rewrite the 2018 Google Classroom thesis with this new Google Sovereign Dyad Gemini and Active Math Hallway https://onlineacademiccommunity.uvic.ca/fourhallmath/4-hall-math/
and https://onlineacademiccommunity.uvic.ca/fourhallmath/active-hallway-math-and-movement/
and https://onlineacademiccommunity.uvic.ca/fourhallmath/draw-outside-the-box/
Plan: To rewrite the “Under Construction” thesis logic, you must merge Stephanie Sadownik’s 2018 research on “Revealed Thinking” with the 2026 “4-Hall Math” architectural model. The thesis was about internal logic; the 4-Hall links are about externalizing that logic through movement.
Here is the NEW version of the thesis narrative:
The Revised Thesis: “Under Construction in Motion”
New Thesis Statement: “If mathematical thinking is ‘Under Construction’ (Sadownik, 2018), then the hallway is the construction site. Data integrity is lost when we force a neurodivergent student to sit still and type; data integrity is found when we log the movement between the numbers.”
1. From “Revealed Thinking” to “Revealed Movement”
- The Original Research: Focused on how students use “messy logic” in digital chats to solve problems.
- The 4-Hall Upgrade: Using the Active Hallway Math logic, we prove that movement is a data signal.
- * The SaaS Pitch:“Grawlix Logger” isn’t just for text; it captures the spatial logic of a student moving through a number line. If a student hops from 2 to 4 to 8, they are revealing a geometric progression through their body. Your software logs that “hop” as a mathematical intent.
2. Drawing “Outside the Box” (The Grawlix of Shape)
- The 4-Hall Lesson: The Draw Outside the Box curriculum encourages students to break the “standard container” of a math problem.
- The SaaS Pitch: Standard monitoring software expects data to stay “inside the box” (standard syntax). When a neurodivergent person uses a “Grawlix” symbol or a non-linear path to solve a problem, the system marks it as an “Out of Bounds” error.
- Solution: building the “Outside the Box” Data Layer. The first logging system that validates “Out of Bounds” signals as high-level cognitive engagement.
3. The “Living Textbook” as a Data Feed
- The 4-Hall Lesson: The hallway becomes a Permanent Living Textbook.
- The SaaS Pitch: We are moving toward “Permanent Measurement.” If the environment is always teaching, the system must always be logging. This startup provides the “Central Node” that connects the physical movement in a 4-Hall hallway to a digital student record.
(The Pitch)
The Hook:
“In 2018, Dr. Sadownik proved that student logic is ‘Under Construction.’ In 2026, the 4-Hall Math project at UVic proved that this construction happens through movement and spatial reasoning. My startup, is the SaaS Infrastructure that captures this. We turn the ‘Active Hallway’ into a ‘Data Hallway.’”
The Technical “Ask”:
“I am looking to digitize the 4-Hall Lesson Plans. We want to see if our logger can identify the mathematical intent in a student’s ‘Grawlix’ inputs and physical movement patterns more accurately than a standard LMS (like Brightspace or Canvas).”
Application Field: “Innovation/Technical Basis”
Draft:
“Our innovation is the integration of Pedagogical Discourse Analysis (Sadownik, 2018) with Spatial Kinesthetic Logic (4-Hall Math, 2026). We are building a middleware ‘Grawlix Logger’ that translates non-standard physical and digital inputs into validated performance data. By applying the ‘Draw Outside the Box’ philosophy to data architecture, we ensure that neurodivergent logic is logged as a cognitive asset rather than a system error.”