# Fou-Lai LinNational Taiwan Normal University | NTNU

Fou-Lai Lin

## About

81

Publications

23,713

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1,376

Citations

Citations since 2017

## Publications

Publications (81)

This study aims to build a framework for affect-focused (or affective) mathematical teaching (AMT), while promoting higher-order mathematical learning (e.g., pattern finding and deep understanding). The data sources were the class mathematics grounding activity designed by Taiwan’s mathematics educators, aiming to enhance students’ affective perfor...

Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students’ mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will...

Students’ negative affective performance in mathematics learning is a global problem, and the situation is especially challenging in high-achieving East Asian countries. Taiwan’s Just Do Math (JDM) program was launched to resolve this problem and to serve as an example of successful scaling up with regard to implementation of innovation. We develop...

Teacher professional development (TPD) is an important topic for school teaching and learning, but the challenging part is how to design quality and sustainable TPD that results in sound teachers’ learning. This research paper presents a cascade model of TPD used by the Just Do Math project and designed to nurture any number of teachers to teach ma...

Language plays an important role in word problem solving. Accordingly, the language in which a word problem is presented could affect its solution process. In particular, East-Asian, non-alphabetic languages are assumed to provide specific benefits for mathematics compared to Indo-European, alphabetic languages. By analyzing students’ eye movements...

In order to develop meaningful mathematics activities for students to enjoy learning and to improve their learning, the mathematics-grounding activity (MGA) modules are developed as part of the JUST DO MATH project which has been funded by the Taiwanese Ministry of Education since 2014. The project consists of three phases: (1) research and develop...

Large-scale studies assess mathematical competence in large samples. They often compare mathematical competence between groups of individuals within or between countries. Although large-scale research is part of empirical educational research more generally, it is also linked to more genuine mathematics education research traditions, because sophis...

This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator–researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implement...

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis revealed...

This paper discusses the effects of large-scale studies, including international comparative studies and national studies using nationally representative samples, on policy making and practices pertinent to mathematics education in Taiwan, through the lens of Taiwanese societal and cultural characteristics. Taiwan has been through several successfu...

The goal of this study aims at introducing an entry course of a 3-year sequential courses module for a secondary mathematics teacher education program in Taiwan. This module is a reformed teacher education curriculum planned for Prospective Secondary Mathematics Teachers (PSMTs) to learn how to teach with the field-study approach. The field-study a...

Responding to students’ performance in TIMSS and PISA in East Asian countries/regions – low interests, low confidence, not seeing the value of mathematics, and high-achieving performance in average but a substantial percentage of “lowest performers”– a project JUST DO MATH has been launched in Taiwan. The themes of the project included developing s...

The chapter begins with the present challenges that mathematics educators in Taiwan are facing. It outlines the hierarchical structure of in-service teacher development and highlights how the top-down approach often adopted may not address the needs of classroom teachers. The authors of the chapter next describe an innovative school-based program,...

In this chapter, we present the current status of mathematics teachers
’ professional development
in Taiwan. We first elaborate three policy directions to outline a holistic view on three types of teachers’ professional development
. The three policy directions are aimed to (1) encourage teachers to take academic degree program, especially master d...

This chapter reports the professional learning of 21 in-service mathematics teachers (MTs), from two junior high schools participating, in the Lighten-Up School-Based Program (LUSBP). The MTs in both the schools chose mathematical conjecturing as the theme of professional development (PD); they also participated in the PD workshops on approaches fo...

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what m...

A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In...

As Adler, Ball, Krainer, Lin and Novotna (2005) remarked in their landmark ICME survey report, research into mathematics teacher education was rather sparse until the mid-1990s. From its roots in mathematics and psychology – witness the name of the sponsor organisation of this handbook – the output of researchers in mathematics (or ‘mathematical’)...

Taiwan has always been one of the top ranked countries in PISA, so initially interest in PISA was mainly concerned with standards monitoring, with some analysis of how instruction could be improved. However, from 2012, PISA became a major public phenomenon as it became linked with proposed new school assessment and competitive entrance to desirable...

In this study, we aimed at examining Indonesian In-Service primary Teachers' Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK) for teaching ratio and proportion. The instruments were administered to 271 in-service primary teachers with various education background. There were three underlined factors on MCK an...

This paper aims to explore the educative power of an experienced mathematics teacher educator-researcher (MTE-R) who displayed his insights and strategies in teacher professional development (TPD) programs. To this end, we propose a framework by first conceptualizing educative power based on three constructs—communication, reasoning, and connection...

