中文文獻
吳秀萍(2003)。國中生對垂直、平行相關用語之理解研究。未出版之碩士論文，國立台灣師範大學數學研究所，台北市。
呂琬萍(2006)。國小二年級學童乘法解題錯誤類型分析之研究。未出版之碩士論文，臺北市立教育大學課程與教學研究所，臺北市。
周鈺淇(2007)。以單位量觀點探討二年級乘法教學活動。未出版之碩士論文，國立臺南大學數學教育學系研究所，台南市。
周筱亭、黃敏晃(主編)(2000)。國小數學教材分析—整數的乘除運算。教育部台灣
省國民學校教師研習會。
洪千惠(2005)。國小二年級學童整數乘法教材教學實驗之研究。未出版之碩士論文，國立新竹師範學院數學教育學系碩士班，新竹市。
陳吟米(2001)。國小一二三年級學童單位量轉換問題解題歷程之研究。未出版之
碩士論文，國立臺南大學國民教育研究所，台南市。
陳淑琳(2000)。談新課程對乘法基本教材的處理。屏師科學教育，12，14-22。
教育部(2018)。十二年國民基本教育課程綱要:國民中小學暨普通型高級中等學校
數學領域。台北市:教育部。
張英傑、周菊美(譯)(2005)。J. A. Van De Walle著。中小學數學科教材教法
(Elementary and Middle School Mathematics：Teaching Developmentally)。台北市：五南。
游麗卿(1998)。從實作表現診斷學生乘除法的錯誤概念。測驗與輔導，149，3094-
3098。
許美華(2000)。國小二年級學生正整數乘法問題解題活動類型之縱貫研究。未出
版之碩士論文，國立屏東師範學院國民教育研究所，屏東縣。
英文文獻
Adler, J. (1998). A language of teaching dilemmas: Unlocking the complex multilingual
secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24–33.
Adler, J. (2001). Teaching mathematics in multilingual classrooms. Dordrecht, The
Netherlands: Kluwer Academic Press.
Altieri, J. L. (2009). Strengthening connections between elementary classroom
mathematics and literacy. Teaching Children Mathematics, 15(6), 346–351.
Anderson-Inman, L., & Horney, M. (1998). Transforming text for at-risk readers. In D.
Reinking, L. D. Labbo, M. C. McKenna, & R. D. Kieffer (Eds.), Handbook of literacy and technology: Transformations in a post-typographic world (pp. 15–43). Mahwah, NJ: Erlbaum.
Anghiler, J. (1989). An investigation of young children’s understanding of
multiplication. Education Studiesin Mathematics, 20, 367-385.
Anthony, A., & Walshaw, M. (2007). Effective pedagogy in mathematics/pangarau.
Best Evidence Synthesis Iteration [BES]. Wellington, New Zealand: Ministry of Education.
Barrouillet, P., Bernardin, S., Portrat, S., Vergauwe, E., & Camos, V. (2007). Time and
cognitive load in working memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(3), 570–585.
Barwell, R. (2011). What works？ Research into practice. A research-into practice
series produced by a partnership between the Literacy and Numeracy Secretariat and the Ontario Association of Deans of Education. Research Monogram, 34, 1–4.
Battista, M. T. (2012). Cognition-based assessment and teaching of multiplication and
division: Building on students' reasoning (Cognition-based asssessment and teaching). Portsmouth, NH: Heinemann.
Bay-Williams, J. M., & Livers, S. (2009). Supporting math vocabulary acquisition.
Teaching Children Mathematics, 16, 238–245.
Boero, P., Douek, N., & Ferrari, J. L. (2008). Developing mastery of natural language:
Approaches to some theoretical aspects of mathematics. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 262–297). New York, NY: Routledge.
Brown, C. L., Cady, J. A., & Taylor, P. M. (2009). Problem solving and the English
language learner. Mathematics Teaching in the Middle School, 14(9), 532–539.
Carpenter, T. P., Fennema, E., Franke, M. L, Levi Linda, and Empson, S. B. (1999)
Children's mathematics: Cognitively Guided Instruction. Restone, VA: The National Council of Teachers of Mathematics, Inc.
Cazden, C. B. (1986). Classroom discourse. In M. C. Wittrock (Ed.), Handbook of
research on teaching (3rd ed., pp. 432–463). New York: Macmillan.
CCSSO/NGO. (2010). Common Core State Standards for Mathematics.Washingston,
DC: Council of Chief State School Officers and the National Governors Association Center for Best Practices. Retrieved from http://corestandards.org.
