|
Ainsworth, S., & Loizou, A. (2003). The effect of self-explaining when learning with text or diagrams. Cognitive Science, 27, 669–681. Aleven, V. A., & Koedinger, K. R. (2002).An effective metacognitive strategy: Learning by doing and explaining with a computer-based Cognitive Tutor.Cognitive science, 26(2), 147-179. Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching and assessing: A revision of Bloom's Taxonomy of educational objectives: Complete edition, New York : Longman. Allen, B. (1991). Using writing to promote students metacognition in muthemutics. Mathematics Education Research Group of Australasia. Western Australia: Perth. Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003).Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps.Journal of Educational Psychology, 95(4), 774–783. Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achievers. Elementary School Journal, 103(1), 51-73. Bangert-Drowns, R. L., Hurley, M. M., & Wilkinson, B. (2004).The Effects of school-based writing-to-learn interventions on academic achievement: A Meta-analysis.Review of Educational Research, 74(1), 29–58. Baroody, A. J., & Ginsburg, H. P. (1990).Children’s mathematical learning: A Cognitive view. In C. Maher & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 51–64). Reston, VA: National Council of Teachers of Mathematics. Berghmans, I, Neckebroeck, F., Dochy, F., & Struyven, K. (2013).A Typology of approaches to peer tutoring. Unraveling peer tutors’ behavioural strategies. European Journal of Psychology of Education, 28(3), 703–723. Bicer, A., Capraro, M. M., & Capraro, R. M. (2014).Integrating writing into mathematics classroom as one communication factor.The Online Journal of New Horizons in Education, 4(2), 58-67. Bloom, Benjamin S. & David R. Krathwohl. (1956). Taxonomy of educational objectives: The classification of educational goals, by a committee of college and university examiners. Handbook 1: Cognitive domain. New York , Longmans. Bonotto, C. (2013). ArtifaCD as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-56. Bossé, M. J., & Faulconer, J. (2008). Learning and assessing mathematics through reading and writing. School Science and Mathematics, 108, 8-19. Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: two preservice teachers’ conceptions and practices. Journal of mathematics teacher education, 3(2), 125-153. Burton, L., & Morgan, C. (2000). Mathematicians writing. Journu1 for Research in Mathematics Education, 31, 429-453. Bruce, C. D., McPherson, R., Sabeti, F. M., & Flynn, T. (2011).Revealing significant learning moments with interactive whiteboards in mathematics.Journal of Educational Computing Research, 45(4), 433–454. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing.The Journal of Mathematical Behavior, 21(4), 401-421. Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students' learning. Educational Studies in Mathematics, 83(1), 57-69. Chan, T. W., Roschelle, J., Hsi, S., Kinshuk, Sharples, M., Brown, T., Patton C., Cherniavsky, J., Pea R., Norris, C., Soloway, E., Balacheff, N., Scardamalia, M., Dillenbourg, P., Looi, C. K., Milrad, M., & Hoope, U. (2006). One-to-one technology enhanced learning: An Opportunity for global research collaboration. Research and Practice in Technology Enhanced Learning, 1(1), 3–29. Chi, M. T. H. (2009). Active-Constructive-Interactive: A Conceptual Framework for Differentiating Learning Activities. Topics in Cognitive Science, 1, 73–105. Chi, M. T. H., Bassok, M., Lewis, M., Reimann, P., & Glaser, R. (1989). How Students Study and Use Examples in Learning to Solve Problems. Cognitive Science, 13, pp. 145-182. Chi, M. T. H., de Leeuw, N., Chiu, M., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18, 439–477. Chi, M. T. H., Roy, M., & Hausmann, R. G. M. (2008).Observing tutorial dialogues collaboratively: Insights about human tutoring effectiveness from vicarious learning.Cognitive Science, 32(1), 301–341. Clarke, D. J., Waywood, A., & Stephens, M. (1993).Probing the structure of mathematical writing. Educational Studies in Mathematics, 25(3), 235-250. Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997).Reflective discourse and collective reflection.Journal for Research in Mathematics Education, 28(3), 258–277. Cooke, B. D., & Buchholz, D. (2005). Mathematical communication in the classroom: A Teacher makes a difference. Early Childhood Education Journal, 32(6), 365–369. Cox, R. (1999).Representation construction, externalised cognition and individual differences.Learning and Instruction, 9(4), 343–363. Dacey, L., & Eston, R. (2002). Show and tell: Representing and communicating mathematical ideas in K–2 classrooms. Sausalito, CA: Math Solutions. De Backer, L., Van Keer, H., & Valcke, M. (2012).Exploring the potential impact of reciprocal peer tutoring on higher education student’s metacognitive knowledge and regulation.Instructional Science, 40(3), 559–588. English, L. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In F. Lester, & R. Charles, Teaching mathematics through problem solving (pp. 187–198). Reston: National Council of Teachers of Mathematics. Fantuzzo, J. W., King, J. A., & Heller, L. R. (1992).Effects of reciprocal peer tutoring on mathematics and school adjustment: A Component analysis.Journal of Educational Psychology, 84(3), 331–339. Fiorella, L., & Mayer, R. E. (2014).Role of expectations and explanations in learning by teaching.Contemporary Educational Psychology, 39(2), 75–85. Forman, E., & Ansell, E. (2002).Orchestrating the multiple voices and inscriptions of a mathematics classroom.Journal of the Learning Sciences, 1, 251–274. Freitag, M. (1997). Reading and writing in the mathematics classroom. The Mathematics Educator, 8, 16-21. Fuchs, L., Fuchs, D., Finelli, R., Courey, S., Hamlett, C., & Sones, E. (2006). Teaching third graders about real-life inathematical problem solving: A randomized controlled study. Elementary School, 106, 293-312. Geist, L., Hatch, P., & Erickson, K. (2014).Promoting Academic Achievement for Early Communicators of All Ages.SIG 12 Perspectives on Augmentative and Alternative Communication, 23(4), 173-181. Griffin, C. C., & Jitendra, A. K. (2008). Word problem solving instruction in inclusive third grade mathematics classrooms. Journal of Educational Research, 102(3), 187-202. Hallgren, K. A. (2012). Computing inter-rater reliability for observational data: an overview and tutorial. Tutorials in quantitative methods for psychology, 8(1), 23. Hausmann, R., Chi, M. T. H., & Roy, M. (2004). Learning from collaborative problem solving: An analysis of three hypothesized mechanisms. In K. Forbus, D. Gentner, & T. Regier (Ed.). (pp. 547–552). Mahwah, NJ: Erlbaum. HegartyM., & KozhevnikovM. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689. Hwang, W. Y., Su, J. H., Huang, Y. M., & Dong, J. J. (2009).A Study of multi-representation of geometry problem solving with virtual manipulatives and whiteboard system.Journal of Educational Technology & Society, 12(3), 229–247. Jitendra, A., Griffin, C., Haria, P., Leh, J., Adams, A., & Kaduvettoor, A. (2005). A comparison of single and multiple strategy instruction on third grade students' mathematical problem solving. Journal of Educational Psychology, 99, 115-127. Johnson, D. W., & Johnson, R. T. (1999).Making cooperative learning work.Theory into Practice, 38(2), 67–73. Keller, J. (1987). Development and use of the ARCS model of motivational design. Journal of Instructional Development, 10(3), 2-10. Keller, J. (2010). Motivational design for learning and performance: The ARCS model approach. New York: Springer. Keller, J. M., & SuzukiK. (2004). Learner motivation and E-learning design: A multinationally validated process. Journal of Educational Media, 29(3), 229-239. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. Schoenfeld, Cognitive science and mathematics education (pp. 123–147). Hillsdale: Lawrence Erlbaum Associates. King, A. (1994). Guiding knowledge construction in the classroom: EffeCD of teaching children how to question and how to explain. American Educational Research Journal, 31(2), 338–368. King, A. (1998). Transactive peer tutoring: Distributing cognition and metacognition.Educational Psychology Review, 10(1), 57–74. King, A., Staffieri, A., & Adelgais, A. (1998). Mutual peer tutoring: Effects of structuring tutorial interaction to scaffold peer learning. Journal of Educational Psychology, 90(1), 134–152. Koedinger, K., Anderson, J. R., Hadley, W. H., & Mark, M. A. