Graduate School Help - What test do I run?

I am working on my independent action research project and need help figuring out what statistical test to use.

I am looking at how my students' waste management knowledge and behaviors change pre- and post- survey. Usually, when I have done something like this, I run a paired t-test since students put a student number on their survey which allows me to pair their pre-and post- test.

However, my instructor, since I don't have a control group, wants me to divide my class. She wants me to categorize the students by their responses to the pre-survey and test whether the students that had low levels of knowledge and waste reduction behaviors prior to the unit had greater/lesser change than the students that were already highly engaged in such behaviors.

This is how she explained my comparative question to me:
By including both knowledge and stewardship levels, you’ve got quite a few ways to look at it – one way could include these factors:
A – high knowledge, low stewardship
B – high knowledge, high stewardship
C – low knowledge, low stewardship
D – low knowledge, high stewardship

As for the comparative question, could it be:
How do pre-existing levels of waste management knowledge and responsible waste stewardship affect the impact of waste management lessons and activities on the knowledge and stewardship of sixth grade students?

So, with this information, I have absolutely no idea what kind of statistical test to use to do what my instructor is asking me to do.

I went through and grouped my students knowledge and behaviors into high, medium, and low levels. I haven't given the post-survey yet. But what test do you run when you are grouping students into levels to compare pre- and post-? How do you know which group of students actually improved the most/least from pre to post survey?
Ignoring the data is never a good idea. Data are money. You should not discretize and view the pre-test data as only 4 possible values instead of many possible values. A non-linear model linking post-test measurements to pre-test measurements would be more appropriate.