The Big Revelation, the Wisconsin context, the equation True or False test

The Big Revelation
I'm glad that Beth asked today how a second grader managed to get to second grade without being taught any strategies. This is actually pretty huge. I thought all of the video children had just been pulled from a regular classroom and asked to solve a word problem or two. Instead they are quite used to solving word problems. This doesn't change whether I think a child of a certain age or grade could do division or multiplication, but I didn't know that context. They have always seemed very comfortable turning to the manipulatives and/or white boards. When I work with my third graders, I have been disappointed that they haven't found my word problems as easy to navigate as the children in the videos.

The Wisconsin negative temperature context
While living in a cold climate could certainly build the concept in children's minds that there ARE such things as negative temperatures, I do not think it explains the familiarity in any way. The difference in temperatures would have to be so extreme like -50 F or 50 F for the negative to have a lot of impact. 14 F and -14 F are both extremely cold. All that said, I haven't grown up in a climate like that. Maybe parents really do go "Oh, 31 F? Just your winter jacket will do. But -5 F, hmmn, yeah, wear all your winter gear." Instead I'd suggest that they are exposed to negative numbers in their classroom.

4 = 3+1 and 3+2=5+1=6 Problems
I was really baffled by the class's response and YOU, Dr. Shih! About these problems. Very puzzled. I realized that I was relating to the questions very differently. HOWEVER: if you get out of it that they think number sentences can only be written one way... Excellent! Fine. The reaction of doing 5 + box = 11 is good.

To me that was the extent of the value of this test/survey. 5+2=3+4 works for me. I understand the idea behind it. It really is a matter of notation and symbols. Even the 3+2=5+1=6, I understand where it is going. If it is bad to think or teach that way, fine, message understood. But if I gave all of my third graders this tomorrow, I wouldn't make much of their answers. I just quizzed my wife over it. It was interesting to me that she would not accept 12 as a possible answer in 8+4=Box+5. She would accept it as less incorrect than 33 or another number, but to her, it was very wrong.

To put it another way. If I gave children 3i = 6... what do I really expect? If I gave it to my classmates what would I expect? It's not that meaningful unless you have been studying the i notation/operation (if that's how you want to approach it. And if it isn't i, then 3! = 6 which I think is 3x2x1 or it's an excited 3 that is so thrilled to be a 6.