A 501(c)(3) Non-Profit Organization

Building the Open Semantic Infrastructure for Mathematics

A collaborative, extensible foundation for K–16 mathematics education

We're creating the computable knowledge infrastructure that enables personalized learning, rigorous assessment, and AI-powered instruction—built on open standards and accessible to all.

Our Mission

To develop and maintain an open, extensible, computable semantic infrastructure for K–16 mathematics that empowers educators, supports learners, and enables the next generation of educational technology.
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Open & Accessible

Our infrastructure is open source and freely available to all educators, researchers, and developers committed to improving mathematics education.

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Research-Based

Grounded in rigorous mathematics, cognitive science, and pedagogical research to ensure conceptual integrity and educational validity.

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Collaborative

Built through partnerships with educators, mathematicians, technologists, and assessment experts working toward a shared vision.

♾️

Extensible

Designed to evolve with new research, accommodate diverse frameworks, and support innovation in educational technology.

The Challenge

Mathematics education operates without a unified, machine-readable representation of mathematical knowledge

Standards Without Structure

Current standards are natural-language descriptions that lack formal mathematical specificity, explicit semantic structure, and machine-actionable coherence.

Fragmented Assessment Systems

Assessment platforms treat standards as flat tags, leading to misalignment, inconsistent rigor, and inability to identify true conceptual understanding.

Shallow Learning Models

Adaptive systems rely on item-level statistics rather than conceptual representations, producing unreliable predictions and and weak trajectory modeling.

The Ontara Infrastructure

A multi-layered semantic architecture that transforms how mathematics is represented and reasoned about

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Computable Knowledge Graph

A semantic network capturing standards, skills, concepts, prerequisites, and learning progressions in machine-readable form—enabling intelligent reasoning about mathematical knowledge.

Mathematical Ontology

Formal definitions of mathematical objects and their relationships, bridging natural language descriptions with rigorous mathematical constructs for both symbolic and conceptual reasoning.

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Problem Archetype Engine

Canonical models of problem families, representations, and transformations that enable assessment generation, scaffolding, diagnostics, and misconception identification.

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Learning Trajectory Models

Probabilistic mastery frameworks tracking conceptual growth, cross-domain interactions, and longitudinal development—scaling to millions of learners while maintaining interpretability.

Transformative Impact

Open infrastructure that fundamentally improves mathematics education for everyone

🎓 Principled Personalization

Enable learning experiences tailored to individual conceptual profiles and developmental trajectories—grounded in mathematical coherence, not proprietary algorithms.

🔗 Coherent Progression

Help students experience mathematics as connected knowledge where topics build logically, prerequisites are clear, and the path forward is visible.

✅ Rigorous Assessment

Support districts and educators in creating assessments that are psychometrically sound, conceptually balanced, and aligned to meaningful learning trajectories.

👨‍🏫 Educator Empowerment

Provide teachers with actionable insights, high-quality resources, automated scaffolding tools, and clear visibility into student thinking and misconceptions.

500+

K–16 Standards

Open

Source & Accessible

All

Educators Welcome

Students Served

Who We Serve

Our open infrastructure supports the entire mathematics education ecosystem

K–12 Educators & Districts

Access rigorous assessment tools, curriculum alignment resources, and data-driven insights—all built on open, validated infrastructure.

EdTech Developers

Build next-generation AI tutors, adaptive platforms, and learning tools on a foundation that prevents hallucination and ensures mathematical soundness.

Assessment Organizations

Create psychometrically robust items, balance rigor across assessments, and ensure construct coverage using shared semantic standards.

Higher Education

Improve placement, remediation, and pathway design with coherent progressions that bridge K–12 and college mathematics.

Curriculum Publishers

Enhance materials with semantic alignment verification, standards mapping, and research-based sequencing recommendations.

Researchers

Study mathematical cognition, learning trajectories, and instructional effectiveness using standardized, computable representations.

Join Us in Building the Future of Mathematics Education

We're seeking partners, contributors, and collaborators who share our vision of open, rigorous educational infrastructure.