Flirting

She doesn't look into my eyes when we talk

Last week one of my friends told me that a girl from my had been talking a lot about me to her friends. The girl was pretty, intelligent, funny so I decided to start talking with her, getting her number, etc.

So after texting each other for like 12 hours straight I noticed that she was the one who was trying to keep the conversation going for example:

Her: Going for my volleyball training. Kisses! :) [19h15]

Me: Have fun, kiss :p [19h15]

Her (ONE OUR LATER): Done training :)))) [20h15]

So at this point I noticed that she was definitely into me. On the next day I told her that I was going for a walk and I asked her if she wanted to join me, she said yes and after walking 10 minutes we sat down at a bench and we started talking (or at least we tried to).

The problem is that whenever she speaks she doesn't look at me. I was sitting next to her and she wouldn't even turn her head to me, she would just look at her cellphone and asking stuff to me and answering me without EVEN LOOKING AT ME. I found it really weird. Still she keeps texting me and stuff.

Is it normal?
She doesn't look into my eyes when we talk
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