The buzzing B

And nonplussed

The end of each semester is a time for reflection and renewal. The school term is over, the new term has yet to begin, and the days are free for contemplation, consideration, and ... complaining students. You can always count on the student who learned the “squeaky wheel” adage better than he learned the subject matter. He imagines that his grade is negotiable and fails to note that no negotiating is actually occurring. It can take weeks for the spate of wheedling communiqués to peter out.

If ever there was a time to consider a grading scheme where if the majority of your exams are A's including the final you get an A. My dad said he got a math teacher to bump him up a grade by doing a card trick.  Are you game?

Family legends and Rudyard Kipling notwithstanding (“If you can make one heap of all your winnings and risk it on one turn of pitch-and-toss”), skill at sleight of hand does not translate into grade points in my class. Sorry about that. He moved on to plan B:

My grandmother would give an A if you got an A on the final but maybe she gave harder finals or something.  

Not to criticize the young man's sainted grandmother, with whom I should never be confused, the old girl was offering her students the ancient “sucker bet” routine. I've seen it often enough before. It's deadly.

When an instructor tells a class at the beginning of the semester that grades will be based on either an overall average or the final exam score, whichever is best, a significant minority of the students immediately falls into the trap: I just need to do well on the final. That'll be enough! Of course it never is. Most such students begin slacking off in that class in order to concentrate on other courses or activities. More immediate concerns take over because I just need to do well on the final. They dig the hole deep, taking comfort in the thought that a single Olympian jump at the end will permit them to escape their subterranean situation, even as they neglect the exercises that would make the feat feasible (and, more to the point, unnecessary, because they would be earning the points that would put them into a position to pass without a miraculously redemptive performance on the final exam).

I never offer my students the sucker bet. My student was undeterred.

Just curious now; did anyone else get two A's on exams and an A on the final and still not get an A?  Is there anyone I can commiserate with or is this an anomaly?

Although misery may love company, privacy considerations intervened. I answered him:

Yes, there were two other students, so it wasn’t exactly an anomaly. It was a matter of getting relatively low A’s that were counterbalanced by lower grades, preventing the composite score from being in the A range. You’d be welcome to commiserate with them, but privacy concerns forbid me from sharing their names. —Z

My student kept harping on his “majority” argument and insisted on ignoring the relative strength of his scores. The semester grade was a weighted average of six scores: one for homework and quizzes, four chapter tests, and one final exam. The composite score was computed thus:

Comp = 0.15*HQ + 0.70*E_average + 0.15*Final

My diligent correspondent had a low A for HQ, a high C for E_average, and a low A for Final. His Comp result was 83.4. That's not A territory. Interestingly, he kept his focus on the exams and ignored the HQ result. Thus his argument was, in effect, three A's on five exams should work out to an A in the class. But here are the exam scores:

Exam 1: 90, Exam 2: 80, Exam 3: 95, Exam 4: 54, Final: 92

That's right: He outright flunked Exam 4. It's really tough to be an A student when you flunk an exam, especially that severely. This never figured into his arguments, for obvious reasons. He fussed over the weights. The final wasn't worth enough! Sorry, but short of going the “sucker bet” route it could hardly ever be worth enough to suit his purposes. Besides, I had already sweetened the pot by building some bonus points into the final exam's grading scheme, giving a perfect paper a value of 105 instead of a mere 100. In reality, his 92 on the final was 87.6%. I had already cut everyone as much slack as I intended to.

He had one more card up his sleeve:

Is there nothing that can be done... a test I can take to challenge?

Lord have mercy! Can you imagine? I tried to be nice:

No, there isn’t anything. If you think about it a little bit, you’ll realize for yourself there couldn’t be any after-the-fact exam that students could take to tweak their grades. Otherwise the college would spend the first several weeks of summer vacation giving the special exams to students who were unsatisfied with the outcome of the semester. Six of your classmates who earned B’s did better than you; ten did more poorly. You earned an unambiguous mid-range B in the class, a good solid grade. —Z

It did not satisfy him. I received one more lengthy message in which he noted his regular attendance, active participation, his “majority” of A's, and his work ethic. “It seems that for one reason or another, I end up coming up short somehow.”

The main reason, as best as I can tell, is that you're a B student whose grades range across the spectrum from A to F. It's not mysterious.

I'm sure you're tired of this by now.

Quite.

One page at a time

The importance of packaging

He seemed smart enough, but he was an extremely unreliable student. He confided to me that he was under treatment for an anxiety condition, but his therapy had clearly not resolved his problem. Still, he started off the semester by powering through the lessons and it looked like he would be all right in the long run.

But looks can be deceiving. His scores on the exams eroded steadily throughout the term, and the erosion was eating away at his chances of passing the class. We met during office hours. We conferred after class. He e-mailed me questions, which I tried to answer promptly. Nothing worked. On top of all that, anxiety feeds on itself, so his emotional condition was not improving.

Of course, we tried that old stand-by of extending his time and letting him linger over the exams, but there was no significant pay-off. The situation was desperate—and so was he.

