RESEARCH PAPER
Examining the Differences of Hong Kong and Taiwan Students’ Performance on the Number Sense Three-tier Test
 
 
More details
Hide details
1
The Education University of Hong Kong, Hong Kong, CHINA
2
National Chiayi University, Chiayi City, TAIWAN
Online publish date: 2018-05-17
Publish date: 2018-05-17
 
EURASIA J. Math., Sci Tech. Ed 2018;14(7):3329–3345
KEYWORDS
ABSTRACT
Assessing elementary students’ performance on number sense provides early predictors and support for interventions in teaching and learning number sense before children fall seriously behind in school. There is no study that concerns the differences between Hong Kong and Taiwan students’ performance on the number sense three-tier test. The purposes of this study were to examine the differences of Hong Kong and Taiwan students’ performance on the number sense three-tier test and the possible misconceptions. A total of 125 fifth graders, 942 sixth graders from Hong Kong, and 819 fifth graders from Taiwan participated in this study. Results show that there are significant differences on the performance of first two-tier test and confidence between the fifth graders of HK and Taiwan, sixth graders of HK and fifth graders of Taiwan, respectively. Strong misconceptions and key differences among the HK fifth graders, HK sixth graders, and Taiwan fifth graders were found and discussed.
 
REFERENCES (69)
1.
Akkaya, R. (2016). An Investigation into the Number Sense Performance of Secondary School Students in Turkey. Journal of Education and Training Studies, 4(2), 113-123. https://doi.org/10.11114/jets.....
 
2.
Alghazo, Y. M., & Alghazo, R. (2017). Exploring common misconceptions and errors about fractions among college students in Saudi Arabia. International Education Studies, 10(4), 133-140. https://doi.org/10.5539/ies.v1....
 
3.
Alves-Martins M, Peixoto F, Gouveia-Pereira M, Amaral V, Pedro I. (2002). Self-esteem and academic achievement among adolescents. Educational Psychology, 22(1), 51–62. https://doi.org/10.1080/014434....
 
4.
America’s Choice. (2012). Mathematics navigator: Misconceptions and errors. Retrieved on January 02, 2018 from https://www.westada.org/cms/li....
 
5.
Ashlock, R. (2006). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Pearson/Merrill Prentice Hall.
 
6.
Aunio, P., Ee, J., Lim, S. E. A., Hautana”kia, J., & Van Luit, J. (2004). Young children’s number sense in Finland, Hong Kong, and Singapore. International Journal of Early Years Education, 12(3), 195-216. https://doi.org/10.1080/096697....
 
7.
Australian Education Council. (1991). A national statement on mathematics for Australian school. Melbourne: Curriculum Corporation.
 
8.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339. https://doi.org/10.1177/002221....
 
9.
Bong, M., & Skaalvik, E. M. (2003). Academic Self-Concept and Self-Efficacy: How Different Are They Really? Educational Psychology Review, 15, 1-40. https://doi.org/10.1023/A:1021....
 
10.
Burton, L. (2004). Confidence is everything”–Perspectives of teachers and students on learning mathematics. Journal of Mathematics Teacher Education, 7(4), 357–381. https://doi.org/10.1007/s10857....
 
11.
Cai, J., & Howson, G. (2013). Toward and International Mathematics Curriculum. In K. Clements et al. (Eds.), Third International Handbook of Mathematics Education (pp. 949–974). New York: Springer.
 
12.
Cai, J., & Ni, Y. (2011). Investigating Curricular Effect on the Teaching and Learning of Mathematics in a Cultural Context: Theoretical and Methodological Considerations. International Journal of Educational Research, 50(2), 65–70. https://doi.org/10.1016/j.ijer....
 
13.
Caleon, I., & Subramaniam, R. (2010). Development and application of a three-tier diagnostic test to assess secondary students’ understanding of waves. International Journal of Science Education, 32, 939–961. https://doi.org/10.1080/095006....
 
14.
Cetin-Dindar, A., & Geban, O. (2011). Development of a three- tier test to assess high school students’ understanding of acids and bases. Procedia-Social and Behavioral Sciences, 15, 600-604. https://doi.org/10.1016/j.sbsp....
 
15.
Clement, J., Brown, D. E., & Zietsman, A. (1989). Not all preconceptions are misconceptions: Finding ‘anchoring conceptions’ for grounding instruction on students’ intuitions. International Journal of Science Education, 11(5), 554-565. https://doi.org/10.1080/095006....
 
16.
Common Core State Standards for Mathematics. (2010). Common Core State Standards for Mathematics. Washington, DC: The National Governors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved on January 02, 2018 from http://www.corestandards.org/t....
 