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education, 8, 30–43. Leung, S. (1994). On analyzing problem-posing processes: A study of prospective elementary teachers differing in mathematics knowledge. In J. da Ponte, & J. Matos, Proceedings of the 18th international conference of the International Group for the Psychology of Mathematics Education (pp. 168–175). Lisbon: University of Lisbon. Leung, S. (2009). Research efforts on probing students’ conceptions in mathematics and reality: Structuring problems, solving problems, and justifying solutions. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay, Words and worlds: Modeling verbal descriptions of situations (pp. 213–225). New York: Sense. Leung, S. (2013). Teachers implementing mathematical problem posing in the classroom: challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. Leung, S., & Silver, E. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24. Lin, C. S., Shann, W. C., & Lin, S. C. (2008). Reflections on mathematical communication from Taiwan math curriculum guideline and PISA 2003. Retrieved from http://www.criced.tsukuba.ac.jp/math/apec/apec2008/papers/PDF/16.Lin_Su_Chun_Taiwan.pdf Lin, Y. H., & Lee, Q. Y. (2004). A study of ability on mathematical communication for students of elementary schools. Journal of Educational Measurement and Statistics, 12, 233-268.(In Chinese) Marks, G., & Mousley, J. (1990). Mathematics, education and genre: Dare we make the process writing mistake again? Language and Education, 4, 117-135. Mason, J. (2010). Effective questioning and responding in the mathematics classroom. Retrieved from http://xtec.cat/centres/a8005072/articles/effective_questioning.pdf McIntosh, M. E. (1991). No time for writing in your class?.The Mathematics Teacher, 84(6), 423-433. McNamara, D. (2004). SERT: Self-explanation reading training. Discourse Processes, 38, 1-30. Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of learning disabilities, 30(2), 164-177. Mooney, C., Hansen, A., Ferrie, L., Fox, S., & Wrathmell, R. (2012).Primary mathematics: Knowledge and understanding. Exeter,UK: Learning Matters. Moschkovich, J. (2012). Mathematics, the common core, and language: Recommendations for mathematics instruction for ELs aligned with the common core. In Understanding Language: Language, Literacy, and Learning in the Content Areas (pp. 17-31) Stanford, CA: Understanding Language. Mosston, M., & Ashworth, S. (2002). Teaching physical education (5th ed.). San Francisco, CA: Benjamin Cummings. Nathan, M. J., & Koedinger, K. R. (2000).An investigation of teachers' beliefs of students' algebra development.Cognition and Instruction, 18(2), 209-237. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.Reston, VA: National Council of Teachers of Mathematics. National Governors Association.(2010). Common core state standards.retrieved on August 20, 2016 at http://www.corestandards.org/Math/Practice/ Neria, D., & Amit, M. (2004). Students preference of non-algebraic representations in mathematical communication'. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 409-416). Newell, S. (2008). Dirty Whites:" Ruffian-Writing" in Colonial West Africa. Research in African Literatures, 39(4), 1-13. OECD (2016), PISA 2015 Assessment and Analytical Framework: Science, Reading, Mathematic and Financial Literacy, PISA, OECD Publishing, Paris. Ottmar, E. R., Rimm-Kaufman, S. E., Larsen, R. A., & Berry, R. Q. (2015). Mathematical knowledge for teaching, standards-based mathematics teaching practices, and student achievement in the context of the responsive classroom approach. American Educational Research Journal, 52(4), 787-821. Pape, S., & Tchoshanov, M. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory into Practice, 40(2), 118-127. Patton, M. (2002). Qualitative research and evaluation methods (3 ed.). Thousand Oaks, CA: Sage.Paiva, F., Glenn, J., Mazidi, K., Talbot, R., Wylie, R., Chi, M. T., ... & Nielsen, R. D. (2014, June). Comprehension seeding: Comprehension through self explanation, enhanced discussion, and inquiry generation. In International Conference on Intelligent Tutoring Systems (pp. 283-293). Springer International Publishing. Paiva, R. O. A., Santa Pinto, I. I. B., da Silva, A. P., Isotani, S., & Jaques, P. (2014, June). A systematic approach for providing personalized pedagogical recommendations based on educational data mining. In International Conference on Intelligent Tutoring Systems (pp. 362-367). Springer International