Mordys Links

From MathWiki

Table of contents

Exploring Spatial Reasoning, Technology, and Teacher Education

Teacher Education Resources

Liping Ma's Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China & the United States - including reference information & links

Son, Ji-Won (2006). “Investigating preservice teachers’ understanding and strategies on a student’s errors of reflective symmetry.” - An interesting and relevant study from last year's PME.

Spatial Abilities & Technology Resources

Wang, H., Chun-Yen, C., & Tsai-Yen, L. (2007). "The comparative efficacy of 2D- versus 3D-based media design for influencing spatial visualization skills" - Wang et al. (2007) compare the usefulness of 2D and 3D computer media in training spatial visualization abilities.

Olkun, S. (2003). "Comparing Computer versus Concrete Manipulatives in Learning 2D Geometry" - This study explores the usefulness of computer or concrete manipulatives to help improve elementary students' spatial ability.

Keehner, M., & Khooshabeh, P. (2005). "Computerized representations of 3D structure: How spatial comprehension and patterns of interactivity differ among learners" - In this more detailed follow-up to Keehner et al. (2004), Keehner & Khooshabeh continue to investigate the use of 3D visualization software, with special attention once again given to software interactivity and prior spatial abilities.

Keehner M, Montello D.R., Hegarty M. & Cohen C. (2004). "Effects of interactivity and spatial ability on the comprehension of spatial relations in a 3D computer visualization" - Keehner et al. explore the effect of one's spatial ability and the interactivity of 3D software on the 'comprehension' of undergraduate students completing a visualization task.

Durmus, S., & Karakirik, E. (2006). “Virtual Manipulatives in Mathematics Education: A Theoretical Framework” - Durmus & Karakirik outline some related theoretical elements when considering the role of virtual manipulatives in mathematics education.

Gutiérrez, A. (1996). “Visualization in 3-dimensional geometry: In search of a framework” - In this relatively dated work, Gutiérrez provides a framework for visualization based on the literature available at the time, and explores the use of technology in helping to develop spatial skills in students. In addition to a definition of visualization and its characterizing elements, there is an implicit discussion for the nature of the use of virtual and physical manipulatives.

Effectiveness of Reading and Mathematics Software Products: Findings from the First Student Cohort ( This is a summary of research driven by the U.S. Department of Education as a Report to Congress, on the effects of using technology for reading and math at the K to 8 level. There are some interesting points made here, for example (pg. xviii-xix)

  • "Nearly All Teachers Received Training and Believed the Training Prepared Them to Use the Products." Teachers were trained, and felt confident in their ability to use the software in their teaching. But once the teachers attempted to actually implement the software into their teaching, teacher confidence dropped from 94% during teacher training to 57% during first classroom use of the software (p.52).
  • "When Products Were Being Used, Students Were More Likely to Engage in Individual Practice and Teachers Were More Likely to Facilitate Student Learning Rather Than Lecture." This would seem to make sense. Interestingly, however, the overall finding of the study (including the use of Grade 6 math software) was that the use of software did not have any significant effect on student performance and ability.

If you choose to scan the report, consider the scope of the software used. The Grade 6 software packages (Larson Pre-Algebra, Achieve Now, and iLearn Math) do include a treatment of "plane and coordinate geometry" but the report does not go into many details. Is anyone in the group familiar with these software packages? [I have just realized that this is the same study for which Tanya reviewed an EdWeek article]. For Tanya's comments and a link to the EdWeek article, please see "Federal Study Finds No Edge for Students Using Technology-Based Reading and Math Products" - By Andrew Trotter.

General Resources

The Landscape of Learning and Learning Trajectories (Fosnot & Dolk, 2002) - Summary & Reference Information

Recommended Professional Reading For Early Numeracy/Mathematics (, compiled by the Ontario Mathematics Coordinators Association (OMCA). While many of these references have to do with numeracy specifically, some of the references are useful as insights into the development of mathematical thinking in students.

-- Farhad Mordy Sabeti