• Research in Mathematical Education
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• v.22 no.3
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• pp.203-222
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• 2019

Despite its importance when it is employed in classrooms, scaffolding is limited in the classrooms. Many researchers have focused on contingent teaching, which is the first component of scaffolding. Given a lack of research on contingent teaching with prospective teachers (PSTs), this paper explores how PSTs intend to do contingent teaching in small groups when they engage in mathematics teaching. Building on research on contingent teaching, I analyzed 26 PSTs' written responses to scenarios in an online open-ended survey. The focus of the analysis was on how the PSTs would do contingent teaching that might support students to learn the subject matter. I present findings in relation to what the PSTs' responses showed in relation to contingent teaching with the subject matter. The findings will be discussed along with implications.

• School Mathematics
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• v.4 no.1
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• pp.49-62
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• 2002

developed by solving practical problems and gradually formalized and abstracted. But school mathematics seemed to stress the formalized and abstracted mathematics. The same is the case with calculus. In particular, it appeared extremely in teaching of calculus. It caused hindrance of learning and indeed, many students had difficulties in teaming of calculus. Therefore this study investigates the various approaches of calculus teaching and the history of calculus which include approaches by Archimedes, Galileo, Newton, Leibniz and Weierstrass etc. This may offer the implication for calculus teaching and we can find the alternative on the method of calculus teaching in historico-genetic principle. Finally we suggest the direction of calculus teaching from this perspective in tile concrete.

• Research in Mathematical Education
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• v.15 no.2
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• pp.105-114
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• 2011

During the 20th century, the secondary school mathematics teaching in China had been developing from the an old-style private school form with individual instruction to classroom teaching with Chinese characteristics, which experienced three stages of development; the stage for the formation of modern teaching system (1902-1949), the stage for development (1950-1976), and the stage for innovation (1977-2000). The characteristics and journey for the transformation will exert great for reference and effects for the reform of secondary school mathematics teaching nowadays.

• International Journal of Computer Science & Network Security
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• v.22 no.5
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• pp.255-265
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• 2022

Educational programs for students with intellectual disabilities have undergone drastic changes in pursuit of the general curriculum. Accordingly, teachers in various fields, including mathematics, strive to find effective methods that enhance learning. The objective of this systematic review is to examine the field of teaching mathematics to students with intellectual disabilities to investigate relevant effective teaching strategies and required teaching skills. To achieve this goal, studies published during the period 2018-2021 were reviewed. Findings indicate the inclusion of nine studies that met the inclusion criteria out of 55 studies. The included studies found that the system of least prompts (SLP) in conjunction with feedback and error correction, and schema-based instruction are generally the most effective strategies in teaching mathematical skills to students with intellectual disabilities. Addition is the most targeted skill, followed by subtraction and algebra problem solving. The least targeted skills are multiplication, recognition of geometric shapes, calculating price after discount, rapid recognition of numbers, and rapid problem solving. The paper provides recommendations and suggests venues of future research.

• Korean Journal of Child Education & Care
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• v.19 no.2
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• pp.19-33
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• 2019

Objective: The purpose of this study is to understand how the experience of studying mathematics education for young children based on picture books is affecting pre-service early childhood teachers with their attitude toward mathematics and mathematics teaching efficiency. Methods: For this, a total of 39 pre-service early childhood teachers majoring in early childhood education at S university located in G metropolitan city participated in the study. 20 of them are randomly assigned to the experimental group while the rest 19 were assigned to the control group. The experimental group participated in the classes of mathematics education for young children based on picture books for 15 weeks, while the control group attended the normal classes of mathematics education for young children for the same period of time. By using SPSS 18.0 Program for the collected data, t-test was conducted for differences in the results of attitude toward mathematics and mathematics teaching efficiency. Results: The results of this study are as follows. Firstly, the experience of studying mathematics education for young children based on picture books had a positive effects on pre-service early childhood teachers' attitude toward mathematics, improved values and interest in mathematics, and reduced anxiety about mathematics. Secondly, the experience of studying mathematics education for young children based on picture books had a positive effects on improving pre-service early childhood teachers' mathematics teaching efficiency. Also, both faith in ability and faith in results have improved significantly. Conclusion/Implications: These results imply that the experience of studying mathematics education for young children based on picture books is an effective teaching-learning method in improving pre-service early childhood teachers' attitude toward mathematics and mathematics teaching efficiency.

