RESEARCH PAPER
Opportunities to Learn Three-Dimensional Shapes in Primary Mathematics: The Case of Content Analysis of Primary Mathematics Textbooks in Hong Kong
 
 
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Department of Mathematics and Information Technology, The Education University of Hong Kong, HONG KONG
 
 
Publication date: 2021-05-07
 
 
EURASIA J. Math., Sci Tech. Ed 2021;17(6):em1971
 
KEYWORDS
ABSTRACT
Textbooks play an important part in teaching and learning mathematics. However, textbook research on spatial ability has so far received little attention. In this study, we investigated whether school mathematics textbooks provide enough opportunities for primary students to learn three-dimensional shapes and help them acquire spatial ability. Three mathematics textbook series used in Hong Kong were analysed through content analysis. Findings showed each series of textbooks contained five domains for introducing solid figures, which included real-life examples, understanding concepts, measurement, finding laws, and developing spatial ability. The development of spatial abilities was mainly shown in the production of three-dimensional graphics. What students experienced in the learning of 3-D shapes was relatively narrow. Geometric graphics were mainly limited to the conventional shapes at the early stage. Activities to explore three-dimensional graphics were insufficient. It was suggested that combining the surrounding world of children with geometry in the classroom was not just a criterion for textbooks but also the focus of classroom teaching. The flexibility of teachers’ adoptions of textbooks is also worthy of further investigation.
 
REFERENCES (47)
1.
Abdullah, A., Ahmad, N., & Nohseth, N. (2020). Investigating student’s learning difficulties in Shape and Space topic: A case study. International Journal of Psychosocial Rehabilitation, 24(5), 5315-5321. https://doi.org/10.37200/IJPR/....
 
2.
Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239-261. https://doi.org/10.1007/s10649....
 
3.
Bishop, A. J. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 125-203). Academic Press.
 
4.
Carter, J., Li, Y., & Ferrucci, B. (1997). A comparison of how textbooks present integer addition and subtraction in China and the United States. The Mathematics Educator, 2(2), 197-209.
 
5.
Charalambous, C., Delaney, S., Hsu, H., & Mesa, M. (2010). A Comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning: An International Journal, 12(2), 117-151. https://doi.org/10.1080/109860....
 
6.
Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning-A project of the National Council of Teachers of Mathematics. Macmillan Publishing Company.
 
7.
Cueto, S., Ramírez, C. & León, J. (2006). Opportunities to learn and achievement in mathematics in a sample of sixth grade students in Lima, Peru. Educational Studies in Mathematics, 62(1), 25-55. https://doi.org/10.1007/s10649....
 
8.
Curriculum Development Council. (2000). Learning to learn: The way forward in curriculum development consultation document. The Council.
 
9.
Curriculum Development Council. (2002). Basic education curriculum guide: Building on strengths. The Council.
 
10.
Dienes, Z. P. (1971). Building up Mathematics (4th Ed.). Hutchinson.
 
11.
Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics, 66(1), 61-75. https://doi.org/10.1007/s10649....
 
12.
Flores-Bascuñana, M., Diago, P. D., Villena-Taranilla, R., & Yáñez, D. F. (2020). On augmented reality for the learning of 3D-geometric contents: A preliminary exploratory study with 6-grade primary students. Education Sciences, 10(1), 4. https://doi.org/10.3390/educsc....
 
13.
Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French, and German Classrooms: Who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567-590. https://doi.org/10.1080/014119....
 
14.
Hallowell, D. A., Okamoto, Y., Romo, L. F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM: The International Journal of Mathematics Education, 47(3), 363-375. https://doi.org/10.1007/s11858....
 
15.
Ho, S. C. (Ed.). (2011). The fourth HKPISA report PISA 2009: Monitoring the quality and equality of education in Hong Kong from an international perspective from PISA 2000 to PISA 2009. HKPISA Centre, The Chinese University of Hong Kong.
 
16.
Hus, W. M., & Lin, M. J. (2008). A content analysis of geometry material in elementary school textbook of Taiwan and Hong Kong. Journal of National Pingtung University of Education, 28, 1-52.
 
17.
Hus, W. M., & Lin, M. J. (2009). A content analysis of geometry materials in elementary mathematics textbook of Taiwan, China and Hong Kong. National Changhua Educational journal, 16, 49-75.
 
18.
Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27.
 
