• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.1
• /
• pp.105-129
• /
• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Journal of the Korean School Mathematics Society
• /
• v.17 no.2
• /
• pp.291-319
• /
• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• Annual Conference on Human and Language Technology
• /
• 2020.10a
• /
• pp.237-240
• /
• 2020

사전학습 언어모델은 다양한 자연어처리 작업에서 높은 성능을 보였다. 하지만, 사전학습 언어모델은 문장 내 문맥 정보만을 학습하기 때문에 단어간 의미관계 정보를 추론하는데는 한계가 있다. 최근에는, 사전학습 언어모델이 어느수준으로 단어간 의미관계를 이해하고 있는지 다양한 Probing Test를 진행하고 있다. 이러한 Test는 언어모델의 강점과 약점을 분석하는데 효율적이며, 한층 더 인간의 언어를 정확하게 이해하기 위한 모델을 구축하는데 새로운 방향을 제시한다. 본 논문에서는 대표적인 사전 학습기반 언어모델인 BERT(Bidirectional Encoder Representations from Transformers)의 단어간 의미관계 이해도를 평가하는 3가지 작업을 진행한다. 첫 번째로 단어 간의 상위어, 하위어 관계를 나타내는 IsA 관계를 분석한다. 두번째는 '자동차'와 '변속'과 같은 관계를 나타내는 PartOf 관계를 분석한다. 마지막으로 '새'와 '날개'와 같은 관계를 나타내는 HasA 관계를 분석한다. 결과적으로, BERT_base 모델에 대해서는 추론 결과 대부분에서 낮은 성능을 보이지만, BERT_large 모델에서는 BERT_base보다 높은 성능을 보였다.

• School Mathematics
• /
• v.17 no.3
• /
• pp.423-446
• /
• 2015

This study aims to look into the characteristics of argumentation in the task context of 'Monty Hall problem' at a high school probability class. As a result of an analysis of classroom discourses on the argumentation between teachers and second-year students in one upper level class in high school using Toulmin's argument pattern, it was found that it would be important to create a task context and a safe classroom culture in which the students could ask questions and refute them in order to make it an argument-centered discourse community. In addition, through the argumentation of solving complex problems together, the students could be further engaged in the class, and the actual empirical context enriched the understanding of concepts. However, reasoning in argumentation was mostly not a statistical one, but a mathematical one centered around probability problem-solving. Through these results of the study, it was noted that the teachers should help the students actively participate in argumentation through the task context and question, and an understanding of a statistical reasoning of interpreting the context would be necessary in order to induce their thinking and reasoning about probability and statistics.

• Journal of The Korean Association For Science Education
• /
• v.37 no.1
• /
• pp.25-37
• /
• 2017

The purpose of this study is to analyze the effects on particulate concept formation based on abductive reasoning model for elementary science class. For this study, an author selected two groups in the sixth grade. One group is an ordinary textbook-based control group (N=26) and the other group is an abductive reasoning model-based treatment group (N=26). After twelve lessons, the scores of Concepts Test for Gas were analyzed by t-test and two-way ANOVA. The result of t-test showed both the control and treatment groups have higher score than before they take the lesson. But after the lesson, an author found out that the treatment group had higher score than that of the control group. And compared to the number of particles expressed, the number of the treatment group were higher than that of the control class. The two-way ANOVA result revealed that the interaction effect between their cognitive level and treatment was not significant. And regardless of the level of cognition, the scores of treatment group are higher than those of control group. Therefore, abductive reasoning model-based elementary science class were found to be more effective for particulate concept formation. Based on the results, an author concluded that abductive reasoning model is very effective in teaching particulate concepts to elementary students.

• Annual Conference on Human and Language Technology
• /
• 2023.10a
• /
• pp.162-167
• /
• 2023

본 논문은 거대언어모델에 대한 한국어 상식추론 기반의 새로운 평가 방식을 제안한다. 제안하는 평가 방식은 한국어의 일반 상식을 기초로 삼으며, 이는 거대언어모델이 주어진 정보를 얼마나 잘 이해하고, 그에 부합하는 결과물을 생성할 수 있는지를 판단하기 위함이다. 기존의 한국어 상식추론 능력 평가로 사용하던 Korean-CommonGEN에서 언어 모델은 이미 높은 수준의 성능을 보이며, GPT-3와 같은 거대언어모델은 사람의 상한선을 넘어선 성능을 기록한다. 따라서, 기존의 평가 방식으로는 거대언어모델의 발전된 상식추론 능력을 정교하게 평가하기 어렵다. 더 나아가, 상식 추론 능력을 평가하는 과정에서 사회적 편견이나 환각 현상을 충분히 고려하지 못하고 있다. 본 연구의 평가 방법은 거대언어모델이 야기하는 문제점을 반영하여, 다가오는 거대언어모델 시대에 한국어 자연어 처리 연구가 지속적으로 발전할 수 있도록 하는 상식추론 벤치마크 구성 방식을 새롭게 제시한다.

