Concept Cloud Extraction for Personalized Math Problem Generation

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Existing math education systems fail to consistently address gaps in mathematical knowledge, leading to misunderstandings and underestimation of students' abilities due to skipped or unclear explanations, hindering world-class results across diverse student populations.

Innovation Solution

A system utilizing the Concept Cloud Extraction/Concept Cloud Reconstitution Module (CCE/CCR) to automatically distill and compose math concepts, dynamically construct problems, and employ branching algorithms to test and map user skills, addressing gaps through customized study and practice programs.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If traditional math education materials are used, then students can access standard curriculum content, but gaps in mathematical knowledge occur due to skipped or unclear explanations

Engineering Contradiction:

Improvecompleteness of math concept explanationsVSAvoidmissing intermediate concepts

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The system segments mathematical knowledge into discrete, granular concepts that can be individually identified, assessed, and taught. By breaking down math problems into component concepts, the system ensures that no intermediate steps are skipped and each concept is explicitly addressed, eliminating the information gaps present in traditional materials.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The system implements continuous feedback loops where student performance on math problems is automatically analyzed to identify which specific concepts are misunderstood or missing. This feedback drives personalized remediation, ensuring that gaps are detected and filled systematically rather than through random review.

Inventive Principle:

Principle #23Feedback

2Adaptability or versatility

If standardized math materials are used, then all students can access the same content, but individualized learning needs are not met

Engineering Contradiction:

Improvepersonalization of learning pathsVSAvoidcomplexity of adaptive system

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The learning system is dynamically adaptive, automatically adjusting the difficulty, pace, and focus of math problems based on real-time performance data. The system evolves the curriculum for each student individually, creating personalized learning paths that adapt to demonstrated mastery levels without requiring manual intervention.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The system performs self-assessment and self-adjustment by automatically analyzing student responses, identifying knowledge gaps, and generating appropriate remediation problems. This self-service capability eliminates the need for teacher intervention to personalize learning, achieving adaptability through automated systems rather than complex human-managed programs.

Inventive Principle:

Principle #25Self-service

3Productivity

If math concepts are taught with skipped steps, then coverage of topics increases, but student understanding and procedural flexibility decrease

Engineering Contradiction:

Improvepace of concept coverageVSAvoidprocedural flexibility

Core Design Contradiction:

ProductivityVSEase of operation

Solution Approach 1:

The system ensures that prerequisite concepts are mastered before advancing to more complex topics by automatically assessing foundational knowledge and blocking progression until gaps are filled. This preliminary action guarantees that students have the necessary procedural flexibility before encountering new material, preventing future misunderstandings.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system maintains continuous engagement with mathematical reasoning by providing unlimited practice problems that reinforce concepts at varying levels of complexity. This continuous practice ensures procedural flexibility is developed and maintained throughout the learning process, rather than relying on discrete textbook examples that may skip critical thinking steps.

Inventive Principle:

Principle #20Continuity of useful action

Data Source

PatentUS12562075B2Systems and methods for automatic distillation of concepts from math problems and dynamic construction and testing of math problems from a collection of math concepts

Publication Date: 2026.02.24 VALUECORP PACIFIC INC

AI summary

Systems and methods of automatically distilling concepts from problems and dynamically constructing and testing the creation of problems from a collection of concepts comprising: providing a user interface to a user; receiving input; extracting and compiling a concept cloud of one or more CLIs that comprise the concepts embodied in the input, describe the operation of the one or more concepts, or relate to the UDP, respectively; applying a mathematical rules engine to the CLIs that define the concept cloud to build one or more additional problems; and returning to the user, through the user interface, the one or more additional problems built from the CLIs that define the concept cloud extracted from the input.