page 1
References
References
Abe, K., & Del Grande, J. (1983). Geometric activities in the elementary school. In M.
Zweng, T. Green, J. Kilpatrick, H. Pollak, & M. Suydam (Eds.), Proceedings of the
Fourth International Congress on Mathematical Education (pp. 161-164). Boston:
Birkhauser.
Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas.
Belmont, CA: Brooks/Cole.
Bell, G. (1995). Asian games and pastimes. Adelaide: Australian Association of
Mathematics Teachers.
Bishop, A. (1973). Structural apparatus and spatial ability. Research in Education, 9,
43-49.
Bishop, A. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of
mathematics concepts and processes (pp. 176-204). New York: Academic Press.
Bishop, A. (1988). Mathematical enculturation: A perspective on mathematics
education. Dordrecht, Kluwer Academic Publishers.
Booth, D. (1994). Art and geometry learning through spontaneous pattern making.
Journal of the Institute of Art Education, 9(2), 28-42.
Boulton-Lewis, G., Wilss, L., & Mutch, S. (1994). An analysis of young children’s
strategies and use of devices for length measurement. In J. da Ponte & J. Matos
(Eds.), Proceedings of the 18th Annual Conference for International Group for the
Psychology of Mathematics Education (Vol. 2, pp. 128-135). Lisbon: Organising
Committee for PME18.
Burden, L., & Coulson, S. (1981). Processing of spatial tasks. Unpublished master's
thesis, Monash University, Melbourne.
Burger, W., & Shaughnessy, J. (1986). Characterizing the van Hiele levels of
development in geometry. Journal for Research in Mathematics Education, 17, 3148.
Carpenter, P., & Just, M. (1986). Spatial ability: An information processing approach to
psychometrics. In R.J. Sternberg (Ed.), Advances in the psychology of human
intelligence (Vol. 3, pp.221-253). Hillsdale, NJ: Lawrence Erlbaum Associates.
Chartres, M. (2005, January). Exploring students’s understanding of angle in primary
schools. Paper presented to 20th Bienniel Conference of the Australian Association
of Mathematics Education.
Chinnappan, M., & Lawson, M. (1995). Organisational features of geometric
knowledge. In B.Atweh & S.Flavel (Eds.), Proceedings of the Eighteenth Annual
Conference of the Mathematics Education Research Group of Australasia (pp. 163169). Darwin, Northern Territory: Mathematics Education Research Group of
Australasia.
Clarke, D. (1996). The case of the mystery bone: A unit of work on measurement for
Grades 5 to 8. Sydney: Mathematical Association of NSW.
Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. Grouws
(Ed.), Handbook of research on mathematics teaching and learning. A project of
the National Council of Teachers of Mathematics (pp. 420-464). New York:
Macmillan.
Clements, M. (1983). The question of how spatial ability is defined, and its relevance to
mathematics education. Zentralblatt fur Didaktik der Mathematik, 1 (1), 8-20.
Clements, M. (1995). The rhetoric/reality gap in school mathematics. Reflections, 20
(1), 29.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 2
Clements, M., & Ellerton, N. (1995). Assessing the effectiveness of pencil-and-paper
tests for school mathematics. In B. Atweh & S. Flavel (Eds.) MERGA18: Galtha
(pp. 184-188). Proceedings of 18th Annual Conference of Mathematics Education
Research Group of Australasia. Darwin: Mathematics Education Research Group of
Australasia.
Close, G. (1982). Children's understanding of angle at the primary/secondary transfer
stage. B.Sc. dissertation Council for National Academic Awards. London:
Department of Mathematical Sciences and Computing, Polytechnique of the South
Bank.
Cox, M. (1977). Teaching perspective ability to five-year-olds. British Journal of
Educational Psychology, 47, 312-321.
Davidson, J. & Sternberg, R. (1985). Competence and performance in intellectual
development. In E. Niemark, R. Delisi & J. Newmans (Eds.) Moderators of
competence (pp. 43-76). Hillsdale, NJ: Erlbaum.
Del Grande, J. (1990). Spatial Sense, Arithmetic Teacher, 27, 14-20.
Del Grande, J. (1992). Geometry and spatial abilities. Paper presented to Subgroup
11.1: Geometry as a part of education in early childhood in Working Group 11: The
role of geometry in general education at the International Congress on
Mathematical Education, ICME 7, Quebec.
