V-Math: Autonomous NHSGME Math Framework

• V-Math is an autonomous exam preparation framework tailored for Vietnamese high school graduates, combining self-paced practice with curriculum-aligned exam generation.
• It employs a planner–executor multi-agent pipeline with a specification matrix to ensure high compliance (96.7%) and innovative question diversity.
• The system enhances learning outcomes with adaptive tutoring that reduces repeated mistakes by 43% and saves teachers up to 70% of exam preparation time.

V-Math is an autonomous agentic framework for the Vietnamese National High School Graduation Mathematics Exams (NHSGMEs). It is designed to support Vietnamese high school students through self-paced practice, detailed step-by-step reasoning, and adaptive tutoring, while also supporting teachers by generating innovative, compliant exam questions and diverse, high-quality question banks. The framework is organized as a planner–executor multi-agent pipeline whose core executors are a specification-matrix-conditioned question generator, a solver/explainer, and a personalized tutor; preliminary evaluation reports matrix-aligned exams, high solution accuracy, coherent explanations, and enhanced variety of practice materials aligned with national standards (Nguyen et al., 12 Sep 2025).

1. Educational setting and system scope

V-Math is explicitly targeted at preparation for the NHSGMEs rather than at generic mathematical problem solving. Its scope is dual-use. On the learner side, it enables self-paced student practice, supports simulation of full NHSGME sessions under time limits, and provides detailed solution traces. On the teacher side, it generates compliant exam questions, helps build question banks, and reduces manual workload by automating a substantial part of exam preparation and resource production (Nguyen et al., 12 Sep 2025).

The framework is therefore best understood as an exam-aligned educational infrastructure rather than a standalone solver. Its alignment is formalized through a specification matrix tied to topics, exam sections, and cognitive levels. This architecture makes V-Math simultaneously a practice environment, an assessment-generation system, and a teacher-facing authoring workflow. The paper’s emphasis on “scalable, equitable mathematics preparation aligned with national standards” places standard compliance at the center of the design rather than treating it as an auxiliary constraint.

2. Planner–executor organization and shared memory

V-Math is built as a “planner–executor” multi-agent pipeline. A high-level Planner Agent decomposes user requests such as “generate a mock exam,” “solve this paper,” and “recommend practice” into ordered subtasks, then selects which executor agent should handle each subtask. The executor layer contains three specialized agents: Agent 1, a creative exam generator; Agent 2, a solver/explainer; and Agent 3, a personalized tutor (Nguyen et al., 12 Sep 2025).

The agents operate over shared memory modules. Main Memory stores the specification matrix, an exam bank of 500 full exam sets, and student profiles. Subtask Memory maintains a task-by-task log of planner–executor interaction. Tool Memory records OCR/LaTeX conversion and CV parsing logs. Case Memory is an episodic store of prior $(\text{state}, \text{action}, \text{reward})$ trajectories in a Memento-style format. This memory design makes the system neither stateless nor monolithic; instead, it combines task decomposition with persistent stores for curriculum structure, execution traces, tool outputs, and prior problem-solving episodes.

A common misconception is to treat “agentic” here as an unconstrained autonomy claim. In V-Math, agenticity is concretely instantiated as structured delegation by a planner over three fixed executor roles plus shared memory, not as open-ended autonomous behavior.

3. Specification-matrix-conditioned exam generation

The question-generation subsystem is defined around a specification matrix $S$, whose rows are topics such as Sequences, Derivatives, and 3D Geometry, and whose columns are Sections I–III crossed with cognitive levels $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$. Formally,

$S \in \{0,1\}^{T \times (C \times L)},$

where $T$ is the number of topics, $C=\{I,II,III\}$, and $L=\{R,C,A\}$ (Nguyen et al., 12 Sep 2025).

The generator $G$ is defined by

$Q = G(S; \theta_G),$

and maps each nonzero cell $S_{t,c,l}=1$ into exactly one question $S$0 with metadata $S$1. This makes the system’s compliance target explicit: generation is not merely prompted by a theme but constrained by a curriculum-and-assessment matrix.

Difficulty control is enforced through prompting templates that specify values such as “Level = Application.” Alignment quality is measured by “Matrix Compliance Rate,” reported as 96.7%. Novelty is encouraged through a low n-gram-overlap regularizer against past exams, with Novelty reported at approximately 7.8%. In the reported experiments, Agent 1 also receives a Teacher Rating of 4.6/5. These values indicate that the generator is evaluated not only for syntactic production but also for distributional fidelity to the target matrix and for pedagogical acceptability.

The same matrix-conditioned mechanism underlies teacher workflows. A teacher selects a target specification matrix $S$2, for example specifying “3 questions in Section III, Application,” and Agent 1 produces a question set $S$3 with IDs and metadata. Review then occurs in a Web interface that supports preview in PDF/LaTeX, adjustment of numerical ranges, and locking of distractors before export in JSON or LaTeX.

4. Solver/explainer design and Memento-style memory

The solver/explainer module is organized as a four-stage workflow: input PDF or images are processed by OCR plus DocLayout-YOLO, normalized into LaTeX, passed to chain-of-thought planning with Gemini 2.5 Pro and Memento-style memory recall, transformed through symbolic reasoning plus NLP into a stepwise solution, and finally rendered as LaTeX with natural-language commentary (Nguyen et al., 12 Sep 2025).

The memory mechanism is formalized by retaining intermediate reasoning states

$S$4

recalling similar past cases $S$5 via $S$6, and adapting the solution through

$S$7

This makes Agent 2 explicitly case-based rather than purely prompt-based. The use of episodic recall is further reflected in the ablation study, where removing memory degrades accuracy on harder items and step completeness.

