... the last problem of a recent homework assignment on perimeter and area had insufficient data to solve the problem. One of the principles of geometric diagrams is that we never go by appearance. We solve using givens and proven facts. Since that particular diagram gave no indicators of equivalent length, bisection, 90-degree angles, etc, no conclusions could be drawn regarding the length of the side opposite the one measuring 15 units, or any other non-given length, without making unsubstantiated assumptions. We are miseducating children if we teach them, even indirectly, bad thinking habits. One of the purposes of math instruction is the logical and critical thinking skills it cultivates. And if we are as worried about high-stakes tests as we say we are, we will teach students to think properly. A favorite trick of bubble tests is to lead the students down a primrose path of faulty assumptions. If you would like discuss ways to help students learn to think, please let me know. I spent a lifetime teaching math, first to junior high and high school, and later, college students.The teacher sent a reply that seemed quite understanding, but showed that she somehow missed the point. She replied,

I completely understand what you are saying in the email. I also concur with what you said, however, I did verbally tell the students that angles that appear to be right are. ..However, if the student drew it out on the grid paper, then that student could find an area for the figure they drew. We are at an entry level with these problems, and so I looked at how the student drew the problem out, and determined if their area and perimeter matched that drawing.Then she asked for suggestions for helping students who are well below grade level. Am I the only one who found the reply disturbing? So I wrote back,

Thank you for your reply. "I did verbally tell the students that angles that appear to be right are." Angles that appear to be right are most decidedly not right just because of appearance. I really think that if the student's math level is lower, then it is all the more critical to precisely teach thinking skills. Drawing on grid paper does not really help, because it only pushes students harder to make unwarranted assumptions.I closed by repeating my offer to help. Then I got this curt dismissal:

Hi again, Thank you for your response, it seems that on this particular problem I did not satisfy your criterion and I am sorry to have let you down. Have a nice day.Okay, so she really does not want any help, I guess. And apparently she is happy to miseducate kids. I figured I would just move on, until....the school's guidance counselor contacted me, and let me know that she considers my communication with the teacher inappropriate and unprofessional. Seriously? She even challenged my right to have any conversation with the teacher by pretending that I was discussing a student, not a math problem. Now when I was teaching, the only time I passed communications on to administration was if it contained a personal insult of some kind, of course, a very rare occasion. Maybe it is unfair to extrapolate from one experience, but I assure you, schools routinely show contempt for parents, let alone the public, even the education-savvy members of the public. We must be careful that we as teachers refrain from thinking we get to define the terms of parental involvement. I know plenty of teachers who actually resent fully involved parents if those parents dare to challenge the teacher or the school. Then teachers vilify the parent as a "helicopter parent" in an ad hominem attempt to dismiss with contempt the parent's concerns. A lot of schools want to limit parent involvement to conferences and making cupcakes.