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Table of Contents

From AI Assistance to Independent Mastery

Project Outline and Step-by-Step Development Plan

Working Project Title: From AI Assistance to Independent Mastery: Designing an AI Learning Coach for College Mathematics Readiness

Primary Goal: Design, prototype, and evaluate an AI-assisted mathematics learning system that helps students identify prerequisite gaps, receive adaptive support, gradually reduce dependence on AI, and demonstrate independent mastery.

Initial Scope: Precalculus skills needed for success in college mathematics, especially calculus.

1. Project Vision

The project will investigate a learning model that goes beyond ordinary online homework, adaptive practice, or conversational tutoring.

The central learning cycle is:

\[
\boxed{\text{Diagnose}}
\rightarrow
\boxed{\text{AI Coaching}}
\rightarrow
\boxed{\text{Graduated Assistance}}
\rightarrow
\boxed{\text{Fade Assistance}}
\rightarrow
\boxed{\text{AI-Free Practice}}
\rightarrow
\boxed{\text{Independent Mastery}}
\rightarrow
\boxed{\text{Retention and Transfer}}
\]

The main design principle is:

AI should help students become increasingly capable of succeeding without AI when independent competence matters.

The project should be approached as both:

an HCI research and design project, and
a mathematics-learning prototype.

2. Main Research and Design Questions

2.1 Learning Questions

How can AI identify the prerequisite skill that is causing a student’s difficulty?
What forms of assistance are most useful at different stages of learning?
When should AI ask a question rather than provide an explanation?
When should hints become more explicit?
When should assistance begin to fade?
How can the system distinguish productive struggle from frustration?

2.2 Mastery Questions

How should the system distinguish AI-assisted proficiency from independent mastery?
How many independent problems are enough to provide reasonable evidence of mastery?
Should mastery include accuracy, efficiency, and retention?
How should students see and understand their own mastery status?

2.3 HCI Questions

Do students understand when and why AI assistance is being reduced?
Do they perceive fading assistance as helpful or frustrating?
How should hints, explanations, mastery checks, and progress be presented?
How much control should students have over the level of AI assistance?
How should an instructor dashboard summarize student weaknesses and progress?

2.4 Longer-Term Questions

Can the system improve later retention?
Can students transfer repaired precalculus skills to authentic calculus problems?
Can AI-assisted grading and personalized feedback eventually be integrated into the same mastery framework?

3. Recommended Scope for the First Version

The first version should be intentionally small. It should not attempt to cover all of precalculus or become a complete LMS.

A good first prototype could focus on approximately 5–8 foundational skills.

Possible choices include:

integer and fraction arithmetic,
exponent rules,
expanding and factoring expressions,
solving linear and quadratic equations,
simplifying rational expressions,
function notation,
basic trigonometric values,
algebra used in difference quotients.

The initial prototype should be designed to answer one central question well:

Can an AI Learning Coach help a student move from needing assistance to demonstrating the same skill independently?

4. Division of Roles

4.1 Your Role: Mathematics and Learning Mentor

Your primary responsibilities would include:

defining the mathematical skills to be included,
identifying prerequisite relationships,
creating or reviewing diagnostic questions,
defining what counts as mastery,
designing mathematically valid examples and assessments,
reviewing AI explanations and feedback for correctness,
advising on pedagogy and calculus readiness,
helping define experimental conditions and outcome measures,
connecting the project with instructors or possible participants when appropriate.

4.2 Intern’s Role: HCI Research and Product Design

The intern’s primary responsibilities would include:

competitive analysis,
user interviews,
journey mapping,
persona or user-type development if useful,
interaction-flow design,
wireframes and Figma prototypes,
usability testing,
design iteration,
front-end prototype development if within her technical skills,
analysis of user behavior and qualitative feedback,
documentation of the HCI process for a portfolio case study.

4.3 Shared Responsibilities

define research questions,
review literature,
interpret findings,
decide which prototype features to prioritize,
plan a pilot study,
evaluate results,
identify future research directions.

5. Phase 1 — Problem Definition and Background Research

Suggested duration: 1–2 weeks

Step 1. Define the target learner

Start with a clearly defined user population. For example:

College students who have completed substantial high-school mathematics but have gaps in algebra, functions, trigonometry, or other precalculus skills that interfere with success in calculus and other STEM courses.