Deregowski, J. (1980). Illusions, patterns and pictures: A cross-cultural perspective.
London: Academic Press
Doig, B., Cheeseman, J., & Lindsey, J. (1995). The medium is the message: Measuring
area with different media. In B. Atweh & S. Flavel (Eds.), Galtha (Proceedings of
18th annual conference of Mathematics Education Research Group of Australasia,
pp. 229-234). Darwin: MERGA.
Egan, D. (1979). Testing based on understanding: Implications from studies of spatial
ability. Intelligence, 3, 1-15.
Eliot, J. (1987). Models of psychological space: Psychometric, developmental, and
experimental approaches. New York: Springer-Verlag.
Eliot, J., & McFarlane-Smith, I. (1983). International directory of spatial tests.
Windsor, England: NFER-Nelson.
Finau K., & Stillman, G. (1995). Geometrical skill behind the Tongan tapa designs.
Frostig, M., & Horne, D. (1964). The Frostig program for the development of visual
perception, Chicago: Follett.
Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in
geometry among adolescents. Journal for Research in Mathematics, Monograph 3.
Reston, Va: National Council of Teachers of Mathematics.
Genkins, E. (1975). The concept of bilateral symmetry in young children. In M. F.
Rosskopf (Ed.), Children's mathematical concepts: six Piagetian studies in
mathematics education (pp. 5-43). Columbia: Teachers College Press.
Giganti, & Cittadino (1990). The art of tessellation. Arithmetic Teacher, 37 (7). 6-16.
Harris, P. (1990). Mathematics in a cultural context. Geelong: Deakin University Press.
Hufferd-Ackles, K., Fuson, K., & Sherin, M. (2004). Describing levels and components
of a math-talk learning community. Journal for Research in Mathematics Education,
25(2), 81-116.
Izard, J. (1990). Developing spatial skills with three -dimensional puzzles. Arithmetic
Teacher, 37 (6), 44-51.
Johnson, E., & Meade, A. (1985). The JM Battery of Spatial Tests: Lower Battery.
Johnson, E., & Meade, A. (1987). Developmental patterns of spatial ability: An early
sex difference. Child Development, 58, 725-740.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 3
Kidder, F. (1978). Conservation of length: A function of the mental operation involved.
In R. Lesh (Ed.), Recent research concerning the development of spatial and
geometric concepts (pp. 213-228). Columbus, Ohio: ERIC.
Kosslyn, S. (1983). Ghosts in the mind's machine. New York: W. W. Norton.
Kouba, V., Brown, C., Carpenter, T., Lindquist, M., Silver, E., & Swafford, J.
(1988). Results of the fourth NAEP assessment of mathematics: Measurement,
geometry, data interpretation, attitudes, and other topics. Arithmetic Teacher, 35
(9), 10-16.
Krutetskii, V. (1976). The psychology of mathematical abilities in schoolchildren. In J.
Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and
teaching mathematics. Vol. II: The structure of mathematical abilities (pp. 5-58).
Survey of recent East European mathematical literature. Chicago: University of
Chicago.
Kurina, F. (1992, August). Geometry in the early childhood education. Paper presented
to Subgroup 11.1: Geometry as a part of education in early childhood in Working
Group 11: The role of geometry in general education at the International Congress
on Mathematical Education, ICME 7, Quebec.
Lean, G. (1984, August). The conquest of space: A review of the research literatures
pertaining to the development of spatial abilities underlying an understanding of 3D geometry. Paper presented at the Fifth International Congress on Mathematical
Education, Adelaide.
Lean, G., & Clements M. (1981). Spatial ability, visual imagery, and mathematical
performance. Educational Studies in Mathematics, 12, 267-299.
Liedtke, W. (1995). Developing spatial abilities in the early grades. Teaching Children
Mathematics 2 (1), 12-18.
Linn, M., & Hyde, J. (1989). Gender, mathematics, and science. Educational
Researcher, 18 (8), 17-19, 22-27.
Lohman, D., Pellegrino, J., Alderton, D., & Regian, J. (1987). Dimensions and
components of individual differences in spatial abilities. In S. Irvine & S. Newstead
(Eds.), Intelligence and Cognition (pp. 253-312). Dordrecht: Martinus Nijhoff.
