課程含括面向：
<br>
<br>1. 兒童數學概念發展總論
<br>Piaget的認知發展階段論
<br>Bruner的認知發展階段論
<br>Vygotsky的認知發展社會歷史論
<br>
<br>2. 不同數學內涵下，從課程設計角度來論述兒童認知發展歷程
<br>整數與四則運算
<br>分數與小數
<br>量與實測
<br>比與比例
<br>幾何
<br>統計概念
<br>不同數學內涵下，兒童的數學認知行為介紹
<br>整數與四則運算
<br>分數與小數
<br>量與實測
<br>比與比例
<br>幾何
<br>統計概念
<br>
<br>3. 兒童數學概念發展的診斷與分析
<br>概念試題的設計
<br>錯誤類型與學習困難分析
<br>假設性學習路徑設計介紹與形成性&總結性評量設計與實施
<br>
<br>課程進行方式：
<br>1.本課程進行以實務為主，理論為輔。除了認知發展的一般性理論之外，其餘均架基在實徵案例分
<br>享
<br>與分析。
<br>2.課堂前或課堂中，學生必須從提出的不同實徵案例中，提出自己的意見，進行案例分析。從中培
<br>養
<br>對兒童數學概念發展及展現認知行為的理解。
<br>3. 課堂也會介紹概念診斷與分析活動設計與實施，希冀培養學生能診斷兒童迷思概念的活動設計與
<br>分析能力。
<br>
<br>課程評量：
<br>1. 選定主題，提供師培生實徵學生解題案例，實際分析學生數學概念認知發展狀況及背後可能存在
<br>的迷思概念。期中、期末各一次作業。作業完成方式為小組作業（60％）.
<br>2. 出席率及課堂參與（40％）。若缺課兩次，會嚴重影響該科總成績。
<br>
<br>參考書目：
<br>Bell, A. (1993). Principles for the design of teaching.Educational Studies in 
<br>Mathematics, 24(1), 5-34.
<br>Bruner, J. (1960).The process of education. Cambridge, MA: Harvard University 
<br>Press.
<br>Bruner, J. S. (1966).Toward a theory of instruction. Cambridge, MA: Harvard 
<br>University.
<br>Piaget, J. (1970).Science of education and the psychology of the child. New 
<br>York: Basic Books.
<br>Vygotsky, L. S. (1978).Mind in society: The development of higher psychological 
<br>processes. Cambridge, MA: Harvard University Press. Published originally in 
<br>Russian in 1930.
<br>Vygotsky, L. S. (1986).Thought and language. Cambridge: MIT Press.
<br>張春興. (1996).教育心理學.台北:東華書局.
<br>Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. 
<br>(1998). A longitudinal study of invention and understanding in children’s 
<br>multidigit addition and subtraction.Journal for Research in Mathematics 
<br>Education, 29(1), 3-20.
<br>Clements, D. H., & Sarama, J. (2004). Learning Trajectories in Mathematics 
<br>Education.Mathematical Thinking and Learning, 6(2), 81-89.
<br>Confrey, J. (1990). A review of the research on student conceptions in 
<br>mathematics, science, adn programming.Review of Research in Education, 16, 3-
<br>56.
<br>Fischbein, E. (1993). The theory of figural concepts.Educational Studies in 
<br>Mathematics, 24(2), 139-162.
<br>Fischbein, E., & Nachlieli, T. (1998). Concepts and figures in geometrical 
<br>reasoning.International Journal of Science Education, 20(10), 1193-1211.
<br>Kieran, C. (1981). Concepts associated with the equality symbol.Educational 
<br>Studies in Mathematics, 12, 317-326.
<br>Mack, N. K. (1995). Confounding whole-number and fraction concepts when 
<br>building 
<br>on informal knowledge.Journal for Research in Mathematics Education, 26(5), 
<br>422-
<br>441.
<br>Mack, N. K. (2001). Building on informal knowledge through instruction in a 
<br>complex content domain: Partitioning, units, and understanding multiplication 
<br>of 
<br>fractions.Journal for Research in Mathematics Education, 32(3), 267-295.
<br>Michener, E. R. (1978). understanding understanding mathematics.Cognitive 
<br>Science, 2, 361-383.
<br>Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. 
<br>(1989). Conceptual ba<x>ses of arithmetic errors: The case of decimal 
<br>fractions.Journal for Research in Mathematics Education, 20(1), 8-27.
<br>Sfard, A. (1989).Transition from operational to structural conception: The 
<br>notion of fuction revised.Paper presented at the Proceedings of XXXX 
<br>International Group for Psychology of Mathematics Educaiton, Paris, France.
<br>Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections 
<br>on 
<br>processes and ob<x>jects as different sides of the same coin.Educational 
<br>Studies in 
<br>Mathematics, 22, 1-36.
<br>Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-
<br>ups cannot see as different?--Early numerical thinking revisited.Cognition and 
<br>Instruction, 23(2), 237-309.
<br>Simon, M., & Tzur, R. (2004). Explicating the role of mathematical tasks in 
<br>conceptual learning: An elaboration of the hypothetical learning 
<br>trajectory.Mathematical Thinking and Learning, 6(2), 91-104.
<br>Stylianides, A. (2007). The notion of proof in the context of elementary school 
<br>mathematics.Educational Studies in Mathematics, 65, 1-20.
<br>Vergnaud, G. (1988). Multiplicative structures. In M. Hiebert & J. Behr 
<br>(Eds.),Number Concepts and Operation in Middle Grades(pp. 141-161). Reston, VA: 
<br>National Council of Teachers of Mathematics.
<br>Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of 
<br>function.Journal for Research in Mathematics Education, 20(4), 356-366.
<br>參考教材
<br>各版本教科書教學指引。
<br>九年一貫數學課程綱要