Despite decades of teaching, I was slow to recognize the significance of an anomaly in my student's performance. Although his exams were increasingly disastrous, his quiz scores remained persistently decent, hovering between B's and C's. It was nearly too late when inspiration finally struck me.

“We're going to do something different on the last chapter test,” I told him.

My announcement did not please him. He mistrusted change. However, he was docile enough and desperate enough to cooperate with whatever I wanted to try.

“I will dole out this exam to you one page at a time,” I continued. “You won't get page two until you return page one to me. If there's time at the end of your extended period, you can ask for individual pages back, but only one page will be on your desk at a time.”

His eyes widened. “It'll be like quizzes!” he said. “A series of quizzes! I can do quizzes!”

“Yes, you can,” I agreed.

On exam day, we followed the one-page-at-a-time protocol rigorously. He never had multiple sheets of paper simultaneously on his desk. When I graded his exam, his score soared into the nineties. I was both astonished and gratified. It had worked ever so much better than I had dared hope.

We did it again on the final exam. He broke discipline this time and filched old pages from my desk when he came up for new pages. I noticed that he sometimes had two or three pages on his desk. He did a lot of flipping between them, making clear to me for the first time what he had been doing on the exams when he had crashed and burned. The one-page approach permitted him to stay focused. Under its restrictions he couldn't compulsively jump back and forth between problems, aborting each solution before he finished. I began to monitor him more closely when he came up to swap pages.

Although he never had the entire final exam on his desk at one time, his occasionally divided attention cost him and his final exam result was not superior. Nevertheless, it was good enough to secure him a passing grade for the course, much to his (and my) relief. He learned a new way to manage his difficulty in expressing his knowledge.

And, obviously, I learned something, too.

Stay of execution

City College gets an extension

The biggest community college in California will not have to shut its doors this year. All of that work in preparing a schedule of classes for fall 2014 was not in vain. As announced this week, the Accrediting Commission for Community and Junior Colleges is promulgating a rule change that will grant the City College of San Francisco a two-year extension in its efforts to resolve the deficiencies identified in the college's most recent accreditation reviews. The San Francisco Chronicle hailed the news with a front-page headline and a detailed article by Nanette Asimov, who has been closely documenting the years-long story.

The innocent bystander may be unaware that the arguments in the City College controversy were as much about the deficiencies of the accrediting agency as they were about the college itself. Make no mistake: City College had plenty to answer for. The ACCJC found that City College was deficient in its planning, accounting, and management processes. The institution's teaching mission was threatened by its inability to track its assets, collect student fees, and address developing needs. Furthermore, CCSF had been warned about its shortcomings in a previous accreditation process but had not bothered to correct them. The college was begging to be disciplined.

Unfortunately for everyone, including itself, the ACCJC proceeded to demonstrate its own inability to manage a difficult case. It imposed the death penalty on CCSF and then stubbornly refused to cooperate with the attempts to implement an emergency rescue of the institution. Nothing underscored this more clearly than the ACCJC's insistence it could not grant an extension even after the federal Department of Education released a stated confirming that it could. As Asimov reported

Last month, [commission President Barbara] Beno and commission Chairwoman Sherrill Amador and Vice Chairman Steven Kinsella refused to extend the revocation deadline despite public assurances from Lynn Mahaffie, a senior accrediting director with the Department of Education, that federal regulations permitted doing so. Nevertheless, the full commission, which meets just twice a year, changed its policy during its meeting June 4-6 in Sacramento. The agency is private and details about its internal decision-making aren't known.

Despite the Chronicle headline, “victory” is too sanguine a conclusion. City College has a lot of work to do before it can be considered fully compliant with ACCJC accreditation standards which other community colleges (like my own) are required to meet. At least the reprieve gives it the opportunity to continue the process under the new leadership that took over in the midst of the debacle. I also expect a painstaking internal review by the ACCJC of its punitive practices. At least, I hope so. If the ACCJC fails to do so, it is merely mirroring the failings of the institution over which it sat in judgment. Anyway, the internal review is necessary in terms of self-defense. Rigorous external review will be imposed by California's state legislature and the Department of Education, so the ACCJC had better get ready.

God's not at all well

The belabors of Hercules

Yes, I slipped in to see God's Not Dead the other day, looking about suspiciously at my fellow movie-goers. It soon became apparent they were there for the Kool-Aid. When Josh Wheaton asks Professor Radisson, “How can you hate someone who doesn't exist?”, the guy a few seats over from me went “Oh, yeah!” Because, you know, it was such a brilliant and devastating riposte to the professor's expressions of disbelief. Theists refuse to believe that anyone actually lacks belief in God; atheists are all sort of pretending, I guess.

The movie has already undergone many trenchant analyses and deconstructions and, yes, it really is an awful piece of tripe. Its cloying earnestness seems to me to be unselfconscious, indicating that the movie's creators are genuinely shallow and lacking in the power of self-reflection. Smug certainty has destroyed their capacity for critical thought.

Since there's no great need for me to add redundant criticisms, let me instead offer some points related to my personal perspective as a college professor, the false notes that regularly pulled me out of the motion picture and made me keenly aware that I was watching a religious tract.