Lovitt, C., & Clarke, D. (1989). Mathematics Teachers and Curriculum Program.
(M.T.C.P.). Professional Development Package 1 and 2. Canberra: Curriculum
Development Centre.
Lowrie, T. (1992, November). Developing talented children's mathematical ability
through visual and spatial learning tasks. Paper presented at the Annual
Conference, Australian Association for Research in Education, Deakin University,
Geelong.
Lowrie, T. (1998). There’s more than meets the eye: The relationships between the user,
the teacher and the technology. In C. Kanes, M. Goos, & E. Warren, Teaching
mathematics in new times, (Proceedings of MERGA21, pp. 319-326). Gold Coast,
QLD: Mathematics Education Research Group of Australasia.
Macmillan, A. (1998). Investigating the mathematical thinking of young children. In A.
McIntosh, & N. Ellerton (Eds.) Research in mathematics education. A
contemporary perspective (pp. 108-133). Perth: Edith Cowan University.
Mansfield, H., & Happs, J. (1992).Estimation and mental-imagery models in geometry.
Mansfield, H., & Scott, J. (1990). Young children solving spatial problems. In G.
Booker, P. Cobb, & T. de Mendicuti (Eds.), Proceedings of the 14th PME
conference (Vol. II, pp. 275-282). Mexico: International Group for the Psychology
of Mathematics Education.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 4
McPhail, D. (1998). Teaching area in years 1 and 2 classrooms. In C. Kanes, M. Goos,
& E. Warren, Teaching mathematics in new times, (Proceedings of MERGA21, pp.
726). Gold Coast, QLD: Mathematics Education Research Group of Australasia.
Mitchelmore, M. (1983). Geometry and spatial learning: Some lessons from a Jamaican
experience. For the Learning of Mathematics, 3 (3), 27.
Mitchelmore, M. (1992). Children's concepts of perpendiculars. In W. Geeslin & K.
Graham (Eds.), Proceedings of 16th Annual Conference of International Group for
the Psychology of Mathematics Education (Vol. 2, pp. 120-127). Durham, NH:
Organising committee for PME16.
Mitchelmore, M. (1992a). What's the right angle? Classroom, 12 (6), 14-16.
Mitchelmore, M. (1992b). Why children do not draw parallels. In B. Southwell, B.
Perry, K. Owens (Eds.), Space - the first and final frontier (pp. 390-397).
Proceedings of 15th Annual Conference of Mathematics Education Research Group
of Australasia. Sydney: Mathematics Education Research Group of Australasia.
Mitchelmore, M. (1993). Abstracting the angle concept. In B. Atweh, C. Kanes, M.
Carss, & G. Booker (Eds.), Contexts of mathematics education (pp. 401-406).
Proceedings of 16th Annual Conference of Mathematics Education Research Group
of Australasia. Brisbane: Mathematics Education Research Group of Australasia.
Mitchelmore, M., & White, P. (1998). Development of angle concepts: A framework for
research. Mathematics Education Research Journal 10 (3), 4-27.
Moses, B. (1990). Developing spatial thinking in the middle grades: Designing a space
station. Arithmetic Teacher, 37 (6), 59-63.
Moyer, (1978). Structure of Euclidean transformations and the spontaneously developed
cognitive structures of young children. Journal for Research in Mathematics
Education 9, 83-92.
Nelson, G., & Leutzinger, L. (1987). Let’s do it: Let’s take a geometry walk. Geometry
for Grades K-6: Readings from the Arithmetic Teacher (pp. 146-148).. Reston, Va:
NCTM.
Nitabach & Lehrer, R. (1996). Developing spatial sense through area measurement.
Teaching Children Mathematics, 2 (8), 473-476.
NSW Department of Education and Training (2003). Quality teaching in NSW public
schools:
A
classroom
practice
guide.
Sydney:
NSW
DET.
http://www.curriculumsupport.nsw.edu.au
Outhred, L. (1987). Left angle or right angel: children's misconceptions of angle.
Research in Mathematics Education in Australia, 14, 41-47.
Outhred, L. (1993). The development in young children of concepts of rectangular area
measurement. Unpublished PhD thesis, Macquarie University.
