本研究設計兩種科學關係圖的教學活動，分別為數學表徵連結科學表徵教學組(學科連結組)與科學實作建構圖形教學組(實作建構組)。前者強調數學函數圖形與科學關係圖建構與詮釋的連結性，後者透過實作活動收集數據、形成圖形，進而產生推理與詮釋。活動結合國中理化課程首章量化單元─「密度」，欲了解科學關係圖的教學、原圖形技能的差異與概念理解之關係。研究對象為高雄市某濱海地區公立國中之八年級生，每教學組別各兩班，共四個班級98人參與。研究資料來源為自行設計與發展的「圖形技能測驗」、「密度概念測驗」及「密度概念延宕測驗」。
研究結果顯示，教學前後兩組別的概念理解皆有顯著進步，圖形技能的表現卻未達顯著差異。不同教學組別對概念整體表現無顯著影響，但原圖形技能的不同，則會顯著反映在概念理解的表現上。將試題分群，概念後測「未涉及科學關係圖」的試題屬性與「記憶、了解」之認知層次，實作建構組的表現較佳；高圖形技能組明顯優於中、低圖形技能組。而「涉及科學關係圖」與「應用、分析」的概念試題，低圖形技能組則明顯低於其他兩能力組別。就學生於概念延宕測驗的表現而言，為學科連結組較佳；原圖形技能的差異亦會影響延宕測驗的概念理解表現，其中低圖形技能組明顯低於中、高技能組別。此外，原圖形技能的高低顯著影響教學後圖形技能及兩大能力指標的表現，教學組別並無顯著影響。
本研究顯示圖形技能對科學學習的重要性，且得知該技能不易於短時間內改變。兩教學組別各有優勢，透過實作活動建構圖形的方式，可顯著提升學生較低階認知層次與未涉及圖形的概念表現。若教學搭配函數圖形與關係圖的連結，則可促進學生於概念延宕測驗的理解表現。

The main purpose of this study was to investigate the relationships between the design of instructional modules, students’ graphing skills, and their conceptual understandings of density. Two instructional modules on the topic of line graphs were used. Module 1 supported students to translate data collected from hands-on activities into graphs, while Module 2 helped students make connections between their mathematic and scientific knowledge. Four classes of 98 eighth graders at a public junior high school in a rural area participated in the study. Data were collected from pre-test and post-test of graphing skills, conceptual understandings of density, and a deferred test of density. The result of this study indicated that students of both modules’ had significant improvement on conceptual understandings, but there was no significant difference on graphing skills. According to the two-way ANCOVA analysis of instructional modules and pre-graphing levels, different pre-graphing skills had significant effect on students’ conceptual understandings but the effect of instructional modules were not found. On the questions that did not involve graphs and were at the remembering-understanding cognitive levels, students of Module 1 performed significantly better than those of Module 2. Students’ pre-graphing levels also significantly influenced their conceptual understandings on questions of different properties and cognitive levels. After the instruction, pre-graphing levels significantly influenced the performance on the post-test graphing skills, but this influence did not vary with different modules. For students’ achievement of the deferred test, Module 2 was better and a significant main effect of pre-graphing levels was also found.
In conclusion, this study suggested the importance of graphing skills in conceptual learning of science and showed that graphing skills connot be improved with in a short period of time. Additionally, different instructional modules could enhance different aspect of conceptual understandings.

