Follow Reference
Battista
M. T.
(2007). The development of geometric and spatial thinking. In LesterF. K. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 843–908). Charlotte, NC: Information Age Publishing Inc.
Follow Reference
Beck
S. A.
Huse
V. E.
(2007). A virtual spin on the teaching of probability.Teaching Children Mathematics, 13(9), 482–486.
Follow Reference
Bodemer
D.
Ploetzner
R.
Feuerlein
I.
Spada
H.
(2004). The active integration of information during learning with dynamic and interactive visualizations.Learning and Instruction, 14, 325–341. 10.1016/j.learninstruc.2004.06.006
Follow Reference
Bolyard, J. J. (2006). A comparison of the impact of two virtual manipulatives on student achievement and conceptual understanding of integer addition and subtraction. (Doctoral dissertation). Available ProQuest Dissertations and Theses database. (UMI No. 3194534)
Follow Reference
Boote, D. N., & Beile, P. (2005). Scholars before researchers: On the centrality of the dissertation literature review in research preparation. Educational Researcher, 34 (6), 3-15.
Follow Reference
Botzer
G.
Yerushalmy
M.
(2008). Embodied semiotic activities and their role in the construction of mathematical meaning of motion graphs.International Journal of Computers for Mathematical Learning, 13(2), 111–134. 10.1007/s10758-008-9133-7
Follow Reference
Bouck
E. C.
Flanagan
S. M.
(2010). Virtual manipulatives: What they are and how teachers can use them.Intervention in School and Clinic, 45(3), 186–191. 10.1177/1053451209349530
Follow Reference
Cavanaugh
C.
Billan
K. J.
Bosnick
J.
(2008). Effectiveness of interactive online algebra learning tools.Journal of Educational Computing Research, 38(1), 67–95. 10.2190/EC.38.1.d
Follow Reference
Clark
R.
Nguyen
F.
Sweller
J.
(2006). Efficiency in learning: Evidence-based guidelines to manage cognitive load. San Francisco, CA: Pfeiffer. 10.1002/pfi.4930450920
Follow Reference
Confrey
J.
Smith
E.
(1994). Exponential functions, rates of change, and the multiplicative unit.Educational Studies in Mathematics, 26, 135–168. 10.1007/BF01273661
Follow Reference
Dienes
Z. P.
(1973). Mathematics through the senses, games, dance and art. Windsor, UK: The National Foundation for Educational Research.
Follow Reference
Drickey, N. A. (2000). A comparison of virtual and physical manipulatives in teaching visualization and spatial reasoning to middle school mathematics students (Doctoral dissertation). Available ProQuest Dissertations and Theses database. (UMI No. 3004011)
Follow Reference
Durmus, S., & Karakirik, E. (2006). Virtual manipulatives in mathematics education: A theoretical framework. Turkish Online Journal of Educational Technology, 5 (1).
Follow Reference
Evans
M. A.
Wilkins
J. L. M.
(2011). Social interactions and instructional artifacts: Emergent socio-technical affordances and constraints for children’s geometric thinking.Journal of Educational Computing Research, 44(2), 141–171. 10.2190/EC.44.2.b
Follow Reference
Gall
M. D.
Gall
J. P.
Borg
W. R.
(2003). Educational research: An introduction (7th ed.). Boston, MA: Pearson.
Follow Reference
Gelman
S. A.
(2004). Psychological essentialism in children.Trends in Cognitive Sciences, 8(9), 404–409. 10.1016/j.tics.2004.07.00115350241
Follow Reference
Goldin
G. A.
(2003). Representation in school mathematics: A unifying research perspective. In KilpatrickJ.MartinW. G.SchifterD. (Eds.), A research companion to principles and standards for school mathematics (pp. 275–285). Reston, Virginia: NCTM.
Follow Reference
Haistings, J. L. (2009). Using virtual manipulatives with and without symbolic representation to teach first grade multi-digit addition (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses database. (UMI No. 3366234)
Follow Reference
Hativa
N.
Cohen
D.
(1995). Self-learning of negative number concepts by lower division elementary students through solving computer-provided numerical problems.Educational Studies in Mathematics, 2(4), 401–431. 10.1007/BF01274081
Follow Reference
Hsiao, P. (2001). The effects of using computer manipulatives in teaching probability concepts to elementary school students (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses database. (UMI No. 3014774)
Follow Reference
Izydorczak, A. E. (2003). A study of virtual manipulatives for elementary mathematics (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses database. (UMI No. 3076492)
Follow Reference
Kaput
J. J.
(1986). Information technology and mathematics: Opening new representational windows.The Journal of Mathematical Behavior, 5(2), 187–207.
Follow Reference
Kaput
J. J.
Roschelle
J.
(1998). The mathematics of change and variation from a millennial prespective: New content, new context. In HoylesC.MorganC.WoodhouseG. (Eds.), Rethinking the mathematics curriculum (pp. 155–170). London: Springer Verlag.
Follow Reference
Kim, S.-Y. (1993). The relative effectiveness of hands-on and computer-simulated manipulatives in teaching seriation, classification, geometric, and arithmetic concepts to kindergarten children (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses database. (UMI No. 9402024)
Follow Reference
Lakoff
G.
Nunez
R. E.
(2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
Follow Reference
Lane, C. (2010). Case study: The effectiveness of virtual manipulatives in the teaching of primary mathematics (Master’s thesis, University of Limerick, Limerick, Ireland) Retrieved from http://hdl.handle.net/10344/450 Follow Reference
Lesh
R.
