What concepts and content should students learn from this activity?
- Understand and experience mathematical pattern by the computer experiment.

How is MATLAB utilized in this activity and how does this improve student learning?
- MATLAB is used for computer experiments for large number of cases of a conjecture.

Are there higher-order thinking skills (e.g. critical thinking, computation, data analysis, synthesis of ideas, model development) that are developed by this activity?
- Finding patterns, conjecture certain rules, and verify them are typical activities in mathematics. This lab is intended more experimental level (analytic level needs more background and skills) of those activities so that any grade level can start with.

Are there other skills (writing, oral presentation, field techniques, equipment operation, etc.) that are developed by the activity?
- We used this project as a group project. As a result, students had an opportunity to compare the result and discuss about their finding, and cross check each other. Naturally, they developed how to reject a certain wild guess (a wrong conjecture) - by finding a counterexample!

The educational level, class size, institution type, etc.
- We used this for a class who are mainly freshmen (1st year) at Minnesota State University. My class size was 18 students.

Is it a lab, classroom activity, or a longer project? How much time is needed?
-It is intended for a 75 minutes computer lab. However, one can easily expand it to use a week long project, or an undergraduate research project for a semester.

What are the technical skills and experience with MATLAB the students need to complete this activity?
- Students only need a readability of the Matlab code. (They no longer do a coding by themselves, at least for basic level, due to the generative AI.)

Are there other disciplinary skills or concepts that students should have already mastered before encountering this activity?
- Basic logic skill. It is designed to develop a pattern finding from computer experiments.

How is this activity situated in the course? How easy (or hard) would it be to adapt the activity for use in other settings?
- It is one of the core part of the course. As it is an open project without a definitive answer, instructor can adjust the difficulty level.

Describe the technical skills and experience with MATLAB the students must have mastered before the beginning of the activity:
- Students should expose basic MATLAB syntax and ability to read a simple MATLAB code. It is not necessary for students' coding skill. However, we found that basic debugging skill would be a big plus for the project. This lab can be done in other popular programing language, such as Python.

This is an open conjecture (no one proved or disproved yet!) and hence there is no definitive answer for the project. It is rather intended that students explore and discuss how to discover/generate an interesting patterns through a computer lab experiment.

Depend on the available time, you may assess in several different ways:
1. If one like to close in one single lab, ask each group present their experiments and findings orally. Some group may like to show certain patterns in picture form.

2. If you can bring it to a week long or longer project, you may ask a short technical report of their findings/ experience in a certain guided format.

Here are some references for Experimental Mathematics:

1. The Computer as Crucible: An Introduction to Experimental Mathematics, by J. Borwein and K. Devlin, 2008, AK Peters

2. Experimental Mathematics in Action, D. Bailey, 2007, AK Peters

3. Experimental Mathematics: A Computational Perspective, M. Richey and M. Wright, 2025, AMS