GEOS-FN-001 — Foundational Numeracy Outcomes Framework
Version: 0.01 Status: Normative Standard
0. Interpretive Basis and Certification Intent ————————————————--
GEOS-FN-001 defines the requirements that an Outcome Signa Portfolio produced by a School System must satisfy in order to be eligible for certification by a GEOSor™ Certified Partner™ as a GEOS Certified Outcome Signal Portfolio (GeOSP™) for Foundational Numeracy under GEOS standards.
This standard:
constrains certifiable artifacts only;
imposes no obligations, duties, or restrictions on any role; and
does not limit what any School System may measure, publish, or use internally.
Certification under this standard is voluntary and applies solely to the Outcome Signal Portfolio artifact submitted for conformity assessment.
1. Purpose and Scope ————————
This document defines the Foundational Numeracy outcome domain for the purposes of results-based funding for education (RBF4Ed) under GEOS standards.
It specifies:
the grade band covered by Foundational Numeracy;
the outcome constructs eligible for use in a certifiable Outcome Signal Portfolio;
the required properties of measurements claiming conformity;
the minimum comparability constraints necessary for cross-jurisdictional finance use; and
the permitted forms of aggregation from raw educational data streams.
This document does not define curriculum, pedagogy, instructional sequencing, or intervention strategies.
This standard applies to Foundational Numeracy outcomes for learners in:
This grade band reflects global practice in defining foundational numeracy and explicitly includes Kindergarten, recognizing the developmental continuity of early mathematical cognition.
This document does not:
prescribe instructional methods;
rank or privilege pedagogical approaches;
define national curriculum standards;
define funding thresholds or disbursement rules;
mandate specific assessment instruments; or
assert normative educational goals beyond measurability and auditability.
2. Institutional Neutrality and Applicability ————————————————-
Outcome signals eligible for certification under this standard may be generated by any School System, including School Systems composed of:
public schools;
private or non-state schools;
faith-based schools;
non-formal education programs; and
digital, blended, or hybrid learning environments.
Eligibility for certification is determined solely by artifact conformity, not by institutional form. This neutrality extends to production method: outcome signals from AI-assisted or AI-generated instructional systems are assessed on the same conformity criteria as signals from traditional instruction (see Essay 12): AI in Africa's DPI-Ed.
GEOS-FN-001 is program-agnostic
The standard makes no assumptions regarding:
instructional time;
delivery modality;
class size;
teacher qualifications; or
technology usage.
3. Foundational Numeracy Outcome Constructs ———————————————--
For the purposes of this standard, Foundational Numeracy is defined as:
The measurable capacity of a learner to understand, represent, and operate on numbers and quantities at levels necessary for continued participation in formal mathematics instruction.
An Outcome Signal Portfolio claiming eligibility for GEOS certification MUST derive its signals from one or more of the following construct families.
No single construct family is required to be used in isolation.
Includes measurable learner capability in:
counting sequences;
one-to-one correspondence;
magnitude comparison;
subitizing (small quantities); and
age-appropriate place value awareness.
Includes measurable learner capability in:
addition and subtraction within age-appropriate ranges;
understanding of operation meaning (not rote memorization); and
decomposition and recomposition of numbers.
Includes measurable learner capability in:
symbolic representation (numerals);
non-symbolic representation (sets, objects); and
transitions between representational forms.
Includes measurable learner capability in:
recognizing patterns;
applying simple quantitative logic; and
explaining numerical relationships at an age-appropriate level.
4. Status and Progress Signal Categories ——————————————--
This standard treats status (attainment) signals and progress (learning gain) signals as co-equal categories within a certifiable Outcome Signal Portfolio.
The standard does not privilege either category a priori.
Status signals represent learner performance at a defined point in time.
Permitted examples include:
proportion of learners meeting a defined proficiency threshold;
distribution of learner performance across defined bands; and
median or percentile attainment values.
Progress signals represent change over time for individual learners or cohorts.
Permitted examples include:
average learning gain over a defined interval;
proportion of learners demonstrating positive growth; and
movement across performance bands between time points.
Any progress signal included in a certifiable Outcome Signal Portfolio MUST specify:
baseline measurement window;
follow-up measurement window; and
elapsed instructional time or exposure proxy.
5. Data Stream Requirements ——————————-
GEOS standards define the required properties of raw educational data streams used for results-based funding.
Any data source may be used, provided that the resulting data stream demonstrably conforms to these properties and passes independent conformity assessment under GEOS-defined procedures.
Raw data streams used to generate signals in a certifiable Outcome Signal Portfolio MUST exhibit:
learner-level traceability prior to depersonalization;
timestamped interaction or assessment events;
curriculum-aligned item tagging where applicable;
reproducible aggregation rules; and
immutable audit logs.
6. Aggregation and Depersonalization —————————————-
Signals included in a certifiable Outcome Signal Portfolio MUST be derived from depersonalized aggregates that:
contain no direct learner identifiers;
comply with applicable national data protection law; and
remain reproducible from raw data under audit.
Aggregation MAY occur at:
school;
district;
regional; or
national level.
Cross-jurisdictional aggregation MAY support funding claims only where the resulting funding applies jointly and exclusively to the same set of aggregated jurisdictions.
Cross-jurisdictional aggregation MUST NOT support funding claims applied to any jurisdiction not fully included in the aggregated dataset.
7. Sentinel Signal Portfolio Requirements ———————————————
An Outcome Signal Portfolio MUST include multiple Sentinel signals in order to be eligible for GEOS certification as a GeOSP™.
No Sentinel signal defined under this standard is intended to be universal.
A certifiable Outcome Signal Portfolio MUST be structured such that the artifact supports anti-gaming strategies, including:
inclusion of signals drawn from multiple outcome construct families;
the ability to rotate or substitute signals across reporting periods;
selective disclosure of signal composition; and
non-deterministic selection of signals by funding counterparties.
This standard does not prescribe which signals any funding counterparty selects, discloses, or acts upon.
The GEOS Organization's role is limited to defining the permissible design space within which such strategies may be implemented.
8. Comparability Constraints ——————————--
Signals included in a certifiable Outcome Signal Portfolio MUST:
map to the construct families defined in Section 3;
apply standardized aggregation logic; and
publish sufficient metadata to enable third-party comparison.
9. Conformity Assessment —————————-
An Outcome Signal Portfolio MUST undergo conformity assessment by:
a GEOSor™ Certified Partner™ operating under GEOS Conformity Assessment procedures; and
published test and audit criteria
in order to qualify for GEOS certification as a GeOSP™.
GEOS certification:
affirms conformity to published standards and processes;
does not assert educational effectiveness;
does not imply funding eligibility; and
remains contestable under defined procedures.
10. Versioning and Evolution ——————————--
This standard prioritizes inter-temporal comparability.
Revisions MUST be:
versioned;
backward-mapped where feasible; and
publicly documented.
This framework is explicitly recognized as a first approximation.
The GEOS Organization expects refinement based on:
pilot evidence;
audit findings;
methodological critique; and
independent research.
11. Interpretive Guidance (Non-Normative) ———————————————
GEOS-FN-001 defines the conditions under which outcome artifacts ma be certified under GEOS standards.
Educational value judgments, policy choices, instructional decisions, and funding determinations remain entirely the responsibility of School Systems, funding counterparties, and implementing institutions.