Using Dynamic Representations to Strengthen Understanding of Linear Functions among Seventh Graders

運用動態表徵強化七年級學生理解線型函數的意義

10.6278/tjme.201810_5(2).003

呂鳳琳(Feng-Lin Lu)；李健恆(Kin Hang Lei)；蕭淑娟(Shu-Chun Hsiao)

computer aided instruction ； dynamic representations ； linear function ； 電腦輔助教學 ； 動態表徵 ； 線型函數

臺灣數學教育期刊

5卷2期（2018 / 10 / 01）

1 - 17

英文

In this study, we investigated the effectiveness of computer-assisted learning when used by students in the seventh grade to learn the linear function y = mx + b. The proposed instructional approach is based on the dynamic linking of multiple representations. The aim of this linking is to provide clarification of the mathematical structure of linear functions and the meaning of parameters m and b. We adopted a quasi-experimental design involving two classes from a junior high school in Taiwan. None of the students possessed prior knowledge of linear functions. The experiment group was exposed to linear functions within a digital learning environment, whereas the control group was subjected to the conventional paper and pencil approach. Results from pre-tests and post-tests revealed significant improvements in both groups; however, the experiment group significantly outperformed those in the control group. In fact, the experiment group obtained higher scores on a delayed posttest than on the initial posttest. This is a clear demonstration of the benefits of computer-assisted learning in terms of concept retention.

本研究旨在闡明七年級學生學習線型函數y = mx + b時，電腦輔助學習對其理解線型函數意義的效果。學習環境主要依據動態鏈結多重表徵之特色，以幫助學生釐清線型函數的數學結構與參數m和b的意義。研究設計是以兩班七年級學生為研究對象進行準實驗研究。實驗組與對照組學生分別採數位學習和傳統紙本兩種不同教學形式學習線型函數。整體而言，實驗組學生在後測與延後測的答對率均高於對照組。更進一步來說，前、後測結果顯示不同教學形式對兩組學生在概念建構的立即效果均具有顯著幫助。此外，由前測與延後測結果顯示，實驗組學生在延後測的答對率顯著優於對照組學生，由此可見在電腦輔助學習中善用動態表徵有助於學生概念保留的長期效果。

1. Ainsworth, S.(2006).DeFT: A conceptual framework for considering learning with multiple representations.Learning and Instruction,16(3),183-198.
2. Bardini, C.,Stacey, K.(2006).Students' conceptions of mand c: How to tune a linear function.Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education,Prague, Czech Republic:
3. Bu, L.(Ed.),Schoen, R.(Ed.)(2011).Model-centered learning: Pathways to mathematical understanding using GeoGebra.Rotterdam, The Netherlands:Sense.
4. Even, R.(1998).Factors Involved in Linking Representations of Functions.Journal of Mathematical Behavior,17(1),105-121.
5. Hitt, F.(1998).Difficulties in the articulation of different representations linked to the concept of function.The Journal of Mathematical Behavior,17(1),123-134.
6. Janvier, C.(1987).Translation Processes in Mathematics Education.Problem of representation in teaching and learning of mathematics,Hillsdale, NJ:
7. Leinhardt, G.,Zaslavsky, O.,Stein, M. K.(1990).Functions, graphs, and graphing: Tasks, learning, and teaching.Review of Educational Research,60(1),1-64.
8. Lesh, R..,Post, T. R.,Behr, M.(1987).Representation and translation among representation in mathematics learning and problem solving.Problem of representation in teaching and learning of mathematics,Hillsdale, NJ:
9. Mayer, R. E.(1997).Multimedia learning: Are we asking the right questions?.Educational Psychologist,32(1),1-19.
10. National Council of Teachers of Mathematics(2000).Principles and standards for school mathematics.Reston, VA:Author.
11. Romberg, T. A.(Ed.),Fennema, E.(Ed.),Carpenter, T. P.(Ed.)(1993).Integrating research on the graphical representation of functions.Hillsdale, NJ:Erlbaum.
12. Rubio, G.,del Castillo, A.,del Valle, Rafael,Gallardo, A.(2008).Cognitive tendencies in the process of constructing meanings in numbers, variables and linear functions.Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education,Morelia, Mexico:
13. Sfard, A.(1991).On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin.Educational Studies in Mathematics,22(1),1-36.
14. Sweller, J.(2010).Element interactivity and intrinsic, extraneous, and germane cognitive load.Educational Psychology Review,22(2),123-138.
15. Sweller, J.,van Merrienboer, J. J. G.,Paas, F. G. W. C.(1998).Cognitive architecture and instructional design.Educational Psychology Review,10(3),251-296.
16. Tso, T. Y.(2001).On the design and implementation of learningsystem with dynamic multiple linked representations.Common Sense in Mathematics Education: Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education,Taipei, Taiwan:
17. Van Labeke, N.,Ainsworth, S.(2002).Representational decisions when learning population dynamics with an instructional simulation.Intelligent tutoring systems: 6th International Conference, ITS 2002 Biarritz, France andSan Sebastian, Spain, June 2-7, 2002 Proceedings,Berlin, Germany:
18. Wilson, M. R.(1994).One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy.Journal for Research in Mathematics Education,25(4),346-370.
19. Wong, W. K.,Yin, S. K.,Yang, H. H.,Cheng, Y. H.(2011).Using computer-assisted multiple representations in learning geometry proofs.Educational Technology & Society,14(3),43-54.