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Opportunities and challenges of mathematics learning in Taiwan: a critical review

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Abstract

In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers’ competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified.

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References

  • Ambussaidi, I., & Yang, Y. F. (2019). The impact of mathematics teacher quality on student achievement in Oman and Taiwan. International Journal of Education and Learning, 1(2), 50–62.

    Article  Google Scholar 

  • Atweh, B., & Clarkson, P. (2002). Globalized curriculum or global approach to curriculum reform in mathematics education. Asia Pacific Education Review, 3(2), 160–167. https://doi.org/10.1007/BF03024909

    Article  Google Scholar 

  • Baker, D. P., Akiba, M., LeTendre, G. K., & Wiseman, A. W. (2001). Worldwide shadow education: Outside-school learning, institutional quality of schooling, and cross-national mathematics achievement. Educational Evaluation and Policy Analysis, 23(1), 1–17. https://doi.org/10.3102/01623737023001001

    Article  Google Scholar 

  • Cai, J., & Howson, G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 949–974). Springer. https://doi.org/10.1007/978-1-4614-4684-2_29

  • Carroll, J. B. (1963). A model of school learning. Teachers College Record, 64(8), 722–733.

    Article  Google Scholar 

  • Chang, Y.-P., Lin, F.-L., & Yang, K.-L. (2021). The development of a workshop for cultivating leaders of mathematics-grounding activities in class. Educational Designer, 4(14), 1–20.

    Google Scholar 

  • Chang, S.-H., Wang, C.-L., Lee, J.-C., & Yu, L.-C. (2018). Who needs entrepreneurial role models? Driving forces of students’ cyber-entrepreneurial career intention. Eurasia Journal of Mathematics, Science & Technology, 14(7), 3083–3098.

    Google Scholar 

  • Charalambous, C. Y., Delaney, S., Hsu, H.-Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. International Journal for Mathematical Thinking and Learning, 12(2), 117–151.

    Article  Google Scholar 

  • Chen, J.-C., Lin, F.-L., & Yang, K.-L. (2018). A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development. Journal of Mathematics Teacher Education, 21(5), 517–539. https://doi.org/10.1007/s10857-017-9396-9

    Article  Google Scholar 

  • Chen, Y.-H., & Yang, K.-L. (2010). The effects of self-reading and text layouts on seventh graders’ mathematical performance concerning the “Pythagorean Theorem” (in Chinese). Journal of Research in Education Sciences, 35, 1–25.

    Google Scholar 

  • Fwu, B.-J., & Wang, H.-H. (2002). The social status of teachers in Taiwan. Comparative Education, 38(2), 211–224. https://doi.org/10.1080/03050060220140584

    Article  Google Scholar 

  • Fwu, B.-J., Wei, C.-F., Chen, S.-W., & Wang, H.-H. (2014). Effort counts: The moral significance of effort in the patterns of credit assignment on math learning in the Confucian cultural context. International Journal of Educational Development, 39, 157–162. https://doi.org/10.1016/j.ijedudev.2014.07.010

    Article  Google Scholar 

  • Hogan, D., Chan, M., Rahim, R., Kwek, D., Maung Aye, K., Loo, S. C., Sheng, Y. Z., & Luo, W. (2013). Assessment and the logic of instructional practice in Secondary 3 English and mathematics classrooms in Singapore. Review of Education, 1(1), 57–106. https://doi.org/10.1002/rev3.3002

    Article  Google Scholar 

  • Hsieh, F.-J., Wang, T. Y., Hsieh, C. J., Tang, S. J., & Chao, G. (2010). A milestone of an international study in Taiwan teacher education preparation-An international comparison of Taiwan mathematics teachers preparation (Taiwan, TEDS-M2008).

  • Hsieh, F.-J. (2020). Senior high school mathematics (III). Tai-Yu Publishing.

  • Hsieh, F.-J., Lin, P.-J., & Wang, T.-Y. (2012). Mathematics-related teaching competence of Taiwanese primary future teachers: Evidence from TEDS-M. ZDM, 44(3), 277–292. https://doi.org/10.1007/s11858-011-0377-7

    Article  Google Scholar 

  • Hsieh, F.-J., Wang, T.-Y., & Chen, Q. (2020). Ideal mathematics teaching behaviors: A comparison between the perspectives of senior high school students and their teachers in Taiwan and Mainland China. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1–15.

    Google Scholar 

  • Hsu, H.-Y., & Silver, E. A. (2014). Cognitive complexity of mathematics instructional tasks in a Taiwanese classroom: An examination of task sources. Journal for Research in Mathematics Education, 45(4), 460–496.