Step 2. Define the core problem

A concise problem statement might be:

Existing AI tools can help students complete mathematics problems, but successful completion with AI assistance does not necessarily demonstrate independent mastery. Students need a learning environment that uses AI productively while deliberately developing durable, independent mathematical competence.

Step 3. Conduct a focused competitive analysis

The intern can examine systems such as:

ALEKS,
McGraw Hill Connect,
WebAssign,
Pearson MyLab Math,
WileyPLUS,
Knewton Alta,
ChatGPT Study Mode,
Khanmigo,
Gemini or other conversational AI tools.

For each system, document:

how it diagnoses student knowledge,
how it selects practice,
how it provides help,
whether it supports conversational tutoring,
how it measures mastery,
whether assistance is faded,
how it communicates progress,
how it supports instructors.

Deliverable

A short competitive-analysis report identifying:

strengths of existing systems,
important missing features, and
the unique design opportunity for this project.

6. Phase 2 — Build a Small Calculus-Readiness Skill Map

Suggested duration: 1–2 weeks

Step 4. Select the first 5–8 skills

Choose skills that are:

important for calculus,
commonly weak among students,
easy to diagnose with a small number of questions,
suitable for short AI-assisted remediation.

Step 5. Identify prerequisite relationships

For example:

\[
\text{Fraction Arithmetic}
\rightarrow
\text{Rational Expressions}
\rightarrow
\text{Rational Equations}
\rightarrow
\text{Calculus Applications}
\]

Another example:

\[
\text{Exponent Rules}
\rightarrow
\text{Algebraic Simplification}
\rightarrow
\text{Difference Quotients}
\rightarrow
\text{Derivatives}
\]

Step 6. Define mastery criteria

For each skill, specify:

what the student should know,
what the student should be able to do,
acceptable accuracy,
whether speed or fluency matters,
whether the skill must be demonstrated without AI,
what later retention check should look like.

A simple initial mastery model could be:

\[
M = f(A,I,R,T)
\]

where:

\(A\) = accuracy,
\(I\) = independence,
\(R\) = retention,
\(T\) = transfer to a new context.

The first prototype does not need a sophisticated mathematical mastery model. These categories can initially be tracked separately.

Deliverable

A small Calculus Readiness Skill Map containing approximately 5–8 skills and their prerequisite relationships.

7. Phase 3 — User Discovery

Suggested duration: 1–2 weeks

Step 7. Interview a small number of students

Approximately 6–10 interviews may be sufficient for the first discovery round.

Topics should include:

what students do when stuck in mathematics,
how they currently use ChatGPT or similar AI,
when AI explanations help,
when AI causes confusion,
whether they sometimes obtain answers without learning,
how they decide whether they really understand a topic,
how they feel about timed or AI-free mastery checks,
what type of feedback they find useful.

Step 8. Interview instructors if possible

Even 3–5 instructor conversations could be valuable.

Questions might include:

Which precalculus weaknesses most interfere with calculus?
How do instructors currently identify prerequisite gaps?
How has generative AI affected homework?
What evidence do instructors trust as proof of mastery?
What student information would they want from an AI learning system?

Step 9. Synthesize findings

The intern can create:

an affinity map,
key user needs,
pain points,
design opportunities,
a student learning journey.

Deliverable

A concise HCI research summary showing how real user needs influence the prototype.

8. Phase 4 — Define the Core Interaction Model

Suggested duration: approximately 1 week

Step 10. Design the assistance ladder

Instead of immediately showing a complete solution, the system could provide increasingly strong support.

For example:

Prompt the student to try again.
Ask a guiding question.
Give a small hint.
Give a more explicit hint.
Demonstrate one substep.
Show a related example.
Provide a full explanation only when necessary.

Step 11. Define fading rules

A possible sequence is:

\[
\text{Worked Support}
\rightarrow
\text{Major Hints}
\rightarrow
\text{Minor Hints}
\rightarrow
\text{Hint on Request}
\rightarrow
\text{No AI}
\]

Assistance should decrease as the student demonstrates competence.

Step 12. Define what happens after an error

The system should distinguish several possibilities:

careless error,
current-topic misunderstanding,
prerequisite weakness,
notation error,
conceptual misconception.

The response should depend on the likely cause.

Deliverable

A written interaction specification describing how the AI coach responds at each stage.

