Students’ understanding of a geometric theorem: A case of grade 9 problem posing
Adriano Jr Villarosa Patac(1*), Louida Penera Patac(2), Nicolas Ensomo Crispo(3)(1) Surigao State College of Technology
(2) Surigao State College of Technology
(3) Department of Education
(*) Corresponding Author
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Abdullah, A. H., & Zakaria, E. (2013). Enhancing students’ level of geometric thinking through van Hiele’s phase-based learning. Indian Journal of Science and Technology, 6(5), 4432-4446.https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1007.5177&rep=rep1&type=pdf
Adarlo, G., & Jackson, L. (2017). For whom is K-12 education: A critical look into twenty-first century educational policy and curriculum in the Philippines. In Educating for the 21st Century (pp. 207-223). Springer, Singapore
https://doi.org/10.1007/978-981-10-1673-8_11
Akay, H., & Boz, N. (2009). Prospective teachers’ views about problem-posing activities. Procedia-Social and Behavioral Sciences, 1(1), 1192-1198.
https://doi.org/10.1016/j.sbspro.2009.01.215
Altakhyneh, B. H. (2018). Levels of Geometrical Thinking of Students Receiving Blended Learning in Jordan. Journal of Education and Learning (EduLearn), 12(2), 159-165.
https://doi.org/10.11591/edulearn.v12i2.8289
Anderson, L. W. (2003). Classroom assessment: Enhancing the quality of teacher decision making. Routledge.
Ayllón, M. F., Gómez, I. A., &Ballesta-Claver, J. (2016). Mathematical Thinking and Creativity
through Mathematical Problem Posing and Solving. Journal of Educational Psychology-Propósitos y Representaciones, 4(1), 195-218.
http://dx.doi.org/10.20511/pyr2016.v4n1.89
Bolden, D. S., Harries, A. V., & Newton, D. P. (2010). Pre service primary teachers’ conceptions of creativity in mathematics. Educational Studies in Mathematics, 73(2), 143-157.
https://doi.org/10.1007/s10649-009-9207-z
Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: conceptualization and initial findings of a problem‑posing project. ZDM–Mathematics Education, 1-14.
https://doi.org/10.1007/s11858-021-01252-3
Cañadas, M. C., Molina, M., & Del Rio, A. (2018). Meanings given to algebraic symbolism in
problem-posing. Educational Studies in Mathematics, 98(1), 19-37.
https://doi.org/10.1007/s10649-017-9797-9
Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415.
https://doi.org/10.1007/s10857-008-9081-0
Cuevas, G. J. (1984). Mathematics learning in English as a second language. Journal for research in mathematics education, 15(2), 134-144.
https://doi.org/10.5951/jresematheduc.15.2.0134
Diezmann, C., & Lowrie, T. (2009). Primary students' spatial visualization and spatial orientation: an evidence base for instruction. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 417-424). PME.
Dindyal, J. (2015). Geometry in the early years: A commentary. ZDM, 47(3), 519-529. https://doi.org/10.1007/s11858-015-0700-9
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1), 103-131. https://doi.org/10.1007/s10649-006-0400-z
English, L. D., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. D. English (Eds.), Advances in Mathematics Education. Theories of mathematics education: Seeking new frontiers (pp. 263–285). New York: Springer.
https://doi.org/10.1007/978-3-642-00742-2_27
Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17(1), 105-121. https://doi.org/10.1016/S0732-3123(99)80063-7
Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education. Monograph, 3, i-196. https://doi.org/10.2307/749957
Gerring, J. (2004). What is a case study and what is it good for?. American political science review, 341-354. https://doi.org/10.1017/S0003055404001182
Gerring, J. (2006). Single-outcome studies: A methodological primer. International sociology, 21(5), 707-734. https://doi.org/10.1177/0268580906067837
Hahn, C. G., Saalbach, H., & Grabner, R. H. (2019). Language-dependent knowledge acquisition: investigating bilingual arithmetic learning. Bilingualism: Language and Cognition, 22(1), 47-57. https://doi.org/10.1017/S1366728917000530
K to 12 Mathematics Curriculum Guide. (2016). Retrieved from Learning Resources Management and Development System: https://lrmds.deped.gov.ph/search?query=curriculum+guide
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from. Cognitive science and mathematics education, 123-147.
