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Research and Development of Mathematics-Grounding Activity Modules as a Part of Curriculum in Taiwan
Abstract
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 development of the MGA modules; (2) cascading to include more teachers and designers; and (3) dissemination to students in Mathematics Camps. The evaluation of the project is still ongoing. Both student feedback and teacher feedback are collected during the MGA modules. At the current stage, data from both qualitative and quantitative results show significant positive influence.
... Classroom activities planned to be carried out within the framework of these plans and purposes characterize the implemented curriculum. Finding the reflections of the applied curriculum in the teaching books, its implementation by the teachers, and the evaluation of the students within the framework of the achievements are within the scope of the attained curriculum (Lin & Chang, 2019). In the teaching model of the TIMSS, which aims to evaluate the knowledge and skills of fourth and eighth-grade students in the fields of mathematics and science and carried out at the international level, there are curriculums as intended curriculum, implemented curriculum and attained curriculum (Mullis & Martin, 2017). ...
... Considering that the intended curriculum in the top-down and bottom-up approach includes learning expectations and ways of guiding learning (Hino & Ginshima, 2019), in this study, the aims, perspective, values, and competencies of the curriculum, as well as the stages of preparation, were considered in the intended curriculum stage. The implemented curriculum includes classroom-oriented application models of planned and intended acquisitions (Lin & Chang, 2019). In the Implemented stage, the focus is on scientists and their studies who contribute to mathematics in the curriculum, associating with real-life and associating with information and communication technologies, and mathematics lesson hours. ...
... In the Implemented stage, the focus is on scientists and their studies who contribute to mathematics in the curriculum, associating with real-life and associating with information and communication technologies, and mathematics lesson hours. Considering that the purposes intended to be achieved by students within through classroom activities are outlined in the curriculum (Çil & Çepni, 2014;Lin & Chang, 2019), the focus is on learning domains, sub-learning domains, and acquisitions in the curriculum within the framework of the attained stage. When the studies e-ISSN: 2536-4758 http://www.efdergi.hacettepe.edu.tr/ on secondary school mathematics curriculum are examined, there are studies in which the opinions of teachers (Aydın et al., 2018;Berkant & Gençoğlu, 2015;Biçer & Ada, 2020;Çiftçi et al., 2013;Çiftçi & Tatar, 2015;Sakallı et al., 2016;Tekalmaz, 2019;Yalçınkaya, 2018) and administrators (Abdioğlu & Çevik, 2018) are taken. ...
This study aims to examine the mathematics curriculum of vocational education centers, secondary education, and science high schools, currently implemented at the secondary education level, in terms of various variables based on the top-down and bottom-up approach. The document review method, a qualitative research method, was employed, and criterion sampling was adopted as the sampling method. Data were obtained through comparisons made by evaluating the purposes, perspective, basic philosophy, general aims, number of acquisitions, and learning domains of the curricula. The ratios of the acquisitions in the curriculums related to real-life situations, "scientists and their studies" emphasized in the general aims of the curriculum and information and communication technologies to all acquisitions were also analyzed. Descriptive statistical methods, such as percentage and frequency, were used to reveal differences between the curricula. As a result of the research, it has been observed that there are similarities in the purposes, competencies, and general aims of the mathematics curriculum of all three curriculums within the framework of the curriculum in which the top-down bottom-up approach is aimed. Within the framework of the applied curriculum, it was concluded that the least association was in the mathematics curriculum of vocational education centers in the examination of the associations made with scientists and their studies, real-life, and information and communication technologies in all three curriculums. In this direction, suggestions have been made for the points that need to be developed in line with the purposes, perspectives, and associations with acquisitions of the curriculums.
... al., 2012;OECD, 2014). Taiwan's Ministry of Education launched the JDM program in collaboration with Shi-Da Institute for Mathematics Education in 2014 to resolve this problem (Lin & Chang, 2019). The program aimed at engaging students in mathematics cognitively and affectively as well as enhancing mathematics teachers' professional development. ...