9. Phase 5 — Design the First HCI Prototype

Suggested duration: 2 weeks

Step 13. Create low-fidelity wireframes

At minimum, design:

diagnostic screen,
skill map,
learning/coaching screen,
hint interface,
independent mastery screen,
student progress dashboard.

Step 14. Consider two distinct modes

Learning Mode

AI encouraged,
questions encouraged,
hints and examples available,
students may explore multiple methods.

Mastery Mode

AI assistance unavailable or highly restricted,
new problems are presented,
performance contributes to independent mastery.

Step 15. Design the progress model

For example:

AI-Assisted Accuracy: 94%
Independent Accuracy: 82%
Recent Hint Use: decreasing
Retention: not yet checked
Status: Nearly Mastered

This distinction should be obvious to students.

Deliverable

A clickable Figma prototype.

10. Phase 6 — First Usability Study

Suggested duration: 1–2 weeks

Step 16. Recruit approximately 5–8 users

At this stage, the primary question is not whether the system improves mathematics learning. The question is whether students understand and can use the design.

Step 17. Give participants realistic tasks

Examples:

Get help without asking for the full solution.
Find out why an answer is wrong.
Complete a mastery check.
Determine whether a skill has been mastered.
Find which prerequisite skill needs more practice.

Step 18. Observe usability problems

Record:

where users hesitate,
what they misunderstand,
which controls they expect,
whether the distinction between learning and mastery is clear,
whether fading AI support feels reasonable.

Deliverable

A usability report followed by a revised prototype.

11. Phase 7 — Build a Small Functional Prototype

Suggested duration: 2–4 weeks

Only after the interaction design has been tested should substantial programming begin.

Step 19. Keep the technical architecture small

A first system might contain:

Student Interface
      |
      v
Learning State Manager
      |
      +---- Skill Model
      |
      +---- Problem Bank
      |
      +---- Student History
      |
      +---- Assistance History
      |
      v
AI Coach
      |
      +---- Diagnose likely error
      |
      +---- Select hint level
      |
      +---- Ask guiding question
      |
      +---- Explain concept
      |
      +---- Generate related example
      |
      v
Math Verification
      |
      v
Mastery Update

Step 20. Use AI only where AI adds value

Use ChatGPT API or Gemini for tasks such as:

conversational coaching,
generating explanations,
generating related examples,
classifying likely misconceptions,
personalizing language and feedback.

Use deterministic methods when possible for:

answer checking,
equivalent-expression checking,
mastery scoring,
time tracking,
problem selection rules.

Step 21. Build a controlled problem bank

For the first research prototype, it may be better to use a curated problem bank rather than allowing the AI to generate every problem dynamically.

This improves:

mathematical reliability,
experimental consistency,
difficulty control,
comparability between participants.

Deliverable

A functional prototype covering approximately 3–5 skills well.

12. Phase 8 — Pilot Learning Study

Suggested duration: 1–2 weeks

Step 22. Conduct a small pilot

A pilot of approximately 10–20 students can reveal problems before a larger study.

A possible sequence is:

\[
\text{Diagnostic}
\rightarrow
\text{AI Coaching}
\rightarrow
\text{Independent Post-Test}
\rightarrow
\text{User Survey}
\]

Possible measures include:

pre/post accuracy,
number of hints used,
time on task,
independent post-test performance,
student confidence,
perceived usefulness,
perceived frustration,
system usability.

Deliverable

A pilot report identifying what should change before a larger study.

13. Phase 9 — Main Comparative Study

This phase can come later and should not delay creation of the initial HCI portfolio project.

Possible experimental comparison

Condition	Learning Environment
A	Conventional ChatGPT-style AI assistance
B	Adaptive AI Learning Coach with graduated assistance and fading

Both groups would eventually complete the same AI-free independent assessment.

The central outcome is not:

Did students complete the learning activity successfully?

Instead:

Can students solve new problems independently after the AI-assisted learning experience?

Possible later retention measure

Students could receive another short test several days later:

\[
\text{Immediate Learning}
\rightarrow
\text{Independent Post-Test}
\rightarrow
\text{Delayed Retention Test}
\]

14. Phase 10 — Instructor-Facing Design

This should be considered a secondary component for the first project.

A simple instructor dashboard could show:

common prerequisite weaknesses,
students who are highly AI-dependent,
students who have demonstrated independent mastery,
skills with unusually high error rates,
students who may need human intervention.