17.
Dehaene, S. (1997). The Number Sense. New York: Oxford University Press.
 
18.
Dhlamini, Z. B., & Kibirige, I. (2014). Grade 9 learners’ errors and misconceptions in addition of fractions. Mediterranean Journal of Social Sciences, 5(8), 236-244. https://doi.org/10.5901/mjss.2....
 
19.
Dunphy, E. (2007). The primary mathematics curriculum: enhancing its potential for developing young children’s number sense in the early years at school. Irish Educational Studies, 26(1), 5-25. https://doi.org/10.1080/033233....
 
20.
Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29. https://doi.org/10.1016/j.lear....
 
21.
Dyson, N. I., Jordan, N. C., & Glutting, J. (2013). A number sense intervention for low-income kindergartners at risk for mathematics difficulties. Journal of Learning Disabilities, 46(2), 166-181. https://doi.org/10.1177/002221....
 
22.
Education Development Center in USA. (2015). Eliciting Mathematics Misconceptions. Retrieved on January 02, 2018 from http://em2.edc.org/sites/defau....
 
23.
Elliot, S. N. (2015). Measuring opportunity to learn and achievement growth: key research issues with implications for the effective education of all students. Remedial & Special Education, 36(1), 58–64. https://doi.org/10.1177/074193....
 
24.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook Research in Mathematics Education: Development Status and Directions. ZDM, 45(5): 633–646. https://doi.org/10.1007/s11858....
 
25.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and intervention for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293-304. https://doi.org/10.1177/002221....
 
26.
Gok, T. (2014). Students’ achievement, skill and confidence in using stepwise problem-solving strategies. Eurasia Journal of Mathematics, Science & Technology Education, 10(6), 617-624. https://doi.org/10.12973/euras....
 
27.
Griffin, L. B. (2016). Tracking decimal misconceptions: Strategic instructional choices. Teaching Children Mathematics, 22(8), 489-494. https://doi.org/10.5951/teacch....
 
28.
Hasan, S., Bagayoko, D., & Kelley, E. L. (1999). Misconceptions and the certainty of response index (CRI). Physics Education, 34, 294–299. https://doi.org/10.1088/0031-9....
 
29.
Hong Kong Curriculum Development Council and the Hong Kong Examinations and Assessment Authority. (2014). Mathematics Education Key Learning Area - Mathematics Curriculum and Assessment Guide (Secondary 4 - 6). Hong Kong: Authors.
 
30.
House, J. D., & Telese, J. A. (2016). Achievement of eighth-grade students in Korea on the TIMSS 2011 Assessment: Effects of confidence in mathematics and engagement in mathematics lessons. Education, 137(1), 77-81.
 
31.
Jones, G. A., Thornton, C. A., Putt, I. J., Hill, K. M., Mogill, A. T., Rich, B. S., & Van Zoest, L. R. (1996). Multidigit number sense: A framework for instruction and assessment. Journal for Research in Mathematics Education, 27, 310-336. https://doi.org/10.2307/749367.
 
32.
Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88. https://doi.org/10.1016/j.lind....
 
33.
Jordan, N. C., Glutting, J., Ramineni, C., & Watkin, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 3(2), 181-195.
 
34.
Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36-46. https://doi.org/10.1111/j.1540....
 
35.
Joseph, K. N. (2014). College students’ misconceptions of the order of operations. Fredonia, NY: Department of Mathematical Sciences, State University of New York.
 
36.
Lin, Y. C., Yang, D. C., & Li, M. N. (2016). Diagnosing Students’ Misconceptions in Number Sense via a Web-Based Two-Tier Test. Eurasia Journal of Mathematics, Science & Technology Education, 12(1), 41-55. https://doi.org/10.12973/euras....
 
37.
Markovits, Z., & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4-29. https://doi.org/10.2307/749290.
 
38.
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2-8.
 
39.
McIntosh, A., Reys, B. J., Reys, R. E., Bana, J., & Farrel, B. (1997). Number sense in school mathematics: Student performance in four countries. Mathematics, Science, and Technology Education Centre, Edith Cowan University.
 
40.
Menon, R. (2004). Elementary school children’s number sense. International Journal for Mathematics Teaching and Learning. Retrieved on January 08, 2018, from http://www.cimt.plymouth.ac.uk....
 
41.
Ministry of Education in Taiwan. (2017). Twelve-year joint mathematics curricula plan in Taiwan. Taiwan: Taipei. (In Chinese).
 
42.
Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International Results in Mathematics. Retrieved on from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/ti....
 
43.
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
 
44.
National Council of Teachers of Mathematics (NCTM). (2000). The principles and standards for school mathematics. Reston, VA: NCTM.
 
