楊德清 國立嘉義大學數理教育研究所 1

Outline 1. ICME (International Congress on Mathematical Education) PME36 (Psychology of Mathematics Education) 2. NSF, JRME, ESM, IJSME 3. 國科會科教處數學教育學門 Call for proposals 4. Personal experiences 2

Topic Study Groups A. Mathematical Literacy & Reading Literacy * Statistical literacy * PISA 「閱讀數學 SIG 」 - 臺師大心輔系 吳昭容教授 1. ICME & PME36 3

科學教育發展處 102 年度「數學教育及閱 讀教育實務研究」計畫徵求書 1. 中學生數學素養教學與評量 2. 中學生閱讀素養教學與評量 4

B. Activities and programs for gifted students C. Activities and Programs for Students with Special Needs --- 國科會科教處徵求 102 年度「原住民科學教育計畫」 --- 弱勢學生相關研究計畫 ( 提升弱勢學生數學學習之相 關教學研究 ) 5

D. Analysis of Uses of Technology in the Teaching of Mathematics E. Analysis of Uses of Technology in the Learning of Mathematics F. Research on Classroom Practice

Discussion Groups Creativity in Mathematics Education (1) What does creativity mean in the process of teaching and learning mathematics? a. How might creativity be defined, recognized, and/or assessed? b. Is creativity an unconscious or intuitive component of doing mathematics? c. Is creativity something that all students can develop or must students be gifted to be creative? 7

(2) How can we develop or stimulate creative activities in and beyond the mathematics classroom? a. Is mathematical creativity something that can be taught? b. What can teachers do to foster creativity? c. How can we use technology to promote mathematical creativity? d. What mathematics activities outside the classroom might be used to develop mathematical creativity? 8

e. What is the role of creativity in assessment, curricula, mathematics competitions, and other aspects of mathematics education? (3) How might we balance mathematical skill training and mathematical creativity? (4) What should be done in teacher training programs at the preservice and inservice levels to foster creativity in the classroom? 9

Issues Surrounding Teaching Linear Algebra 1. What is the meaning of understanding linear algebra? 2. How can we improve students’ conceptual understanding of linear algebra concepts? 3. How can we encourage students to think in the formal world of mathematics? 4. What are some of the major difficulties that linear algebra students encounter? 5. What skills do we want students to take away from a linear algebra course? Do our exams really test these skills? 10

6. Can one see linear algebra (visualization, geometry)? How can we educate the students to see the beauty of Linear Algebra and its importance? 7. Discussion of constructive and innovative ways to use technology in the teaching of linear algebra (Sage, MATLAB, clickers, etc.). 8. Should a second course in linear algebra be required for all undergraduate mathematics majors/ science students / engineering students? If so, how do we go about convincing departments to require a second course in linear algebra? 11

Uses of History of Mathematics in School (pupils aged ) 1. Which ideas from HPM can be used with children (aged 6- 13) in such a way that produces a god result (e.g. improved student engagement, positively impacted student learning)? 2. What would be criteria for finding, developing and selecting materials to be used with children (aged 6-13)? 3. How does the HPM community in particular (and mathematics education community more broadly) assure that high quality material that cover a variety of topic are produced and shared? 12

Improving Teacher Professional Development Through Lesson Study A. What are the key elements of Lesson Study that can help teachers gain mathematical knowledge for teaching? B. What are the key elements of Lesson Study that can help teachers develop expertise in teaching mathematics effectively? C. How can an established effective professional development model such as Lesson Study be translated for use in different cultures? D. How can a professional development model such as Lesson Study be adapted for use in pre-service teacher education? 13

Theory and Perspective of Mathematics Learning and Teaching from the Asian Regions How mathematics is taught and learned in the Asian regions for primary and secondary mathematics? Under what influence or theories does the pedagogical content knowledge or didactical knowledge in mathematics is developed in the Asian classroom? Are there any different approach/frameworks between primary and secondary levels teaching in the Asian classrooms? 14

