• Research in Mathematical Education
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• v.23 no.3
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• pp.149-164
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• 2020

This study aimed to establish an observation protocol for mathematical modeling as an alternative way to examine instructional alignment to the Common Core State Standards for Mathematics. The instructional alignment observation protocol (IAOP) for mathematical modeling was established through careful reviews on the fidelity of implementation (FOI) framework and prior studies on mathematical modeling. I shared the initial version of the IAOP including 15 items across the structural and instructional critical components as the FOI framework suggested. Thus, the IAOP covers what teachers should do and know for practices of mathematical modeling in classrooms and what teachers and students are expected to do. Based on the findings in this study, validity and reliability of the IAOP should be evaluated in follow-up studies.

• Research in Mathematical Education
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• v.17 no.3
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• pp.181-198
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• 2013

Teaching and learning mathematics in a classroom setting is based on the interactions between the teacher and her students. Using classroom observations and interviews of students and the teacher, this research examines a first-year teacher and her students' interactions in the mathematics classroom. In this mathematics classroom, teacher and students interaction had inconsistency between mathematical topics and non-mathematical topics. For non-mathematical topics, their interactions were very active but for mathematical topics their interactions were very limited. This paper ends with raising questions for future research and calling for the opportunities for first-year teachers to reflect on their interactions with their students, in particular about mathematical topics.

• The Mathematical Education
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• v.52 no.1
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• pp.19-41
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• 2013

What is the foundation of mathematical thinking? Is it logic based symbolic language system? or does it rely more on mental imagery and visuo-spatial abilities? What kind of neural changes happen if someone's mathematical abilities improve through practice? To answer these questions, basic cognitive processes including long term memory, working memory, visuo-spatial perception, number processes are considered through neuropsychological outcomes. Neuronal changes following development and practices are inspected and we can show there are neural networks critical for the mathematical thinking and development: prefrontal-anterior cingulate-parietal network. Through these inquiry, we can infer the answer to our question.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.163-180
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• 2002

The purpose of this paper is to reconsider the meaning of mathematical literacy based on the investigation of the nature of mathematical knowledge communicated in university level mathematics classes. The analysis of classroom discourse has revealed three different kinds of mathematical knowledge circulated in mathematics class, which include 'factual mathematics', 'mathematical fantasy', and 'mathematical savior faire.' The fact that a mathematics teacher delivers diverse categories of mathematics knowledge suggests that the mathematical literacy is not confined to the development of technical competence. More specifically, the kinds of mathematical knowledge identified above tell that mathematical literacy developed through learning mathematics reflects the cultural norms and values of doing mathematics. This means that mathematical literacy is not merely involve with technical competence but rather with cultural competence. In this regard, this paper highlights the meaning of mathematical literacy as a cultural identity, which has been underestimated in the theory and practice of mathematics education dominated by technocracy of the twentieth century In particular, the notion of mathematical savior faire implies that teaching and teaming mathematics ultimately deals with a system of cultural meaning. Hence, through learning mathematics, a learner gets transformed as a whole person according to the cultural norms and values. In this regard, it is concluded that mathematical literacy can be considered as a necessary condition to become a competent member of mathematics community sharing cultural norms of doing mathematics as well as a repertoire of mathematical skills.

• Coupled systems mechanics
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• v.11 no.1
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• pp.79-91
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• 2022

Models for water treatment processes include simulation, i.e., modelling of water quality, flow hydraulics, process controls and design. Water treatment processes are inherently dynamic because of the large variations in the influent water flow rate, concentration and composition. Moreover, these variations are to a large extent not possible to control. Mathematical models and computer simulations are essential to describe, predict and control the complicated interactions of the water treatment processes. An accurate description of such systems can therefore result in highly complex models, which may not be very useful from a practical, operational point of view. The main objective is to combine knowledge of the process dynamics with mathematical methods for processes estimation and identification. Good modelling practice is way to obtain this objective and to improve water treatment processes(its understanding, design, control and performance- efficiency). By synthesize of existing knowledge and experience on good modelling practices and principles the aim is to help address the critical strategic gaps and weaknessesin water treatment models application.

