Cross-Reality Mathematics:Becoming Aware

of theVisual Instinct

The Physical Educational EnvironmentCentimeter 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.

The Virtual Educational Environment

Itonlytakes1.org interacts with Discover 0 through 4 to facilitate subQuan learning.

Discover 0

Discover 1

Discover 2

Discover 3

Discover 4

The Immersive Educational Environment

Second Life allows us toprototype, collaborate, and implement

lessons.

The ResearchNine children,

between the ages of three and five, spent 45 minutes learning how to subQuan.

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.

The Initial QuizPhysical Virtual Immersive

The Environments

Physical

Virtual

Immersive

The Post-Survey

Each child was asked which environment was their favorite.

The Follow-up Quiz

2-weeks later

Physical

Virtual

Immersive

The ResultsAccuracy of subQuans in the initial assessment.

Accuracy of subQuans in the final assessment.

SubQuan Capability by Age

Ease of Environments

As noted by researcher per:1. Time delay in

completion2. Facial consternation3. Timidity of response

Fun of Environments

As noted by researcher per:1. Cognitive engagement2. Desire to continue toward

completion3. Enthusiasm

Survey Results

Responses when askedwhich environment was their favorite.

The ModificationsDid 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.

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.

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.

Counting vs. Subitizingin

subQuan

How much does counting enhance or detract from our natural ability to subitize and what ramification does this have on subQuanning?

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.

Up next:

1. 5th/6th grade research

2. High school online math research

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-Realiz

ations/149516305074487