While in bed this "morning", I tried to do some math in my head two different ways: allowing myself to tense up, and not allowing myself to tense up.
tensing up: I multiplied 150 * 25. My first strategy was to break the numbers into prime factors: 3 * 5 * 5 * 2 * 5 * 5, but I couldn't see an easy way of combining them. Next, I converted the problem to 15 * 250, and then did 250 * (10 + 5), which was 2500 + 1250 = 3750.
not tensing up: I multiplied 71 * 35. My strategy was to imagine a whiteboard, and just do the problem "normally", writing 71 above 35, multiplying 5 * 1, then 5 * 7, and writing 355 on the top row, then adding a 0 to the next row and multiplying 3 * 1, then 3 * 7, and writing 213 in front of the 0, and then adding 355 to 2130 to get 2485. This was all trusting memory and instinct, so to confirm, I did the calculation again writing 35 above 71, and again got 2485.
Tensing up, I felt like I had more power to manipulate ideas. Not tensing up, I felt like I had to follow my instincts, but oddly enough, I felt like my "whiteboard" memory was pretty good, perhaps better. That is to say, I could imagine the act of physically writing on a whiteboard, and using the writing on the whiteboard as "memory", better while not tensing up.
I tried again just now, writing something on my mental whiteboard while tensing versus not tensing, and it does seem easier while not tensing. The difference seems to be that while I'm tensing, I want to store the information differently than on a whiteboard — I sortof want to have a more compressed, more "understood" representation of the information — whereas when I'm not tensing, I'm more ok with not understanding the information, and just writing it down, and following wrote rules of manipulation. That is, it sortof comes down to trust. When I'm tensing, I don't trust my mental whiteboard. When I'm relaxed, I do.. though I suppose I'm still not sure under which circumstance my mental whiteboard actually works better. It could be that it works better while I'm tensed, if I decided to try trusting it, and just seeing whether I got the right answer.