• School Mathematics
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• v.10 no.3
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• pp.423-441
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• 2008

The purpose of this study was to examine the Pedagogical Content Knowledge(PCK) of teachers and their educational practice in the category of plane figure, to make a comparative analysis of their PCK and educational practice, and to discuss the relationship between their PCK and the characteristics of their instruction. Instruction of four selected elementary school teachers was analyzed to find out their educational practice. In conclusion, the characteristics of the PCK and actual instruction of the teachers could be listed as below: First, as a result of comparing their PCK and educational practice on plane figure by applying selected analysis criteria, there was a close correlation between their PCK and actual instruction. Second, the teachers had various levels of PCK on different areas. Especially, there was a large disparity in mathematical content knowledge and knowledge of teaching methods. Third, the teachers who had plenty of PCK were more excellent in textbook reconstructing, and those who fell behind in terms of PCK were more reliant on textbooks as if the textbooks had been the Bible.

• East Asian mathematical journal
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• v.32 no.4
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• pp.465-482
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• 2016

This study aims to investigate research trends relevant to mathematics teachers and discuss implications on professional development of mathematics teachers. For the purpose of this study, we review 156 articles written between 2006 and 2015 related to mathematics teachers. The articles are analyzed using the model of professional growth suggested by Goldsmith, Doerr, Lewis(2014). The model discusses personal domain, external domain, domain of practice, and domain of consequence. In the results of this study, articles focusing on the personal domain of mathematics teachers appear a lot in reviewed ones, whereas studies relevant to external domain or domain of practice of mathematics teachers are relatively small.

• Research in Mathematical Education
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• v.14 no.3
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• pp.281-297
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• 2010

This paper pretends to study the potentialities of feedback, particularly in the development of a written report in two phases and in portfolio; and the main difficulties that teachers has to face concerning this assessment practice. Through a meta-analysis concerning different studies, it is possible to say that oral or written feedback, intentionally provided to students of several ages, may enable them to develop their self-assessment capacity and to get close of the expected product. However, the type of student and his or her perceptions may influence the effectiveness of feedback. Even for experience teachers, this practice maintains complex.

• School Mathematics
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• v.4 no.3
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• pp.415-433
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• 2002

The mathematics education community is seeking to change a teacher-centered class-room culture to a student-centered culture. However, the real transition is not easy, even for teachers who are eager and willing to teach differently. The challenge for teachers is to use the social structure of the classrooms to nurture students' development toward mathematical ways of thinking and communicating as well as their under-standing of mathematical concepts and processes. By introducing an elementary teacher's teaching practice and professional develop-ment along with her classroom episodes, this paper is to make strides toward an enriched understanding of the culture of the elementary mathematics classrooms in which students may have a lot of opportunities to develop conceptual under standing and math-ematical disposition. This paper first provides a detailed description of the classroom flow in terms of general social norms and sociomathematical norms in order to explore how the teacher and the students have established such a student-centered math-ematics microculture. This paper then analyzes the teacher's teaching approach and professional development.

• Research in Mathematical Education
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• v.8 no.1
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• pp.19-30
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• 2004

This research applies the discursive approach to investigate the social transformation of students' conceptual model of differential equations. The analysis focuses on the students' use of metaphor in class in order to find kinds of metaphor used, their characteristics, and a pattern in the use of metaphor. Based on the analysis, it is concluded that the students' conceptual model of differential equations gradually becomes transformed with respect to the historical and cultural structure of the communal practice of mathematics. The findings suggest that through participating in the daily practice of mathematics as a historical and cultural product, a learner becomes socially transformed to a certain kind of a cultural being with historicity. This implies that mathematics education is concerned with the formation of historical and cultural identity at a fundamental level.