... Until mid-2018, there have been 175 MGAs designed and evaluated to accept. The mathematical content of these MGAs is connected to numbers, algebra, measurement, geometry and probability (Lin & Chang, 2019). ...
... MGAs were designed under careful consideration of mathematics content, mediated tools, and student learning to help students establish the fundamental prerequisite ideas before learning a mathematics topic in regular classes. The theories referred to the design of MGAs included to provide students opportunities for meaningful learning (Ausubel, 1961), for schema construction (Skemp, 1989), for experiencing different abstract levels of concepts with enactive, iconic and symbolic representations (Bruner, 1964), and for game-based learning adapted from Dienes (1973) in the mode stage of the JDM program (Lin & Chang, 2019). However, these theories were reactively related to the elaboration of MGAs rather than proactively referred to facilitating and improving the design of MGAs. ...
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 be derived in terms of the key processes. The key processes of designing MGAs, the criteria for evaluating quality MGAs and the design steps also emerged from the reciprocal relationships between theories and practices in the context of the Just Do Math (JDM) program. The processes and steps of designing MGAs suggested in this article can benefit researchers and educators to develop original activities for advancing the learning of mathematics in line with the enactivist perspective. Additionally, the key processes can be further referred to for explanations of how metaphorical grounds of mathematics can emerge under systemic interactions between learners, tasks and social contexts, and how learners’ motivation is integrated into the evolving tasks. Criteria could be applied for not only evaluating the potential of MGAs but also for identifying the weaknesses needed to be modified.
... To overcome the identified educational challenge, the JDM project, supported by the MOE and the Ministry of Science and Technology (MOST), was initiated in 2014 to provide students with opportunities to experience mathematics outside classrooms (Lin & Chang, 2019). The project focuses on designing a variety of mathematics grounding activities (MGAs) in line with mathematics content in the curriculum. ...
In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers’ competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified.
... The JDM project started in the mode stage with Fun-Math Camps based around mathematics-grounding activities (MGA-for-camp). The camps aim at providing opportunities for students to learn mathematics with fun, use their own mathematical sense, and to think mathematically via dialogues among peers (Lin & Chang, 2019;Lin, Wang & Yang, 2018). Schools apply to host Fun Math camps, and all fees are covered by the Ministry of Education, Taiwan. ...
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 mathematics in a more student-centered approach, rather than teaching mathematics in an inflexible way. The one-day workshop for cultivating leaders of mathematics-grounding activities in class (MGA-in-class), discussed in this article, is built on our previous TPD cascade model of scaling up the cultivation of designers, leaders, and teachers of mathematics-grounding activities for camps (MGA-for-camp). This paper focuses on presenting the process of developing and evaluating the one-day workshop for leaders of MGA-in-class. The development includes the processes of (1) how to transform activities designed for use in special camps to activities for use in regular classes, (2) how to cultivate the designers of MGA-in-class to be the facilitators in the one-day workshop for leaders of MGA-in-class, and (3) how to organize and evaluate the one-day workshop. Though the evidence shows that the one-day workshop has not recruited as many participants as previous TPD, the collected evidence provides useful information for future adjustment.
... Beberapa penelitian pengembangan modul, menyatakan pembelajaran matematika menggunakan modul sangat efektif bagi siswa (Devesh & Nasseri, 2014) dan dapat meningkatkan disposisi matematis (Chotimah et al., 2018). Penelitian pengembangan untuk siswa sekolah menengah, seperti pengembangan modul pembelajaran matematika pada materi statistika terintegrasi nilai-nilai keislaman (Ekawati et al., 2019) pengembangan modul matematika berbasis strategi metakognitif dalam meningkatkan kemampuan pemecahan masalah matematika siswa valid dan efektif (Telaumbanua et al., 2017), penelitian dan pengembangan modul aktivitas matematika-grounding sebagai bagian dari kurikulum di Taiwan (Lin & Chang, 2019). ...
