Fou-Lai Lin

Societal differences and their influences on children's mathematics understanding

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 childrens mathematical understanding? This problem will be my main concern in this paper.

Assessing Science Students' Attitudes to Mathematics: A Case Study on a Modelling Project with Mathematical Software.

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 mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.

Defining a rectangle under a social and practical setting by two seventh graders

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.

Teachers’ Professional Learning of Teaching Proof and Proving

This chapter 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 discuss the challenges teachers may face in teaching proof and proving, as well as teachers’ professional learning activities. Throughout, we argue that the three components are interrelated in successful teaching of proof and proving. This argument raises a new challenge for further research.

Designing a Competence-Based Entry Course for Prospective Secondary Mathematics Teachers

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 approach provides abundant opportunities for PSMTs to cultivate their competencies in teaching. In this chapter, we take the first year course to deliberate why the Psychology of Mathematics Learning is selected as an entry course for the teacher education program and how it works. Considering the importance to raise PSMTs’ awareness of students’ mathematical thinking and to cultivate their competencies of sensitizing students’ mathematical thinking, and ultimately to bear the competencies as the habitus in their future teaching professional, the mission of the course focuses on PSMTs’ learning of understanding students’ mathematical thinking through the process of cyclic learning. The quality of PSMTs dynamic learning in the field study can be evaluated by their study work. This chapter provides one example of PSMTs’ survey study in one complete learning cycle, and summarizes several criteria of evaluating how PSMTs conduct a study to understand students’ mathematical thinking in a holistic perspective.

Facilitating Professional Growth of Taiwanese In-service Mathematics Teachers Through an Innovative School-Based Program

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, Lighten-up School-Based Program (LUSBP), they initiated for facilitating professional growth of mathematics teachers in Taiwan. The core for LUSBP is that all tiers of educators, teachers, and students learn through active participation whilst interacting with each other. The project employs a design-based approach with teachers as designers who learn from the process of creating tasks, enacting tasks with classroom students, and revising tasks based on students’ learning. The school-based model enables the creation of a friendly learning environment where teachers take it for granted to make changes and are willing to share their experiences with one another. The outcomes of LUSBP are positive and hold promise for the future.

The Effects of PISA in Taiwan: Contemporary Assessment Reform

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 schools. Students, along with their parents and teachers, worried about the ability to solve PISA-like problems and private educational providers offered additional tutoring. This chapter reports and explains these dramatic effects. Increasingly, the PISA concept of mathematical literacy has been used, along with other frameworks, as the theoretical background for thinking about future directions for teaching and assessment in schools. This is seen as part of an endeavour to change the strong emphasis on memorisation and repetitive practice in Taiwanese schools.

TSG 13: Mathematical Learning and Cognitive Processes

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 above theme. The situations about students’ learning of number operations, solving quadratic equations, concepts of place-value, concept of infinite, concept of definition, mental calculation, problem solving and mathematical induction have been analyzed.