Browse > Article
http://dx.doi.org/10.7468/mathedu.2020.59.2.113

An analysis on middle school students' space geometrical thinking based on cylinder  

Chang, Hyun Suk (University of Ulsan)
Hong, Jeong Ae (Janggok middle school)
Lee, Bongju (Kyungpook National University)
Publication Information
The Mathematical Education / v.59, no.2, 2020 , pp. 113-130 More about this Journal
Abstract
The purpose of this study is to analyze how well middle school students understand space geometrical concept related to a cylinder. To this end, we developed the test tool based on prior research and examined 433 middle school students in November and December, 2018. And in March 2019, we interviewed 4 students who showed some type of errors. The difference in the correct answer rate of the questions by the grade and gender was tested, and the error type was analyzed based on the student's responses to the questions to evaluate the spatial reasoning ability. The results of this study are as follows. First, the difference by graders was not statistically significant in the questions evaluating spatial visual ability. On the other hand, in the case of the two questions for evaluating spatial measurement ability and spatial reasoning ability, the difference in the correct answer rate between the 7th graders and 8th is not significant, but the difference between lower graders and 9th was significant. Second, there was no significant difference in the spatial geometric ability of all girls and boys participating in this study. Third, analyzing the student's error type for an item which assessed spatial reasoning ability, we found that there are various error types in relation to visual, manipulative, and reasoning errors.
Keywords
spacial geometrical thinking; cylinder; middle school students;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Van Hiele, P. M. (1985). The child's thought and geometry. In D. Geddes & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243-252). Brooklyn: Brooklyn College, School of Education (Original work published 1959).
2 Widder, M. & Gorsky, P. (2013). How students use a software application for visualizing 3D geometric objects to solve problems. Journal of Computers in Mathematics and Science Teaching, 32(1), 89-120.
3 Ministry of Education (2015). Mathematics Curriculum. Ministry of Education Notification No. 2015-74 [Vol.8]. Seoul: Author.
4 Ambrose, R. & Kenehan, G. (2009). Children's evolving understanding of polyhedra in the classroom. Mathematical Thinking and Learning, 11(3), 158-176.   DOI
5 Bielinski, J. & Davison, M. N. (1998). Gender differences by item multiple-choice mathematics items. American. Educational Research Journal, 35, 455-476. doi.org/10.3102/00028312035003455   DOI
6 Bruce, C. & Hawes, Z. (2015). The role of 2D and 3D mental rotations in mathematics for young children: what is it? why does it matter? and what can we do about it? ZDM Mathematics Education, 47(3), 331-343. doi:10.1007/s11858-014-0637-4   DOI
7 Fennema, E. & Tartre, L. A. (1985). The use of spatial visualization in mathematics by girls and boys. Journal for Research in Mathematics Education, 16, 184-206.   DOI
8 Clements, D. H. & Sarama, J. (2011). Early childhood teacher education: the case of geometry. Journal of Mathematics Teacher Education, 14(2), 133-148.   DOI
9 Delgado, A. R. & Prieto, G. (2004). Cognitive mediators and sex-related differences in mathematics. Intelligence, 32(1), 25-32.   DOI
10 Farmer, G., Verdine, B., Lucca, K., Davies, T., Dempsey, R., Newcombe, ..., & Golinkoff, K. (2013). Putting the pieces together: spatial skills at age 3 predict to spatial and math performance at age 5. Seattle: SRCD poster presentation.
11 Fujita T., Kondo Y., Kumakura H., & Kunimune S. (2017). Students' geometric thinking with cube representations: assessment framework and empirical evidence. The J. of Mathematical Behavior, 46, 96-111. doi: 10.1016/j.jmathb.2017.03.003   DOI
12 Hoffer, A. (1981). Geometry in more than proof. Mathematics Teacher, 74, 11-18.   DOI
13 Jansen, P., Schmelter, A., Quaiser-Pohl, C., Neuburger, S., & Heil, M. (2013). Mental rotation performance in primary school age children: are there gender differences in chronometric tests? Cognitive Development, 28(1), 51-62.   DOI
14 Kim, N. G. & Oh, E. S. (2008). A study on the elementary school student's abilities. Education of Primary School Mathematics, 11(1), 21-38.
15 Kim, S. H. (2009). Analysis of plane figure and solid figure 6th grader misconceptions and reasons for these misconceptions. Master's thesis, Korea National University of Education, Seoul.
16 Kim, S. M. (2008). On the gap of revision and the 7th national mathematics curriculum according to shifts in contents. Education of Primary School Mathematics, 11(2), 95-103.
17 Kim, J. M. & Ju, Y. J. (2008). Development of web-based three-dimensional structure learning programs using AVA 3D. Journal for History of Mathematics, 21(1), 121-138.
18 Kim, Y. K. & Pang, J. S. (2007). An investigation on 6th grade students' spatial sense and spatial reasoning. School Mathematics, 9(3), 327-352.
19 Lee, B. J. (2009). The trend of gender differences in variability in national assessment of educational achievement on mathematics. Journal of Educational Research in Mathematics, 19(2), 273-288.
20 Lee, M. Y. (2014). A study on programs using a net for the development of spatial visualization ability of mathematically gifted elementary. Master's thesis, Seoul National University of Education, Seoul.
21 Lee, S. J. (2019). An analysis of gender differences in primary, middle school and college students' academic achievements in mathematics. Journal of Educational Innovation Research, 29(2), 1-16, DOI: http://dx.doi.org/10.21024/pnuedi.29.2.201906.1
22 Lee, Y. B. & Cho, C. S. (2014). A study of representing activities of preservice secondary mathematics teachers in 3D geometric thinking and spatial reasoning. The Mathematical Education, 53(2), 275-290.   DOI
23 National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston: Author.
24 Lee, C. H. & Jeon, S. K. (1998). A study for spatial visualization ability of middle school students. Journal of Research in Curriculum Instruction, 2(2), 214-234.
25 Lee, H. H. & Kim, R. Y. (2013). SketchUp, spatial visualization, spatial orientation, 3D geometric thinking, spatial structuring, measurement, solid figures. The Mathematical Education, 52(4), 531-547. DOI: http://dx.doi.org.libproxy.knu.ac.kr/10.7468/mathedu.2013.52.4.531   DOI
26 McLellan, J. A. & Dewey, J. (1895). The Psychology of Number: and its Applications to Methods of Teaching Arithmetic. New York: D. Appleton & Company.
27 Pang, ]. S. & Hwang, H. M. (2010). An analysis of elementary mathematics textbooks on threedimensional figures. Journal of the Korean School Mathematics Society, 13(4), 549-568.
28 Piaget, J. & Inhelder, B. (1956). The Child's Conception of Space. London: Routledge & Kegan Paul.
29 Ryue, H. A., Chong, Y. O., & Song, S. H. (2007). Analysis of the mathematically gifted 6th and 7th graders' spatial visualization ability of solid figures. School Mathematics, 9(2), 277-289.
30 Sinclair, N. & Bruce, C. (2015). New opportunities in geometry education at the primary school. The International Journal on Mathematics Education, 47(3), 319-329.
31 Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers' concept images and concept definitions: triangles, circles, and cylinders. ZDM Mathematics Education, 47(3), 497-509. doi:10.1007/s11858-014-0641-8   DOI