In this study, we aimed at demonstrating the power of Variation Theory in exploring the local situation of Indonesian teachers and Teacher Professional Development program. The projection of Variation theory regarding the enterprise of teaching results on the need of sensitivity of students and exemplary teaching strategy that differ with teachers...

In this study, we developed an instrument for assessing teachers’ mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher’s MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences. Te...

This study compared the effects of reading-oriented tasks and writing-oriented tasks on students’ reading comprehension of geometry proof (RCGP). The reading-oriented tasks were designed with reading strategies and the idea of problem posing. The writing-oriented tasks were consistent with usual proof instruction for writing a proof and applying it...

From the sociocultural perspective, this research utilized activity theory as the theoretical framework to analyze the influences of cultural factors for Taiwanese Atayal junior high school students’ study in mathematics. The research methodology adopted grounded theory, theoretical and methodological approaches which are illustrated through episod...

Principles of task design should have both the fundamental function of a clear relation to the learner’s rules, learning powers or hypothetical learning trajectories and the practical function of easy evaluation of many similar tasks. Drawing on some theories and practical tasks in the literature, we developed a total of 11 principles of task desig...

This paper reviews studies on teachers’ professional learning of teaching proof and proving. From them we conceptualise three essential components of successful teaching: teachers’ knowledge of proof, proof practices and beliefs about proof. With respect to each component, we examine research studies of primary and secondary teachers. We also discu...

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathem...

The teaching and learning of mathematics in schools has drawn tremendous attention since the education reform in Taiwan. In
addition to assessing cognitive abilities, Taiwan Assessment of Student Achievement in Mathematics (TASA-MAT) collects background
information to help depict average student achievement in schools in an educational context. The...

This study uses classroom videotapes to examine the phenomenon of students who are left behind during whole-class teaching.
Zooming in via these videos enabled us to analyze these classroom situations by means of a compact, multi-perspective set
of theories – van Hiele theory, conceptualization, and visual perception. The analysis provided a pictur...

Conference Proceedings with papers of ICMI Study 19 Conference.

Contains al the papers of ICMI Study 19 Conference: Proof and Proving in Mathematics Education.

In this article, we discuss the complexity of geometric proofs with respect to a theoretical analysis and empirical results
from studies in Taiwan and Germany. Based on these findings in both countries, specific teachings experiments with junior
high school students were developed, conducted, and evaluated. According to the different classroom and...

A model of reading comprehension of geometric proofs (RCGP) has recently been proposed by the authors. This article further
investigates students’ development of such comprehension based on this model, looking at the relationship between students’
reading comprehension and their prior knowledge and logical reasoning. The results show that (1) stude...

This study aims to investigate a construct of reading comprehension of geometry proof (RCGP). The research aims to investigate
(a) the facets composing RCGP, and (b) the structure of these facets. Firstly, we conceptualize this construct with relevant
literature and on the basis of the discrimination between the logical and the epistemic meanings o...

This paper presents a cross-cultural study on the intuitive rules theory. The study was conducted in Australia (with aboriginal
children) in Taiwan and in Israel. Our findings indicate that Taiwanese and Australian Aboriginal students, much like Israeli
ones, provided incorrect responses, most of which were in line with the intuitive rules. Also, d...

The paper presents a study aimed to inquire the factors and reasons causing a relatively big group of low achieving Taiwanese students to be left behind, while others have gained one of best results in the world (TIMSS, 2003). Using the methodology of Problematic Learning Situation (Gal & Linchevski, 2000), we characterised 9th grade geometry lesso...

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education confe...

We first discern three different sources to describe the non-modelling friendly environment in Taiwan: the background of mathematics teachers and students, examinations, and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis o...

Based on a national survey and some further studies of mathematical proof and refutation of 7th through 9th graders, this paper will show evidence of the existence of continuity between refuting as a learning strategy and the production of conjectures, and between a more effective teaching strategy and the traditional teaching strategy. A detailed...

This chapter summarizes some research-based evidence that characterizes how Chinese learn mathematics, and then points out needed directions to understand Chinese learners and their learning of mathematics. The discussion is situated in a comparative context by focusing on the following four important issues: (1) Are Chinese learners really higher...

Three issues about students reasoning, proving and understanding proof in number patterns are investigated in this paper. The first is to elaborate the features of junior high students reasoning on linear and quadratic number patterns. The second is to study the relationships between 9th graders justification of mathematical statements about number...

