• Journal of Educational Research in Mathematics
• /
• v.18 no.1
• /
• pp.123-135
• /
• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• The Journal of the Korea Contents Association
• /
• v.7 no.6
• /
• pp.161-168
• /
• 2007

In this paper, we proposed the mathematics learning evaluation system between teachers and students using the web. The proposed web-based evaluation system lets learners make up their lesson in a self-oriented and effective way, by letting instructors diagnose learners level of understanding learned contents and letting learners take part in evaluation as well. The system also lets instructors easily make out items for evaluation by using hangul(word processor) and present them on the web. With the help of this web-based mathematics learning site and mathematics learning evaluation system, learners can perform self-oriented loaming and approach various kinds of problems. In addition, students can check with answers and have feedback on the spot. As a result, students can solve lack of understanding on the learned contents.

• Journal of Digital Convergence
• /
• v.14 no.10
• /
• pp.53-60
• /
• 2016

This study investigated the effect of visual mathematics education using smartphones and immediate feedback through SNS on students' understanding of basic mathematical concept and academic achievement at the tertiary level. Researchers analyzed the test results of 214 students' mid-term and final examination in 4 classes consisted of 16 weeks' classes with two hours per week. Also their 30 questionnaire survey results were analyzed. The result reveals that classes using smartphones promoted understanding mathematical concepts and induced students' motivation and affirmative reaction. This study implies that an appropriate use of technology will support dynamic visualization of mathematical modeling and its interpretation, which enables students' active participation and deeper understanding.

• Research in Mathematical Education
• /
• v.6 no.2
• /
• pp.159-170
• /
• 2002

The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing developmental research effort to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the teaching and learning of differential equations at Ewha Womans University. The RME theory based on the design heuristic using context problems and modeling was developed for primary school mathematics. However, the analysis of this study indicates that a RME design for a differential equations course can be successfully adapted to the university level.

• Journal of Educational Research in Mathematics
• /
• v.12 no.1
• /
• pp.29-48
• /
• 2002

The purpose of this paper is to investigate the transfer in mathematics learning, especially focussing on arithmetic and algebra. There are many obstacles at the stage of transfer in learning. In the case of mathematics, each learning contents are definitely categorized by the learning level, therefore these obstacles are more happened than other subjects. First of all, this paper investigates the historical transfer from arithmetic to algebra by Sfard's perspectives. And we define prealgebra as the stage between arithmetic and algebra, which may be revised obstacles or misconceptions happened in the early algebra learning. Also, this paper discusses various obstacles and concrete examples happened in the transfer from arithmetic to algebra. To advance the understanding in the learning of algebra, we consider the core contents of the algebra learning which should be stressed at the prealgebra stage. Finally we present the teaching units of (pre)algebra which are sequenced from the variable concepts to equations.

• Communications of Mathematical Education
• /
• v.18 no.1 s.18
• /
• pp.1-18
• /
• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation as elaborated for mathematics education by Krummheuer, provide us with means to analyze aspects of explanation justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• The Mathematical Education
• /
• v.43 no.1
• /
• pp.97-107
• /
• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmin's scheme for argumentation, as elaborated for mathematics education by Kummheuer, provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Journal of the Korean School Mathematics Society
• /
• v.20 no.2
• /
• pp.77-89
• /
• 2017

Although it is not necessary to have much mathematical knowledge in Major Courses of Animal Resources curriculums in agricultural high school, the function of mathematics class has a much effect on Major Courses. Therefore, we extracted the mathematics contents included in Major Courses of Animal Resources curriculums in agricultural high school, and also evaluated students' understanding according to the description method in textbooks of Major Courses. Furthermore, we analyzed students' preference about the description method in textbooks related to the Major Courses. As a result, it turns out that the level of mathematics contents of Animal Resources major curriculums does not break bounds of middle school level. Furthermore, many students are not able to solve the middle school level of problems. It is also shown that the most preferred description method in textbooks of Animal Resources major curriculums is the sentence-equation mixed type. In this study, we propose to reconstruct the mathematics contents with basic knowledge needed to complete the Major Courses in order that students can complete them more easily, and furthermore, to choose the description method in textbooks of Major Courses as sentence-equation mixed type and detailed explanation about terms should be included into the bargain.

• School Mathematics
• /
• v.5 no.2
• /
• pp.223-240
• /
• 2003

The purpose of this study was to investigate the preservice elementary teachers' knowledge of division through open-ended problems focused on the following perspectives in understanding division : connectedness between procedural and conceptual knowledge as well as the knowledge of units. Results indicates that the preservice elementary teachers showed low level of understanding of division such as the making word problem including division of fractions and the identification of the units in division operation.

• East Asian mathematical journal
• /
• v.38 no.2
• /
• pp.257-275
• /
• 2022

Recently, there are studies the argument that arithmetic rules established by the four fundamental arithmetic operations, in other words, commutative laws, associative laws, distributive laws, should be explicitly described in mathematics textbooks and the curriculum. These rules are currently implicitly presented or omitted from textbooks, but they contain important principles that foster mathematical thinking. This study aims to evaluate the current level of understanding of these computation rules and provide implications for the curriculum and textbook writing. To this end, the correct answer ratio of the five arithmetic rules for 1-4 grades 398 in five elementary schools was investigated and the type of error was analyzed and presented, and the subject to learn these rules and the points to be noted in teaching and learning were also presented. These results will help to clarify the achievement criteria and learning contents of the calculation rules, which were implicitly presented in existing national textbooks, in a new 2022 revised curriculum.