Koichu, B., &Kontorovich, I. (2012). Dissecting success stories on mathematical problem
posing: A case of the billiard task. Educational Studies in Mathematics, 83(1), 71–86. https://doi.org/10.1007/s10649-012-9431-9
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149-161. https://doi.org/10.1016/j.jmathb.2011.11.002
Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23(4), 341-361. https://doi.org/10.1007/s10857-018-09425-w
Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. https://doi.org/10.1016/j.ijer.2019.04.002
Leung, S. S., & Silver, E. A. (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. https://doi.org/10.1007/BF03217299
Lin, P. J. (2004). Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning. International Group for the Psychology of Mathematics Education. https://files.eric.ed.gov/fulltext/ED489580.pdf
Ma, H. L., Lee, D. C., Lin, S. H., & Wu, D. B. (2015). A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a
Matus, P. (2018). Discursive representation: Semiotics, theory, and method. Semiotica, 2018(225), 103-127. https://doi.org/10.1515/sem-2017-0019
Mestre, J. P. (2002). Probing adults' conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23(1), 9-50. https://doi.org/10.1016/S0193-3973(01)00101-0
Mielicki, M. K., Kacinik, N. A., & Wiley, J. (2017). Bilingualism and symbolic abstraction: Implications for algebra learning. Learning and Instruction, 49, 242-250. https://doi.org/10.1016/j.learninstruc.2017.03.002
Montebon, D. T. (2014). K12 science program in the Philippines: Student perception on its implementation. International Journal of Education and Research, 2(12), 153-164. https://www.researchgate.net/profile/Darryl-Montebon/publication/280234350_K12_Science_Program_in_the_Philippines_Student_Perception_on_its_Implementation/links/55ae591b08aee0799220d900/K12-Science-Program-in-the-Philippines-Student-Perception-on-its-Implementation.pdf
Nadjafikhah, M., Yaftian, N., & Bakhshalizadeh, S. (2012). Mathematical creativity: some
definitions and characteristics. Procedia-Social and Behavioral Sciences, 31, 285-291. https://doi.org/10.1016/j.sbspro.2011.12.056
Nazari, A., & Allahyar, N. (2012). Grammar Teaching Revisited: EFL Teachers between Grammar Abstinence and Formal Grammar Teaching. Australian Journal of Teacher Education, 37(2). https://doi.org/10.14221/ajte.2012v37n2.6
Orbe, J. R., Espinosa, A. A., & Datukan, J. T. (2018). Teaching chemistry in a spiral progression approach: Lessons from science teachers in the Philippines. Australian Journal of Teacher Education (Online), 43(4), 17-30. https://ro.ecu.edu.au/ajte/vol43/iss4/2/
Peng, A., & Luo, Z. (2009). A framework for examining mathematics teacher knowledge as used in error analysis. For the learning of mathematics, 29(3), 22-25. Retrieved from: https://flm-journal.org/Articles/46B191D39748441966D26939BDDA07.pdf
Plucker, J. A., & Makel, M. C. (2010).Assessment of creativity. In J.C. Kaufman & R. J. Sternberg (Eds.), The Cambridge handbook of creativity. New York, NY: Cambridge University Press. Prayitno, L. L., Purwanto, P., Subanji, S., & Susiswo, S. (2018). Identification Errors of Problem Posed by Prospective Teachers About Fraction Based Meaning Structure. International Journal of Insights for Mathematics Teaching, 01(1), 76–84. Retrieved from http://journal2.um.ac.id/index.php/ijoimt/article/viewFile/3018/1828
Pohl, M., & Doppler Haider, J. (2017). Sense-making strategies for the interpretation of visualizations—bridging the gap between theory and empirical research. Multimodal Technologies and Interaction, 1(3), 16. https://doi.org/10.3390/mti1030016
Prayito, M., Suryadi, D., & Mulyana, E. (2019). Geometric thinking level of the Indonesian seventh grade students of junior high school. In Journal of Physics: Conference Series (Vol. 1188, No. 1, p. 012036). IOP Publishing. https://iopscience.iop.org/article/10.1088/1742-6596/1188/1/012036/pdf
Robertson, S. A., & Graven, M. (2020). Language as an including or excluding factor in mathematics teaching and learning. Mathematics Education Research Journal, 32(1), 77-101. https://doi.org/10.1007/s13394-019-00302-0
Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The Effects of Problem Posing on Student
Mathematical Learning: A Meta-Analysis. International Education Studies, 7(13).
https://doi.org/10.5539/ies.v7n13p227
Shaughnessy, J. M., & Burger, W. F. (1985). Spadework prior to deduction in geometry. The Mathematics Teacher, 78(6), 419-428. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.648.9878&rep=rep1&type=pdf
Silver, E. A. (1994). On mathematical problem posing. For the learning of mathematics, 14(1), 19-28. https://www.jstor.org/stable/40248099
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
Škrbec, M., & Čadež, T. H. (2015). Identifying and fostering higher levels of geometric thinking. EURASIA Journal of Mathematics, Science and Technology Education, 11(3), 601-617. https://doi.org/10.12973/eurasia.2015.1339a
Tyler, R. (2016). Discourse-shifting practices of a teacher and learning facilitator in a bilingual mathematics classroom. Per Linguam: a Journal of Language Learning= Per Linguam: Tydskrif vir Taalaanleer, 32(3), 13-27. https://hdl.handle.net/10520/EJC-80edafa7e
Vacc, N. (1993). Questioning in the mathematics classroom. Arithmetic Teacher, 41(2), 88–91.
Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117-132. https://doi.org/10.1007/s10649-012-9456-0
Van Harpen, X. Y., & Sriraman, B. (2012). Creativity and mathematical problem posing: an
analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201–221 https://doi.org/10.1007/s10649-012-9419-5
Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching children mathematics, 5(6), 310-317. https://doi.org/10.5951/TCM.5.6.0310
Voica, C., & Pelczer, I. (2010). Problem posing by novice and experts: Comparison between students and teachers. CERME 6–WORKING GROUP 12, 2356.
Volmer, E., Grabner, R. H., & Saalbach, H. (2018). Language switching costs in bilingual mathematics learning: Transfer effects and individual differences. Zeitschrift für Erziehungswissenschaft, 21(1), 71-96. https://doi.org/10.1007/s11618-017-0795-6
Wechsler-Kashi, D., Schwartz, R. G., & Cleary, M. (2014). Picture naming and verbal fluency in children with cochlear implants. Journal of Speech, Language, and Hearing Research, 57(5), 1870-1882. https://doi.org/10.1044/2014_JSLHR-L-13-0321
Xu, B., Cai, J., Liu, Q., & Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j.ijer.2019.04.005
Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’
creativity and mathematical problem-posing abilities: Comparing Chinese and US students. In The elements of creativity and giftedness in mathematics (pp. 5-28).Brill Sense.
http://hs.umt.edu/math/research/technical-reports/documents/2010/22_YuanSriraman.pdf
Yunus, M., Suraya, A., Ayub, M., & Fauzi, A. (2019). Geometric Thinking of Malaysian Elementary School Students. International Journal of Instruction, 12(1), 1095-1112. https://files.eric.ed.gov/fulltext/EJ1201177.pdf
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