These four interacts were created for an experiment on advanced mathematical thinking. Some teachers may find them useful for an abstract (modern) algebra course. I am moving away from researching math education, so I figure I should open these files up to the world to at least make it possible some of this work will go to use. I'm sorry for the sparse comments; if you have any questions, I can probably answer them.
These interacts are setup for a SageMath notebook. For each file without an extension, its contents can be copied into one of the notebook's worksheets by clicking on a worksheets edit button and saving the text there. Alternatively, the text for the interacts (inside the triple curly braces starting with "@interact" in the files for the interacts) can be copied on its own into a worksheet cell. Some files (like interacts 1 and 4) will need the code for the attached files (near the top) to give the path for the relevant sage file. The file labeled problem4.sage doesn't run in polynomial time, so I put limits on the number of factorizations it could find. For each problem number, the first problem of problem set a (in the LaTeX files) uses the interact (with the same number), and the second problem is given in full in problem set b. The files in the folder labeled experiment are for the original experiment. If for some reason you are interested in the experiment, it would probably be better if you get the entire set of .sws (worksheet) files from me in a zip, so you can upload them to Sage all at once (I can also get you more info on the concepts behind the experiment). To get the project working properly you would need to follow the directions in the section labeled organization at the end of the read me. This section is also the key for interpreting the randomly assigned ids each page has.
Theory:
Each student completes 3 randomly selected problem sets with the condition (a being a baseline control, b being standard treatment type control, and c being the experimental condition) randomly selected for each. Since I don't want to assume students can TeX, as much of their work is written as possible. The quality of proof for the second question, the amount of time spent on it, and the amount of time spent total on a problem set (both recorded in this program) are the DVs. Each type of problem will be collapsed across the 4 problem sets (three for each student) for analysis. My hypothesis is that the conjecturing problem will be as valuable to the final proof, as a standard method, compared to simply doing a two problem problem set with the problems 'unrelated'.
Organization:
To configure these worksheets correctly: make sure all the problem and problem set worksheets other than interacts are published; record the new URLs (they seem to be randomly given when uploading the worksheets from a zip) based on the Worksheets' name (I only use the second URL for the published worksheets). Now type the URLs into the urls array near the top of the javascript for the "Experiment Home" page in the order corresponding to the order given below. Then record that worksheets URL and put it in for the URL on the fourth line. You may want to adjust the three right most entries (currently 5000) of the timeLimits array (last item in the variables section) to 1000 each for testing purposes.
Problem 1.1a
WS Title: First Problem (id# 71171) Type: conjecture, system of congruence Current URL: http://localhost:8000/home/admin/7/
Problem 1.1b
WS Title: First Problem (id# 39760) Type: proof, system of congruence example Current URL: http://localhost:8000/home/admin/18/, http://localhost:8000/home/pub/5/
Problem 1.1c
WS Title: First Problem (id# 86869) Type: proof, factor 7^24-1 Current URL: http://localhost:8000/home/admin/6/, http://localhost:8000/home/pub/6/
Problem 1.2
WS Title: Second Problem (id# 57268) Type: proof, System of Congruence Current URL: http://localhost:8000/home/admin/14/, http://localhost:8000/home/pub/7/
Problem Set 1a