• The Mathematical Education
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• v.57 no.2
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• pp.179-196
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• 2018

The purpose of this study was to investigate the measurement equivalence and to suggest application ways in teaching aptitude and personality test results for pre-service mathematics teachers between a graduate school of education and a college of education. This study analyzed the scores of the teaching aptitude and personality test of 36 pre-service mathematics teachers enrolled in a graduate school of education and 111 pre-service mathematics teachers in a college of education by performing a multivariate generalizability analysis. The main results were as follows. First, graduate's pre-service mathematics teachers had a higher level of teaching aptitude and personality than that of college's pre-service mathematics teachers based on the total scores. In addition, graduate's pre-service mathematics teachers had higher levels of teaching aptitude and personality than those of college's pre-service mathematics teachers except for a creativity application domain based on the sub-domain scores. Second, cognitive domains were measured more precisely but affective domains were measured less precisely for graduate's pre-service mathematics teachers than for college's pre-service mathematics teachers. Third, regardless of school levels, Cronbach's ${\alpha}$ values, which might be overestimated by applying the classical test theory, were higher than dependability coefficients. Fourth, this study showed a somewhat negative result in ensuring the measurement equivalence for a problem solving exploration domain. However, regardless of school levels, this study indicated that the overall measurement was generally reliable on composite scores. Based on these results, it was confirmed that multivariate generalizability methodologies' approach can be useful for exploring the measurement equivalence issues. Finally, this study suggests how to utilize the results of the test, how to apply a multivariate generalizability analysis for detecting the measurement equivalence, and how to develop future research based on limitations.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.323-338
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• 2010

In this study we analyzed the teaching units for the area of geometrical figures by the same method in the previous research of Kang, Wan and Kim, Nam Jun in 2010, where they extracted the teaching units based on the mathematics curriculum based on the theory of Wittmann (1984). Teaching units are a systematic organization of the essential contents for mathematics education according to 4 elements, objectives, data, functions, and backgrounds. In this study, the features and titles of the teaching units, extracted from the area of geometrical figures in revised mathematics curriculums in 2007, are analyzed and categorized as accepting of concept type, application of concept type, and acquiring of relation type. Their meanings for education are investigated, in addition, the way of their practical application to research of education for the area of geometrical figures. The teaching units are a model consistently compensated and evolved rather than fixed. It will be an important material for establishing new educational courses if the teaching units are more systematically studied by mathematics researchers and teachers in educational fields.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.45-56
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• 2010

This research analyzes the elementary school mathematics curriculum in Korea in accordance with the teaching units devised by the German mathematics pedagogue, Wittmann(1984). Teaching units, a systematic teaching content organized according to the 4 elements of objectives, data, functions, and backgrounds, helps educators and professors plot for the systematic organization and structural understanding of the materials necessary in teaching. This research presents the extracting process of teaching units step by step based on the 2007 revised mathematics curriculum and also demonstrates the new alternative method to analyze and review the entire education courses through it. Teaching units is not immutable, but rather pursuing and developing a model that consistently through the constant complementary efforts by the research experts. On that account, many researchers and field professors continuously devote their efforts to develop and innovate it so that it can be practically used as an essential tool to establish a new mathematics curriculum.

• Education of Primary School Mathematics
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• v.3 no.1
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• pp.47-54
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• 1999

The development of computer software accelerates the change of teaching-learning method in primary school mathematics. In this paper, we discuss how to apply the software GSP to teach mathematics in primary school and suggest some examples fur the creative and active loaming. Moreover, we give the efficient teaching method for the primary school mathematics.

• Research in Mathematical Education
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• v.19 no.4
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• pp.247-265
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• 2015

Mathematics textbook plays a significant role in shaping students' learning of mathematics. Logic, rigor and abstraction as typical features of the formalization of mathematics, dominate mathematics textbooks around the world, which is regarded as one of the important origins of students' learning difficulties in mathematics. An innovative series of Chinese mathematic textbooks is presented in this paper. Supported by the supplementary materials excerpts from the textbooks, it gives a comprehensive theoretical analysis of the principles of design and implementation of this series of mathematics textbooks. The effectiveness of this series of textbooks is demonstrated by student achievement and secondary research data. It shows that series of Chinese mathematic textbooks has largely decreased students' learning difficulties in mathematics and enhance classroom teaching efficiency. It suggests that prioritizing the essence of mathematics and reducing abstraction is an important notion for mathematics textbook design and implementation.