• Research in Mathematical Education
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• v.13 no.4
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• pp.349-377
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• 2009

In this work we present a study undertaken with in-service mathematics teachers of primary and secondary school where we describe and analyze the didactical competences needed to implement an innovative design in geometry applying Van Hiele's models. The relationship between such competences and an ideal teacher profile is also studied. Teachers' epistemology is established in terms of didactical competences and we can see that this epistemology is an element that helps us understand the difficulties that teachers face in practice when implementing an innovative curriculum, in this case, geometry based on the Van Hiele theory.

• Human Ecology Research
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• v.58 no.1
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• pp.105-120
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• 2020

This study helps infant teachers practice a constructivism-based teacher education program that supports infant mathematical inquiry activities and examines improvements in mathematical teaching knowledge, mathematical teaching initiatives, mathematical interaction, constructivism belief and mathematical teaching efficacy. Twenty two experiment group infant teachers and twenty two comparison group infant teachers were chosen at two workforce educare centers. The experiment group infant teachers participated in 18 sessions of a constructivism teacher training program for 8 weeks, but the comparison group infant teachers did not take part in the program. Pretest and post-tests were implemented for the mathematical teaching knowledge, mathematical teaching initiatives, mathematical interactions, constructivism belief and mathematical teaching efficacy in the experiment group. Independent sample t-test and ANCOVA were tested using Windows SPSS statistics 21.0. The homogeneity test for the experiment and comparison group revealed significant differences. ANCOVA was carried out after the pretest score was controlled as a co-variance. Significant differences were indicated in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. The results indicated that a constructivism-based teacher education program to support infant mathematical inquiry activities influenced improvements in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. This study proved the effects of the program based on constructivism theory content for the knowledge, skills and attitude about infant teaching of mathematical initiatives and practiced a program of exploration, investigation, application and assessment for infant teachers. The results can help infant teachers teach mathematical exploration activities and help activate infant mathematical exploration activities.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.309-327
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• 2018

This study is a case study of an elementary school teacher's reflection and practice in the process of planning, executing and criticizing his lesson on division with decimals. The purpose of this study was to clarify what kinds of problems an elementary school teacher was thinking about and how his focus was changing in the process of planning and executing a lesson and criticizing his lesson with his peers. The teacher was set in three periods: a teacher planning a lesson, a teacher executing a lesson, and a teacher criticizing his or her own lesson. Each period was analyzed in eight aspects: Establishing the goals for mathematics, implementing tasks, connecting mathematical representations, facilitating mathematical discourse, posing questions, building procedural fluency from conceptual understanding, supporting productive struggles, and using evidences of students' thinking.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.195-203
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• 1998

In [3], we showed that overintegration may be needed to obtain the optimal $H^1$ error rate for the $p$ version. In this paper, we examine the convergence of the $p$ version in practice, and comment on the implementation of the $p$ version in commercial codes. Also, we give an example of a problem with extremely rough coefficients, for which overintegration is necessary to obtain the optimal $H^1$ convergence rate.

• Research in Mathematical Education
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• v.18 no.3
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• pp.223-234
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• 2014

Research shows that formative assessment has a more powerful effect on student learning than summative assessment. This case study of an 8th grade algebra classroom focuses on how the implementation of Formative Assessment Lessons (FALs) and the participation in teacher learning communities related to FALs changed in the teacher's instructional practices, over the course of a year, to promote students' mathematical reasoning and justification. Two classroom observations are analyzed to identify how the teacher elicited and built on students' mathematical reasoning, and how the teacher prompted students to respond to and develop one another's mathematical ideas. Findings show that the teacher solicited students' reasoning more often as the academic year progressed, and students also began developing mathematical reasoning in meaningful ways, such as articulating their mathematical thinking, responding to other students' reasoning, and building on those ideas leading by the teacher. However, findings also show that teacher change in teaching practices is complicated and intertwined with various dimensions of teacher development. This study contributes to the understanding of changes in teaching practices, which has significant implications for teacher professional development and frameworks for investigating teacher learning.

• Research in Mathematical Education
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• v.26 no.3
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.

• 전기의세계
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• v.29 no.1
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• pp.58-64
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• 1980

In this paper, this objective is to obtain the mathematical model which describes the dynamic characteristics of variable reluctance(VR) step motor, the most important and most widely used motor in practice. In the development of the mathematical model for VR step motor, first the general nonlinear dynamic equations which describe the N-phase VR step motor are derived. These general equations are then applied to the multiple-step type of VR step motor in case, for simplicity, maynetic saturation and core lossess in the iron are neglected. These nonlinear dynamic equations are numerically analysed by the computer simulation, through which the performance characteristics of a step motor undertest are investigated under the various operating conditions.

• Research in Mathematical Education
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• v.2 no.2
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• pp.71-78
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• 1998

This paper investigates the practices of proof education in Korea by analyzing the teaching and learning of proofs in classes in the second year of middle school. With this purpose, this study examines the features and deficiencies of the ways of teaching proofs and investigates the difficulties which students have in learning them. Furthermore, it suggests methods for the improvement of teaching proofs.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.111-119
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• 2001

Over the years, the benefits of instructional manipulatives in mathematics education have been verified by classroom practice and educational research. The purpose of this paper is to introduce how the instructional material, specifically, geoboard could be used and integrated in elementary mathematics classroom in order to develop student's mathematical concepts and process in terms of the following areas: (1) Number '||'&'||' Operation : counting, fraction '||'&'||' additio $n_traction/multiplication (2) Geometry : geometric concepts (3) Geometry : symmetry '||'&'||' motion (4) Measurement : area '||'&'||' perimeter (5) Probability '||'&'||' Statistics : table '||'&'||' graph (6) Pattern : finding patterns Further, future study will continue to foster how manipulatives will enhance children's mathematics knowledge and influence on their mathematics performance.

• The Mathematical Education
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• v.42 no.3
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• pp.337-352
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• 2003

In this paper, we have studied the ways to enhance students' interest in infant math education. Firstly, we explain to the students the relation between the infant math skills and the college math contents. Next, the students practiced the subject about the infant education and the infant math education in real environment. Finally, the results of the practice are analyzed. From this study, we could find that the students got good experiences in infant math education activities and had the chance to change their mind in affirmative way for the infant math education and mathematics itself through performing given projects and investigations.