一、 中文部分
彭嘉妮（2007）。國小六年級學童在分數符號、小數符號和圖形表徵三者間轉譯表現之研究（未出版碩士論文）。國立屏東教育大學，屏東。
賴勤薇、林碧珍（2011，12月）。數學遊戲融入國中數學科函數單元教學成效之研究。論文發表於中華民國第 27 屆科學教育研討會，高雄市。
李昌汶（1997）。國中學生密度概念的診斷與探討（未出版碩士論文）。國立台灣師範大學，臺北市。
顧炳宏、陳瓊森、溫媺純（2011）。從學生的表現與觀點探討引導發現式教學作為發展探究教學之折衷方案角色的成效－以密度概念為例。科學教育學刊，19（3），257-282。
何明昇(1999)。國中與國小學生體積概念之診斷與教學（未出版碩士論文）。國立台灣師範大學，臺北市。
洪素姿(2012)。結合學習環與三角架構表徵的密度概念教學活動對八年級生學習成效之影響（未出版碩士論文）。國立彰化師範大學，彰化縣。
黃楷文(2012)。教具融入高中平面向量教學之成效研究（未出版碩士論文）。國立中央大學，桃園市。
教育部（2003）。國民中小學九年一貫課程綱要。臺北市：作者。
祁明輝（2014）。國中教育會考自然科（理化）試題分析。臺灣化學教育，（2）。
邱志堅（2009）。國中學生密度概念之調查研究（未出版碩士論文）。國立高雄師範大學，高雄市。
莊緯彬（2002）。高雄市中小學生與密度相關概念及概念圖示之認知樣式、模式、層次、頻率分佈以及認知發展的分析研究（未出版碩士論文）。國立高雄師範大學，高雄市。
陳麗婷（2005）。從符號表徵與圖像表徵雙向轉譯的觀點探討國小四年級學童的二位小數概念—以四名學童為例（未出版碩士論文）。屏東師範學院，屏東。
左台益與蔡志仁（2001）。高中生建構橢圓多重表徵之認知特性。科學教育學刊， 9(3)，281–297。
姚珩、許貫中、方崇雄、陳世煌、李通藝編（2014）。國民中學自然與生活科技(第三冊)。臺南市：翰林。
楊宗達(2001)。國小學童對「密度」相關概念理解之研究：數學與科學的對話（未出版碩士論文）。國立臺北教育大學，臺北市。
二、 西文部分
Adams, D. D., & Shrum, J. W. (1990). The effects of microcomputer-based laboratory exercises on the acquisition of line graph construction and interpretation skills by high school biology students. Journal of Research in Science Teaching, 27(8), 777-787.
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183-198.
Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning teaching. and assessing: A revision of Bloom's educational objectives. New York: Longman.
Arons, A. B. (1983). Student patterns of thinking and reasoning: Part One of Three Parts. Physics Teacher, 21(9), 576-81.
Ates, S., & Stevens, J. T. (2003). Teaching line graphs to tenth grade students having different cognitive developmental levels by using two different instructional modules. Research in Science & Technological Education, 21(1), 55-66.
Barclay, W. L. (1985). Graphing misconceptions and possible remedies using microcomputer-based labs. Paper presented at the 7th National Educational Computing Conference, University of San Diego, San Diego, CA.
Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62, 750-762.
Berg, C. A., & Smith, P. (1994). Assessing students' abilities to construct and interpret line graphs: Disparities between multiple‐choice and free‐response instruments. Science Education, 78(6), 527-554.
Brasell, H. M., & Rowe, M. B. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93(2), 63-70.
Clement, J. (1986, April). Adolescents' graphing skills: A descriptive analysis. Paper presented at the annual meeting of American Education Research Association, San Francisco, CA.
Coleman, J. M., McTigue, E. M., & Smolkin, L. B. (2011). Elementary teachers’ use of graphical representations in science teaching. Journal of Science Teacher Education, 22(7), 613-643.
Cox, R., & Brna, P. (1995). Supporting the use of external representations in problem solving: The need for flexible learning environments. Journal of Artificial Intelligence in Education, 6, 239-302.
Culbertson, H., & Powers, R. (1959). A study of graph comprehension difficulties. Audio Visual Communication Review, 7(2), 97-110.
Danish, J. A., & Enyedy, N. (2007). Negotiated representational mediators: How young children decide what to include in their science representations.Science Education, 91(1), 1-35.
Dori, Y. J., & Sasson, I. (2008). Chemical understanding and graphing skills in an honors case‐based computerized chemistry laboratory environment: The value of bidirectional visual and textual representations. Journal of Research in Science Teaching, 45(2), 219-250.
