• East Asian mathematical journal
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• v.33 no.4
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• pp.431-451
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• 2017

This is a descriptive study with the intent of providing a rich characterization of teachers' perceptions of rate of change. The nature of teachers' perceptions and differences among teachers were examined by collecting data through a survey on teachers' conceptions of rate of change in terms of learning goals, prerequisites, and beliefs about teaching and learning of rate of change, and an interview individually assessing teachers' concept images and definitions. The participating 13 teachers were selected to provide a range of similar and contrasting levels of experiences based on the teachers' educational background and the number of years they had been teaching. Findings and implications of this study are discussed.

• IE interfaces
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• v.12 no.2
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• pp.237-246
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• 1999

The Automated Storage/Retrieval System(AS/RS) is very expensive to be built. But there are few tools available which can be used to design the storage systems optimally considering overall system building costs and constraints. In this paper, we propose a design support system for optimal design of AS/RS which includes different sized cells using expert systems and mathematical models considering customer's demands. The optimization models are to be used to minimize the total cost including building, equipment and operation costs. Expert system technique is utilized for using the experiences of skilled designers. By using the proposed system, AS/RS can be designed accurately, economically and efficiently.

• Research in Mathematical Education
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• v.24 no.3
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• pp.201-228
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• 2021

Teacher noticing has been termed consequential to teaching because what you see and do not see impacts decisions made within the classroom. Further, how a teacher responds to student thinking depends on what a teacher sees in student thinking. Within this study we sought to understand what teachers noticed within an engineering lesson and the decisions made as a result of that noticing. Findings indicate that student teachers and cooperating teachers drew on their pedagogical knowledge for decisions, rather than taking up the integrated content of student thinking and understanding. These findings serve as a guide for the experiences needed to engage in the complex work of teaching or, more specifically, implementing engineering into instruction through a responsive teaching frame.

• Research in Mathematical Education
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• v.24 no.1
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• pp.29-47
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• 2021

The purpose of this study was to examine what factors affect the construction of preservice white mathematics teachers' racial identities and the relationship between their racial identities and Culturally Relevant Teaching (CRT) practices. We examined five white female preservice teachers who enrolled in an elementary mathematics methods course at a private university in the US. We collected data consisting of lesson plans, semi-structured interviews, and reflection of a taught lesson in the 2018 fall term and examined them using qualitative research methods. We found that preservice teachers' racial identities were affected by their backgrounds, K-12 school experiences, and practicum school environment. We also found a relationship between teachers' sensitivity to racial issues and their endorsement of CRT strategies. The findings also revealed that the relationships were mediated by practicum school contexts. Based on the findings, we provided practical implications for the teacher education programs.

• Research in Mathematical Education
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• v.25 no.2
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• pp.117-133
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• 2022

Examining ways to interact with students in small groups is an important topic for researchers to understand. Existing studies pertaining to the topic have not shed light on knowing why teachers interact with students in small groups the way they do. Given that teacher identity shapes teaching practices, this study explores how teacher identity shapes teachers' interaction with students in small groups. Working with two beginning teachers, I conducted four interviews to collect the data related to reasons behind their interactions with students in small groups in the interview. I analyzed the interview transcripts using a thematic analysis. I found that one teacher's teacher identity was related to her personal experiences as a child and a learner and another teacher's teacher identity was related to her view of teachers' roles as a teacher. I provide discussion and implications of this study.

• Research in Mathematical Education
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• v.26 no.1
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• pp.31-38
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• 2023

Mathematics educators have emphasized the importance of language use in mathematics education. However, previous studies have predominantly focused on the spoken language used in mathematics classrooms, which provides limited information on the written language used by mathematics teachers. The written language reflects the characteristics of the teacher community and social, cultural, and political contexts. Moreover, the written language affects teachers' instructional practices and their students' mathematics learning experiences. Therefore, this study aims to review a study conducted by Lee and Kim (2022) investigating changes in mathematics teachers' pedagogical lexicons.

• Research in Mathematical Education
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• v.26 no.4
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• pp.311-331
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• 2023

This article explores how mathematics teacher educators (MTEs) engaged in collaborative inquiry into the microteaching experiences of preservice teachers (PSTs), ultimately developing a noticing framework through collective MTE inquiry. We delve into the specifics of what MTEs notice focusing on three emerging categories of noticing on PST's microteaching videos-lesson structure, task quality, and teaching practices. Each category, along with MTEs' noticing within these components, is elaborated through vignettes. This approach positions MTEs' noticing as a crucial element in the overarching vision to enhance the teaching practices of PSTs.

• School Mathematics
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• v.15 no.4
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• pp.701-721
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• 2013

In this study, I set the 5th grade children mathematically gifted in elementary school to pose freely the creative and difficult mathematical problems by using their knowledges and experiences they have learned till now. I wanted to find out that the math brains in elementary school 5th grade could posed mathematical problems to a certain levels and by the various and divergent thinking activities. Analyzing the mathematical problems of the mathematically gifted 5th grade children posed, I found out the math brains in 5th grade can create various and refined problems mathematically and also they did effort to make the mathematically good problems for various regions in curriculum. As these results, I could conclude that they have had the various and divergent thinking activities in posing those problems. It is a large goal for the children to bring up the creativities by the learning mathematics in the 2009 refined elementary mathematics curriculum. I emphasize that it is very important to learn and teach the mathematical problem posing to rear the various and divergent thinking powers in the school mathematics.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.149-163
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• 2011

While the affective aspects are emphasized in the current mathematics curriculum in Korea, it is just indicated a superficial degree. Therefore in this study, based on consideration for internal representational system theories, a dynamic viewpoints of self-system processes, socio-constructivist perspectives, and motivation theories, we discuss the meaning of affective competency, the motive of mathematics learning, mathematical identity of students, social environments and affective experiences, then we suggest an affective frame in mathematical learning. Hereby, we suggest what should be considered in affect instructions and the alternative goal of mathematical education in affective aspects.