1. Cross-Reality Mathematics: Becoming Aware of the Visual Instinct

2. The Physical Educational Environment Centimeter cubes and Base Number Sheets (BNS) comprise the physical manipulatives. Students can build numbers to visually see quantities. Numbers must remain small due to time, matter, and space.

3. The Virtual Educational Environment Itonlytakes1.org interacts with Discover 0 through 4 to facilitate subQuan learning. Discover 0Discover 1Discover 2 Discover 3Discover 4

4. The Immersive Educational Environment Second Life allows us to prototype, collaborate, and implement lessons.

5. The Research Nine children, between the ages of three and five, spent 45 minutes learning how to subQuan.

6. The Set-up P = Physical V = Virtual I = Immersive G1A for the first child in Group 1 at 5 years and 3 months old, etc.

7. The Initial Quiz PhysicalVirtualImmersive

8. The Environments Physical Virtual Immersive

9. The Post-Survey Each child was asked which environment was their favorite.

10. The Follow-up Quiz 2-weeks later Physical Virtual Immersive

11. The Results Accuracy of subQuans in the initial assessment. Accuracy of subQuans in the final assessment.

12. SubQuan Capability by Age

13. Ease of Environments As noted by researcher per: 1.Time delay in completion 2.Facial consternation 3.Timidity of response

14. Fun of Environments As noted by researcher per: 1.Cognitive engagement 2.Desire to continue toward completion 3.Enthusiasm

15. Survey Results Responses when asked which environment was their favorite.

16. The Modifications Did change: Grouping children in pairs. Re-evaluating subQuan capability after two-weeks. Would like to have changed: Use of consistent vocabulary (small, medium, large). More examples in the physical environment. Participant background data. Better camera angles. Memory enhancers.

17. Differentiation Between Media Inconclusive: one child from each group noticeably grasped subQuanning. Most fluidity was found in Group 5: P-I-V. Physical environment found to be most difficult. Immersive environment found to be the most interesting. Virtual environment found to be the easiest.

18. Implications for Future Research How would the ability to subitize affect the ability to subQuan? (memory) Using colors to denote positive and negative, a ‘combining’ study at this age level would be fascinating. Using subQuan as a tool for discovery of students with dyscalculia would allow for early intervention. Longer duration of learning sessions with subQuan need to be investigated.

19. Counting vs. Subitizing in subQuan How much does counting enhance or detract from our natural ability to subitize and what ramification does this have on subQuanning?

20. Conclusion SubQuan has been successfully demonstrated to bypass the normal process of learning large numbers: i.e. first teaching counting to twenty, then to a hundred, followed by teaching place values. All realities are important for the absorption and connection of this new foundation in mathematics to the individual learner. This research could lead to a paradigm shift in math education.

21. Up next: 1.5 th /6 th grade research 2.High school online math research

22. Contacts utefrenburg@gmail.com coopermacbeth@gmail.com alexsiskamala@gmail.com http://dreamrealizations.org http://itonlytakes1.org http://twitter.com/iot1 http://www.facebook.com/pages/Dream- Realizations/149516305074487http://www.facebook.com/pages/Dream- Realizations/149516305074487