This building of structure is what we are trying to design when we talk about cognition and learning. Hart K. opened this study group with the above citation that describes the theme of TSG 13 properly. During the two sessions of TSG 13, eight speakers from the East and West countries are selected and invited to present their studies related to the...

Two hundreds and two students of 17~20 years old were surveyed on their understanding of proof by contradiction. Five abilities were identified for interpreting their understanding. A two-streamed model of understanding proof by contradiction was constructed statistically. To analyze the negating of a statement with quantifier 'only have one', inte...

Regarding defining as a mathematical activity bridging informal to formal proof, two seventh graders will reinvent the definition
of rectangles under a social and practical setting based on their informal argumentation. Their apprehensions of figures,
implicit concepts/theorems and the cognitive architecture of defining are discussed in this paper....

This chapter addresses the role of values in mathematics teachers’ thinking, and the relationship of those values to teachers’ classroom practices, in order to examine the assumption raised in Bishop’s chapter that the more teachers understand about their own value positions the better teachers they will be. Studying values from two aspects, referr...

This is a research-based book on mathematics teacher education. It is about the learning of prospective and inservice mathematics teachers, mathematics educators, and researchers. The text is intended for a broad audience including teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers at all...

A teaching model on learning refuting and conjecture making is established based on the performance of Taiwanese junior high school students on argumentation. The main data was taken from a national survey, together with two small-scale studies. Students' behaviors on giving examples with respect to false propositions were classified. Based on that...

England and Taiwan are two societies in which the languages, the rationales of education, the teaching orientations and the learning motivations in school are very different. Would such differences influence children's mathematical understanding? This problem will be my main concern in this paper.

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learnt this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing, symboliz...

In a previous article (Chin & Lin, 2000a) we reported the substance and structure of mathematics teachers' pedagogical values as well as methodological issues of conducting research into such values, based on a case study of an expert mathematics teacher. We considered values education from the level of clarification/articulation. In this follow-up...

This paper describes a form of value-loaded activities emerged in teaching and learning of mathematical induction in which the value of pleasure is shared by an expert teacher and his students. Using case study method, values are explored with classroom observation, teacher and student interview, and questionnaire survey. Conceiving identity theory...

Considering values from different aspects of the nature of mathematics and mathematics learning, this paper addresses the issues of students' values emerged in learning the concept of mathematical induction. Using three batteries of questionnaire survey and interviews, the primitive value of "uncertainty", "fun", and "certainty" and some derivative...

Abstract The impact that mathematics teachers’ pedagogical beliefs, whether consistent or not, have on their classroom instructional practices and student conceptions have been well documented. A probable source for the (in)consistencies of such beliefs is considered to be teachers ’ mathematical and pedagogical values as expressed in the deeper af...

The reading and coloring (RC) strategy has been verified that it can enhanced incomplete provers' performance to Taiwan junior high students while they had learnt the multi-steps formal geometry proof. In this study, we transfer the RC strategy into whole class regular teaching and explore its effectiveness and limitation. The results show that the...

Mathematical software has been playing an important role in teaching and learning. This paper reports the students' performance and reaction on the use of MATLAB for a modeling project at the National Taiwan Normal University. It was the first time a mathematical modeling project had been incorporated into the Applied Mathematics course for such st...

## Projects

Projects (3)

Research on the learning and teaching on proof in mathematics has largely developed along the past decades. Hundreds of research projects and PhD theses have documented its complexity from multiple perspectives, within different theoretical frameworks, and with different methodologies. Moreover, this domain is very sensitive to epistemological viewpoints and cultural contexts.
The objective of the "Proof in Mathematics Education: Reflection and Institutionalization" Research Gate meta-project is to engage in a conversation and sharing resources to bridge the different approaches and the related outcomes. As a community, our objective is to turn objections and differences into research problems. Specifically, we aim at:
• Exploring the diversity of the definitions in order to understand the impact of our different languages, culture, institutions on sharing research
• Eliciting the different problématiques and their possible relationships
• Eliciting the theoretical commonalities and divergences
• Commenting on the different methodologies, their benefit, and their possible limits
• Institutionalizing accepted results
The method will consist in sharing research papers, commenting and discussing them using the RG platform. More could be expected if successful, for example writing a synthesis of some of the debates and discussions. But the idea is to be pragmatic first. So let's see how it works...
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Nicolas Balacheff, Gila Hanna, Guershon Harel, Patricio Herbst, Christine Knipping, Fou-Lai Lin, Carolyn Maher, M. Alessandra Mariotti, Takeshi Miyakawa, David Reid, Andreas J. Stylianides, Keith Weber