Clarkson, P. C. (2007). Australian Vietnamese students learning mathematics: High
ability bilinguals and their use of their languages. Educational Studies in Mathematics, 64, 195–215.
Cobb, P., & Bowers, J. (1998). Cognitive and situated learning perspectives in theory
and practice. Educational Researcher, 28(2), 4–15.
Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the
development of students’ statistical reasoning. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375–395). Dordrecht, The Netherlands: Kluwer. https://doi.org/10.1007/1-4020-2278-6_16
Cobb, Paul, Terry Wood, and Erna Yackel. (1994). Discourse, Mathematical Thinking,
and Classroom Practice. In Contexts for Learning: Sociocultural Dynamics in Children’s Development Oxford: Oxford University Press.
Common Core State Standards Initiative (CCSSI). (2010). Common Core State
Standards for Mathematics (CCSSM). Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
Chapman, A. (2003). A Social Semiotic of Language and Learning in School
Mathematics. In Semiotic Perspectives on Mathematics Education, edited by Victor Ciferalli. West Lafayette, Ind.: Purdue University Press.
Clarkson, P. C. (2007). Australian Vietnamese students learning mathematics: High
ability bilinguals and their use of their languages. Educational Studies in Mathematics, 64(2), 191–215.
Crowhurst, M. (1994). Language and learning across the curriculum. Instructor’s
manual. Scarborough, Canada: Allyn & Bacon.
Greer, B. (1992). Multiplicaton and division as models of situations.In D. A. Grouws
(Ed.), Handbook of research on mathematics teaching and learning (pp.276-295). New York: Macmillan Puvlishing Company.
Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford:
Oxford University Press.
Ebby, C. B. (2005). The powers and pitfalls of algorithmic knowledge: A case study.
The Journal of Mathematical Behavior, 24(1), 73-87.
Empson, S., & Levi, L. (2011). Extending children's understanding of fractions and
decimals. Portsmouth, NH: Heinemann.
Fosnot, C., & Dolk, M. (2001). Young mathematics at work: Multiplication and
divison. Portsmouth, NH: Heinemann.
Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom
practice. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp.225–256). Charlotte, NC: Information Age.
Gee, J. P. (1996). Sociolinguistics and literacies: Ideology in discourses. London,
United Kingdom: Falmer Press.
Gough, J. (2007). Conceptual complexity and apparent contradictions in mathematics
language, Australian Mathematics Teacher, 63(2), 8-16.
Greer, B. (1992). Multiplication and division as models. In D. Grouws (Ed.), Handbook
of research on mathematics teaching and learning (pp. 276-296). Reston, VA: National Council of the Teachers of Mathematics.
Greer, B. (1994). Extending the meaning of multiplication and division. In G.Harel &
J. Confrey(Eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics (pp. 61-85). State University of NewYork Press. Albany.
Halliday, M. A. K., & Hasan, R. (1989). Language, context, and text: Aspects of
language in a social-semiotic perspective. Geelong, Australia: Deakin University Press.
Harmon, J. M., W. B. Hedrick, and K. D. Wood. “Research on Vocabulary Instruction
in the Content Areas: Implications for Struggling Readers.” Reading & Writing Quarterly 21, no. 3 (2005): 261–80.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In
D. A. Groups (Ed.), Handbook of research on mathematics teaching and learning (p.p. 65-98). New York: Macmillan.
Herbel-Eisenmann, B. (2002). Using student contributions and multiple representations
to develop mathematical language. Mathematics Teaching in the Middle School, 8(2), 100–105.
Hulbert, Elizabeth & Petit, Marjorie & Ebby, Caroline & Cunningham, Elizabeth &
Laird, Robert. (2017). A Focus on Multiplication and Division: Bringing Research to the Classroom. London: Routledge.
Kamii, C. (1998). The harmful effects of algorithms in grades 1-4. In L. J. Morrow &
M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 yearbook (pp. 130-140). Reston, VA: National Council of Teachers of Mathematics.
Kaput, J. (1989). Supporting concrete visual thinking in multiplicative reasoning:
Difficulties and opportunities. Focus on Learning Problem in Mathematics, 11(2), 35-47.
Kazima, M. (2007). Malawian students meaning for probability vocabulary.
Educational Studies in Mathematics, 64(2), 169–189. https://doi.org/10.1007/s10649-006-9032-6
Kieran, C., Forman, E., & Sfard, A. (Eds.). (2002). Learning discourse: Discursive
approaches to research in mathematics education. Dordrecht, The Netherlands: Kluwer.
