AI Generated Tools in the Mathematics Classroom

LLMs, Claude Artifacts & Custom Simulations

Who Am I?

Nathanael Reveal

Teacher of CS & Mathematics · MLK Magnet at Pearl High

  • Vygotskyan Social Constructivist
  • Luddite with an M.S. in Computer Science
  • 25 years of industry experience in data science
  • 18 months of teaching experience
  • Does not use AI in the classroom
  • Does use AI generated tools in the classroom

Agenda

  1. Large Language Models — What they are and how they work
  2. Claude Artifacts — Interactive content generation
  3. Custom Math Simulations — Explorations built with AI assistance

Part 1

Large Language Models

What is a Large Language Model?

A Large Language Model (LLM) is a tool for transforming one kind of language into another.

  • Learns statistical patterns across words and symbols
  • Can summarize, translate, and generate text
  • Examples: OpenAI ChatGPT, Google Gemini, Anthropic Claude

Deterministic vs. Non-Deterministic Behavior

Deterministic

Humans · Desktop software

Same input → same output

  • Ask a colleague a simple factual question
  • A spreadsheet formula is deterministic

Non-Deterministic

Humans · Gen AI

Same input → different output

  • Ask a colleague an open-ended question twice → two different answers
  • Prompt a model twice → two different answers

Language models are non-deterministic generators of probable speech.

What is a Feature Space?

Words aren't stored as definitions — they're stored as points in a high-dimensional space.

Every dimension captures some quality: gender, formality, concreteness, domain…

The model learns these dimensions by reading billions of sentences.

Where is "Queen" in the Feature Space?

What characteristics does the word "Queen" have?

Feature Embedding

Noun · Female · Monarch · Power · Wealth · Beyoncé

Feature Space Navigation

She advanced her pawn to the last row and said, "Queen me."

Feature Embedding

Verb · Chess · Game · Success

Probable ≠ Correct


Language models produce likely speech, not correct speech.

Our goal: increase the probability that likely speech is also correct speech.


Three levers we control:

  1. What you put in the context window — your documents, your exemplars
  2. How you explain your expectations — clear, specific, structured prompts
  3. What tool you choose — Claude Code

Part 2

Claude Artifacts

What Are Claude Artifacts?

Artifacts are self-contained pieces of content generated by Claude that live alongside the conversation:

  • Documents with text and mathematical formulae
  • Interactive HTML/JavaScript apps
  • Code files (Python, React, etc.)
  • SVG graphics and diagrams

Think of them as live outputs — not just text answers.

Why Artifacts Matter for Math

Traditional AI responses give you text and static code.

Artifacts give you running, interactive applications — instantly.

You: "Create a visualization of the unit circle"
Claude: [generates a live, interactive unit circle explorer]

No setup. No installation. No copy-paste.

What Artifacts Look Like

Type Example Use
HTML App Interactive graphing tool
Python Script Computation or simulation
SVG Diagram Geometric figure or graph
Markdown and Latex Structured proofs or solutions

Demo: Artifact in Action

Prompt:

"Build an interactive slider that shows how changing a, b, c affects the graph of y = ax² + bx + c"

Result:

  • Sliders for each parameter
  • Live graph update
  • Vertex and root labels
  • All in one browser window — no install needed

Pedagogical Power of Artifacts

  • Immediate feedback — students see changes in real time
  • Low floor, high ceiling — usable by all ability levels
  • Exploratory learning — "What happens if I change this?"
  • Teacher efficiency — generate a tool in seconds

Artifacts turn a conversation into a laboratory.

Prompting for Artifacts

Good prompts are specific and contextual:

❌ "Graph a parabola"

✓ "Create an interactive HTML app with sliders for a, b, c that graphs y = ax² + bx + c, labels the vertex and x-intercepts, and works in a browser"

The more context you give, the more targeted the artifact.

Part 3

Custom Math Simulations & Explorations

Beyond the Textbook

Static textbook diagrams show a snapshot.

Simulations show behavior over time and across parameters.

  • How does the period of a pendulum change with length?
  • What patterns emerge in the Collatz conjecture?
  • How does sample size affect the Central Limit Theorem?

Building Simulations with Claude

You don't need to be a programmer.

Describe what you want → Claude builds it.

"Create a simulation that shows how the sum of n dice rolls
approaches a normal distribution as n increases.
Include a slider for n and show the histogram updating live."

Example: Central Limit Theorem Explorer

A Claude-generated artifact can:

  • Simulate rolling n dice thousands of times
  • Plot the distribution of sums as a histogram
  • Overlay the theoretical normal curve
  • Allow students to drag a slider and watch the shape change

Students discover the theorem before it is formally stated.

Example: Transformations Explorer

Prompt:

"Build a tool where students can apply translations, rotations, reflections, and dilations to a polygon on a coordinate grid. Show the transformation matrix alongside."

Result: A full interactive geometry tool — in under 60 seconds.

Example: Slope Fields & Differential Equations

"Generate a slope field visualizer for dy/dx = f(x, y).
Let the teacher type in a custom function.
Draw solution curves that pass through clicked points."
  • Students explore ODEs visually before the algebra
  • No Desmos subscription needed
  • Fully customizable to your curriculum

Workflow: From Idea to Tool

1. Identify a concept students find abstract
2. Describe the interaction you want
3. Paste the prompt into Claude
4. Review the artifact — test it
5. Iterate: "Change the color scheme / add labels / fix the axis"
6. Embed or share with students

Total time: 5–10 minutes for a polished tool.

Tips for Better Simulations

Do Avoid
Specify input controls (sliders, buttons) Vague prompts like "make it interactive"
Name the output visuals explicitly Assuming Claude knows your layout preference
Ask for labels, axes, and units Forgetting accessibility (font size, contrast)
Iterate in the same conversation Starting over from scratch each time

A Growing Simulation Library

math5120.netlify.app

A collection of my personal custom-built explorations:

  • with Dr. Mary Dalton at APSU
  • Immediate goal is to cover the exercises of Dr. Jo Boaler's Mathematical Mindsets.

Teacher as Curator

Teachers build the tools — students use them to explore.

  • Verify mathematical accuracy before sharing
  • Test edge cases and boundary values
  • Decide what controls students need
  • Embed or link from your LMS

Students benefit most when they can focus on the mathematics, not on debugging a simulation.

Putting It All Together

Tool Role
LLM Explanation, tutoring, problem generation
Artifacts Interactive visualizations, instant tools
Simulations Deep exploration of mathematical concepts

These work together — and they are available today, for free.

Key Takeaways

  1. LLMs understand mathematics and can tutor, explain, and generate problems
  2. Claude Artifacts turn AI responses into live, interactive tools
  3. Teachers build and curate simulations — students use them to explore
  4. You don't need to code — you need to describe clearly and verify carefully

Questions?

Try it yourself:
claude.ai → New conversation → "Create an interactive math exploration of [your topic]"

Resources

Claude Documentation