Penelitian ini bertujuan untuk mengembangkan Modul Pembelajaran Mata Kuliah Teori Peluang untuk mahasiswa Pendidikan Matematika yang valid, praktis dan efektif. Jenis penelitian ini adalah penelitian pengembangan (Research & Development). Penelitian ini mengembangkan modul mata kuliah dengan menggunakan model pengembangan 4D (Define, Design, Develop, Dessiminate) yang dikembangkan oleh Thiagarajan, Dorothy S. Semmel, dan Melvyn I Semmel. Instrumen penelitian yang digunakan terdiri dari lembar validasi yang diisi oleh ahli bidang pendidikan matematika, lembar penilaian kepraktisan mahasiswa, angket disposisi matematis dan tes hasil belajar siswa. Kualitas modul yang dikembangkan ditinjau dari aspek kevalidan, aspek kepraktisan dan aspek keefektifan. Aspek kevalidan berdasarkan penilaian ahli menunjukkan bahwa modul pada kategori valid. Aspek kepraktisan berdasarkan penilaian mahasiswa adalah baik. Aspek efektifitas berdasarkan angket disposisi matematis pada kategori tinggi dan tes hasil belajar mahasiswa sebanyak 75% mendapat nilai minimal 60. Hasil pengembangan merupakan produk modul pembelajaran mata kuliah teori peluang yang valid, praktis dan efektif dan layak digunakan untuk mahasiswa pendidikan matematika.
Abstract
This study aims to develop tthe learning module design of Probability Theory for students of Mathematics Education that is valid, practical and effective. This type of research is research and development method. This study developed a module using the 4D development model (Define, Design, Develop, Dessiminate) developed by Thiagarajan, Dorothy S. Semmel, and Melvyn I Semmel. The research instrument consisted of validation sheets filled out by experts in the field of mathematics education, student practicality assessment sheets, mathematical disposition questionnaires and student learning outcomes tests. The quality of the modules developed is evaluated from the aspects of validity, practical aspects and effectiveness aspects. The validity aspect based on expert judgment shows that modules in the category are valid. The practicality aspect based on student assessment is good. The effectiveness aspect is based on a mathematical disposition questionnaire in the high category and a 75% student learning achievement test gets a minimum score of 60. The results of the development are a product of the learning module of probabilityy theory that are valid, practical and effective and are suitable for use in mathematics education students.
Numerous studies have explored the impact of game-based learning (GBL) on mathematics education. This teaching experiment endeavors to develop a mathematics grounding activity (MGA) mobile application focused on cube nets and to assess whether this MGA app enhances students' understanding of mathematical concepts and their attitude toward learning mathematics. To achieve this, a combination of quantitative and qualitative research methods was employed, involving a cohort of 506 students spanning grades four to six. Findings revealed that the MGA app effectively motivated students and added an element of intrigue to mathematics classes. Additionally, it was observed that students were able to facilitate their own learning, rendering redundant exercises unnecessary. Furthermore, the application demonstrated the potential to bridge age and gender gaps, suggesting that its implementation in a coeducational and mixed-age classroom setting is viable and convenient.
This chapter, corresponding to Theme D in the conference, is dedicated to tools and resources used in, designed for and resulting from teacher collaboration, and is composed of six more sections after this brief one. Section 5.2 introduces the essential issues to be addressed. Sections 5.3 through 5.6 are dedicated to tools and resources: designed for teacher collaboration (Sect. 5.3); for learning to improve teaching practice in collaboration (Sect. 5.4); for fostering collaboration (Sect. 5.5); for studying collaboration (Sect. 5.6). Section 5.7 looks to the future, considering not only the discussion at the conference, but also other possible topics of interest for research.
