It must always begin with organic thinking

Interesting! You are right; every math project starts with organic thinking. In general, organic thinking might be defined as free-flowing, intuitive exploration that connects ideas. Do you know a simple definition about the organic thinking?

Well i agree with you and add that learners need to stretch the mind first before interacting with AI. This means that as they develop organic thinking we only introduce AI in bits and strategically. Full blown AI is a cognitive mess. Out come would be dependency in thinking and programmed thought .

High school students can effectively use AI computational tools for math projects by integrating them into the research, exploration, and presentation phases. Here's how they can do it:

1. Problem Exploration and Idea Generation

AI Chatbots (like ChatGPT): Ask for math project ideas based on interests (geometry, algebra, calculus, etc.).

Example: "Give me a math project idea involving real-world applications of quadratic equations."

2. Concept Understanding and Tutorials

Use AI tools to explain math concepts step-by-step.

Example: "Explain how to use matrices in real-world problems."

3. Data Analysis and Visualization

Tools: Wolfram Alpha, Python (with NumPy, Matplotlib), GeoGebra, Desmos.

Use AI to generate data sets or simulate models, and visualize patterns or graphs.

Example: Analyzing the growth of a population using exponential functions.

4. Code Writing and Automation

Use AI tools to help write and debug Python code for mathematical simulations or algorithms.

Example: Writing a script to solve a system of equations using matrix operations.

5. Proof Assistance and Verification

Ask AI to verify steps in a proof or suggest alternate methods.

Example: "Check this proof of the Pythagorean Theorem for logical consistency."

6. Presentation and Report Writing

Use AI to draft reports, format equations in LaTeX, or create slides with clear explanations and visuals.

Example: "Create a presentation slide summarizing the use of calculus in predicting motion."