• Journal of Educational Research in Mathematics
• /
• v.23 no.2
• /
• pp.117-133
• /
• 2013

Mathematical misconception is one of the big obstacles of the underachieving students to learn mathematics correctly. This study aims to develop the instruction materials for secondary school students who are underachieving in mathematics to reduce the occurrence of the misconception and to help them to build the correct concept in the mathematical learning. Before developing the material, we tried to collect the misconception cases occurring in common mathematics lesson. This materials tries to provide key educational contents for mathematics teachers who is responsible for teaching underachieving student and help them to creative interesting ideas for lessons. The materials could be used not only as an teaching materials for underachieving students or students with the misconceptions, but also could be used as training materials for mathematics teachers.

• School Mathematics
• /
• v.5 no.1
• /
• pp.115-133
• /
• 2003

Investigation of the students' mathematical misconceptions is very important for improvement in the school mathematics teach]ng and basis of curriculum. In this study, we categorize second-grade middle school students' misconceptions on the learning of linear function and make a comparative study of the error-remedial effect of students' collaborative learning vs explanatory leaching. We also investigate how to change and advance students' self-diagnosis and treatment of the milton ceptions through the collaborative learning about linear function. The result of the study shows that there are three main kinds of students' misconceptions in algebraic setting like this: (1) linear function misconception in relation with number concept, (2) misconception of the variables, (3) tenacity of specific perspective. Types of misconception in graphical setting are classified into misconception of graph Interpretation and prediction and that of variables as the objects of function. Two different remedies have a distinctive effect on treatment of the students' misconception under the each category. We also find that a misconception can develop into a correct conception as a result of interaction with other students.

• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.1
• /
• pp.179-198
• /
• 2011

The understanding of mathematical concepts should be backed up on a constant basis in oder to grow problem-solving skills which is one of the ultimate goals of math education. The purpose of the study was to provide readers with the information which could be considered valuably for the math educators trying both to prevent mathematical misconceptions and to develop curricular program by estimating the actual conditions and developing backgrounds of the mathematical misconceptions held by the gifted education learners. Accordingly, this study, as the first step, theoretically examined the meaning and the developing background of mathematical misconception. As the second step, this study examined the actual conditions of mathematical misconceptions held by the participant students who were enrolled in the CTY(Center for Talented Youth) program run by a university. The results showed that the percentage of the correct statements made by participant students is only 35%. The results also showed that most of the participant students belonged either to the level 2 requiring students to distinguish examples from non-examples of the mathematical concepts or the level 3 requiring students to recognize and describe the common nature of the mathematical concepts with their own expressions based on the four-level of concept formulation. The causes could be traced to the presentation of limited example, wrong preconcept, the imbalance of conceptual definition and conceptual image. Based on the estimation, this study summarized a general plan preventing the mathematical misconceptions in a math classroom.

• Journal of the Korean School Mathematics Society
• /
• v.13 no.1
• /
• pp.69-88
• /
• 2010

This paper is the case study how we can apply the appropriate teaching method in order to correct the misconception of middle and high school students in preservice teachers' education. Through the review of previous research and literature, we categorized students' misconception and sought the teaching method to teach preservice teachers. During this process, we did according to PBL and preservice teachers also tried to find the teaching method for students. And thus we were able to suggest the appropriate teaching method which was effective in correcting the misconception of middle & high school students along with their fine understanding of mathematical concepts. Further, preservice teachers acknowledged cooperative teaching & learning and the importance of it as well as the self-directed teaching and learning.

• Communications of Mathematical Education
• /
• v.32 no.3
• /
• pp.297-314
• /
• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• Journal of the Korean School Mathematics Society
• /
• v.15 no.3
• /
• pp.453-465
• /
• 2012

In this paper, we first analysis definition of continuity of functions in high school textbooks, the mathematics high school curriculum and university mathematics textbooks. We surveyed what was causing the students to struggle in their concept image of continuity of functions. We arrived at that students' concept for errors in images of continuity of function were caused by definition of continuity of functions in high school textbooks.

• Journal of Educational Research in Mathematics
• /
• v.19 no.2
• /
• pp.233-256
• /
• 2009

The notions of conditional probability and independence are fundamental to all aspects of probabilistic reasoning. Several previous studies identified some misconceptions in students' thinking in conditional probability. However, they have not analyzed enough the nature of conditional probability. The purpose of this study was to analyze conditional probability and students' knowledge on conditional probability. First, we analyzed the conditional probability from mathematical, historico-genetic, psychological, epistemological points of view, and identified the essential aspects of the conditional probability. Second, we investigated the high school students' and undergraduate students' thinking m conditional probability and independence. The results showed that the students have some misconceptions and difficulties to solve some tasks with regard to conditional probability. Based on these analysis, the characteristics of reasoning about conditional probability are investigated and some suggestions are elicited.

• School Mathematics
• /
• v.9 no.1
• /
• pp.119-139
• /
• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• Communications of Mathematical Education
• /
• v.13 no.2
• /
• pp.591-623
• /
• 2002

본 연구에서는 우리 나라의 학교 수학에서 실제적으로 CBL, CBR과 같은 실시간 테크놀로지와 MathWorld와 같은 소프트웨어를 활용한 활동 중심의 실험 학습의 가능성을 탐색하고, 이를 통하여 수학 학습의 기초가 되는 함수적 개념의 이해와 그 표상과의 연관성, 그리고 기존의 형성되어 있던 함수에 대한 오개념에 어떠한 영향을 미치는지를 분석하고자 하였다.

• Journal of Educational Research in Mathematics
• /
• v.20 no.1
• /
• pp.1-20
• /
• 2010

Conditional probability may look simple but it raises various misconceptions. Preceding studies are mostly about such misconceptions. However, instead of focusing on those misconceptions, this paper focused on what the mathematical essence of conditional probability which can be applied to various situations and how good teachers' understanding on that is. In view of this purpose, this paper classified conditional probability which have different ways of defining into two-relative conditional probability which can be get by relative ratio and if-conditional probability which can be get by the inference of the situation change of conditional event. Yet, this is just a superficial classification of resolving ways of conditional probability. The purpose of this paper is in finding the mathematical essence implied in those, and by doing that, tried to find out how well teachers understand about conditional probability which is one integrated concept.