GEOS-FN-002 — Foundational Numeracy Outcome Domain Taxonomy
Version: 0.01 Status: Normative Standard (Definition — Def)
1. Purpose and Position in the GEOS Standards Stack ——————————————————-
GEOS-FN-002 defines the formal outcome domain taxonomy fo Foundational Numeracy referenced by GEOS-FN-001.
This document:
enumerates the recognized Foundational Numeracy outcome domains;
defines each domain at a level suitable for finance-grade measurement;
establishes domain boundaries and relationships; and
provides a stable semantic layer to which Sentinel signals may map.
This taxonomy exists to ensure that Outcome Signal Portfolios submitted for GEOS certification are:
internally coherent;
comparable across School Systems and jurisdictions; and
auditable over time.
GEOS-FN-002 does not define
curriculum standards;
learning progressions;
pedagogical approaches;
assessment instruments; or
performance thresholds.
2. Design Principles ————————
The taxonomy defined in this document adheres to the following principles:
Conservatism Domains reflect constructs that are already widely accepted in the mathematics education and cognitive development literature.
Orthogonality (Where Feasible) Domains are defined to minimize conceptual overlap, recognizing that perfect orthogonality is not achievable in early numeracy.
Measurability Each domain admits observable learner behaviors that can be measured repeatedly and aggregated.
Curricular Agnosticism Domains are independent of any national curriculum sequence or instructional model.
Signal Compatibility Domains are defined at a granularity suitable for use in multi-signal portfolios rather than single composite metrics.
3. Taxonomy Structure ————————-
The Foundational Numeracy taxonomy consists of four primary outcome domains, each of which may contain sub-domains for measurement and reporting purposes.
The domains are:
Number Sense and Quantity
Numerical Operations
Numerical Representation and Symbolization
Foundational Mathematical Reasoning
Each domain is defined below.
4. Outcome Domains ———————-
*Domain Definition* Number Sense and Quantity refers to a learner's intuitive and emerging formal understanding of numbers as representations of quantity, magnitude, and order.
*Scope Includes* Observable learner capability in:
recognizing quantities without counting (small sets);
counting with stable order and one-to-one correspondence;
comparing quantities and determining "more," "less," or "equal";
understanding numerical order and relative magnitude; and
developing age-appropriate place value awareness.
Scope Excludes
formal arithmetic procedures;
symbolic manipulation beyond age-appropriate numerals; and
abstract number theory concepts.
*Rationale* This domain is universally recognized as foundational to later mathematical learning and is extensively documented across diverse education systems.
*Domain Definition* Numerical Operations refers to a learner's ability to perform and reason about basic arithmetic operations appropriate to early grade levels.
*Scope Includes* Observable learner capability in:
addition and subtraction within age-appropriate ranges;
understanding operations as transformations of quantity, not rote procedures;
decomposing and recomposing numbers;
solving simple quantitative problems involving operations.
Scope Excludes
formal multiplication and division algorithms;
symbolic algebraic manipulation; and
memorization of advanced procedures without conceptual grounding.
*Rationale* Operational competence is necessary for practical numeracy but is explicitly distinguished from higher-order procedural fluency.
*Domain Definition* Numerical Representation and Symbolization refers to a learner's ability to represent quantities and relationships using symbols, objects, diagrams, or other representations — and to translate between them.
*Scope Includes* Observable learner capability in:
recognizing and using numerals;
representing quantities using objects, marks, or visual models;
mapping between symbolic and non-symbolic representations; and
interpreting simple numeric representations presented by others.
Scope Excludes
formal notation systems beyond early numerals;
abstract symbolic manipulation; and
advanced representational conventions.
*Rationale* This domain supports comparability across instructional contexts and provides a bridge between intuitive quantity and formal mathematics.
*Domain Definition* Foundational Mathematical Reasoning refers to a learner's emerging capacity to reason quantitatively, identify patterns, and explain numerical relationships at an age-appropriate level.
*Scope Includes* Observable learner capability in:
recognizing simple patterns and regularities;
making basic quantitative inferences;
explaining numerical choices using informal reasoning;
applying logic to simple number-based situations.
Scope Excludes
formal proof;
abstract logical systems; and
advanced problem-solving strategies.
*Rationale* Reasoning is included as a distinct domain to avoid conflating procedural skill with conceptual understanding, while remaining measurable at early ages.
5. Domain Relationships and Overlap —————————————
The GEOS Organization recognizes that Foundational Numeracy domains are developmentally interdependent.
Accordingly:
Signals may map to multiple domains simultaneously;
No domain is assumed to develop independently of the others; and
Outcome Signal Portfolios may include signals that reflect cross-domain interactions.
This taxonomy does not require that signals be uniquely assigned to a single domain.
6. Use in Sentinel Signal Construction ——————————————
To be certified under GEOS, Outcome Signal Portfolios:
MUST map each included signal to one or more domains defined in this taxonomy;
MUST document the domain mapping explicitly; and
MUST NOT introduce novel outcome domains outside this taxonomy without GEOS revision.
This document defines the semantic envelope within which GEOS-FN-003 (Sentinel Signal Families) operates.
7. Stability and Evolution ——————————
This taxonomy is intentionally stable.
Revisions to domain definitions:
will occur infrequently;
will be versioned and backward-mapped; and
will be informed by empirical evidence, audit experience, and cross-jurisdictional use.
The GEOS Organization anticipates refinement of sub-domains and mappings over time, while preserving the primary domain structure.
8. Non-Normative Clarification ———————————-
This taxonomy defines what may be measured and certified under GEOS standards.
It does not define:
what learners should be taught;
how learning should occur; or
what constitutes "good" education.
Those judgments remain external to the GEOS Standards.