Student X wrote:  

Given that nobody got the first question correctly on the midterm, and bearing in mind what you posted on your site regarding this matter, I was wondering if you could possibly consider throwing that question out.

Dr. Beeson replied:

Absolutely not.   That material was on the syllabus, on the practice midterm,  you were told it would be on the exam,  it was on the reading list,  you were told to take responsibility for ensuring that you could solve those problems.   If third-year students have to be treated like second-graders before they actually will study something,  it is definitely their own faults. I regret, to some extent, that I did not treat the class more like second-graders,  but $%^&,  you guys are only one year away from becoming professional people, entrusted with  building systems that society must rely on.   SOME of you must become algorithm designers!  Or do you want to leave those jobs to the people who went to Stanford and Berkeley and actually learned how to solve recurrence relations,  while you guys just are at the bottom of the totem pole and have to implement the algorithms those people design?
Your question perfectly illustrates the problem I am up against.  Your reaction to this situation is to hope that "it won't count".   I am telling you,  in the future with that attitude, somebody else will be the algorithm designer,  and you will just be the implementor.  Your reaction should instead be a decision to FINALLY  take the personal responsibility to learn this material.   Far from throwing this question out,  there will be another question testing the same skill on the final exam.   I hope that is clear.

Student X replied:

Perhaps instead some of us will become professors who actually teach what they test on. I can read the book or tutorials on this and learn it myself for free if I had to - instead of paying thousands of dollars for someone to suggest a topic I should go research. While I do understand where you're coming from, and for the most part I agree, you should also understand that if no student in two sections got a question right, maybe the problem is not with the students. I'm sure at least a few of the 52 people who got the question wrong put a serious effort into trying to understand it.

Dr. Beeson replied:

I devoted an entire week of class to this subject.  Monday,  September 28, and Wednesday, Sept. 30  I devoted 2.5 hour of class time to recurrence relations. I solved several examples at the board.  I then gave ONE problem on the midterm on this subject, hardly  a disproportionate amount of testing for two  class periods of material.   The accusation that I did not teach what I tested on  is completely unfounded.   I DID teach it.   You just didn't learn it,  and neither did any other student.    

Now,  what IS the root of that problem?   It is this:   I did not assign GRADED HOMEWORK  requiring students to PRACTICE solving recurrence relations. Why not?  Because,  although in the past homework graders were provided,  now there is no money for homework graders.  My time is fully occupied with  my other duties.  (I assure you I do not sit around toasting my toes by the fire during working hours.  Note that I am working right now, at 8 am on a Sunday morning.) I do not have time to grade 55 papers each ten pages long containing solutions of many recurrence relations.   And if students are not assigned GRADED HOMEWORK, they simply WILL NOT STUDY a subject.   Hence,  they did not study this subject, and hence they did not learn it.  It's very simple.   Frankly,  I resent your attempt to fasten the blame on me.

In regard to your comment that "I can read the book or tutorials on this and learn it myself for free if I had to - instead of paying thousands of dollars for someone to suggest a topic I should go research.":   I didn't suggest that you "research"  that topic.   I suggested instead that you "study" that topic.   That is,  actually practice the methods I showed you in class on ten or twenty examples until you were confident that you could solve such problems.  Now,  I repeat that suggestion.  I suggest that you study this topic in time for the final examination.

Dr. Beeson to the class:

  Student X says "I'm sure at least a few of the 52  people who got the question wrong put a serious effort into understanding it." That is a question that can be empirically tested.   Can any student produce written solutions of ten to twenty different recurrence relations, testing different values of a,b, and f in the recurrence relation T(n) = a T(b n) + f(n), written out before the second midterm exam?   If so I would like to see those solutions.  I will add to this posting later, telling whether or not any student came forward to demonstrate their serious effort. The midterm question had a = 3 and b = 2/3, with f constant, not a particularly esoteric case, and one occurring in the textbook exercises.