Frederiksen, J. R., White, B. Y., & Gutwill, J. (1999). Dynamic mental models in learning science: The importance of constructing derivational linkages among models. Journal of research in science teaching, 36(7), 806-836.
Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in mathematics Education, 124-158.
Gallagher, J. J. (1979). Basic skills common to science and mathematics. School Science and Mathematics, 79, 555-565.
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The roles of representation in school mathematics, 2001, 1-23.
Graham, T., & Sharp, J. (1999). An investigation into able students' understanding of motion graphs. Teaching Mathematics and its Applications, 18(3), 128-135.
Guidugli, S., Gauna, C. F., & Benegas, J. (2005). Graphical representations of kinematical concepts: A comparison of teaching strategies. The Physics Teacher, 43(6), 334-337.
Hawkes, S. J. (2004). The concept of density. Journal of Chemical Education, 81(1),14-15.
Kwon, O. N., Rasmussen, C., & Allen, K. (2005). Students' retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105(5), 227-239.
Lunetta, V. N., Hofstein, A. & Clough, M. P. (2007). Learning and teaching in the school science laboratory: An analysis of research, theory, and practice. In S. K. Abell & N. G. Lederman (Eds.). Handbook of research on science education (pp. 393-441). Mahwah, NJ: Lawrence Erlbaum Associates.
McDermott, L. C., Rosenquist, M. L., & Van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American journal of Physics, 55(6), 503-513.
McKenzie, D. L., & Padilla, M. J. (1984). Effects of laboratory activities and written simulations on the acquisition of graphing skills by eighth grade students. Paper presented at the National Association for Research in Science Teaching, New Orleans, Louisiana.
McKenzie, D. L., & Padilla, M. J. (1986). The construction and validation of the test of graphing in science (TOGS). Journal of Research in Science Teaching, 23(7), 571-579.
Meltzer, D. E. (2002). The relationship between mathematics preparation and conceptual learning gains in physics: A possible “hidden variable” in diagnostic pretest scores. American Journal of Physics, 70(12), 1259-1268.
Mokros, J. R., & Tinker, R. F. (1987). The impact of microcomputer‐based labs on children's ability to interpret graphs. Journal of Research in Science Teaching, 24(4), 369-383.
Onwu, G. O. (1993). Line graphing ability of some Nigerian secondary science students. International Journal of Mathematical Education in Science and Technology, 24(3), 385-390.
Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A., & Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. International Journal of Science and Mathematics Education, 10(6), 1393-1414.
Potgieter, M., Harding, A., & Engelbrecht, J. (2008). Transfer of algebraic and graphical thinking between mathematics and chemistry. Journal of Research in Science Teaching, 45(2), 197–218.
Pribyl, J. R., & Bodner, G. M. (1987). Spatial ability and its role in organic chemistry: A study of four organic courses. Journal of Research in Science Teaching, 24(3), 229-240.
Rieck, W. (1996). Density: An extended investigation. Science Activities: Classroom Projects and Curriculum Ideas, 33(3), 13-19.
Roth, W.-M., & McGinn, M. K. (1997). Graphing: Cognitive ability or practice? Science Education, 81(1), 91-106.
Roth, W. -M., & McGinn, M. K. (1998). Inscriptions: Toward a theory of representing as social practice. Review of Educational Research, 68(1), 35–59.
Schnotz, W. (2002). Commentary: Towards an integrated view of learning from text and visual displays. Educational Psychology Review, 14(1), 101-120.
Suth, J., & Moyer-Packenham, P. S. (2007). Developing students' representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155.
Vekiri, I. (2002). What is the value of graphical displays in learning?. Educational Psychology Review, 14(3), 261-312.
Wavering, M. J. (1989). Logical reasoning necessary to make line graphs. Journal of Research in Science Teaching, 26, 373-379.
Woolnough, J. (2000). How do students learn to apply their mathematical knowledge to interpret graphs in physics? Research in Science Education, 30(3), 259-267.
Wu, H.-K., & Puntambekar, S. (2012). Pedagogical affordances of multiple external representations in scientific processes. Journal of Science Education and Technology, 21(6), 754-767.