Kotsopoulos, D. (2007). Mathematics discourse: “It’s like hearing a foreign language”.
Mathematics Teacher, 101(4), 301–305.
Kouba, V. L. (1989). Children's solution strategies for equivalent set multiplication
and division word problems. Journal for Research in Mathematics Education, 20(2), 147-158.
Laborde, C., Conroy, J., De Corte, E., Lee, L., & Pimm, D. (1990). Language and
mathematics. In P. Nesher & J. Kilkpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology ofMathematics Education (pp. 53–69). Cambridge, UK: Cambridge University Press.
Lampert, M. (1986). Knowing, doing, and teaching multiplication. Cognition and
teaching multiplication. Cognition and instruction, 3(4), 305-342.
Lavy, I., & Mashiach-Eizenberg, M. (2009). The interplay between spoken language
and informal definitions of statistical concepts. Journal of Statistics Education, 17(1).
Lee, J., Lee. Y., & Amaro-Jiménez, C. (2011). Teaching English language learners
(ELLs) mathematics in early childhood. Childhood Education, 87(4), 253–260. https://doi.org/10.1080/00094056.2011.10523187
Lsger, C. A. (2006). Types of mathematics-language reading interactions that
unnecessarily hinder algebra learning and assessment.Reading Psychology, 27(2-3), 165-204.
Marzano, R.J. (2004) Building Background Knowledge For Academic Achievement:
Research on What Works in Schools. Alexandria, VA: Association for Supervision and Curriculum Development.
Mayer, R.E. (1987). Educational Psychology: A cognitive approach. Boston: Little,
Brown and Company.
Monroe, E. E. (1998). Using graphic organizers to teach vocabulary: Does available
research inform mathematics instruction. Education, 118, 538–542.
Monroe, E., & Panchyshyn, R. (2005). Helping children with words in word problems.
Australian Primary Mathematics Classroom, 10(4), 27–29.
Morin, J. E., & Franks, D. J. (2010). Why do some children have difficulty learning
mathematics？ Looking at language for answers. Preventing School Failure, 54, 111–118.
Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual
mathematics learners.Mathematical Thinking and Learning, 4(2/3), 189–212.https://doi.org/10.1207/S15327833MTL04023_5
Moschkovich, J. N. (2005). Using two languages when learning mathematics.
Educational Studies in Mathematics, 64, 121–144. https://doi.org/10.1007/s10649-005-9005-1
Moschkovich, J. N. (2007). Examining mathematical discourse practices. For the
Learning of Mathematics, 27(1), 24–30.
Moschkovich, J. N. (2010). Language(s) and learning mathematics: Resources,
challenges, and issues for research. In J. N. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 1–28). Charlotte, NC: Information Age.
Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners.
Journal of Mathematical Behavior, 40, 43–62.
Moschkovich, J. N., & Nelson-Barber, S. (2009). What mathematics teachers need to
know about culture and language. In B. Greer, S. Mukhopadhyay, A. B. Powell, & S. Nelson- Barber (Eds.), Culturally responsive mathematics education (pp. 111–136). New York, NY: Routledge.
Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children’s intuitive models of
multiplication and division.Journal for Research in Mathematics Education, 28(3), 309-330.
National Council of Teachers’ of English. (2008). English language learners: A policy
research brief produced by the National Council of Teachers of English. Retrieved from http://www.ncte.org/library/NCTEFiles/Resources/Policy Research/ELLResearchBrief.pdf
National Council of Teachers of Mathematics. (NCTM). (1989). Curriculum and
Evaluation Standards for School Mathematics. Reston, Va.: NCTM.
National Council of Teachers of Mathematics. (NCTM). (2000). Principles and
Standards for School Mathematics. Reston, Va.: NCTM.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions:
Ensuring Mathematical Success for All. Reston, Va.: NCTM.
National Research Council. (2001). Adding it up: Helping children learn mathematics.
J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Nguyen, H. T., & Cortes, M. (2013). Focus on middle school: Teaching mathematics
to ELLs: Practical research-based methods and strategies childhood education. Childhood Education, 89(6), 392–395.http://dx.doi.org/10.1080/00094056.2013.854130
Nunes, T., & Bryant, P. (1996). Children doing mathematics. Malden, MA: Wiley-
Blackwell.