19.
Kan, P. W., Ma, S. Y., So, W. Y., & Wong, K. M. (1995). An analysis of the Hong Kong primary mathematics textbooks: The learning dimension of shape and space (1). EduMath, 1, 16-18.
 
20.
Kan, P. W., Ma, S. Y., So, W. Y., & Wong, K. M. (1996). An analysis of the Hong Kong primary mathematics textbooks: The learning dimension of shape and space (2). EduMath, 2, 39-45.
 
21.
Kolovou, A, van den Heuvel-Panhuizen, M. & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks: A needle in a haystack. Mediterranean Journal for Research in Mathematics Education, 8(2), 31-68.
 
22.
Krippendorff, K. (1980). Content analysis: An introduction to its methodology. Sage.
 
23.
Lohman, D. F. (1988). Spatial abilities as traits, processes, and knowledge. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 40, pp. 181-248). Erlbaum.
 
24.
Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks. Educational Studies in Mathematics, 56, 255-286. https://doi.org/10.1023/B:EDUC....
 
25.
Mullis, I. V. S., Martin, M. O., & Foy, P. (2008). TIMSS 2007 international mathematics report: Findings from IEA’s Trends in International Mathematics and Science Study at the eighth and fourth Grades. Boston College.
 
26.
Mullis, I.V.S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Boston College.
 
27.
Ng, O., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: Dynamic geometry and 3D Printing. International Journal of STEM Education. https://doi.org/10.1186/s40594....
 
28.
OECD (2014). PISA 2012 results: What students know and can do (Volume I). OECD. https://www.oecd.org/pisa/keyf....
 
29.
OECD (2019). PISA 2018 Assessment and Analytical Framework. OECD Publishing. https://doi.org/10.1787/b25efa....
 
30.
Ozdemir, G. (2010). Exploring visuospatial thinking in learning about mineralogy: spatial orientation ability and spatial visualization ability. International Journal of Science and Mathematics Education, 8(4), 737-759. https://doi.org/10.1007/s10763....
 
31.
Ping, O. W., & Hua, A. K. (2016). A case report of educational in 3D and 2D towards primary mathematics. Asia Pacific Journal of Education, Arts and Science, 3(2), 8-12. https://doi.org/10.6084/m9.fig....
 
32.
Pingel, F. (1999). UNESCO guidebook on textbook research and textbook revision. Hahn.
 
33.
Reys, B., Reys, R., & Koyama, M. (1996). The development of computation in three Japanese primary-grade textbooks. The Elementary School Journal, 96(4), 423-437. https://doi.org/10.1086/461837.
 
34.
Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement. Journal for Research in Mathematics Education, 34(1), 74-95. https://doi.org/10.2307/300347....
 
35.
Rezat, S. (2009). The utilization of mathematics textbooks as instruments for learning. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME6 (Vol 6, pp. 1260-1269), Lyon France.
 
36.
Stein, M., Remillard, J., & Smith, M. (2007). How curriculum influences students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Information Age.
 
37.
Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Sage Publications, Inc.
 
38.
Sun, X. (2011). Variation problems and their roles in the topic of fraction division in Chinese Mathematics textbook examples. Educational Studies in Mathematics, 76(1), 65-85. https://doi.org/10.1007/s10649....
 
39.
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247-280. https://www.jstor.org/stable/3....
 
40.
Törnroos, 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....
 
41.
Van Hiele, P. M. (1986). Structure and insight. A theory of mathematics education. Academic press Inc.
 
42.
Vincent, J., & K. Stacey (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS Video Study criteria to Australian Eighth-grade mathematics textbooks. Mathematics Education Research Journal. 20(1), 82-107. https://doi.org/10.1007/BF0321....
 
43.
Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over fifty years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817-835. https://doi.org/10.1037/a00161....
 
44.
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....
 
45.
Wong, K. L. (2014). Mathematical literacy. In S. C. Ho (Ed.), The fifth HKPISA report: PISA2012 (pp. 45-93). The Chinese University of Hong Kong, Hong Kong: Hong Kong PISA Centre.
 
46.
Wong, N. Y. (1990). Spatial mathematical games and the training of spatial ability [in Chinese]. Math Media, 56, 78-96.
 
47.
Wong, N. Y., Han, J. W., & Lee, P. Y. (2004). The mathematics curriculum: Towards globalisation or Westernisation? In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 27-70). World Scientific. https://doi.org/10.1142/978981....
 
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