The module also incorporates inference rules and proof templates. Examples listed in the paper include linear combination $S$8 row reduction in matrices, vector parametric form $S$9 extraction of direction vector $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$0 from $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$1, and area computation via

$$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$2

A sample derivative-style inference step identifies

$$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$3

then concludes that the horizontal asymptote is $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$4. These examples show that the solver/explainer is intended to produce pedagogically legible intermediate steps, not only final answers.

5. Adaptive tutoring and teacher-facing operation

The personalized tutoring agent tracks a student state $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$5 over $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$6 topics. After each practice session $$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$7, containing scores and errors, the posterior state is updated through a Bayesian-RL hybrid:

$$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$8

Operationally, V-Math uses a Memory-Based MDP

$$\{\text{Recognition}, \text{Comprehension}, \text{Application}\}$$9

with reward $S \in \{0,1\}^{T \times (C \times L)},$0 balancing immediate score gains and long-term mastery (Nguyen et al., 12 Sep 2025).

Its recommendation policy includes error-driven remediations that focus drills on weak skills and the simulation of full NHSGME sessions under time limits. The reported educational metrics for Agent 3 are Learning Improvement $S \in \{0,1\}^{T \times (C \times L)},$1 points pre→post, Engagement $S \in \{0,1\}^{T \times (C \times L)},$2 measured by completion rate/time, and Path Effectiveness defined as a 43% reduction in repeated mistakes.

Teacher-oriented functionality is integrated rather than separated from the student pipeline. The Web interface permits direct review and editing of generated items and exports question banks either as JSON or as LaTeX for print. The sample output schema includes fields for id, topic, section, level, stem, choices, answer, solution, and skills, with the example skills field containing "conditional probability" and "Bayes’ rule". This schema indicates that generated items are intended to be reusable as structured assessment assets rather than ephemeral chat outputs.

6. Empirical evaluation, impact, and limitations

The reported experiments use two datasets: NHSGMEs, consisting of 500 full exams in 2025+ MOET format, and VNHSGE, consisting of 250 public items from 2019–2023. Evaluation is reported at the subsystem level and at the end-to-end system level (Nguyen et al., 12 Sep 2025).

Subsystem	Metrics	Results
Agent 1	Matrix Compliance; Novelty; Teacher Rating	96.7%; 7.8%; 4.6/5
Agent 2	Solution Accuracy; Step Completeness; Explanation Quality	90.4%; 82.1%; 4.5/5
Agent 3	$S \in \{0,1\}^{T \times (C \times L)},$3Score; Engagement; Path Effectiveness	+11.8; 0.76; 43%

At the end-to-end level, VNHSGE exact match is reported as 100% for 2019–2023, versus GPT-4 Omni at approximately 86.4%. On full-exam evaluation, set-level perfect is 64%, with Item Acc = 92.1% and Expl. Q = 4.6, reported as +6–8 points over the next best system. The memory ablation for Agent 2 shows the following progression: without Memory, VNHSGE Acc = 88.1%, Hard-Item Acc = 74.5%, Step Comp = 77.3%, Latency = 7.2 s; with + ReadNP, 89.6%, 78.4%, 80.9%, 8.1 s; with + ReadP, 90.4%, 80.3%, 82.1%, 8.7 s. Improvements in Hard-Item accuracy and step-completeness are reported as significant at $S \in \{0,1\}^{T \times (C \times L)},$4 by paired bootstrap.

The educational impact claims extend beyond raw benchmark numbers. Average pre→post gain is reported as +11.8 points with effect size $S \in \{0,1\}^{T \times (C \times L)},$5, and error recurrence is reduced by 43%. On the teacher side, automatic bank generation saves approximately 70% of preparation time in a pilot study, with teacher satisfaction reported at 4.2/5. Deployment is described as plug-and-play on any base LLM via API, with the memory-augmented pipeline incurring modest latency of approximately 8 s per exam.

The principal stated limitation is dependence on scanned PDFs, with diagram-heavy pages remaining noisy. Future work is specified as lighter planners, more robust CV for graphs, multi-subject extension, and privacy/audit trails. A further misconception is that high item-level accuracy implies uniformly solved complete exams; the reported 64% set-level perfect score shows that exam-level reliability remains materially harder than single-item correctness.

7. Terminological context and related usages

The label “V-Math” is not unique across the literature. In the educational-agent sense, it denotes the NHSGME-oriented framework described above (Nguyen et al., 12 Sep 2025). However, nearby naming conventions can refer to different problem classes.

“MV-MATH” is a benchmark for multimodal math reasoning in multi-visual contexts, consisting of 2,009 K–12 problems with multiple images interleaved with text (Wang et al., 28 Feb 2025). “VisioMath” is a benchmark of 1,800 multiple-choice questions in which answer options are images, and its overview explicitly describes it as a “V-Math benchmark” (Li et al., 7 Jun 2025). An earlier and unrelated usage appears in VEST, “Vector Einstein Summation Tools,” whose summary characterizes it as providing a “V-Math” (vector-math) solution inside Mathematica for abstract vector calculus simplification (Squire et al., 2013).

This terminological overlap matters because the 2025 V-Math framework is neither a generic visual-math benchmark nor a vector-calculus package. It is a specialized agentic educational system centered on Vietnamese national-exam preparation, curriculum-constrained generation, memory-augmented solution explanation, and adaptive tutoring.