• Journal of KIISE:Databases
• /
• v.27 no.2
• /
• pp.141-150
• /
• 2000

There are three significant drawbacks in extant fuzzy rule-based expert system languages. First, they lack the functionality of composite object inference. Second, they do not support fuzzy reasoning semantically easy to understand and conceptually simple to use. Third, knowledge representation and reasoning style of their model have a great semantic gap with those of current database models. Therefore, it is very difficult for the two models to be seamlessly integrated with each other. This paper provides the formal specification of a fuzzy object inference model to solve the three drawbacks. GIS(Geographic Information System) application domain is used to demonstrate that our model naturally models complex GIS information in terms of composite objects and successfully performs fuzzy inference between them.

• Journal of Educational Research in Mathematics
• /
• v.13 no.2
• /
• pp.159-178
• /
• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• Journal of The Korean Association For Science Education
• /
• v.37 no.1
• /
• pp.39-48
• /
• 2017

In this study, we investigated the characteristics of analogs generated by high school students to explain ionic bonding in the perspectives of the number of analogs, the understanding of mapping, and the source and type of analogs. We also compared the results by students' conceptual understanding, logical thinking ability, and analogical reasoning ability. Participants in this study were 395 11th graders in Seoul. The results of the study showed that the higher the conceptual understanding, the logical thinking ability, and the analogical reasoning ability, the more the students generated the analogs. The understanding of mapping was related to logical thinking ability and analogical reasoning ability. It is noteworthy that the sources of analogs differed only depending on their conceptual understanding of the target concept among the cognitive variables studied. Students who had higher conceptual understanding also generated analogs from more diverse sources. Some types of the generated analogs were related to the cognitive variables. For examples, the students who had higher conceptual understanding and logical thinking ability generated more verbal/pictorial analogs. The types of analogs were not related to cognitive variables in terms of artificiality, abstraction, and systemicity. Educational implications of these findings were discussed.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2018.05a
• /
• pp.377-380
• /
• 2018

인간의 추론 능력이란 문제에 주어진 조건을 보고 문제 해결에 필요한 것이 무엇인지를 논리적으로 생각해 보는 것으로 문제 상황 속에서 일정한 규칙이나 성질을 발견하고 이를 수학적인 방법으로 법칙을 찾아내거나 해결하는 능력을 말한다. 이러한 인간인지 능력과 유사한 인공지능 시스템을 개발하는데 있어서 핵심적 도전은 비구조적 데이터(unstructured data)로부터 그 개체들(object)과 그들간의 관계(relation)에 대해 추론하는 능력을 부여하는 것이라고 할 수 있다. 지금까지 딥러닝(deep learning) 방법은 구조화 되지 않은 데이터로부터 문제를 해결하는 엄청난 진보를 가져왔지만, 명시적으로 개체간의 관계를 고려하지 않고 이를 수행해왔다. 최근 발표된 구조화되지 않은 데이터로부터 복잡한 관계 추론을 수행하는 심층신경망(deep neural networks)은 관계추론(relational reasoning)의 시도를 이해하는데 기대할 만한 접근법을 보여주고 있다. 그 첫 번째는 관계추론을 위한 간단한 신경망 모듈(A simple neural network module for relational reasoning) 인 RN(Relation Networks)이고, 두 번째는 시각적 관찰을 기반으로 실제대상의 미래 상태를 예측하는 범용 목적의 VIN(Visual Interaction Networks)이다. 관계 추론을 수행하는 이들 심층신경망(deep neural networks)은 세상을 객체(objects)와 그들의 관계(their relations)라는 체계로 분해하고, 신경망(neural networks)이 피상적으로는 매우 달라 보이지만 근본적으로는 공통관계를 갖는 장면들에 대하여 객체와 관계라는 새로운 결합(combinations)을 일반화할 수 있는 강력한 추론 능력(powerful ability to reason)을 보유할 수 있다는 것을 보여주고 있다. 본 논문에서는 관계 추론을 수행하는 심층신경망(deep neural networks) 중에서 Sort-of-CLEVR 데이터 셋(dataset)을 사용하여 RN(Relation Networks)의 성능을 재현 및 관찰해 보았으며, 더 나아가 파라미터(parameters) 튜닝을 통하여 RN(Relation Networks) 모델의 성능 개선방법을 제시하여 보았다.