Procedural and relational understanding of pre-service mathematics teachers regarding spatial perception of angles in pyramids

References

• Wai J, Lubinski D, Benbow CP. Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. J Educ Psychol. 2009;101(4):817–835. doi: 10.1037/a0016127
   Web of Science ®Google Scholar
• Stieff M, Uttal D. How much can spatial training improve STEM achievement? Educ Psychol Rev. 2015;27(4):607–615. doi: 10.1007/s10648-015-9304-8
   Web of Science ®Google Scholar
• Cohen N. (2007). Analytical-visual integration in 3-D tasks. [dissertation]. Beer-Sheba (Israel): Ben-Gurion University of the Negev; 2007. Hebrew.
   Google Scholar
• Gutiérrez A. Visualization in 3-dimensional geometry: in search of a framework. In: Puig L, Gutiérrez A, editors. Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education. Valencia: Universidad de Valencia; 1996. p. 3–19.
   Google Scholar
• Halpern FD. Sex, brains & hands: gender differences in cognitive abilities. eSkeptic. 2005;2(3):96–103. Available from: http://www.skeptic.com/eskeptic/05-03-15/.
   Google Scholar
• Linn MC, Petersen AC. Emergence and characterization of sex differences in spatial ability: a meta-analysis. Child Dev. 1985;56:1479–1498. doi: 10.2307/1130467
   PubMed Web of Science ®Google Scholar
• Presmeg NC. Research on visualization in learning and teaching mathematics: emergence from psychology. In: Gutiérrez A, Boero P, editors. Handbook of research on the psychology of mathematics education. Rotterdam: Sense Publishers; 2006. p. 205–235.
   Google Scholar
• Sorby SA, Wysocki AF, Baartmans BG. Introduction to 3D spatial visualization. New York (NY): Cengage Learning; 2002.
   Google Scholar
• Patkin D, Dayan E. The intelligence of observation improving high school students’ spatial ability by means of intervention units. Int J Math Educ Sci Technol. 2013;44(2):179–195. doi: 10.1080/0020739X.2012.703335
   Google Scholar
• Barkai R, Patkin D. An investigation of the visual-mental capability of pre-and in-service mathematics teachers: A tale of two cones and one cube. Res Math Educ. 2014;18(1):41–54. doi: 10.7468/jksmed.2014.18.1.41
   Google Scholar
• Ben-Chaim D, Lappan G, Houang RT. The effect of instruction on spatial visualization skills of middle school boys and girls. Am Educ Res J. 1988;25(1):51–71. doi: 10.3102/00028312025001051
   Web of Science ®Google Scholar
• Ben-Chaim D, Lappan G, Houang RT. Adolescents’ ability to communicate spatial information: analyzing and effecting students’ performance. Educ Stud Math. 1989;20(2):121–146. doi: 10.1007/BF00579459
   Google Scholar
• Medina AC, Gerson HBP, Sorby SA. Identifying gender differences in the 3D visualization skills of engineering students in Brazil and in the United States. Proceedings of the International Conference for Engineering Education; 1998; Rio de Janeiro, Brazil.
   Google Scholar
• Shriki A, Barkai R, Patkin D. Developing mental rotation ability through engagement in activities that involve solids of revolution. Math Enthus. 2017;14(1,2&3):541–562. ISSN 1551-3440.
   Web of Science ®Google Scholar
• Sorby SA, Baartmans BG. The development and assessment of a course for enhancing the 3D spatial visualization skills of first year engineering students. J Eng Educ. 2000;63(2):21–32.
   Google Scholar
• Turos J, Ervin A. Training and gender differences on a web-based mental rotation task. Penn State Behrend Psychol J. 2000;4(2):3–12.
   Google Scholar
• Patkin D, Fadalon L. Developing 3rd grade boys and girls’ spatial ability by means of an extra-curricular teaching unit. Res Math Educ. 2013;17(2):99–118. doi: 10.7468/jksmed.2013.17.2.099
   Google Scholar
• Zacks JM. Neuroimaging studies of mental rotation: a meta-analysis and review. J Cogn Neurosci. 2008;20:1–19. doi: 10.1162/jocn.2008.20013
   PubMed Web of Science ®Google Scholar
• Keller B, Wasburn-Moses J, Hart E. Improving students’ spatial visualization skills and teachers’ pedagogical content knowledge by using on-line curriculum-embedded applets: overview of a research and development project. 2002. Available from National Council of Teachers of Mathematics Illuminations Project website: http://illuminations.nctm.org/downloads/IsoPaperV4.pdf.
   Google Scholar
• Piaget J, Inhelder B. The child’s conception of space. New York (NY): WW Norton.
   Google Scholar
• Fischbein E. The theory of figural concepts. Educ Stud Math. 1993;24(2):139–162. doi: 10.1007/BF01273689
   Google Scholar
• Skemp R. Relational understanding and instrumental understanding. Math Teach. 1976;77:20–26.