    Article  Google Scholar 

  • Huang, H.-M. (2004). Effects of cram schools on children's mathematics learning. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 282–306). World Scientific Publishing. https://doi.org/10.1142/9789812562241_0011

  • Husén, T. (1967). International study of achievement in mathematics: A comparison of twelve countries. Hoboken: Wiley.

    Google Scholar 

  • Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646–686. https://doi.org/10.5951/jresematheduc.44.4.0646

    Article  Google Scholar 

  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Erlbaum.

    Google Scholar 

  • Kilpatrick, J. (1964). Cognitive theory and the SMSG program. Journal of Research in Science Teaching, 2(3), 247–251. https://doi.org/10.1002/tea.3660020321

    Article  Google Scholar 

  • Kuan, P.-Y. (2011). Effects of cram schooling on mathematics performance: Evidence from junior high students in Taiwan. Comparative Education Review, 55(3), 342–368. https://doi.org/10.1086/659142

    Article  Google Scholar 

  • Kung, F. W. (2017). Teaching and learning English as a foreign language in Taiwan: A socio-cultural analysis. TESL-EJ, 21(2), 1–15. http://www.tesl-ej.org/wordpress/issues/volume21/ej82/ej82a4/

  • Laschke, C., & Blömeke, S. (2016). Measurement of job motivation in TEDS-M: Testing for invariance across countries and cultures. Large-Scale Assessments in Education, 4(1), 16. https://doi.org/10.1186/s40536-016-0031-5

    Article  Google Scholar 

  • Li, Y.-S. (2021). Teacher's manual for 2 grade mathematics. Nan-I Book Enterprise Cooperation.

  • Lin, F.-L., Cheng, Y.-H., & et al. (2003). The competence of geometric argument in Taiwan adolescents. International Conference on Science & Mathematics Learning, Taipei, Taiwan.

  • Lin, F.-L., & Wu Yu, J.-Y. (2005). False proposition as a means for making conjectures in mathematics classrooms. Invited speech in Asian Mathematical Conference, Singapore.

  • Lin, F.-L. (2005). Modeling students' learning on mathematical proof and refutation. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Melbourne.

  • Lin, F.-L., & Chang, Y.-P. (2017). Mathematics teachers professional development in Taiwan. In B. Kaur, O. N. Kwon, & Y. H. Leong (Eds.), Professional development of mathematics teachers: An Asian perspective (pp. 109–117). Springer. https://doi.org/10.1007/978-981-10-2598-3_9

  • Lin, F.-L., Yang, K.-L., & Chang, Y.-P. (2018). Designing a competence-based entry course for prospective secondary mathematics teachers. In M. E. Strutchens, R. Huang, D. Potari, & L. Losano (Eds.), Educating prospective secondary mathematics teachers: Knowledge, identity, and pedagogical practices (pp. 189–203). Springer. https://doi.org/10.1007/978-3-319-91059-8_11

  • Lin, F.-L., & Chang, Y.-P. (2019). Research and development of mathematics-grounding activity modules as a part of curriculum in Taiwan. In School Mathematics Curricula (pp. 151–168). Springer.

  • Lin, F.-L. (2020). Perspectives and goals of mathematics curriculum. Taipei, Taiwan: Mathematics Monthly of MOE Curriculum & Instruction Consulting Team

  • Lin, F.-L., & Hsu, H.-Y. (2018). Using mathematics-pedagogy tasks to facilitate the professional growth of pre-service elementary teachers. In G. J. Stylianides & K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers: An international perspective (pp. 3–17). Cham: Springer. https://doi.org/10.1007/978-3-319-68342-3_1

    Chapter  Google Scholar 

  • Lin, F.-L., Hsu, H.-Y., & Chen, J.-C. (2017). Facilitating professional growth of Taiwanese in-service mathematics teachers through an innovative school-based program. In B. Kaur, O. N. Kwon, & Y. H. Leong (Eds.), Professional development of mathematics teachers: An Asian perspective (pp. 209–222). Singapore: Springer. https://doi.org/10.1007/978-981-10-2598-3_15

    Chapter  Google Scholar 

  • Lin, F.-L., Wang, T.-Y., & Yang, K.-L. (2018). Description and evaluation of a large-scale project to facilitate student engagement in learning mathematics. Studies in Educational Evaluation, 58, 178–186.