WS Title: Problem Set (id# 81465) Type: system of congruence: conjecture, proof Current URL: http://localhost:8000/home/admin/20/, http://localhost:8000/home/pub/8
Problem Set 1b
WS Title: Problem Set (id# 73447) Type: system of congruence: proof example, proof generalization Current URL: http://localhost:8000/home/admin/4/, http://localhost:8000/home/pub/9
Problem Set 1c
WS Title: Problem Set (id# 92810) Type: system of congruence: other proof, proof Current URL: http://localhost:8000/home/admin/19/, http://localhost:8000/home/pub/10
Problem 2.1a
WS Title: First Problem (id# 01554) Type: conjecture, continued fraction Current URL: http://localhost:8000/home/admin/0/
Problem 2.1b
WS Title: First Problem (id# 24102) Type: proof, Euclid's Algorithm and the Fibonacci Sequence Current URL: http://localhost:8000/home/admin/15/, http://localhost:8000/home/pub/11/
Problem 2.1c
WS Title: First Problem (id# 25555) Type: proof, mersenne prime Current URL: http://localhost:8000/home/admin/9/, http://localhost:8000/home/pub/12/
Problem 2.2
WS Title: Second Problem (id# 59332) Type: proof, Continued Fraction Fibonacci Current URL: http://localhost:8000/home/admin/12/, http://localhost:8000/home/pub/13/
Problem Set 2a
WS Title: Problem Set (id# 90478) Type: Continued fraction, fibonacci: conjecture, proof Current URL: http://localhost:8000/home/admin/26/, http://localhost:8000/home/pub/14
Problem Set 2b
WS Title: Problem Set (id# 56934) Type: Continued fraction, fibonacci: related proof, proof Current URL: http://localhost:8000/home/admin/23/, http://localhost:8000/home/pub/15
Problem Set 2c
WS Title: Problem Set (id# 11303) Type: Continued fraction, fibonacci: other proof, proof Current URL: http://localhost:8000/home/admin/22/, http://localhost:8000/home/pub/16
Problem 3.1a
WS Title: First Problem (id# 39022) conjecture, number of divisors Current URL: http://localhost:8000/home/admin/1/
Problem 3.1b
WS Title: First Problem (id# 18363) Type: proof, divisors square-free Current URL: http://localhost:8000/home/admin/8/, http://localhost:8000/home/pub/17/
Problem 3.1c
WS Title: First Problem (id# 47844) Type: proof, n chooose k Current URL: http://localhost:8000/home/admin/17/, http://localhost:8000/home/pub/18/
Problem 3.2
WS Title: Second Problem (id# 87588) Type: proof, number divisors Current URL: http://localhost:8000/home/admin/11/, http://localhost:8000/home/pub/19/
Problem Set 3a
WS Title: Problem Set (id# 00477) Type: number of divisors: conjecture, proof Current URL: http://localhost:8000/home/admin/25/, http://localhost:8000/home/pub/20
Problem Set 3b
WS Title: Problem Set (id# 49909) Type: number of divisors: square free, proof generalization Current URL: http://localhost:8000/home/admin/24/, http://localhost:8000/home/pub/21
Problem Set 3c
WS Title: Problem Set (id# 68110) Type: number of divisors: other proof, proof Current URL: http://localhost:8000/home/admin/21/, http://localhost:8000/home/pub/22
Problem 4.1a
WS Title: First Problem (id# 58031) Type: conjecture, factors in 4Z Current URL: http://localhost:8000/home/admin/5/
Problem 4.1b
WS Title: First Problem (id# 22674) Type: proof, factors in 4Z Current URL: http://localhost:8000/home/admin/16/, http://localhost:8000/home/pub/23/
Problem 4.1c
WS Title: First Problem (id# 90985) Type: Pythagorean triple Current URL: http://localhost:8000/home/admin/10/, http://localhost:8000/home/pub/24/
Problem 4.2
WS Title: Second Problem (id# 44530) Type: proof, Factors into 2 in 4Z Current URL: http://localhost:8000/home/admin/13/, http://localhost:8000/home/pub/25/
Problem Set 4a
WS Title: Problem Set (id# 65112) Type: Factors in 4Z: conjecture, proof Current URL: http://localhost:8000/home/admin/29/, http://localhost:8000/home/pub/26
Problem Set 4b WS Title: Problem Set (id# 35970) Type: Factors in 4Z: related proof, main proof Current URL: http://localhost:8000/home/admin/28/, http://localhost:8000/home/pub/27
Problem Set 4c
WS Title: Problem Set (id# 14877) Type: Factors in 4Z: other proof, proof Current URL: http://localhost:8000/home/admin/27/, http://localhost:8000/home/pub/28