Leong, Y. H., Kaur, B., Choy, B. H., Yeo, J. B. W., & Chin, S. L. (Eds.). (2021). Proceedings of the 43rd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA): Excellence in Mathematics Education: Foundations and Pathways. Singapore: MERGA. Available online at https://www.merga.net.au/Public/Publications/Annual_Conference_Proceedings/2021-MERGA-conference-proceedings.aspx
The "development of human intellectual functioning from infancy to such perfection as it may reach is shaped by a series of technological advances in the use of mind. Growth depends upon the mastery of techniques and cannot be understood without reference to such mastery. These techniques are not, in the main, inventions of the individuals who are growing up; they are, rather, skills transmitted with varying efficiency and success by the culture—language being a prime example. Cognitive growth, then, is in a major way from the outside in as well as from the inside out." The "growth of symbolic functioning links a unique set of powers to man's capacity." (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This book offers in-depth information resulting from the Third International Mathematics and Science Study (TIMSS). Launched in 1995, the TIMSS examines elementary and secondary mathematics and science achievement in 40 countries. The book explains that curriculum has a profound effect on student achievement and plays a crucial role in providing opportunities for student learning. The 11 chapters examine: (1) "How Does Curriculum Affect Learning?"; (2) "A Model of Curriculum and Learning"; (3) "Measuring Curriculum and Achievement"; (4) "The Articulation of Curriculum"; (5) "Curriculum Variation"; (6) "The Structure of Curriculum"; (7) "A First Look at Achievement"; (8) "Learning and the Structure of Curriculum"; (9) "Curriculum and Learning Gains across Countries"; (10)"Curriculum and Learning Within Countries"; and (11) "Schools Matter." The book concludes that reform efforts should be redirected to create challenging curriculum across all years of schooling for all students. The four appendixes focus on: TIMSS mathematics and science curriculum frameworks; relationship between content measurement categories for TIMSS framework, teachers, and TIMSS test; TIMSS framework codes and number of items for each mathematics and science test sub-area; and supplemental material related to the two-level analysis of mathematics achievement: chapter 10. (Contains 96 references, 56 tables, and 32 figures.) (SM)
In the mid- 1970s the curriculum development boom in mathematics was to end almost as rapidly as it had begun. In this book the authors, who come from countries with differing educational traditions and patterns, consider these developments in their historical, social and educational context. They give not only a descriptive account of developmental work in a variety of countries, its aims and the patterns of management utilised, but also attempt to identify trends and characteristics and thus provide a theoretical base for criticism and analysis. The reader will find numerous case studies, including extracts from such renowned authors as Bruner, Dieudonne and Piaget.
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 students’ fundamental prerequisite mathematical ideas before regular classes, employing concrete manipulative representations as a starter for learning, and embedding learning activities in games. The design and implementation of the project involved the development of grounding activity modules and facilitation of professional development of mathematics teachers to implement instruction according to modules to engage students in learning mathematics. The findings – confirming the project significantly facilitated students’ cognitive and affective engagement in learning mathematics – can inform the government regarding educational reform and can suggest teachers and educators feasible instructional approaches to facilitate student engagement in East Asian countries/regions.
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 degree of teaching, to afford benefits for teaching; (2) provide one-shot or semester-based workshops for teachers’ lifelong learning for them to catch up on contemporary educational issues and reforms; and (3) incorporate teachers’ professional, evaluation, and growth into one system for the convenience of teachers’ learning, herein the network platform. We summarize the three types with a framework to show the structure of professional development programs
involving teachers, their facilitators and contexts. Next, to enhance mathematics teachers
’ motivation and professions in learning from the workshops, we give two examples of ongoing professional development program
, conducted nationally, which assist mathematics teachers
in designing tasks and teaching practice, while cultivating their active thinking and learning. Finally, we make a concluding remark on the three types of teachers professional programs in Taiwan.
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.
Through our work in mathematics and science education we have observed that students react similarly to a wide variety of conceptually unrelated situations. Our work suggests that many responses which the literature describes as alternative conceptions could be interpreted as evolving from common, intuitive rules. This paper describes and discusses one such rule, manifested when two systems are equal with respect to a certain quantity A but differ in another quantity B. We found that in such situations, students often argue that Same amount of A implies same amount of B. Our claim is that such responses are specific instances of the intuitive rule Same A—same B. This approach explains common sources for students'; conceptions and has strong predictive power.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
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