Der-Ching Yang

• PhD
• Professor at National Chiayi University

The study was designed to enable researchers the opportunities to investigate the number sense performance and methods used by both the gifted and general students. A mixed-method design was used, and 48 gifted students and 95 general students in fourth grade from two elementary schools in Southern Taiwan were selected. The sample was chosen using...

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with onl...

This study is part of the international survey studies on teachers’ beliefs concerning the integration of children’s literature in mathematics teaching and learning, and this paper reports the findings of the thematic analysis of open-ended survey responses elicited from 287 primary school teachers and teacher trainees in Taiwan. Using the seminal...

This study reports on the development and application of an online four-tier test designed to assess elementary students' number sense and their conceptual understanding of numbers and operations. A total of 982 students completed the test, which was developed and validated to evaluate their number sense and conceptual understanding based on declar...

In this study, the author enrolled 982 fourth graders in Taiwan to investigate the differences (a) in confidence ratings between the answer and reason tier and (b) between students who provided correct and incorrect responses. This study administered a four-tier number sense test comprising an answer, confidence, reason, and confidence tier (the fi...

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with onl...

The purpose of this study is to compare the differences of four essential aspects (i.e., representational forms, contextual features, cognitive demand levels, and response types) embedded in mathematical problems within the topics of numbers and operations in mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This st...

This study examined the differences in the presentation of geometry concepts and characteristics of geometry questions among elementary mathematics textbooks in Finland, Singapore, and Taiwan. Horizontal and vertical analysis methods were used to collect and analyze the data. A popular Mathematics textbook from a dominant publisher in each country...

This study analysed the designs of algebraic problems in elementary mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This study employed a content-analysis method that focused on four dimensions: representational forms, cognitive demand levels (CDLs), contextual features, and types of responses. The result of the c...

Numbers and operations is widely considered the most essential domain in elementary school grades. Nevertheless, elementary students in Indonesia have consistently performed unsatisfactorily on this domain in several international mathematics assessments. This study examined 308 Indonesian sixth grade students’ current performance(s), misconception...

This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An analytical framework was developed comprising four perspectives: representational forms, cognitive demand levels, contextual features, and organization...

To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response, an...

Lay Description What is already known about this topic: Students must be instilled with conceptual understanding to achieve mastery of mathematical understanding and be able to properly solve complex or novel problems. Students would likely exhibit misconceptions if they do not have sufficient conceptual understanding. Students' conceptual understa...

To examine prospective teachers’ number sense performance, two-hundred and eighty prospective teachers who majored in elementary teaching from one teacher training institution of southern Taiwan were selected to participate in this study. Results showed that about one-fifths of the prospective teachers could apply number sense based method (such as...

Judging the reasonableness of computational results is pivotal for students to understand mathematical concepts. This domain is the most sensitive to the presence of misconceptions in mathematics. Confidence ratings can serve as a measure of the strength of students’ conceptual understanding. This study investigated the performance, misconceptions,...

This study examined the performance of sixth graders in Hong Kong on a number sense three-tier test (NSTTT) and identified their possible misconceptions about number sense. The NSTTT comprises a content tier, which assesses the content knowledge of number sense; a reason tier, which assesses the reasons for the first-tier responses; and a confidenc...

Assessing elementary students' performance on number sense provides early predictors and support for interventions in teaching and learning number sense before children fall seriously behind in school. There is no study that concerns the differences between Hong Kong and Taiwan students' performance on the number sense three-tier test. The purposes...

This research examined the presentation of fractions in textbooks used by fifth and sixth graders in Singapore, Taiwan, and the United States. The specific textbooks examined were My Pals Are Here! Maths (MPHM) in Singapore; Kung Hsung (KH) in Taiwan; and Mathematics in Context (MiC) in the USA. Results show the problems posed in MiC put more empha...

This chapter focuses on the neuro-cognitive, cognitive and developmental analyses of whole number arithmetic (WNA) learning. It comprises five sections. The first section provides an overview of the working group discussion. Section 7.2 reviews neuro-cognitive perspectives of learning WNA but looks beyond these to explain the transcoding of numeral...

This study examined the methods used by fourth graders when answering number sense-related questions. Eighth fourth graders who were classified as high, medium, and low achievers in mathematics were recruited from three public elementary schools in south Taiwan. Semi-structured interviews were conducted with all students, in which they responded to...

