Aleman, B. P. (2007). The effect of a proportional reasoning-based test preparation instructional treatment on mathematics achievement of eight grade students. A dissertation submitted in partial fulfillment of the requirements for degree of Doctor of Education. Faculty of the college of Education, University of Houston. URL: https://www.proquest.com/openview/034a8f2147716897c8aaf1bf035f74d6/1?pq-origsite=gscholar&cbl=18750
Artut, P. D., Pelen, M. S. (2015). 6th grade gtudents’ golution gtrategies on proportional reasoning problems.
Journal of Procedia-Social and Behavioral Sciences, 197(11), 113-119.
https://doi.org/10.1016/j.sbspro.2015.07.066
Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. pre-and in-service mathematics teachers of elementary and middle school classes. Rotterdam, the Netherlands: Sense.
Ben-Chaim, D., Keret, Y., & Ilany, B. S. (2007). Designing and implementing authentic investigative proportional reasoning tasks: The impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes.
Journal of Mathematics Teacher Education,
10(4), 333-340.
https://doi.org/0.1007/s10857-007-9052-x
Clark, M. R., Berenson, S. B.& Cavey. L. O. (2003). A comparison of ratios and fractions and their roles as tools in proportional reasoning
. Journal of Mathematical Behavior. 22(3): 297-317.
https://doi.org/10.1016/S0732-3123(03)00023-3
Cramer, K. A., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications: Middle grades mathematics. In Research ideas for the classroom: Middle grades mathematics (pp.159-178), New York: Macmillan.
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students.
Journal for research in mathematics education,
39(4), 372-400.
https://doi.org/ 10.5951/jresematheduc.39.4.0372
Hines, E., McMahon, M. T. (2005). Interpreting middle school students' proportional reasoning strategies: Observations from preservice teachers.
School Science and Mathematics,
105(2), 88-105.
https://doi.org/10.1111/j.1949-8594.2005.tb18041.x
Howe, C., Luthman, S., Ruthven, k., Mercer, N., Hofman, R., Ilies, S., & Guardia, P. (2015). Rational number and proportional reasoning in early secondary school: towards principled improvement in mathematics.
Research in Mathematics Education. 17(1), 38-56.
https://doi.org/10.1080/14794802.2015.1019914
Howe, C., T. Nunes, and P. Bryant. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science.
International Journal of Science and Mathematics Education, 9(2), 391-417.
https://doi.org/10.1007/s10763-010-9249-9
Lamon, S, J. (1993). Ratio and proportion: Connecting content and children's thinking.
Journal for research in mathematics education,
24(1), 41-61.
https://doi.org/10.2307/749385
Lamon, S, J. (1999). Teaching fractions and ratios for understanding: Essentiol content knowledge and instructional strategies for teachers. Mahwah. NJ: Lawrence Erlbaum.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. Second handbook of research on mathematics teaching and learning, 1, 629-667. Reston, VA: NCTM
Lim, K. H. (2009). Burning the candle at just one end. Using nonproportional examples helps students determine when proportional strategies apply.
Mathematics Teaching in the MiddleSchool, 14(8): 492–500.
https://doi.org/10.5951/MTMS.14.8.0492
Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader.
Journal for research in mathematics education,
28(2), 216-236.
https://doi.org/10.2307/749762
Lobato J. Orrill, H, Ch. Druken, B., Jacobson, E. ( 2011). Middle school teachers’ knowledge of proportional reasoning for teaching. in Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA. Abstract retrieved from
http://www. kaputcenter. umassd. edu/ downloads/ products/ workshops/ AERA2011/ Lobato_Orrill_Druk en_Erikson_AERA_July12-13.
Nagar, G. G., Weiland, T., Orrill, C. H, & Burke, J. P. (2015). Teachers’ understanding of ratios and their cinnections to fractions. Hands book of PMENA-37. Bartell, T.G., Bieda, K. N., Putnam, R.T., Bradfield, K., & Dominguez, H.(Eds), pp 764-771. (Proceedings of the 37th Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University).
NCTM (1989). National Council of Teachers of mathematics. Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. URL: https://nap.nationalacademies.org/read/5844/chapter/5
NCTM (2013). Research Brief: Teaching Ratio and Proportion in the Middle Grades. Available from: https://www.nctm.org
Orrill, C. H., & Burke, J. P. (2013). Fine-grained analysis of teacher knowledge: proportion and geometry. Hands book of PMENA-35. Martinez, M. & Castro Superfine, A. (Eds.), pp 605-612. (Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago).
Parish, L. (2010). Facilitating the Development of Proportional Reasoning through Teaching Ratio. Mathematics Education Research Group of Australasia, 469-476. URL: https://files.eric.ed.gov/fulltext/ED520962.pdf
Pearce, D. L., Bruun, F., Skinner, K., & Lopez-Mohler, C. (2013). What Teachers Say About Student Difficulties Solving Mathematical Word Problems in Grades 2-5. International Electronic Journal of Mathematics Education, 8(1),3-19.
https://doi.org/10.29333/iejme/271
Pitta-Pantazi, D., & Christou, C. (2011). The structure of prospective kindergarten teachers’ proportional reasoning.
Journal of Mathematics Teacher Education,
14(2), 149-169.
https://doi.org/10.1007/s10857-011-9175-y
Radford, L. (2011). Grade two students’ non-symbolic algebraic thinking. In Early algebraization Springer, Berlin, Heidelberg.
Riley, K. R. (2010). Teachers’ understanding of proportional reasoning. In Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 6, 1055-1061.
Ruiz Ledesma, E. F. R. (2011). Primary and Secondary Teachers’ Knowledge, Interpretation, and Approaches to Students Errors about Ratio and Proportion Topics.
Creative Education,
2(03), 264-269.
https://doi.org/10.4236/ce.2011.23035
Ruiz Ledesma, E. F. R. (2013). Activities to learn the proportion concept using technology. Journal of International Review of Social Sciences and Humanities, 5(1), 175-184.
Sen, C., Guler, G. (2017). Effect of Strategy Teaching for the Solution of Ratio Problems on Students' Proportional Reasoning Skills. Malaysian Online Journal of Educational Sciences, 5(2)1-15. URL: https://mojem.um.edu.my/index.php/MOJES/article/view/12621
Silvestre, A. I. da Ponte J. P. (2012). Missing value and comparison problems: What pupils know before the teaching of proportion? PNA, 6(3), 73-83.
Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles.
Educational studies in mathematics,
84(1), 49-70.
https://doi.org/10.1111/j.1949-8594.2009.00005.x
Spanoudi, A., & Misailidou, C. (2015). Teachers encountering challenging word problems: How do they solve them?
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