Outhred. L. (1997). Classroom views of length, area and volume. In B. Doig & J.
Lokan, Learning from children (pp. 103-122). Melbourne: ACER Press.
Outhred, L., & Mitchelmore, M. (1992). Representation of area: A pictorial perspective.
In W. Geeslin & K. Graham (Eds.), Proceedings of 16th annual conference of the
International Group for the Psychology of Mathematics Education (Vol. 2, pp.
194201). Durham, NH: Program Committee.
Owens, K. (1992). Spatial mathematics: A group test for primary school students. In M.
Stephens & J. Izard (Eds.) Reshaping assessment practices: Assessment in the
mathematical sciences under challenge, (pp. 333-354) Melbourne: Australian
Council for Educational Research.
Owens, K. (1993). Spatial thinking employed by primary school students engaged in
mathematical problem solving. Unpublished PhD thesis, Deakin University.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 5
Owens, K. (1994). Concrete materials: Why they do or don't work. In D. Rasmussen &
K. Beesey (Eds.) Mathematics Without limits, (pp. 342-347). Melbourne: The
Mathematical Association of Victoria.
Owens, K. (1996). Recent research and a critique of theories of early geometry learning:
The case of the angle concept. Nordisk Matematikk Didaktikk-Nordic Studies in
Mathematics Education 4 (2/3), 85-106.
Owens, K. (1997). Classroom views of space. In B. Doig & J. Lokan, Learning from
children (pp. 125-148). Melbourne: ACER Press.
Owens, K., & Clements, M. A. (1998). Representations used in spatial problem solving
in the classroom, Journal of Mathematical Behavior 17 (2), 197-218.
Owens, K., Mitchelmore, M., Outhred, L., & Pegg, J. (1996). Space, geometry,
measurement, and visualisation. In B. Atweh, K. Owens, & P. Sullivan (Eds.),
Research in mathematics education in Australasia 1992-1995, (pp. 311-343).
Sydney: Mathematics Education Research Group of Australasia.
Owens, K., & Outhred, L. (1998). Covering shapes with tiles: Primary students’
visualisation and drawing. Mathematics Education Research Journal 10(3), 28-41.
Perham, F. (1978). An investigation into the effect of instruction on the acquisition of
transformation geometry concepts in first grade children and subsequent transfer to
general spatial ability. In R. Lesh (Ed.), Recent research concerning the
development
of
spatial
and
geometric
concepts
(pp.
229-242).
Columbus, Ohio: ERIC.
Perry, B., & Conroy, J. (1996). Early childhood and primary mathematics – A
participative text for teachers. Sydney: Harcourt Brace.
Peters, S. (1992). Spatial ability: An investigation into the spatial ability and play
preferences of four year old children. In B. Bell, A. Begg, F. Biddulph, M. Carr, J.
McChesney, & J. Young-Loveridge (Eds.), SAMEpapers 1992 (pp. 117-129).
Auckland: Longman Paul.
Piaget, J., & Inhelder, B. (1956). The child's conception of space. London: Routledge &
Kegan Paul.
Piaget, J., & Inhelder, B. (1971). Mental imagery in the child: A study of the
development of imaginal representation. London: Routledge & Kegan Paul.
Piaget, J., Inhelder, B. & Szeminska, A. (1960). The child's conception of geometry.
New York: Basic Books.
Poltrock, S., & Agnoli, F. (1986). Are spatial visualization ability and visual imagery
ability equivalent? In R.J. Sternberg (Ed.), Advances in the psychology of human
intelligence, (Vol. 3 pp. 255-296). Hillsdale, NJ.: Lawrence Erlbaum Associates.
Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of
Mathematics, 6 (3), 42-46.
Researching numeracy project team (2004). Researching numeracy teaching approaches
in primary schools. Australian Primary Mathematics Classroom, 9 (4), 27-29.
Rogers, A. (1999). Children and block play. Mathematical learning in early childhood.
In K. Baldwin & J. Roberts (Eds.) Mathematics: The next millennium.(Proceedings
of the 17th biennial conference of Australian Association of Mathematics Teachers,
pp. 162-185). Adelaide: AAMT.
Rosser, R., Lane, S., & Mazzeo, J. (1988). Order of acquisition of related geometric
competencies in young children. Child Study Journal, 18 (2), 75-89.