The purpose of this study was to analyze the cognitive demand levels required for learning algebra in secondary-level mathematics textbooks in Singapore and Indonesia. The research employed qualitative data and vertical analysis. The findings indicated that both Singaporean and Indonesian textbooks predominantly feature algebraic questions with low...

This study investigates algebraic instruction for eighth graders in Indonesia, Singapore, and the United States based on the algebraic content in their mathematics textbooks, which were identified as potentially implementable curricula (Varvelde et al., 2002). In these three countries, algebraic instruction goes beyond merely understanding algebrai...

This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The res...

This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students' learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation forms...

Organization for Economic Co-operation and Development (OECD) (2016) released the results of Programme for International Student Assessment (PISA) 2015 and reported that the students' performance in mathematics of Singapore and Indonesia had significant differences. There is a strong relationship between textbooks used and mathematics performance o...

The average undergraduate does not specifically calculate the total tuition or miscellaneous fees spent during their four-year study at university. Besides tuition and miscellaneous fees, few undergraduates record their basic living expenses or additional expenses, resulting in some unnecessary expenses. Using multimedia animation about expenditure...

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help c...

Most students thinking mathematics is a difficult subject. This study aims to enhance students' motivation and efficiency in learning mathematics. This study developed 3D animation on the binomial theorem with historical stories of mathematics as the plot. It also examined the effect of animation on students' learning willingness and comprehension....

With the advancement of information technology, mathematics and science have enriched the meaning of vocational education. The researchers developed 3D-animated teaching materials about mathematics that include stories about two mathematicians, Leibniz and Pascal, and upload them onto the website of a mathematical education system. The teaching mat...

The Organisation for Economic Co-operation and Development (OECD) has highlighted a significant disparity in mathematics performance between students in Indonesia and Singapore. This study investigates the role of national curricula, particularly through mathematics textbooks, in shaping students' achievement in statistics for grades 9-12. Employin...

This study applied the content analysis method to compare the differences of addition and subtraction for two digit numbers in grade one textbook. The published mathematics textbook of “Nani” in Taiwan and “My Pals Are Here [MPAH]” in Singapore were selected to be compared. They are the most popular elementary mathematics textbooks in each country....

The purposes of this study were to compare the differences in the use of geometry in elementary school mathematics textbooks among Finland, Mainland China, Singapore, Taiwan, and the USA and to investigate the relationships between the design of the textbooks and students' performance on large-scale tests such as TIMSS-4 geometry, TIMSS-8 geometry,...

This study analyzed geometry problems in middle-grade mathematics textbook series, considered as potentially implemented curriculum (Valverde et al., 2002), from Singapore and Indonesia, while exploring the expectations for students’ learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysi...

This study compared the mathematics curricula and textbooks used in Singapore and Indonesia that cover statistics at the tenth-grade level. The specific textbooks compared were "Mathematics" (Shinglee) from Singapore and "Buku Guru Matematika" (Mathematics Teacher Textbook) from Indonesia. The textbooks were evaluated based on their content in (a)...

The Organization for Economic Co-operation and Development (OECD) (2016) released the results of the Programme for International Student Assessment (PISA) 2015, highlighting significant differences in mathematics performance between students in Singapore and Indonesia. There is a strong relationship between the textbooks used and students' mathemat...

This study compared 6th-grade mathematics textbooks from the United States and Indonesia, focusing on the topic of data and probability. The specific textbooks analyzed were "Everyday Mathematics" (The University of Chicago School Mathematics Project) from the United States and "Belajar Matematika itu Mudah" (Learning Mathematics is Easy) from Indo...

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to participat...

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b) applicati...

Background: Number sense is a key topic in mathematics education, and the identification of children’s misconceptions about number is, therefore, important. Information about students’ serious misconceptions can be quite significant for teachers, allowing them to change their teaching plans to help children overcome these misconceptions. In science...

To examine the relative performance in number sense among low-SES students, new immigrant students, and typical learners in grades 4 through 6, data were collected through a number sense web-based, two-tier test. A total of 628 fourth graders, 535 fifth graders, and 524 sixth graders in Taiwan participated in this study. Results showed that there w...