Publishing. Pigott, H. E., Fantuzzo, J. W., & Clement, P. W. (1986). The Effect of reciprocal peer tutoring and group contingencies on the academic performance of elementary school children.Journal of Applied Behavior Analysis, 19(1), 93–98. Poch, A. L., van Garderen, D., & Scheuermann, A. M. (2015). Students’ Understanding of Diagrams for Solving Word Problems A Framework for Assessing Diagram Proficiency. TEACHING Exceptional Children, 47(3), 153-162. Polya, G. (1973). How to solve it: A New aspect of mathematical method. Princeton, NJ: Princeton University Press. Porter, M., & Masingila, J. (2000). Examining the effect of writing on conceptual and procedural knowledge in calculus. Educutional Studies in Mathematics, 42, 165-177. Presmeg, N. (1986a). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297–311. Presmeg, N. (1986b). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46. Pugalee, D. K. (2004).A comparison of verbal and written descriptions of students' problem solving processes.Educational Studies in Mathematics, 55(1-3), 27-47. Ririe, J., & Redford, K. (2008). Communication and Discourse. Retrieved from Strategies for Teaching Elementary Mathematics: http://mathteachingstrategies.wordpress.com/2008/11/24/communication-discourse/ Roscoe, R. D., & Chi, M. T. H. (2007). Understanding tutor learning: Knowledge building and knowledge telling in peer tutors’ explanations and questions. Review of Educational Research, 77(4), 534–574. Roscoe, R. D., & Chi, M. T. H. (2008).Tutor learning: The role of explaining and responding to questions.Instructional Science, 36(4), 321–350. Rosenthal, D. J., & Resnick, L. B. (1974). Children's solution processes in arithmetic word problems. Journal of Educational Psychology, 66(6), 817. Roy, M., & Chi, M. (2005). The self-explanation principle in multimedia learning. In R. Mayer, The Cambridge handbook of multimedia learning (pp. 271-286). Cambridge: Cambridge University. Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16, 475-522. Sedig, K. (2008). From play to thoughtful learning: A design strategy to engage children with mathematical representations. Journal of Computers in Mathematics and Science Teaching, 27(1), 65-101. Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2, 157-189. Shepard, R. G. (1993). Writing for conceptual development in mathematics. The Journal of Mathematical Behavior,12(3), 287-293. Shimizu, Y., & Lambdin, D. V. (1997). Assessing students’ performance on an extended problem-solving task: A Story from a Japanese classroom.The Mathematics Teacher, 90(8), 658–664. Siegler, R. (2005). Children's learning. American Psychologist, 60, 769-778. Sierpinska, A. (1998). Three epistemologies, three views of communication: Constructivism, social cultural approaches, interactionism. In H. Steinbring, M. G. Bartonlini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 30–62). Reston, VA: National Council of Teachers of Mathematics. Silver, A. E. (1994). On Mathematical Problem Posing. For the learning of mathematics, 14(1), 19-28. Silver, E. A., & Smith, M. S. (1996). Building discourse communities in mathematics classrooms: A worthwhile but challenging journey. In P. C. Elliott, Communication in mathematics, K-12 and beyond: 1996 yearbook (pp. 20-28). Reston, VA: National Council of Teachers of Mathematics. Silver, E., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. Silver, E., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135. Siswono, T. (2010). Leveling students’ creative thinking in solving and posing mathematical problem. Indonesian Mathematical Society Journal on Mathematics Education, 1(1), pp. 20–41. Smith, G. G., Ferguson, D., & Caris, M. (2003). The web versus the classroom: Instructor experiences in discussion-based and mathematics-based disciplines. Journal ofEducational Computing Research, 29(1), 29–59. Sorsana, C. (2005). Beliefs and conversational skills among children: Reflections on the dialogic management disagreements within reasoning. Psychology of Interaction, 19/20, 39-97. Sriraman, B. (2009). The characteristics of mathematical creativity. Zentralblatt für Didaktik der Mathematik, 41(1-2), pp. 13–27. Stahl, G. (2006). Supporting group cognition in an online math community: A cognitive tool for small-group referencing in text chat. Journal of Educational Computing Research, 35(2), 1–16. Stahl, G. (2009). Social practices of group cognition in virtual math teams. In S. Ludvigsen, A. Lund, & R. Säljö (Eds.), Learning in social practices. ICT and new artifacts: Transformation of social and cultural practices (pp.190-205). London, UK: Pergamon. Steele, D. (2005). Using writing to access students' schemata knowledge for algebraic thinking. School Science and Mathematics, 105(3), 142–154. Steele, D. F., & Arth, A. A. (1998). Math instruction and assessment: Preventing anxiety, promoting confidence. Schools in the Middle, 7(3), 44-48. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. C. Clarkson, Technology in mathematics education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia. Sür, B., & Delice, A. (2016, January). The examination of teacher student communication process in the classroom: mathematical communication process model. In SHS Web of Conferences (Vol. 26).EDP Sciences. Taiwan, M. O. E. (2003). General Guidelines of Grade 1-9 Curriculum of Elementary and Junior High School Education—mathematics learning areas. Taipei, Taiwan: Author. Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., & Maruno, S. (2007). Effects of self‐explanation as a metacognitive strategy for solving mathematical word problems1. Japanese Psychological Research, 49(3), 222-233. Teuscher, D., Kulinna, P. H., &Crooker, C. (2016). Writing to Learn Mathematics: An Update. The Mathematics Educator, 24(2), 56–78 Thompson, D. R., & Chappell, M. F. (2007). Communication and Representation as Elements in Mathematical Literacy. Reading & Writing Quarterly: Overcoming Learning Difficulties, 23(2), 179-196. Topping, K. J. (2005).Trends in peer learning.Educational Psychology, 25(6), 631–645. Tsuei, M. (2012).Using synchronous peer tutoring system to promote elementary students’ mathematics learning.Computers & Education, 58(4), 1171–1182. Uesaka, Y., & Manalo, E. (2011). The effeCD of peer communication with Diagrams on students’ math word problem solving processes and outcomes. Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 312–317). Austin, TX: Cognitive Science Society. Van de Walle, J. (2007). Elementary and middle school mathematics: Teaching developmentally (6 ed.). Boston: Allyn and Bacon: Texas. van Garderen, D., & Montague, M. (2003). Visual-Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities. Learning Disabilities Research & Practice, 18(4), 246–254. van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145-160. VanLehn, K., Jones, R. M., & Chi, M. T. (1992).A model of the self-explanation effect.The journal of the learning sciences, 2(1), 1-59. Verschaffel, L., Van Dooren, W., Chen, L., & Stessens, K. (2009). The relationship between posing and solving division-with-remainder problems among flemish upper elementary school children. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay, Words and worlds: Modelling verbal descriptions of situations (pp. 143–160). Rotterdam: Sense. Walker, E., Rummel, N., & Koedinger, K. R. (2011). Designing automated adaptive support to improve student helping behaviors in a peer tutoring activity. International Journal of Computer-Supported Collaborative Learning, 6(2), 279–306. Webb, N. M., & Mastergeorge, A. M. (2003). The development of students’ helping behavior and learning in peer-directed small group. Cognition and Instruction, 21(4), 361–428. Whitin, D., & Whitin, P. (2000a). Exploring mathematics through talking and writing. In M. Burke, & F. Curcio, Learning mathematics for a new century: 2000 yearbook (pp. 213–222). Reston, VA: National Council of Teachers of Mathematics. Whitin, P., & Whitin, D. J. (2000b).Math is language too: Talking and writing in the mathematics classroom. Reston, VA: National Council of Teachers of Mathematics. Wilcox, B., & Monroe, E. E. (2011). Integrating Writing and Mathematics. The Reading Teacher, 64(7), 521-529. Yuan, X., & Sriraman, B. (2010). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities. In B. Sririman, & K. Lee, The elements of creativity and giftedness in mathematics (pp. 5-28). Rotterdam: Sense. Zhe, L. (2012). Survey of Primary Students'. Mathematical Representation Status and Study on the Teaching Model of. Mathematical Representation. Journal of Mathematics Education, 5(1), 63-76. Zinsser, W. (1998). Writing to learn. New York: Harper and Rowe.
|