I am not doing that

Yesterday, I worked with the child who told me she did not want to be taught anything.  In fact, if you remember she did not want to learn anything.  We worked longer because she was not ready to quit reading.
I told her yesterday that we were going to add math to our tutoring.  No, we are not was her reply.  I explained that it would not be math like she thought it would.  I used a dry eraser board to show her the new concept.  We only did 5 cards on the board.  I did not use the packet of cards as it would have overwhelmed her.  It is using triangle flashcards.  I drew a triangle on the board.  An example is 5 plus 3.  5 goes in one bottom corner and 3 in the other bottom corner.  The 8 goes in the top of the triangle.  As I wrote I explained that we were making a picture with math so she would be able to remember it better. 
I asked her what 5 plus 3 was and then replied 8. Working one on one or one on two, I can do this and it does not allow her to fail.  I do not know how this would work in a classroom.  After I did 5 plus 3 and 3 plus 5, I did 8 minus 5 and 8 minus 3.  Then I covered up a corner and did them again.  This does not take long.  I did not use the balance board as I had to hurry and sneak this in and she was not going to expose herself to be considered dumb. Next time I will try balance board and flashcards.  I also asked her to do tangrams.  She refused as these are really hard for her.  I did not push this as I had already succeeded with one new concept she was not comfortable did not want to lose the positive.  I allowed her to draw on the board and ignored her while I worked with another child.  I will need to work one on one with her with the tangrams as she learns how to do them.  I will also need to be gentle so she lets her guard down enough to have the confidence to learn. This is sometimes hard as I can let myself tell her to obey when she appears rude instead of listening to what she is really saying when she says, "I am not!"