This study integrated the 3D graphic animations for mathematics and sciences designed by Python and VPython with the methods of cooperative learning to conduct teaching experiment. A mixed scale (Likert 5 point + 10-point + structural items) was used to collect data. Multiple regression analysis was conducted to verify the path of effect of positiv...

The purpose of this study was to use calculator-assisted instruction to help two fifth-grade low-achievers learn number sense. The research process includes three stages: (1) pre-test interview to detect what kinds of number sense the students did not have; (2) calculator-assisted instruction to help them develop number sense; and (3) post-test int...

This paper describes how number sense was taught with interactive multimedia in a primary classroom in Taiwan and reports the differences of interviewed students' use of number sense strategies before and after the instruction. One sixth grade class which contains 32 students (18 boys and 14 girls) was selected to join the teaching experiment in a...

This study aimed to examine the effects of remedial instruction on low-SES & low-math first graders’ basic mathematics competence as well as their interest and confidence in mathematics learning. Fourteen participants of low-SES & low-math were selected from two classes totaling fifty-seven first graders at a public elementary school in central Tai...

The object of this study is applying the mathematical concepts to help students for learning the deflection analysis of beams. We integrate the concepts and techniques of calculus, derivative, programming writing, and deflection of beam device manufacture to achieve the purpose of this work. The results show the computer dynamic teaching and simula...

The authors compared the mental computation performance and mental strategies used by an experimental Grade 2 class and a control Grade 2 class before and after instructional intervention. Results indicate that students in the experimental group had better performance on mental computation. The use of mental strategies (counting, separation, aggreg...

The purpose of this study was to examine the relative effectiveness of two different learning modes; namely, a computer animation self-directed learning approach and a paper version of the self-directed learning approach, to 5th-graders’ number sense development. Two 5th-grade classes, 30 students each, were selected from a public elementary school...

The purpose of this study was to examine the relative effectiveness of two different learning modes; namely, a computer animation self-directed learning approach and a paper version of the self-directed learning approach, to 5th-graders' number sense development. Two 5th-grade classes, 30 students each, were selected from a public elementary school...

The purpose of this study was to investigate the performance and difference of fifth graders in Taiwan between contextual and numerical fractional problems. 355 students from 7 elementary schools in Southwest area of Taiwan were selected to join this study. The t-test result indicates that the fifth graders performed significantly better on numeric...

The key purpose of this study was how we taught the use of benchmark strategy when comparing fraction for fifth-graders in Taiwan. 26 fifth graders from a public elementary in south Taiwan were selected to join this study. Results of this case study showed that students had a much progress on the use of benchmark strategy when comparing fraction af...

This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowl...

Two 12-question estimation instruments were designed to compare the differences of estimating strategies used by the 8th-graders when solving contextual and numerical problems. Both instruments are parallel, meaning that the numbers used in both instruments are the same; however, they were presented differently. One hundred and ninety-eight 8th-gra...

本研究採質性研究法探討國小一年級學生進行心算教學活動之成效、策略改變情形及教學活動的實施歷程。研究樣本為實驗組學生21 人，進行二位數加減一位數的心算策略教學。對照組學生16人，依照教科書規劃的方式進行二位數加減一位數的教學，兩班各進行12 節課教學。研究結果顯示：教學後實驗組學生在心算之表現顯著優於對照組學生。同時，結果亦顯示教學後實驗組學生能夠發展多元之解題策略，如分離策略、集合策略，以及整體策略等。相反地，對照組學生在教學前、後，所使用之策略以數數策略、圖像與直式心像為主，改變較少，且少有心算策略的使用。教學過程中，藉由高分組學生的回答帶動中分組與低分組學生的思考，同時學生對於能夠上臺分享自己的策略感到興奮。最後根據研究結果，針對心算教學活動融入一年級數學課程及未來研究提出建議。 Th...

A quasi-experimental design was adopted to investigate the effect of integrating technology into mathematics teaching on students ’ number sense and their learning attitudes. Two sixth-grade classes were selected from an elementary school in Taiwan for participation in this study. The control group with 32 students followed their usual mathematics...

The authors compared the performance of students who received integration of number sense activities in instruction with students who received instruction using regular mathematics textbooks. Two classes of third-grade students (N = 60) were randomly assigned to experimental and control groups. Students in each group were given a pretest, post I te...

