I am still observing. Yesterday and today I saw something that seems recurrent, so I have to comment/ask. In a process of solving a problem my teacher gets to:
Or, let's have even simpler example:
She proceeds to multiply 6 and 50, and then divide by 3. I saw identical process in the first classroom that I observed. In fact, kids (9 grade, I believe, possibly even 10) there couldn't do things like -4-2 or 7*3 without a calculator (the latter we figured out, and then two minutes later we had 8*3 in a problem and the student couldn't do it even after I reminded her that she knew 7*3). The teacher there said "Their mental math skills are terrible"?! I wouldn't call that mental math. Should I? Regardless of what we may call it though, I was terrified. I still am.
Back to my examples, I can understand using the long process when teaching it, but this was not an introductory lesson. Why do the teachers not use the "shortcuts"? Is it out of some consideration for the students? Do they think the students can't handle it? Or they'd be confused? Or is there some other explanation?