6QRC™ System Identity Manual: Public Research Edition (Limited Release)

Scope: Mathematical Tasks (all solvable problem-types)

Intended Audience

Researchers and reviewers evaluating 6QRC. Teams running reliability, validity, or implementation studies.

Document Purpose

This document previews the schema‑level definitions of 6QRC™ for research and review. It includes the core operators and raw information elements needed to understand the structure of the system.

The full 6QRC™ System Identity Manual: including the complete decomposition protocol, implementation rules, diagnostic procedures, and operational guidance is proprietary and available only by agreement with Axiron LLC.

Researchers may request access to the full manual for study use, schema‑level mapping work, or participation in pilot‑site evaluations.

For access inquiries: channing@axironsystems.com

Ultimate Purpose (Learner Courtesy): Make the schema level of a Prompt explicit (via Task Extraction) before solving. Disentangle Prompt (surface text) from Task (cognitive event). Specify the *Objective and the Cognitive Verbs. Specify the six raw elements: Quantities, Relationships, Conditions, Constraints, *Objective, and Representations. And establish a compact, load-bearing language for math problem structure to tighten teacher and student communication.

Clarification: In 6QRC, “Objective” is NOT an instructional goal, student skill achievement, or outcome expectation. It is the Task's governing completion criterion as a raw information element, recovered from the Prompt but held and operated on in the cognitive layer, because it is the mentally represented target the learner must stabilize before solving. This is a technical construct unique to 6QRC, and distinct from how ‘objective’ is used in curriculum or instructional terminology.

Primary use cases:

Structure: In a given Prompt, specify the element set the Task depends on, and what’s not there.
Sequence: Specify the expected verb progression, plus permissible variation.
Communication: Supply a load-bearing language for talking about what a problem requires before solving.
Diagnosis: Localize breakdowns to a specific 6QRC element.
Design: Make required elements guaranteed at Task-entry.
Assessment: Eliminate false equivalence: same words ≠ same Task.

Terminology (heads up): Terms are ordered by conceptual dependency, not alphabetically.

Introduction:

6QRC draws a hard boundary between the Prompt and the Task: it supplies a precise vocabulary for describing the cognitive event (Task) a student performs when solving a math problem (Prompt). In this manual, 6QRC is presented as a schema-level analytic framework: a decomposition model for mapping surface Prompts to their underlying cognitive structure and information elements. It targets the cognitive event, not just the words on the page. In many classrooms, the Prompt becomes the default stand-in for a problem’s meaning, because it is the only layer made explicit. 6QRC aims to make the schema level of a Prompt (mapping to Task) explicit and speakable: the information elements that are present (6QRC: Quantities, Relationships, Conditions, Constraints, Objective, and Representations), what reasoning actions those elements require, and how the governing Objective structures the cognitive event, so that learners can see through surface variation to the invariant and enter a Task with a clear cognitive survey before reasoning, planning, or solving.

This preview ends here.

The purpose statement, use cases, and introduction above constitute the full scope of this limited release. They establish what 6QRC™ is designed to accomplish and why. Nothing more. The components that make the system operational are not contained in this document and remain proprietary to Channing Cornell Powers and Axiron LLC. These include its schema-level operators, raw information elements, decomposition protocol, Cognitive Verb sequences, implementation rules, and diagnostic procedures.

This material may not be reproduced, adapted, or used as the basis for derivative work without express written authorization from Axiron LLC.

To request access to the full 6QRC™ System Identity Manual, contact: channing@axironsystems.com