To investigate the structure of number sense and then to assess its uses in fifth-grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and substantial...

The aim of this article was to (a) describe how a teacher helped his students develop fractional number sense through a process-oriented activity, and (b) illustrate how a teacher included a worthwhile, interesting, and challenging mathematics question in his class to create a good learning environment for children. The results indicate that studen...

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings a...

This research examined the presentation of fractions in textbooks used by fifth and sixth graders in Singapore, Taiwan, and the United States. The specific textbooks examined were My Pals Are Here! Maths (MPHM) in Singapore; Kung Hsung (KH) in Taiwan; and Mathematics in Context (MiC) in the USA. Results show the problems posed in MiC put more empha...

This study reports on two excerpts from a 6th grade Taiwanese class, describing how a teacher examined and promoted his students' development of number sense. It illustrates an effort to integrate number sense activities into the mathematics curriculum in ways that encourage exploration, discussion, thinking and reasoning. The results indicate that...

The main purpose of this study was to investigate the number sense performance of 3rdgraders in Taiwan, and to diagnose areas of weakness or deficiency in number sense development. A total of 808 3rd-graders participated in this study. The results indicated that these students did not perform well on each of the five number sense components (correc...

This study was to develop a computerized number sense scale (CNST) to assess the performance of students who had already completed the 3rd-grade mathematics curriculum. In total, 808 students from representative elementary schools, including cities, country and rural areas of Taiwan, participated in this study. The results of statistical analyses a...

This study examined number sense strategies and misconceptions of 280 Taiwanese pre-service elementary teachers who responded to a series of real-life problems. About one-fifth of the pre-service teachers applied number sense-based strategies (such as using benchmarks appropriately or recognizing the number magnitude) while a majority of pre-servic...

In order to investigate the performance of number sense and its relationships with mathematics achievement of Taiwanese students who had just completed the 5th-grade mathematics curriculum, a computerized number sense scale has been developed. This number sense scale includes four factors which are recognizing relative number size, using multiple r...

This study examined the strategies used by pre-service teachers when responding to number sense related questions. 15 pre-service teachers from one University in Southern Taiwan were interviewed. Results indicated that about one-third of these pre-service teachers were able to use number sense strategies (such as recognizing the number size, using...

Developing number sense through real-life situations in school

In an interview setting, 21 6th‐graders from four public schools in south Taiwan were asked a series of questions, related to whole and decimal numbers, designed to assess their number sense. Eight students were randomly selected from both low and middle performance levels, and five were selected from a high‐performance level, according to their ma...

The author advocates for writing as an essential communication skill for learning mathematics. Mathematical diary writing is cited as a good way for students to privately represent their thinking through pictures, language, or symbols, and also as a channel for children to communicate with themselves and with their teachers. Cited research demonstr...

Two public schools (A and B) from two cities in southern Taiwan were selected to participate in this study. In each school, two sixth grade classes (an experimental and a control class) were studied. Number sense activities were conducted in the experimental classes through process-oriented teaching model to help children develop number sense, whil...

Twenty classes in ten schools with 627 sixth-grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One-way ANOVA analysis indicate that significant difference wa...

Two classes (one experimental and one control) in a public elementary school located in southern Taiwan participated in this study. Number sense activities were conducted in the experimental class as supplementary teaching materials, while the control class followed the standard mathematics curriculum. Data indicate that there are statistically sig...

Developing number sense is an important goal of mathematics programs. For example, the Number and Operations Standard in NCTM's Principles and Standards for School Mathematics states, “Central to this Standard is the development of number sense”(NCTM 2000, p. 32). Number sense is a complex process involving many different components of number and o...

This research provides information on the number sense of Taiwanese students in Grades 6 and 8. Data were collected with separate tests on written computation and number sense. Seventeen students were interviewed to learn more about their knowledge of number sense. Taiwanese students' overall performance on number sense was lower than their perform...

This research provides information on the number sense of Taiwanese students in Grades 6 and 8. Data were collected with separate tests on written computation and number sense. Seventeen students were interviewed to learn more about their knowledge of number sense. Taiwanese students' overall performance on number sense was lower than their perform...

Typescript. Thesis (Ph. D.)--University of Missouri-Columbia, 1995. Vita. Includes bibliographical references (leaves 181-197). Microfilm.