i think the record keeping is a good idea- it helps to be objective. I tend personally tend to beat myself up over how i interact with people, I'm not always quite sure if it's irrational or not, (like sometimes it's over small details). It's important to see if there is a relationship between what actually happens and how we feel about it. And the therapist can help to say what's ok and what might be irrational.
Keeping tabs is about being committed to helping yourself & the process. And it also gives you a record of your attempts, and it can be something you reflect on and try to improve a little each day- and if lo and behold you have a positive interaction, it's a good thing to look at (because we do tend to overlook our accomplishments). It's important to do things the way your counselor says because if we could do everything right on our own, then we wouldn't have had issues to begin with. And also too, it helps the therapist to know when does the anxiety kick in and what reactions you have (what you feel physically, how you feel emotionally, and what goes through your mind consciously.) and begin the process of tying those reactions into behaviors, and if you become aware of these things specifically, you can start to find ways to change them into something more positive.
(I've started to keep a record to help with my gambling issues (which is heavily related to my anxiety and times when i feel rejected), and for me, every day I don't gamble is a good day, so maybe everyday you can say hi to someone can be a good day?)
An assignment like that would terrify me to the bone. It's like I can't say hi to friends sometimes (like if i see them from afar in a pubic place), let alone strangers (but then again, you wouldn't have to see them again so it might be easier).
I really commend you for being willing to take on the assignment!! Let us know your results! (I think it's important to realize how many people don't run away screaming or freak out.)
And in response to gardnerj, (sorry this is long... you don't have to read it hahaha) that's part of the problem is that we are emotional beings. We need a little bit of detachment from our emotions to see what's really going on, because emotions can distort that image- especially the negative things we feel about ourselves. So sometimes a little flow chart of how things are going is helpful to see. Also too, if you try for 20 people and get 5, that can still be pretty good. If you try for one, and can't get one, at least for me, i'd feel like a total failure... it could make for too much pressure- like i wouldn't be able to stop thinking about all day who i would say hi to, and if i did say hi to someone, then i would immediately retreat back into my shell right afterwards. I think maybe that's the fear- is that we will immediately go into old habits. And if the interaction goes wrong, we only have one thing to base it off of... and we wouldn't know if that was a typical or atypical reaction to us. And hey, if you are able to say hi to a new person each day, let us know how it goes!
(sorry for the fatty post
... i am really not good at being concise... i need to work on that :/)