• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.67-88
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• 2020

This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.85-104
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• 2019

The purpose of this study is to analyze the tasks developed through task development activities with emphasis on mathematical connectivity, and to provide implications for teacher education to enhance teacher's competence. For this purpose, I analyzed the task developed by 52 pre-teachers through the activities. As a result, they combined mathematics with 'other subjects', 'mathematics', 'phenomenon', 'technology' and 'real life'. And they also made various internal connections of 'Different representation', 'Part-whole relationship', 'Implication', 'Procedure', and 'Instruction-oriented connection'. From the point of view of teacher knowledge, the study revealed that CCK and SCK were positive in terms of 'logical' and 'expression', and KCT as 'strategic' was meaningful but disappointing in diversity; however in terms of 'level', the KCS was limited due to tasks that did not meet the level of students. As such, this analysis reveals that teachers continue to struggle with understanding students' level, but exhibit little difficulty with 'logic', 'expression' and 'strategy. This being the case, teacher education needs to place additional emphasis in understanding students' levels and planning corresponding activities.

• School Mathematics
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• v.6 no.3
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• pp.267-281
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• 2004

The purpose of this study is to understand Preservice elementary teachers' knowledge about multiplication of fractions by focusing on their computation abilities, understanding of meanings, generating appropriate problem contexts and representations. A total of 115 preservice elementary teachers participated in the present study. The results of this study indicated that most of preservice elementary teachers have little difficulty in computing multiplication of fractions for right answers, but they have big difficulty in understanding meanings and generating appropriate problem contexts for multiplication of fractions when the multiplier is not an integer, called 'multiplier effect.' Likewise, the rate of appropriate representations surprisingly decreased for multiplication of fractions when the multiplier is not an integer. The findings also point out that an ability to make problem contexts is highly correlated with representations and meanings. This study implies that teacher education programs need to improve preservice elementary teachers' profound understanding of elementary mathematics in order to fundamentally improve the quality of teaching practices in classrooms.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.61-78
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• 2016

The purpose of this study was to investigate the perceptions and perspectives on meanings and use of manipulatives in mathematics lessons. For the investigation, the researcher reviewed related literature and analyzed the perceptions of preservice teachers on the meanings and use of manipulatives in mathematics lessons. The participants were 75 preservice elementary school teachers who took a teaching practice course at the 1st or the 2nd semester in 2015. These preservice teachers observed mathematics lessons for two weeks during the student teaching periods. They were requested to observed the use of manipulatives in mathematics lessons and wrote about their ideas on the meanings and use of manipulatives. Result of the research was that the perceptions on the meanings and use of manipulatives from the preservice teachers' perspectives are as follows. Manipulatives in mathematics lessons were self-made or pre-made manufactures. The using time of manipulatives during lessons varies, and the teachers provide the manipulatives with contexts. Providing in-depth observation during a teaching practice course is allowed opportunities for preservice teachers to reflect their mathematics teaching and learning methods in the classroom.

• The Mathematical Education
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• v.61 no.1
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• pp.179-198
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• 2022

Teaching is delicate, complicated, and demanding work, and especially beginning teachers set forth their difficulties in preparing and implementing mathematics instruction. It is important to ensure the quality of beginning mathematics teachers' instruction above a consistent level because such affirmation justifies the national policy on teacher education as well as the individual efforts of preservice teachers in South Korea. The current study collected mathematics lessons of the two beginning teachers who graduated from the same teacher training institute and worked at the same high school. The findings reported what features their lessons have with regard to the learning environment, engaging students in learning, deepening student learning, and using representations of the edTPA in order to identify what can or cannot be expected in their mathematics instruction. The instruction of the one teacher was assessed middle or more than middle scores throughout the rubrics, but the other one had lower scores. Based on these findings, this study suggested the implications for teacher education in ways of improving the quality of instruction of beginning mathematics teachers.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.153-166
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• 2017

164 preservice elementary teachers' decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

• School Mathematics
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• v.16 no.3
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• pp.491-502
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• 2014

This paper analyzed pre-service teachers' justification of $0.99{\cdots}$=1 from their disproof of $0.99{\cdots}$ <1. Some pre-service teachers thought of the difference between $0.99{\cdots}$ and 1 as an infinitesimal. On the contrary, the others claimed that the difference between $0.99{\cdots}$ and 1 was zero as the standard real, but were content with their intuitive justifications. The pre-service teachers' limitation revealed in the process of disproving $0.99{\cdots}$ <1 can be closely related to the orthodox view: the standard real number system is the only absolutely true number system. The existence of nonstandard real number system in which $0.99{\cdots}$ is less than 1, shows that the plain question of whether or not $0.99{\cdots}$ equals 1, cannot be properly answered by common explanations of textbooks or teachers' intuitive justification.

• The Mathematical Education
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• v.59 no.3
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• pp.271-294
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• 2020

The purpose of this study was to explore the possibility of digital simulation by which pre-service teachers (PSTs) can approximate the core teaching practice of eliciting student thinking. This study examined PSTs' questions to elicit student thinking, their use of "pause" session and peer feedback, and their reflections on doing a digital simulation. We analyzed a two-hour digital simulation session with 13 PSTs who enrolled in the elementary mathematics methods course. The results showed that PSTs shifted their general questions to more content-specific questions throughout the simulation and made a quick transition to comparing students' strategies. The number of lead PST-initiated "pause" ranged one to four times for various reasons. Their peer-coaches did not voluntarily "pause" the simulation session but actively shared what they noticed from the student work samples and suggested the next teaching moves. Without utilizing the pause session, the dramatic improvement of questioning was not observed. Even though the PSTs felt overwhelmed with interacting with the student-avatars in real-time, they highlighted the benefits of simulations, appreciated the opportunity to learn the core teaching practice, and viewed this digital simulation as "real" and "authentic" experience. The findings of this study provide implications for re-designing a practice-based teacher education program.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.535-555
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• 2012

The aim of this study is to analyze how the context problems by prospective teachers are solved. In order to achieve this aim, this study examined the conceptual nature of context based on previous studies. I developed context problems about linear programming with reference to the results of the examination about the natural characterization of context. These problems were given to 44 prospective teachers and qualitative methods were used to analyze the data obtained from the written solutions by the participants. This study also developed the framework descriptors for this analysis in the light of the Mathematics Scoring Rubric from Illinois Department of Education(2005). The data was analyzed and interpreted in terms of this framework and the specific characteristics shown in the process of problem solving by the teachers were categorized into four types as a result.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.43-55
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• 2022

It is critical to examine changes in teachers' beliefs on how to teach and learn mathematics through teacher education programs. This study aims to develop an instrument measuring elementary pre-service teachers' beliefs on student- and teacher-centered instruction. After developing questionnaires with mathematics education experts, the structural validity of the instrument was evaluated by collecting and analyzing data from 166 pre-service teachers. Parallel analysis and exploratory factor analysis were applied sequentially to collect validity and reliability evidence. The results showed that this instrument can be used to examine changes in pre-service teachers' two different types of belief: student- and teacher-centered instruction. We also suggested how to interpret scores appropriately.