Hi potential advice givers

Context

I am undertaking a study in mathematics educations, one of the aspects which involves exploring the impact of different teaching approaches on student persistence. The intervention involved three different classes of students (i.e., Grade A, Grade B, Grade C), each of which experienced a distinct type of teaching approach. 

Prior to the intervention (pre-program), I assessed students on their willingness to persist and collected the following data (the numbers represent the number of students in each category):

Pre-program data

Teaching approach        Not willing to persist          Willing to persist     Total

Approach 1 (Grade A)              13                                     11                   24

Approach 2 (Grade B)              4                                       17                   21

Approach 3 (Grade C)              4                                       17                   21

After the intervention, I assessed students again:

Post-program data

Teaching approach        Not willing to persist          Willing to persist     Total

Approach 1 (Grade A)              8                                     16                   24

Approach 2 (Grade B)              7                                     15                   22

Approach 3 (Grade C)              5                                      16                  21

What I would like to know

My research question: Does teaching approach impact on student's willingness to persist, once we account for prior willingness to persist (i.e., pre-program data)?

I know we can use ANCOVA to account for pre-program performance, however obviously not when the dependent variable is categorical. Does anyone know what analysis I can run? Can I use chi-square, and somehow alter the expected counts for the post-program analysis so they reflect the distribution of persistence apparent in the pre-program data (i.e., rather than the expected accounts reflecting the null hypothesis that post-program persistors should be randomly allocated across teaching approach)?

Thanks a lot!