    Article  Google Scholar 

  • Lin, F.-L., & Yang, K.-L. (2002). Defining a rectangle under a social and practical setting by two seventh graders. Zentralblatt Fur Didaktik Der Mathematik, 34(1), 17–28. https://doi.org/10.1007/bf02655689

    Article  Google Scholar 

  • Lin, F.-L., & Yang, K.-L. (2007). The reading comprehension of geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education, 5, 729–754.

    Article  Google Scholar 

  • Lin, F.-L., Yang, K.-L., Hsu, H.-Y., & Chen, J.-C. (2018c). Mathematics teacher educator-researchers’ perspectives on the use of theory in facilitating teacher growth. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-018-9804-9

    Article  Google Scholar 

  • Lin, H.-L., Gorrell, J., & Taylor, J. (2002). Influence of culture and education on U.S. and Taiwan preservice teachers’ efficacy beliefs. The Journal of Educational Research, 96(1), 37–46. https://doi.org/10.1080/00220670209598789

    Article  Google Scholar 

  • Lin, S.-W., & Tai, W.-C. (2015). Latent class analysis of students’ mathematics learning strategies and the relationship between learning strategy and mathematical literacy. Universal Journal of Educational Research, 3(6), 390–395.

    Article  Google Scholar 

  • Lin, S.-W., Tzou, H.-I., Lu, I.-C., & Hung, P.-H. (2021). Taiwan performance in the programme for international student assessment. In N. Crato (Ed.), Improving a country’s education: PISA 2018 results in 10 countries (pp. 203–226). Springer.

    Chapter  Google Scholar 

  • Liou, P.-Y. (2014). Investigation of the big-fish-little-pond effect on students’ self-concept of learning mathematics and science in Taiwan: Results from TIMSS 2011. The Asia-Pacific Education Researcher, 23(3), 769–778.

    Article  Google Scholar 

  • Ministry of Education. (2010). Education report of the Republic of China. Retrieved from https://www.naer.edu.tw/files/15-1000-2976,c551-1.php

  • Ministry of Education. (2014). Curriculum guidelines of 12-Year Basic Education: General guidelines. Retrieved from https://www.naer.edu.tw/eng/PageSyllabus?fid=148

  • Ministry of Education. (2018a). 12-year basic education: Mathematics curriculum. Taipei: Author.

    Google Scholar 

  • Ministry of Education. (2018b). Adaptive teaching platform for promoting students’ mathematics learning. Taipei: Ministry of Education.

    Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. TIMSS & PIRLS International Study Center.

  • Mullis, I., Martin, M., Foy, P., Kelly, D., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. https://timssandpirls.bc.edu/timss2019/international-results/

  • Nachlieli, T., & Tabach, M. (2019). Ritual-enabling opportunities-to-learn in mathematics classrooms. Educational Studies in Mathematics, 101(2), 253–271. https://doi.org/10.1007/s10649-018-9848-x

    Article  Google Scholar 

  • NCTM. (1989). Curriculum and evaluation standards for school mathematics. The National Council of Teachers of Mathematics.

  • OECD. (2014). PISA 2012 results: What students know and can do-Student performance in mathematics, reading and science (Vol. 1). OECD Publishing.

  • OECD. (2019). PISA 2018 results: Combined executive summaries. OECD. https://www.oecd.org/pisa/publications/pisa-2018-results.htm

  • Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: Exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15(5), 381–403. https://doi.org/10.1007/s10857-012-9218-z

    Article  Google Scholar 

  • Schmidt, M., Blomeke, S., Tatto, M. T., Hsieh, F.-J., Cogan, L. S., Houang, R., Bankov, K., Santillan, M., Cedillo, T., Han, S.-I., Carnoy, M., Paine, L., & Schwille, J. (2011). Teacher education matters: A study of middle school mathematics teacher preparation in six countries. Teacher College Press.

  • Shih, S.-C., Li, J.-S., & Kuo, B.-C. (2019). The effect of remedial instructional using adaptive-learning platform on mathematical achievements of seventh graders. Education and New Development. https://pdfs.semanticscholar.org/a387/6d06d2a22787259c80db6f64c79317726d8a.pdf

  • Sianturi, I. A. J., Ismail, Z., & Yang, D.-C. (2021). A cross-national comparison of mathematical problems on numbers and operations-related topics in five countries. School Science and Mathematics, 121(2), 72–84. https://doi.org/10.1111/ssm.12451

    Article  Google Scholar 

  • Stevens, F. I. (1993). Applying an opportunity-to-learn conceptual framework to the Investigation of the effects of teaching practices via secondary analyses of multiple- case-study summary sata. The Journal of Negro Education, 62(3), 232–248. https://doi.org/10.2307/2295463

    Article  Google Scholar 

  • Tate, W. F. (1995). School mathematics and African American students: Thinking seriously about opportunity-to-learn standards. Educational Administration Quarterly, 31(3), 424–448. https://doi.org/10.1177/0013161x95031003006

    Article  Google Scholar 

  • Usiskin, Z. (1992). Thoughts of an ICME regular. For the Learning of Mathematics, 12(19–20).