O’Halloran, K. (2005). Mathematical discourse: Language, symbolism and visual
images. London, United Kingdom: Continuum.
Peled, L., and P. Nesher. (1988). What children tell us about multiplication word
problem. Journal of Mathematical Behavior, 7(3), 239-262.
Piaget, J. (1970). Science of education and the psychology of the child. New York:
Viking.
Pimm, D. (1987). Speaking mathematically: Communication in mathematics
classrooms. London, United Kingdom: Routledge.
Planas, N., & Setati-Phakeng (2014). On the process of gaining language as resource
in mathematics education. ZDM Mathematics Education, 46, 883–893. https://doi.org/10.1007/s11858-014-0610-2
Riccomini, P. J., Sanders, S., & Jones, J. (2008). The key to enhancing students’
mathematical vocabulary knowledge. Journal on School Educational Technology, 4(1), 1–7.
Rubenstein, R. (2000). Word origins: Building communication connections.
Mathematics Teaching in the Middle School, 5(8), 493–498.
Russel, S. J. (2000). Developing computational fluency with whole numbers.
Teaching Children Mathematics, 7(3), 154.
Schleppegrell, M. J. (2011). Language in mathematics teaching and learning: A
research review. In J.Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 73–112). Charlotte, NC: Information Age.
Seeger, F., Voigt, J., & Waschescio, U. (1998). The culture of the mathematics
classroom. Cambridge, United Kingdom: Cambridge University Press.
Seethaler, P. M., Fuchs, L. S., Star, J. R., & Bryant, J. (2011). The cognitive predictors
of computational skill with whole versus rational numbers: An exploratory study. Learning and Individual Differences, 21, 536–542.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of
discourses, and mathematizing. Cambridge, United Kingdom: Cambridge University Press.
Siemon, D., Breed, M., & Virgona, J. (2005). From additive to multiplicative thinking:
The big challenge of the middle years. Proceedings of the 42nd Conference of Mathematical Association of Victoria. Retrieved December 12, 2016, from www.eduweb.vic.gov.au/edulibrary/public/ teachlearn/ student/ppaddmulti.pdf.
Siemon, D., & Virgona, J. (2001). Roadmaps to numeracy: Reflections on the Middle
Years Numervacy Research Project. Paper presented at Australian Association for Research in Education Conference, Fremantle, Perth.
Steffe, L. P. (1992). Schemes of action and operations involving composite units.
Learning and Indi vidual Differences, 4(3), 259-309.
Swanson, Lee, H., & Lee, C. S. (2001). Mathematical problem solving and working
memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology, 79(3), 294–321.
Ulrich, C. (2015). Stages in coordinating units additively and multiplicatively. For the
Learning of Mathematics, 35(3), 2-7
United Nations Educational, Scientific and Cultural Organization. (1974). Interactions
between linguistics and mathematics education: Final report of the symposium sponsored by UNESCO, CEDO and ICMI. Nairobi, Kenya: Author.
van der Walt, M. (2009). Study orientation and basic vocabulary in mathematics in
primary school. South African Journal of Science and Technology, 28, 378–392.
Vygotsky, L.S. (1986). Thought and language. (A. Kozulin ed. and trans.). Cambridge,
MA: MIT Press.
Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A
review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516–551.
Wong, M., & Evans, D. (2007). Improving basic multiplication fact recall for primary
school students. Mathematics Education Research Journal, 19(1), 89-106.
Xi, C., & Yeping, L. (2008). Language proficiency and mathematics learning. School
Science & Mathematics, 108(3), 90–93. https://doi.org/10.1111/j.1949-8594.2008.tb17811.x
Xin, Y. P. (2012). Conceptual model-based problem solving: Teach students with
learning difficulties to solve math problems. https://doi.org/10.1007/978- 94-6209-104-7_1 Rotterdam, Netherlands: Sense.
Xin, Y. P., Park, J. Y., Tzur, R., & Si, L. (2020). The impact of a conceptual model-
based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities. The Journal of Mathematical Behavior, 58. doi:10.1016/j.jmathb.2020.100762
Yackel, E., Cobb, P. and Wood, T. (1991). Small group interactions as a source of
learning opportunities in second-grade mathematics. Journal for Research in Mathematics Education, 22(5), 390–408.
Zimmerman, B. J., & Campillo, M. (2003). Motivating self-regulated problem solvers.
In J. E. Davidson & R. J. Sternberg (Eds.), The psychology of problem solving (pp. 233-262). New York, NY: Cambridge University Press.