Can't learn how to learn

Last year, Bella had fabulous religion grades. I could always count on her to have an 'E' (equivalent of an 'A') in religion. This year, she has been having some problems, and I was trying to get to the root of them the other day.

We were studying for her religion test last week, and I knew that it was all material that had been covered last year, so I was fairly confident. Things like the Holy Family, etc. While I was quizzing her from the study guide her teacher sent home, I noticed she was agitated, and the agitated turned into being flat-out freaked out. She didn't know any of the answers, and she was getting very, very upset. So we took a breather, and I asked her what was wrong. This was her answer:

"Last year, we learned the answers in order and the test was in the same order and as long as we knew the order that was how we passed the test! But this year the answers aren't in order and I don't know how to learn them!".

Say whaaaaaat?

I had encountered this last year - we were studying for her religion test and I asked a question out of order and she recognized it immediately. "That's not in the right order! I only know them in the right order!" Panic ensued. I calmed her down and just asked her the questions in the right order and everything was fine. I didn't think about it at the time, but I now know I wasn't doing her any favors.

So I told her last week that it was no big deal, we would work on them together. And we studied over the week, and I thought she had the material down (it was only about seven questions) and then when the test came home, she got a 'D'. I'm not too worried about it at the moment, because it's early yet and we have time to work on it, but this concerns me.

She also freaked out about her math homework. They are doing fast math facts, where they have to just look at a problem and know the answer immediately. The other night we were working on numbers 1-9 plus 0 and 0-9 plus 1. I started asking her questions out of order again, and she lost it again. "I can't do it that way! That's not how we learned it last year!" I tried explaining that she is in second grade now, and that things will be different this year, but it was to no avail.

When I say she gets upset, she gets really upset. She cries, her breathing speeds up, and she is terribly agitated. It seems to really stress her out. And I'm not pressuring her, yelling at her or anything like that. Just a casual, "What does the word 'divine' mean?" and she falls to pieces. She doesn't do that with spelling words. I am at a loss.

My question is: how do I help her actually learn the material, not just memorize the answers?