For example:

Skill	AI-Assisted Success	Independent Mastery	Students Needing Support
Factoring	92%	78%	6
Rational Expressions	88%	64%	11
Function Notation	96%	90%	3

15. Future Extension: AI-Assisted Grading and Feedback

A natural second project would investigate AI-assisted evaluation of written mathematical work.

The system could eventually analyze:

\[
\text{Student Written Solution}
\rightarrow
\text{Mathematical Verification}
\rightarrow
\text{Rubric Evaluation}
\rightarrow
\text{Error Diagnosis}
\rightarrow
\text{Personalized Feedback}
\]

Rather than asking AI simply to assign a score, the system could evaluate individual rubric criteria and produce a suggested score with a confidence estimate.

Low-confidence or unusual responses would be sent to the instructor for review.

This creates a longer-term architecture:

\[
\boxed{\text{AI-Assisted Learning}}
\rightarrow
\boxed{\text{Independent Assessment}}
\rightarrow
\boxed{\text{AI-Assisted Grading}}
\rightarrow
\boxed{\text{Personalized Feedback}}
\rightarrow
\boxed{\text{Targeted Relearning}}
\]

16. Future Extension: Assessment and Online Exam Integrity

Another later research direction is how to verify independent student mastery in an environment where generative AI is readily available.

Possible approaches include combinations of:

timed mastery checks,
randomized but equivalent problems,
written reasoning requirements,
secure assessment environments,
identity verification,
short oral follow-up questions,
comparison of current work with prior demonstrated mastery.

The goal should not simply be increased surveillance. A more important research question is:

How can an online learning system provide credible evidence of independent mastery while remaining fair, practical, and respectful of students?

17. Suggested 10–12 Week Initial Schedule

Week	Main Activity	Primary Lead
1	Define scope, target users, and central research question	Both
2	Competitive analysis and literature scan	Intern
3	Create initial skill map and mastery definitions	Mentor
4	Student/instructor discovery interviews	Intern
5	Synthesize findings and define design requirements	Intern + Mentor
6	Wireframes and interaction-flow design	Intern
7	Clickable Figma prototype	Intern
8	First usability testing	Intern
9	Design revision and technical prototype	Both
10	Functional prototype and internal testing	Both
11	Small pilot with users	Both
12	Analyze results and prepare HCI case study	Intern + Mentor

18. Minimum Viable Project

If time becomes limited, the project can still be successful with the following minimum scope:

5 precalculus skills,
one small prerequisite map,
student discovery interviews,
competitive analysis,
Figma prototype,
adaptive hint/fading interaction design,
5–8 usability participants,
one small functional AI demonstration,
portfolio case study.

A complete LMS is not necessary for this project to be valuable.

19. Strong Portfolio Story for the Intern

The final HCI case study could follow this sequence:

\[
\text{Problem}
\rightarrow
\text{Competitive Research}
\rightarrow
\text{User Research}
\rightarrow
\text{Design Requirements}
\rightarrow
\text{Prototype}
\rightarrow
\text{Usability Testing}
\rightarrow
\text{Iteration}
\rightarrow
\text{Functional AI Prototype}
\rightarrow
\text{Pilot Evaluation}
\]

The portfolio narrative could emphasize:

Students increasingly use generative AI for mathematics, but successful AI-assisted performance does not necessarily indicate independent learning. We investigated how an AI Learning Coach could provide adaptive support while progressively fading assistance, then verify whether students could independently solve new mathematics problems.

This is a stronger HCI story than simply designing an AI tutoring interface because it connects:

an authentic educational problem,
user research,
learning science,
AI interaction design,
adaptive systems,
usability testing,
measurable learning outcomes.

20. Recommended Immediate Next Steps

Before programming anything substantial, complete these five tasks:

Select the first 5–8 precalculus skills.
Construct the first prerequisite skill map.
Define assisted proficiency versus independent mastery.
Have the intern conduct competitive analysis and initial user discovery.
Design and test the learning-to-mastery interaction in Figma before building the full prototype.

If these five steps are done carefully, the resulting evidence should determine which features are genuinely worth implementing.

21. Guiding Principle

The project should not ask how much AI can do for a student. It should ask how AI can help a student become capable of doing increasingly more without it.

This principle can guide both the initial HCI prototype and the larger long-term vision for AI-supported mathematics learning, assessment, grading, and personalized feedback.

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