Cai has always had public speaking anxiety, but her new job will require her to be in front of large audiences on a regular basis. To deal with her public speaking anxiety, Cai begins offering her opinion at staff meetings and speaking at small group gatherings at her church. What method is Cai using to overcome her public speaking anxiety?

desensitizing herself.

Explanation:

Anxiety of public speaking, also popularly named as glossophobia, is one of the most recorded social anxieties. Signs of public-speaking anxiety are like those occurring for social anxiety disorder, but what makes them unique is that they only take place in the context of public speaking. Systematic Desensitization refers to a strategy of hierarchy used to manage anxiety or phobias based on changes in behavior. As per the question, Cai is speaking at small group gatherings at her church to overcome her public speaking anxiety.

Cai is using 'Learning by Doing' method to improvise her public speaking skills.

Explanation:

Cai has had issues like anxiety in public speaking. However, her new job requires public speaking skills.

So, by beginning to offer opinion at staff meetings & speaking at small group gatherings at church : She has adopted 'Learning by Doing' methodology.

Learning by doing is a theory by an educational american philosopher John Dewey. This learning approach involves :  learning taking place by learner being physically indulgent in practically carrying out the activity in reality,  rather than listening to lessons or lectures on the topic.

Cai could have learned 'public speaking' by attending communication enhancement classes or she could have directly started practicing public speaking in real. Instead of attending class lectures, she took the second alternative of actual real world practice, so she adopted 'Learning by Doing' method.