   Google Scholar
• Hiebert J, Lefevre P. Conceptual and procedural knowledge in mathematics: an introductory analysis. In: Hiebert J, editor. Conceptual and procedural knowledge: the case of mathematics. Hillsdale (NJ): Lawrence Erlbaum Associates; 1986. p. 1–27.
   Google Scholar
• National Council of Teachers of Mathematics. Principles and standards for school mathematics. Reston (VA): NCTM; 2000.
   Google Scholar
• Rittle-Johnson B, Wagner M. Conceptual and procedural knowledge of mathematics: does one lead to the other? J Educ Psychol. 1999;91(1):175–189. doi: 10.1037/0022-0663.91.1.175
   Web of Science ®Google Scholar
• Star J, Seifert C. Re-conceptualizing procedural knowledge: flexibility and innovation in equation solving. New Orleans (LA): Annual Meeting of the American Educational Research Association (AERA); 2002 Apr. p. 1–50.
   Google Scholar
• Stephens M. Describing and exploring the power of relational thinking. Proceedings of the Mathematics Education Research Group of Australia Incorporated (MERGA 29); 2006. p. 479–486.
   Google Scholar
• Kent G, Foster C. Re-conceptualising conceptual understanding in mathematics. Proceedings of the Ninth Congress of European Research in Mathematics Education (CERME 9), 2015 Feb 4–8; Prague, Czech Republic. p. 97–107.
   Google Scholar
• Boaler J. Open and closed mathematics: student experiences and understandings. J Res Math Educ. 1998;29(1):41–62. doi: 10.2307/749717
   Web of Science ®Google Scholar
• Stigler JW, Hiebert J. The teaching gap; best ideas from the world’s teachers for improving education in the classroom. New York (NY): The Free Press; 1999.
   Google Scholar
• Donevska-Todorova A. Procedural and conceptual understanding in undergraduate linear algebra. Proceedings of the First Conference of International Network for Didactic Research in University Mathematics; 2016 March; Montpellier (France). Available from: https://hal.archives-ouvertes.fr/hal-01337932.
   Google Scholar
• Fujii T, Stephens M. Fostering an understanding of algebraic generalisation through numerical expressions. In: Chick H, Stacey K, Vincent J, Vincent J, editors. Proceedings of the 12th Conference of the International Commission on Mathematics Instruction. Melbourne: ICMI; 2001. p. 258–264.
   Google Scholar
• Stephens M. Some key junctures in relational thinking. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA, 2). 2008. p. 479–486. Available from: https://www.researchgate.net/publication/236661294.
   Google Scholar
• Leikin R. Towards high quality geometrical tasks: reformulation of a proof problem. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. 2004;3:209–216.
   Google Scholar
• Prusak N, Hershkowitz R, Schwarz B. From visual reasoning to logical necessity through argumentative design. Educ Stud Math. 2012;79(1):19–40. doi: 10.1007/s10649-011-9335-0
   Web of Science ®Google Scholar
• Patkin D. Global van Hiele (GVH) Questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. Res Math Educ. 2014;18(2):103–128. doi: 10.7468/jksmed.2014.18.2.103
   Google Scholar
• Van Hiele PM. La pensee de l'enfant et la Geometrie. Bulletin de l'Association des Professeurs de Mathematiques de l'Enseignement Public. 1959;198:199–205.
   Google Scholar
• Van Hiele PM. A method to facilitate the finding of levels of thinking in geometry by using the levels in arithmetic. Proceeding of the Conference of Learning and Teaching Geometry: Issues for Research and Practice; 1987; New York (NY): Syracuse University.
   Google Scholar
• Plaksin O, Patkin D. Exploring the minimum conditions for congruency of polygons. Learning Teach Math. 2016;21:42–46.
   Google Scholar
• Patkin D. Various ways of inculcating new solid geometry concepts. Int J Educ Math Sci Technol. 2015;3(2):140–154. doi: 10.18404/ijemst.99466
   Web of Science ®Google Scholar
• Harris J, Hirsh-Pasek K, Newcombe NS. A new twist on studying the development of dynamic spatial transformations: mental paper folding in young children. Mind Brain Educ. 2013;7(1):49–55. doi: 10.1111/mbe.12007
   Web of Science ®Google Scholar
• Shea DL, Lubinski D, Benbow CP. Importance of assessing spatial ability in intellectually talented young adolescents; a 20-year longitudinal study. J Educ Psychol. 2001;93(3):604–614. doi: 10.1037/0022-0663.93.3.604
   Web of Science ®Google Scholar
• Seago N, Jacobs J, Driscoll M. Transforming middle school geometry: designing professional development materials that support the teaching and learning of similarity. Middle Grades Res J. 2010;5(4):199–211. Available from: https://www.researchgate.net/publication/236661303.
   Google Scholar
• Walker CM, Winner E, Hetland L, et al. Visual thinking: art students have an advantage in geometric reasoning. Creat Educ. 2011;2(1):22–26. doi: 10.4236/ce.2011.21004
   Google Scholar