main class and unit assessment, specialized class, and mathematical expression required word problems. Based on the analysis results, didactical implications related to the linguistic expression of the mathematical word problems were derived.

• School Mathematics
• /
• v.11 no.3
• /
• pp.497-511
• /
• 2009

This study compared two problem solving instructional approaches, schema based sequence instruction and schema based parallel instruction on word problem solving performance of elementary school students who were in general students group. The subjects totaled 48 third grade students who were exposed to a test that consisted of 9 word problem items of three types for 4 sessions. First of all, the baseline of word problem performance level was measured without any training. During session 1, 2 and 3 participants were put into strategic training groups. The experiment was designed by two between factor(two intervention group and two within factors(two problem types, three sessions). The results of experiment were as follows. Schema based sequence instruction group performed significantly better than students in another group on word problem solving performance. The effect of strategic schema based Instruction revealed that solving word problems relied upon problem types, sessions and input orders which were of great value.

• Journal of Elementary Mathematics Education in Korea
• /
• v.12 no.2
• /
• pp.185-204
• /
• 2008

The purposes of this study are to analyze sentence structures of word problems suggested in educational math programs for the 2nd grade elementary students and error patterns in sentence interpretation, and examine how sentence structures influence on errors during sentence comprehension. Based on the results of the analysis on 168 word problems suggested in math textbooks for the 2nd grade elementary students and error patterns observed while 160 the 2nd grade elementary students attempted to solve math word problems, easy and simple vocabularies are repeatedly used in the sentence structures of word problems and specific real life materials such as fruits, books, the number of people and etc. were repeatedly used. 51.56% of errors in sentence interpretation observed was higher than 39.20% of calculation errors and backtracking operation, a length of sentences, the numbers used in questions and off were analyzed to be involved in the errors in interpretation. Therefore, it is very important to make word problems from a student's points of view rather than a teacher's point of view and the study suggests that teachers help students learn basic sentence interpretation skills.

• Journal of Educational Research in Mathematics
• /
• v.14 no.3
• /
• pp.267-281
• /
• 2004

Many students feel the word problems are very difficult. This study analyzes the linguistic and cognitive factors that affect word problem solving so that we help students bring through the difficulty. There are a text base, a situation model, and a real world in the linguistic aspects. Students have a difficulty at the transition from text base to situation model(equation), and make lots of errors at the situation model. In the cognitive aspects, I investigated problem solving schemes, strategies, and complexity level. Students are likely to choose strategy by the contents which teacher instructed, but not by low complexity level, and mix up the amount of sugar and sugar water, and concentration. We can recognize how complex the types of word problems are to solve, which strategies students choose largely, and what errors that students make in the problem solving are.

• Education of Primary School Mathematics
• /
• v.26 no.1
• /
• pp.29-43
• /
• 2023

The purpose of this study was to synthesize intervention studies, which utilized single case experimental design, on teaching mathematical word problems for elementary school students with disabilities and evaluate each of their methodological rigor. The researchers reviewed all studies from 2000 to 2022 that involved teaching mathematical word problems to individuals with disabilities. A total of 12 studies was included for a final analysis. Most of the interventions were delivered by researchers for about 30-40 minutes per session to elementary school students with disabilities. Schema-based instruction, cognitive-metacognitive strategy, and technology-based instruction were used as intervention methods, and explicit instruction was mostly used in conjunction with them. On the other hand, the researchers found that none of research articles met quality indicators for single case experimental design according to Cook et al. (2015). Limitation and directions for future research were also discussed.