‧ Are there any theoretical perspectives or conceptual frameworks for mathematics teaching at the Asian classroom? ‧ How and why such teaching / learning practice in the Asian classroom? ‧ What is the training of a mathematics teacher in the Asians regions? ‧ How to analyze the possible trend in the classroom teaching in the Asian region, with respect to individual circumstances of local theories of learning? 15

‧ What is the context of the existing theories of learning in mathematics in Asian classroom? ‧ What is the possible development of the theory and framework of the theories used in the Asian classrooms? ‧ What kind of topics (secondary/primary) in mathematics are being taught based on certain theories, and which kind of topics are less likely to employ using a theory in teaching? 16

Using Technology to Integrate Geometry and Algebra in the Study of Functions What are the potential advantages and disadvantages of integrating a geometric approach into the study of function? What role does technology play in integrating a geometric approach into the study of functions? Twenty years after the introduction of dynamic mathematics software, why have there not been more research studies on this approach, and why has there been so little adoption in schools? 17

What research has actually been done, and what additional research needs to be done, to validate this approach? How well are students able to integrate the geometric and algebraic views of various concepts? For instance, how well does a student’s understanding of covariation in the geometric context transfer to the symbolic context? What factors bear on this transfer of learning? How can we best encourage students to connect their learning in the two realms? 18

What other cognitive obstacles must students overcome? Which aspects of the study of function can be developed geometrically, and which cannot? What approaches to professional development are likely to be effective in helping teachers understand the approach and develop enthusiasm for it? How does this approach relate to ongoing curriculum- reform efforts in various regions or countries? How can we in our professional roles best help move this process forward? 19

New Challenges in Developing Dynamic Software for Teaching and Learning Mathematics What are the most important challenges in developing mathematical software for teaching? How do new hardware platforms (e.g. smart phones, tablets, IWB) alter the functionality and features of mathematical software? How best to cater for cultural differences? How best to implement localization of software? 20

How can software be developed which is both increasingly more powerful, but also easy to use? What can we learn from the successes and failures of software applications? What are the research priorities for software development? What kinds of research projects are necessary to support the development of software? What kinds of hardware are best suited for effective use of software? How can the design of mathematical software best be developed to support STEM/MST education? 21

Discussion groups Equilateral Triangle: A Study and Demonstration of the Properties Using GeoGebra Software Right Angle Triangle Trigonometry: An Activity Using GeoGebra Software Circle, Circumference and Trigonometric Arc: A Methodological Approach Using GeoGebra Software 22

Teaching Mathematics and Statistics with the New features of GeoGebra 4.0 and 4.2 Teaching Mathematics with GeoGebra Tube (Online Environment for Dynamic Mathematics) and Experiencing 3D Algebraic Space with GeoGebra 5 Building and Exploring Parabola Using GeoGebra Software Symmetry of Figures: An Activity Using GeoGebra Software 23

NSF, JRME, ESM, IJSME Two Trends o Interdisciplinary Research o Mixed Methods 24

國科會科教處數學教育學門 Call for proposals 一、數學教育 ( 學門代碼： SSS01) （一）數學文化與教育相關議題的研究 ( 重點代號： 101) （二）提高國民統計素養的研究 ( 重點代號： 102) （三）數學師資培育及教師專業學習與發展研究 ( 重點 代號： 103) （四）數學課程、教學與學習相關議題的研究 ( 重點代 號： 104) （五）數學學習成效評量的研究 ( 重點代號： 105) 25

（六）資訊科技在數學教育相關議題的研究 ( 重點代號： 106) （七）認知神經科學與數學學習與教學的整合研究 ( 重 點代號： 107) 26

Personal experiences 課程教科書之相關研究 科技融入數學教與學之研究 創造力 (Creativity) 與數學教育 27

謝謝聆聽！ 28