Rowe, M. (1982). Teaching in spatial skills requiring two- and three-dimensional
thinking and different levels of internalization and the retention and transfer of
these skills. Unpublished doctoral thesis, Monash University, Melbourne.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 6
Sanok, G. (1987). Living in a world of transformations. Geometry for Grades K-6:
Readings from the Arithmetic Teacher (pp. 50-54). Reston, Va: NCTM.
Saunderson, A. (1973). The effect of a special training programme on spatial ability test
performance. New Guinea Psychologists, 5, 15-23.
Schultz, K. (1978). Variables influencing the difficulty of rigid transformations during
the transition between the concrete and formal operational stages of cognitive
development. In R. Lesh (Ed.), Recent research concerning the development of
spatial and geometric concepts (pp.195-212). Columbus, Ohio: ERIC.
Sedgewick (1988). Learning through drawing, Local buildings, Art and Craft, June, pp.
22-23, 18-19.
Shepard, R., & Metzler, J. (1971). Mental rotation of three dimensional objects.
Science, 171, 701-703.
Tartre, L. (1990a). Spatial skills, gender, and mathematics. In E. Fennema & G. Leder
(Eds.), Mathematics and gender. New York: Teachers College Press.
Thomas, D. (1978). Students' understanding of selected transformation geometry
concepts. In R. Lesh (Ed.), Recent research concerning the development of spatial
and geometric concepts (pp. 177-174). Columbus, Ohio: ERIC.
Thorpe, T. (1995). How young children learn spatial concepts. In B. Atweh & S. Flavel
(Eds.), Galtha (Proceedings of 18th Conference of Mathematics Education
Research Group of Australasia, pp.517-523). Darwin: MERGA.
Toh Seong Chong (1993). Use of microcomputer simulations to overcome student
misconceptions about displacement of liquids. Proceedings of the Annual
Conference of the Australian Association for Research in Education [On-line].
Available: www.swin.edu.au/AARE/conf93.html File: TOHS93.222
van Hiele, P. (1986). Structure and insight: A theory of mathematics education. New
York: Academic Press.
Vurpillot, E. (1976). The visual world of the child. New York: International Universities
Press.
Wheatley, G., & Cobb, P. (1990). Analysis of young children's spatial constructions. In
L. P. Steffe & T. Wood (Eds.), Transforming children's mathematics education (pp.
161-173). Hillsdale, NJ: Lawrence Erlbaum Associates.
Whitton, D. (1998). Investigating patterns with patchwork. PAMphlet, 39.
Willis, S. (2005). Oversights and insights: Mathematics teaching and learning. In M.
Coupland, J. Anderson, T. Spencer, Making Mathematics Vital, Proceedings of 20th
Bienniel Conference of the Australian Association of Mathematics Education (pp.
32-42). Adelaide: AAMT..
Wilson, P. (1986). Feature frequency and use of negative instances in a geometry task.
Journal for Research in Mathematics Education, 17, 130-139.
Wilson, P. (1992). A dynamic way to teach angle and angle measure. Arithmetic
Teacher, 39 (5), 6-13.
Wood, T. (1999). Creating a context for argument in mathematics class. Journal for
Research in Mathematics Education, 30(2), 171-191.
Wood, T. (2003). Complexity in teaching and children’s mathematical thinking. In N.
Pateman, B. J. Doherty, & J. Zilliox (Eds.) Proc. 27th Conf. of the Int. Group for the
Psychology in Mathematics Education (Vol. 4, pp. 435-442). Hawaii: PME.
Yackel, E., & Wheatley, G. (1990). Promoting visual imagery in young pupils.
Arithmetic Teacher, 37 (6), 52-58.
Yelland, N. & Masters, J. (1997). Learning mathematics with technology. Young
children’s understanding of paths and measurement. Mathematics Education
Research Journal, 9(1), 83-99.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens
References
page 7
Zevenbergen, R. (1992). The construction of spatial meaning and social disadvantage.
In B. Southwell, B. Perry, & K. Owens (Eds.) Space - The first and final frontier
(Conference Proceedings of Mathematics Education Research Group of
Australasia, pp. 599-608). Sydney: MERGA.
Creating Space: Professional Knowledge and Spatial Activities for Teaching Mathematics
Kay Owens