I received this email from Gary Davis with some very points in response to my post on student attention and justification of answers. I think the points are important and I want to pursue them when I have a little more time:
* The teacher (that's you!) said that many of the students showed serious misunderstandings of variables and constants and of fractions and the algebra tiles after he completed a unit. One might say that it comes from many years of rote learning in earlier grades.
* If he is their first teacher who is asking them to think and build their own ideas, it could be that they are in an early cycle of learning these mathematical ideas and need more experiences. We are also not sure by reading this about this particular teacher's expertise in guiding students in developing conceptual knowledge.
* He speaks about putting his foot down and insisting on justification. I'm not sure what that means to him. We have many teachers in our courses that know the buzz words and can talk the talk but when we go in to observe their classes, their actions do not match their words.
* The other thing he speaks about is the students being inattentive so the ways the students are engaged during different moments of his classes and how he handles this may also be factoring into the equation.
* I think it is common for parents not to understand this approach to learning and many teachers receive parent resistance. You remember I did too, when I was a teacher.