• Research in Mathematical Education
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• v.25 no.2
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• pp.135-158
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• 2022

This study aimed to building models to understand the relationships between reasoning resources and content knowledge. We applied Support Vector Machine and linear models to the data including fifth graders' scores in the Cornel Critical Thinking Test and the Iowa Assessments, demographic information, and learning science approach (a student-centered approach to learning called the Science Writing Heuristic [SWH] or traditional). The SWH model showing the relationships between critical thinking domains and academic achievement at grade 5 was developed, and its validity was tested across different learning environments. We also evaluated the stability of the model by applying the SWH models to the data of the grade levels. The findings can help mathematics educators understand how critical thinking and achievement relate to each other. Furthermore, the findings suggested that reasoning in mathematics classrooms can promote performance on standardized tests.

• School Mathematics
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• v.13 no.4
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• pp.615-632
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• 2011

The purpose of the study was to investigate the mathematical knowledge for teaching (MKT) of pre-service and in-service mathematics teachers on the concept of vector. 80 pre-service and 124 in-service mathematics teachers were asked to perform three questions based on MKT's subdomain. The results show that pre-service teachers have stronger common content knowledge(CCK). On the other hand, in-service teachers have stronger specialized content knowledge(SCK), knowledge of content and teaching(KCT) compared to those of pre-service teachers. The paper proposes CCK, SCK and KCT about the concept of vector and discusses the relationships between subdomains of MKT.

• School Mathematics
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• v.1 no.1
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• pp.123-133
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• 1999

For an appropriate assessment in mathematics, students should play an active role in their learning by becoming aware of what they have learned in mathematics and by being able to assess their attainment of mathematical knowledge. The process of actively examining and monitoring students' own progress in learning and understanding of their mathematical knowledge, process, and attitude is called self-assessment, Researchers in mathematics education have found some important facts about the meta-cognitive process which is related to self-assessment : i. e. meta-cognition progress is composed of being aware of ones' own personal thinking of content knowledge and cognitive process(self-awareness) and engagement in self-evaluation. Tipical method for self-assessment in mathematics developed upon above finding about meta-cognitive progress is describing about students' knowledge and their problem solving strategies. In the beginning of the description in mathematics about themselves, students are required to answer which part they know and which part they don't know. Self-assessment of students' attitudes and dispositions can be just as important as assessment of their specific mathematical abilities. To make the self-assessment method a success, teachers should let students' have confidence and earn their cooperation by let them overcoming fear to be known the their ability to other students. In conclusion, self-assessment encourages students to assume an active role in development of mathematical power. For teachers, student self-assessment activities can provide a prism through which the development of students' mathematical power can be viewed.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.285-294
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• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.

• East Asian mathematical journal
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• v.36 no.2
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• pp.229-251
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• 2020

Problem Based learning(PBL) is a teaching and learning method to increase mathematical ability and help achieving mathematical concepts and principles through problem solving using the learner's mathematical prerequisite knowledge. In addition, the recent instructional situations or environments have focused on the learner's self construction of his learning and its process. In spite of such a quite attention, it is not easy to apply and execute PBL program actually in class. Especially, there are some difficulties in actually applying and practicing PBL in the areas of mathematics education in not only secondary school but also in college. Its reason is that in order to conduct PBL instruction constantly in real or experimental class there is no more concrete and detailed instructional content during the consistent and long period. However, to whom is related to mathematics education including instructors called scaffolders, investigation and recognition on the degree of the learner's acquisition of mathematical thinking skills and strategies is an very important work. By the reason, in this study, the instructional content was to be explored and developed to be conducted during 15 weeks in one semester, which was based on Problem Based Learning environment by the subject of the theories relevant to mathematics education in the college of education.

• School Mathematics
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• v.16 no.4
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• pp.827-845
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• 2014

This study aims to investigate how the university educational programs about quadratic curves are operated in relation to the high school curriculum and what their effects may be, and the degree of understanding for the prospective and current teachers of the mathematical content knowledge about quadratic curves. To solve this research questions, we randomly selected three universities and one high school. Then we investigated the curricula of each department of mathematics education, compared them with the high school curricula, and conducted surveys of the professors' and students' conception on how much mathematical content knowledge they need to know about quadratic curves. The study resulted in the following conclusions. First, the curriculum on the subject of quadratic curves in the college of education is closely connected to the high school programs. This study's results showed that the college of education's curriculum includes a series of lectures regarding quadratic curves, and that within them, the mathematical content about quadratic curves associated with high school mathematics was thoroughly covered. Also, a large number of students who attended the lecture reported a significant increase in their understanding in regards to the quadratic curves. Second, it is strongly recommended to strengthen the connection between the college of education's curriculum and the actual high school education field. The prospective teachers think that there is a substantial need to learn about the quadratic curves because it is closely connected with the high school curriculum. But they find it challenging to put what they were taught into practical use in the high school education field, and feel that an improvement in this area is much needed. Third, it is necessary to promote, encourage and support the voluntary efforts to expand the range of the content knowledge in quadratic curves to cover the academic content associated with the high school mathematics.

• The Mathematical Education
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• v.60 no.3
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• pp.297-319
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• 2021

The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.215-241
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• 2017

This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.

• Research in Mathematical Education
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• v.14 no.2
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• pp.173-194
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• 2010

This study examines the differences and similarities of mathematics teachers' subject matter knowledge among England, the Chinese mainland and Hong Kong. Data were collected from a ten-item test in the SKIMA subject matter audit instrument [Rowland, T.; Martyn, S.; Barber, P. & Heal, C. (2000). Primary teacher trainees' mathematics subject knowledge and classroom performance. In: T. Rowland & C. Morgan (eds.), Research in Mathematics Education, Volume 2 (pp.3-18). ME 2000e.03066] from over 500 participants. Results showed that participants from England performed consistently better, with those from Hong Kong being next and then followed by those from the Chinese mainland. The qualitative data revealed that participants from Hong Kong and the Chinese mainland were fluent in applying routines to solve problems, but had some difficulties in offering explanations or justifications.

• School Mathematics
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• v.16 no.4
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• pp.763-782
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• 2014

The purpose of this study is to investigate mathematics content knowledge(MCK) of pre-service teachers about the area of a circle. 53 pre-service teachers were asked to perform four tasks based on the central ideas of measurement for the area of a circle. The results of this study are as follows. First, pre-service teachers had some difficulty in describing the meaning of the area of a circle. Quite a few of them didn't recognize the necessity of counting the number of area units. Secondly, pre-service teachers had insufficient content knowledge about the central ideas of measurement for the area of a circle such as partitioning, unit iteration, rearranging, structuring an array and approximation. Lastly, few pre-service teachers understood the concept of actual infinity. Most students regarded the rectangle as the figure having the approximation error instead of the limitation from rearranging the parts of a circle.