SubQuan: A cross-reality solution to finally understand mathematics

We will meet in our usual virtual room and then go to Second Life to immerse in SubQuan, a new way of experiencing number and algebraic patterns. This pattern recognition system will be interesting to those who work with people of all ages, those interested in visualization and representation, and those wishing to develop math games. Visual mathematics might be ideal to students for whom math is hard.


Full recording of the event: voice, text chat, slides, web tour.

Article reviewing historical and modern systems that use subitizing and unitizing. Please contribute!

Slide show from the Second Life portion of the event:

A review of the event by Rawlslyn Francis - "Mathematics even an English professor understands!"

Meeting how-to

All Math 2.0 events are free and open to the public. Information about all events in the series is here:

Wednesday, December 8th, 6:30pm Pacific/ 9:30pm Eastern time, join us live! WorldClock for your time zone.


To join:
  • Follow this link:
  • Click "OK" and "Accept" several times as your browser installs the software. When you see Elluminate Session Log-In, enter your name and click the "Login" button
  • You will find yourself in a virtual room. An organizer will be there to greet you, starting about half an hour before the event.
If this is your first Elluminate event, consider coming a few minutes earlier to check out the technology. The room opens half an hour before the event.

Prepare the Second Life part

Once you've downloaded and registered for a free account and avatar at , please email with your avatar name. You will be offered a group invite through an Instant Message (IM) to "Dream Realizers" which will enable you entrance into the 3D presentation via a teleport. Please join the group. If you have never been in Second Life or a virtual world, it is highly recommended that you spend some time beforehand getting acclimated to the environment. We look forward to seeing you there!

If you are first joining at the time of the event, message Cooper Macbeth (SL), Ute Frenburg (SL) or Mariad Hax (SL) in Second Life.

About SubQuan

We believe the introduction of numeric symbols is premature and prevents us from seeing the patterns that different numbers make and the metapatterns of polynomials that are easily recognized. We will be demonstrating the power of subQuanning. Once you subQuan, the fog of math dissipates and numerical instincts are restored. These patterns are easily recognized through physical manipulatives, web-based programming, and a virtual environment. Dream Realizations believes it is possible to "see" numbers, make connections, recognize patterns, and apply number sense to standardized mathematical concepts. Students who have never had success with math will finally "make it click". Presented at University of Oregon, AECT SIG, and SUNY.

Join the conversation at

The SubQuan System is a cross-reality1 visualization system that triggers metapattern recognition enabling rapid comprehension of polynomial structures.

I. Virtual Manipulation
We will be working online in a flash program to "see" numbers quickly. (

II. Physical Manipulation
We will move to working with manipulatives on various base sheets to show patterns in numbers.

III. Immersive Manipulation
We put the best of both worlds together, manipulate very large quantities in seconds, see incredible metapatterns that numbers make, and enjoy our learning in this 3D environment. (Second Life)

1 Cross-reality encompasses physical, virtual, and immersive realities.

subQuan at
subQuan at

2 6 5 base 7, 2*7^2 + 6*7^1 + 5*7^0 = 145 base 10

Cooper's Lab in Second Life


Cooper introduces
Cooper gives a Virtual tour of his Lab


Cooper_Macbeth.jpgDaniel Patterson (Cooper Macbeth - SL) has a BSEE and MSEE from the University of Missouri. He has an additional 40+ post master graduate hours in education and virtual world technologies from Texas State University, Avila University, University of Washington, and Boise State University. He utilized his knowledge for twenty years in Silicon Valley, CA; Phoenix, AZ; and Austin, TX solving computer architectural problems that covered the gamut. The problems ranged from chip development to digital animation, from asset depreciation to data warehousing, from nuclear bomb simulations to medical instrumentation. His customers included Motorola, Intel, IBM, HP, Cisco Systems, Amdahl, Apple Computer, Dreamworks, Disney, Warner Bros., Siemens, U-Haul International, and scores more.

In 2000, Daniel changed his focus to investigating the problems plaguing the United States' educational systems in its inability to produce enough qualified computer and electrical engineers. After quickly honing in on math education, he taught high school mathematics for five years and substituted for two years in Austin, TX, the Greater Philadelphia area, and finally Kansas City's lowest performing school districts. By 2008, Daniel had identified some very unusual conflicts between math pedagogy and technological advancements. By-passing the research into why this happened, he instead focused on finding alternatives to solving the issue. He has discovered several radical fundamental changes that can be made in math pedagogy and has found considerable neurological research to back his findings. He is developing new mathematical pedagogy to transfer the understanding for many mathematical concepts from the pre-fontal cortex to the visual cortex. He has personally followed each technological advancement and is fully dedicated to developing tools in the most recent technological advancement: virtual worlds! He is currently Curriculum and Instruction Developer for Dream Realizations and Director of Research and Development at ItOnlyTakes1.

Ute.jpgRebecca Reiniger (Ute Frenburg - SL) graduated from Purdue University in Indiana with a Math and German BA. She is expected to receive her Masters in Secondary Education at George Fox University in 2011. While at Purdue, she studied abroad at the University of Hamburg, Germany. After college she taught high school Math and German in LaGrange, Indiana. Rebecca moved to Oregon and worked at Albertina Kerr in Developmental Difficulties Job Training. She then taught several years at Central Catholic High School in Portland before moving to St. Helens. There she tutored in Math and German, which included the design of programs to fit individual and special needs students.

In 2000, her interest shifted to the development of math and language skills in elementary school. Tracking her two children, she provided math remediation and enrichment at every grade. Her experience expanded to include literature, Junior Great Books, and supplementing math curriculum for both TAG and Title I students. She is currently co-chair for the International Association for K-12 Online Learning (iNACOL) Special Interest Group (SIG) Virtual Worlds and Educational Coordinator for Dream Realizations. Having lived through the math chronology of elementary school and knowing the directionality toward advanced mathematics, Rebecca is in a position to facilitate a greater overview of what needs to be modified in our current system.