Cramer
K.
Doerr
H.
Post
T.
Zawojewski
J.
(2003). Using a translation model for curriculum development and classroom instruction. In LeshR.DoerrH. (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates.
Follow Reference
Lesh
R.
Zawojewski
J.
(2007). Problem solving and modeling. In LesterF. K. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 763–804). Charlotte, NC: Information Age Publishing Inc.
Follow Reference
Lin
C.
Shao
Y.
Wong
L.
Li
Y.
Niramitranon
J.
(2011). The impact of using synchronous collaborative virtual tangrams in children’s geometric.The Turkish Online Journal of Educational Technology, 10(2), 250–258.
Follow Reference
Manches
A.
O'Malley
C.
Benford
S.
(2010). The role of physical representations in solving number problems: A comparison of young children's use of physical and virtual materials.Computers & Education, 54, 622–640. 10.1016/j.compedu.2009.09.023
Follow Reference
Marrades
R.
Gutierrez
A.
(2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment.Educational Studies in Mathematics, 44(1/2), 87–125. 10.1023/A:1012785106627
Follow Reference
Martin
T.
Schwartz
D. L.
(2005). Physically distributed learning: Restructuring and reinterpreting physical environments in the development of fraction concepts.Cognitive Science, 29, 587–625. 10.1207/s15516709cog0000_1521702786
Follow Reference
Miles
M. B.
Huberman
A. M.
(1994). Qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage Publications.
Follow Reference
Moyer
P. S.
Bolyard
J. J.
Spikell
M. A.
(2002). What are virtual manipulatives?Teaching Children Mathematics, 8(6), 372–377.
Follow Reference
Moyer
P. S.
Niezgoda
D.
Stanley
J.
(2005). Young children’s use of virtual manipulatives and other forms of mathematical representations. In MasalskiW. J.ElliottP. C. (Eds.), Technology-supported mathematics learning environments: Sixty-seventh yearbook (pp. 17–34). Reston, VA: NCTM.
Follow Reference
Moyer
P. S.
Salkind
G.
Bolyard
J. J.
(2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity.Contemporary Issues in Technology & Teacher Education, 8(3), 202–218.
Follow Reference
Moyer-Packenham
P. S.
(2010). Teaching mathematics with virtual manipulatives. Rowley, MA: Didax.
Follow Reference
Moyer-Packenham
P. S.
Suh
J. M.
(2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups.Journal of Computers in Mathematics and Science Teaching, 112(3), 133–146.
Follow Reference
National Council of Teachers of Mathematics
. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Follow Reference
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel . Retrieved on March 1, 2012, from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf Follow Reference
Noss
R.
Hoyles
C.
(1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht, Germany: Kluwer. 10.1007/978-94-009-1696-8
Follow Reference
Reimer
K.
Moyer
P. S.
(2005). Third graders learn about fractions using virtual manipulatives: A classroom study.Journal of Computers in Mathematics and Science Teaching, 24(1), 5–25.
Follow Reference
Sarama
J.
Clements
D. H.
(2009). Concrete computer manipulatives in mathematics education.Child Development Perspectives, 3(3), 145–150. 10.1111/j.1750-8606.2009.00095.x
Follow Reference
Schoenfeld
A. H.
(1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance.Cognitive Science, 7, 329–363. 10.1207/s15516709cog0704_3
Follow Reference
Shaffer
D. W.
Kaput
J. J.
(1998). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education.Educational Studies in Mathematics, 37(2), 97–119. 10.1023/A:1003590914788
Follow Reference
Suh
J. M.
Moyer
P. S.
(2007). Developing students’ representational fluency using virtual and physical algebra balances.Journal of Computers in Mathematics and Science Teaching, 26(2), 155–173.
Follow Reference
Suh
J. M.
Moyer
P. S.
Heo
H.-J.
(2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials.The Journal of Interactive Online Learning, 3(4), 1–22.
Follow Reference
Terry, M. K. (1995). An investigation of differences in cognition when utilizing math manipulatives and math manipulative software . (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 9536433)
Follow Reference
Thompson
P. W.
(1985). A Piagetian approach to transformation geometry via microworlds.Mathematics Teacher, 78, 465–471.
Follow Reference
Trespalacios
J.
(2010). The effects of two generative activities on learner comprehension of part-whole meaning of rational numbers using virtual manipulatives.Journal of Computers in Mathematics and Science Teaching, 29(3), 327–346.
Follow Reference
Urdan
T. C.
(2010). Statistics in plain English (3rd ed.). New York, NY: Routledge.
Follow Reference
Wiley
D. A.
(2000). Connecting learning objects to instructional design theory: A definition, a metaphor, and a taxonomy. The Edumetrics Institute.
Follow Reference
Yerushalmy
M.
(1991). Student perceptions of aspects of algebraic function using multiple representation software.Journal of Computer Assisted Learning, 7, 42–57. 10.1111/j.1365-2729.1991.tb00223.x
Follow Reference
Yuan
Y.
Lee
C. Y.
Wang
C. H.
(2010). A comparison study of polyominoes explorations in a physical and virtual manipulative environment.Journal of Computer Assisted Learning, 26(4), 3007–3016. 10.1111/j.1365-2729.2010.00352.x
Follow Reference
Zbiek
R. M.
Heid
M. K.
Blume
G. W.
Dick
T. P.
(2007). Research on technology in mathematics education: The perspective of constructs. In LesterF. K. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 1169–1207). Charlotte, NC: Information Age Publishing Inc.