I think he was enraged that he was failing her class. In my experience as a math teacher, I never had a student who was completely checked out mentally from class whom I did not flunk for almost total lack of math proficiency. I think most nonteachers as well as any teachers who have not worked in both low academic standard and well as high academic standard schools would not understand how deficient in math Chism would have been in comparison to most of the other students at Danvers.
I checked on Chism's previous schools in Tennessee online. As just one indicator (I don't care to discuss the others since it would likely lead to inflammatory political discussions) their test scores are bad, really bad. Having worked in those types of schools I can tell you for a fact that both the academic and behavioral standards are low. The academic content, especially in mathematics, is watered down to the point that the courses have almost no resemblance to their description in the state curriculum guides. By watered down course content, I mean that not only are key parts of the course not taught, but easier topics from earlier levels of math are substituted and what is taught is not approached with proper depth or rigor.
In my school, instead of teaching actual algebra in algebra, most of the teachers were teaching how to manipulate fractions and basic arithmetic for most of the term. This meant they never got to the actual topics of algebra like completing the square, factoring equations, the quadratic equation. Or they only covered some of these topics in a shallow and cursory manner. This meant that most of the algebra II teachers then were teaching algebra i material. Worse, the students still could not do basic arithmetic or manipulate fractions so the algebra ii teachers were still teaching this. Calculus was a complete watered down joke that resembled nothing like any authentic calculus course. This is the math program at schools with low academic standards. Education in these schools is something that George Orwell or Ayn Rand would have imagined and then written in a book people would have read as a piece of fiction.
But the lack of academic rigor does not stop there in these types of schools. There is also a great deal of grade inflation occurring. By this I mean that students are often not required to complete homework for accuracy. Instead they usually receive full credit on their homework for "effort", which does not even mean real effort. If the student simply copies a few homework problems (that can be incomplete and incorrect) on their paper but does not even bother to make "effort" on all the problems, that is considered sufficient as effort and they get a 100. I have seen this over and over. It is standard practice in those types of schools because the administrators want the students passed on not flunked back. Of course, there are exceptional teachers who do not go along with this but they are the exception that proves the rule.
It does not end there. It is not uncommon at these schools for students to be allowed to take the same test over and over until they pass it. This mainly happens in math. I was required to allow students to take tests over and over an unlimited amount of times. This of course meant that some (maybe most) of them had no incentive to study for their test since they just figured that maybe they would get lucky and pass and if they didn't, well, they got a free look at the test and would get as many other tries as they want. Often, the teachers are also required to weight homework heavier than test and quiz grades so that would virtually ensure almost everybody would pass automatically regardless of genuine effort or competence in the subject.
So Philip Chism came from schools like that. Then after years of watered down academics and grade inflation, he suddenly has to hit the ground running academically at a school that had much higher academic standards. Unless you have seen what I have seen, you can't imagine how academically unprepared he would have been. The subject that would have been the most difficult and the most impossible to catch up in would have been math. The real world is not like the movie Stand and Deliver that pretended kids could gain math proficiency in only a year because the math teacher was so great. That was never what Jaime Escalante did and the movie twisted the truth into a terrible lie to make an exciting movie. The truth was far less glamorous. The truth was that Escalante and his principal arranged for the feeder schools and courses for calculus to be beefed up so that a select group of capable students could succeed in his calculus class.
In real life, students like Philip Chism do not catch up in math quickly. They struggle for a long time. As Chism's math teacher, Ms. Ritzer would most definitely have been very aware of how severely deficient he was in math even if she didn't have the experiences to understand why.
Just as one example of this, I was discussing the low standards at our school with a parent once, the parent suddenly exclaimed, "Oh! My nephew used to go here and had all A's without ever doing any work. He was so lazy. Now he is at S.C. (a suburb school out of the county with much higher academic standards and exactly the kind of "good" school I was describing to the parent as a contrast to ours) and he is flunking almost everything except now he is really trying. I mean he is really trying and he just can't pass." I replied, "You've got it."
Currently, there is an epidemic of students who go to college believing they are academically prepared only to find that they place into remedial math or English, which they proceed to flunk repeatedly before dropping out of college. Their prior academic experiences in k-12 left them not only unprepared for real academics but with an unrealistic perception of their competence and abilities.
Philip Chism and his mother would have easily believed that he was much more academically advanced than he really was and may have also had an inflated sense of his intelligence. When he found himself to be behind academically at Danvers he would have been shocked, afraid, and distressed. He might have felt that the world came off its axis. Nobody besides Philip himself, God, and Colleen Ritzer would have understand how seriously deficient he was in mathematics.
She singled him out for staying after school because she understood how severely deficient he was in math. By the first week of school I generally knew which students were struggling. Even a clueless teacher would know by week three. They were several weeks into the school year so she would have known absolutely that he was academically in serious trouble. She was motivated by being a good teacher not by some lascivious intentions. Nobody with any ability to read people could look at her or read her postings and think she was other than a well intentioned and good hearted person.
But Philip could have still felt anger and hatred toward her. It it not uncommon for students and their parents to be angry or enraged at the teacher when the student is doing poorly academically. They will even tells lies about the teacher, tell lies about themselves, blame the teacher and try to get the teacher in trouble. Of course, they don't generally try to kill the teacher but then Philip Chism is not every student. He probably has some underlying pathology that just needed to be awakened.
I am not saying that rage at Colleen Ritzer over failing at math was his only motivation for the crime, but I think it was a distinct possibility and one of several contributing factors. Who knows with somebody who is a powder keg what the ignition might be.
P.S. Not only are there marked differences between how Danvers and his previous schools performed on their state assessments for academics but that is true within a larger picture in which the two states have marked differences in the proficiency required on those tests. This makes the performance disparity even more meaningful. You can check the state test scores at GreatSchools and I found this online which specifically names the two states in question.
From:
http://educationnext.org/few-states-set-worldclass-standards/
"Comparing the States
Three statesMassachusetts, South Carolina, and Missourihave established world-class standards in math and reading as the goal for all students. Every other state has established a lower proficiency standard, and some states (for example, Georgia and Tennessee) declare most students proficient even when their performance is miles short of the NAEP standard."
In other words, Danvers High School scores very highly on its state assessments of academics within a state (Massachusetts) that has some of the highest performance standards among all states. On the other hand, Chism's former school scored poorly on its state assessments of academics within a state (Tennessee) that has THE lowest performance standards among all states. According to the website, Tennessee has the worst standards of all 51 states and the District of Columbia. Naturally no school can get away with flunking the majority of its students so each state is giving a lot of passing grades. The difference is that the school in Tennessee is passing a large proportion of students who have no academic competence. The students do not know this and neither do their parents so they have a false sense of competence.