  • Valdes, M. (1986). Culture bound: Bridging the culture gap in language teaching. Cambridge: Cambridge University Press.

    Google Scholar 

  • Walkowiak, T. A., Pinter, H. H., & Berry, R. Q. (2017). A reconceptualized framework for “opportunity to learn” in school mathematics. Journal of Mathematics Education at Teacher College, 8(1), 7–18. https://doi.org/10.7916/jmetc.v8i1.800

    Article  Google Scholar 

  • Wang, T.-Y., Lin, F.-L., & Yang, K.-L. (2021). Success factors for a national problem-driven program aimed at enhancing affective performance in mathematics learning. ZDM– Mathematics Education, 53(5), 1121–1136. https://doi.org/10.1007/s11858-021-01285-8

    Article  Google Scholar 

  • Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1

    Article  Google Scholar 

  • Wu, H.-M., Kuo, B.-C., & Wang, S.-C. (2017). Computerized dynamic adaptive tests with immediately individualized feedback for primary school mathematics learning. Educational Technology & Society, 20(1), 61–72.

    Google Scholar 

  • Yang, K.-L., & Lin, F.-L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59–76. http://140.122.97.100:3210/sfxlcl3?sid=google&auinit=KL&aulast=Yang&atitle=A%20model%20of%20reading%20comprehension%20of%20geometry%20proof&id=doi%3A10.1007%2Fs10649-007-9080-6&title=Educational%20studies%20in%20mathematics&volume=67&issue=1&date=2008&spage=59&issn=0013-1954

  • Yang, K.-L., & Lin, F.-L. (2012). Effects of reading-oriented tasks on students' reading comprehension of geometry proof. Mathematics Education Research Journal, 24(2), 215–238. http://140.122.97.100:3210/sfxlcl3?sid=google&auinit=KL&aulast=Yang&atitle=Effects%20of%20reading-oriented%20tasks%20on%20students%E2%80%99%20reading%20comprehension%20of%20geometry%20proof&id=doi%3A10.1007%2Fs13394-012-0039-2

  • Yang, K.-L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80(3), 307–326. https://doi.org/10.1007/s10649-011-9350-1

    Article  Google Scholar 

  • Yang, K.-L. (2016). Analyzing mathematics textbooks through a constructive-empirical perspective on abstraction: The case of Pythagoras’ Theorem. Eurasia Journal of Mathematics, Science & Technology Education, 12(4), 913–930.

    Google Scholar 

  • Yang, K.-L., Hsu, H.-Y., Lin, F.-L., Chen, J.-C., & Cheng, Y.-H. (2015). Exploring the educative power of an experienced mathematics teacher educator-researcher. Educational Studies in Mathematics, 89(1), 19–39. https://doi.org/10.1007/s10649-014-9589-4

    Article  Google Scholar 

  • Yang, K.-L., Lin, F.-L., & Tso, T.-Y. (2021). An approach to enactivist perspective on learning: Mathematics-grounding activities. The Asia-Pacific Education Researcher. https://doi.org/10.1007/s40299-021-00616-3

    Article  Google Scholar 

  • Zhang, Q., Barkatsas, T., Law, H.-Y., Leu, Y.-C., Seah, W. T., & Wong, N.-Y. (2016). What primary students in the Chinese Mainland, Hong Kong and Taiwan value in mathematics learning: A comparative analysis. International Journal of Science and Mathematics Education, 14(5), 907–924.

    Article  Google Scholar 

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Funding

This research was supported by Ministry of Science and Technology (Grants MOST 110-2511-H-003-008-MY3 and MOST 107-2511-H-007-001-MY3).

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  1. National Taiwan Normal University, Taipei, Taiwan

    Kai-Lin Yang

  2. National Tsing Hua University, Hsinchu, Taiwan

    Hui-Yu Hsu

  3. University of Taipei, Taipei, Taiwan

    Ying-Hao Cheng

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Yang, KL., Hsu, HY. & Cheng, YH. Opportunities and challenges of mathematics learning in Taiwan: a critical review. ZDM Mathematics Education 54, 569–580 (2022). https://doi.org/10.1007/s11858-021-01326-2

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