45.
Organization for Economic Co-operation & Development (OECD). (2016). PISA 2015 Results in Focus. Paris: OECD.
 
46.
Pesman, H., & Eryilmaz, A. (2010). Development of a three-tier test to assess misconceptions about simple electric circuits. The Journal of Educational Research, 103, 208-222. https://doi.org/10.1080/002206....
 
47.
Resnick, L. B. (1989). Defining, assessing and teaching number sense. In Sowder & Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference. San Diego, CA: San Diego State University, Center for Research in Mathematics and Science Education.
 
48.
Reys, B. J. (1994). Promoting number sense in middle grades. Teaching Mathematics in the Middle School, 1(2), 114–120.
 
49.
Reys, B. J., Reys, R. E., & Havez, O. (2004). Why Mathematics Textbooks Matter. Educational Leadership, 61(5), 61–66.
 
50.
Reys, R. E., & Yang, D. C. (1998). Relationship between Computational Performance and Number Sense among Sixth- and Eighth-Grade Students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. https://doi.org/10.2307/749900.
 
51.
Şengül, S., & Gülbağcı, D. H. (2012). Evaluation of number sense on the subject of decimal numbers of the secondary stage students in Turkey. International Online Journal of Educational Sciences, 4(2), 296-310.
 
52.
Şengül, S., & Gülbağcı, D. H. (2014). The strategies of mathematics teachers when solving number sense problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 5(1), 73-88. https://doi.org/10.16949/turco....
 
53.
Sood, S., & Jitendra, A. K. (2007). A comparative analysis of number sense instruction in reform- based and traditional mathematics textbooks. Journal of Special Education, 41(3), 145-157. https://doi.org/10.1177/002246....
 
54.
Sowder, J. (1992). Estimation and number sense. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). New York, NY: Macmillan.
 
55.
Stein, M., Remillard, J., & Smith, M. (2007). How Curriculum Influences Student Learning. In F. Lester, Handbook of Research on Mathematics Teaching and Learning (pp. 319–369). Greenwich, CT: Information Age.
 
56.
Tan, K. C. D., Goh, N. K., Chia, L. S., & Treagust, D. F. (2002). Development and application of a two-tier multiple choice diagnostic instrument to assess high school students’ understanding of inorganic chemistry qualitative analysis. Journal of Research in Science Teaching, 39(4), 283-301. https://doi.org/10.1002/tea.10....
 
57.
Tarr, J. E., Grouws, D. A., Chávez, Ó., & Soria, V. M. (2013). The effects of content organization and curriculum implementation on students’ mathematics learning in second-year high school courses. Journal for Research in Mathematics Education, 44(4), 683–729. https://doi.org/10.5951/jresem....
 
58.
The Hong Kong Curriculum Development Council. (2000). Learning to learn: The way forward in curriculum development. Hong Kong: Author.
 
59.
The Hong Kong Curriculum Development Council. (2014). Mathematics Education Key Learning Area. Hong Kong: Author. Retrieved on January 08, 2018 from http://334.edb.hkedcity.net/do....
 
60.
The Hong Kong Curriculum Development Council. (2017). Mathematics Education Key Learning Area Curriculum Guide (Primary 1 – Secondary 6). Hong Kong: Author. Retrieved on January 08, 2018 from http://www.edb.gov.hk/attachme....
 
61.
Törnrros, J. (2005). Mathematics Textbooks, Opportunity to Learn and Student Achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stue....
 
62.
Trivena, V., Ningsih, A. R., & Jupri, A. (2017). Misconception on addition and subtraction of fraction at primary school students in fifth-grade. Journal of Physics: Conference Series, 895(1), 1-7. https://doi.org/10.1088/1742-6....
 
63.
Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Charlotte, NC: Information Age.
 
64.
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, 41-65. https://doi.org/10.1007/s10649....
 
65.
Yang, D. C. (2003). Teaching and Learning Number Sense - An Intervention Study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, 1(1), 115-134. https://doi.org/10.1023/A:1026....
 
66.
Yang, D. C., & Li, M. N (2013). Assessment of Animated Self-Directed Learning Activities Modules for Children’s Number Sense Development. Journal of Educational Technology and Society, 16(3), 44-58.
 
67.
Yang, D. C., & Li, M. N. (2017). A study of fifth graders’ performance on the three-tier number sense test. Paper presented at the 41st Annual Meeting of the International Group for the Psychology of Mathematics Education, Singapore, July 17-22, 2017.
 
68.
Yang, D. C., & Wu, W. R. (2010). The study of number sense realistic activities integrated into third-grade math classes in Taiwan. The Journal of Educational Research, 103(6), 379-392. https://doi.org/10.1080/002206....
 
69.
Yang, D. C., Li, M. N., & Lin, C. I. (2008). A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807. https://doi.org/10.1007/s10763....
 
eISSN:1305-8223
ISSN:1305-8215