Kevin Sorbo depicted Professor Radisson as a self-important authoritarian, a dispenser of “truth” who hates to be questioned. Such professors are not unknown in academia, but they are rare. Most of us like students to think about what they are told, to question dogma and to discuss these matters with classmates and instructors. Of course, the movie could have merely chosen to depict one of these curmudgeonly professors as a device for conveying a lesson—except in this case it's less of a lesson and more of an unrelenting harangue.

I nearly laughed out loud at the end of the scene involving the first day of philosophy class. The professor adds Bertrand Russell's Why I am not a Christian to the reading list for the next session. Apparently the students had already been assigned David Hume on “The Problem of Induction” (presumably an excerpt from An Enquiry Concerning Human Understanding) and Discourse on the Method (Discours de la méthode) by René Descartes. How often does the class meet? This is a daunting reading list even assuming the students have a week in which to plow through it. Perhaps Radisson had distributed a syllabus in which only certain pages were indicated for the week's reading, but his addition of Russell to the list carried no such limitation. I can imagine the screenwriter congratulating himself on using Russell's book as Radisson's shot across Wheaton's bow: “Heh, heh. This'll raise the audience's hackles! Even though most of them won't know who Russell is, the title will do the trick!”

No one has commented, to my knowledge, on Radisson's office. Although it's made clear that he is considered the prohibitive frontrunner for the position of department chair, he has yet to achieve that status. Nevertheless, his office is large enough to serve as a hangar for a 747 and his desk is long enough to land jet fighters. Radisson must work for one of the most prestigious and most richly endowed universities in the western world. It's like those television sitcoms where impoverished young people live in deluxe apartments while subsisting on ramen and cheap beer. I was most impressed.

Dean Cain's character could have been ripped from the pages of an Ayn Rand novel. Unbelieving and self-absorbed, “Mark” has no time for altruism. He is a “superman” who rapidly sheds any inconveniences that arise between him and his goals. His girlfriend develops cancer? Ex-girlfriend! His mother descends into the fog of Alzheimer's? Time to forget her just as she's involuntarily forgotten him! (Of course, when Mark is hectored by his sister into paying Mom a visit in the nursing home, Mom manages to emerge from her dementia just long enough to deliver a lucid little sermonette to shame her unbelieving son. A miracle!)

The subplot depicting the Arab girl who converted to Christianity was especially disturbing. Of course, her Muslim father beat her and ejected her from the house. We got to see him cry afterward, so I imagine the movie producers felt they had gone the extra mile in humanizing the devout believer in a false religion. (See, kids! This is how you behave when you follow Allah instead of Yahweh!) I managed not to hoot aloud when a close-up revealed that the girl had been listening to lessons recorded by Franklin Graham. Franklin! A pale imitation of the real thing, but apparently good enough to cost a young woman her family and her home.

I won't dwell on the ghoulish ending, which was embarrassing in the extreme. When the preachers were crouching over the dying Professor Radisson, I was half-expecting them to sprout vampire fangs, they were so eager to sink their teeth into him. Instead I want to point out the ridiculousness of the final scene in Radisson's philosophy class. Since it was foreordained that Wheaton had to win, humiliating his atheist professor, it was impossible that the end of the debate would offer any surprises. And it didn't. Right on cue, the Asian boy who had befriended Wheaton was the first to rise to his feet to declare “God's not dead!” and Wheaton the winner. But then every single student stood up and joined the chorus. Really? Every student? I watched closely, looking for the students who would stubbornly keep their seats, rolling their eyes at their suddenly faithful classmates—all of whom had been willing only a few weeks before to scrawl their names on God's obituary. I didn't see a one.

Fake, fake, fake. Nothing short of a fire drill or the end of class will get every student to pop up from his or her desk. My neighbors in the movie theater may have noticed I was chuckling, but so were some of them. Perhaps they thought I was participating in their joy at Wheaton's David-vs.-Goliath triumph.

Nope.

The template student

When thinking is too much trouble

My exams seldom contain surprises, but my students' answers do. Since I'm a firm believer in keeping track of student progress with frequent quizzes, I telegraph my punches. Students have plenty of opportunity to discern what facts, techniques, procedures, and calculations I deem the most important. (They also—most of them—learn the importance of regular attendance so as not to miss these pre-exam rehearsals.)

Of course, some students take it too far. These are the students who have had the unfortunate educational experience of intensely patterned teaching to “the test.” These are also the students who badger me for “practice tests” in advance of each exam. What do they want? Problems that are exactly like the ones they'll encounter on the exam.(I presume I'm permitted to change the numbers a little bit.)

What surprised me most this past school year was the discovery of this tendency among my calculus students. I was used to seeing it in my lower-level classes like algebra, but in multivariate calculus? An example of the behavior of the template-driven student will suffice. You'll see the problem, even if the terms are mysterious.

On a quiz I asked multiple questions about the gradient of a function of two variables. In part (a) I asked them to compute the gradient and evaluate it at a given point. In part (b) I asked them to use the gradient to compute the directional derivative in a given direction. In part (c) I asked them to calculate the greatest possible value of the directional derivative. In part (d) I asked them to find the direction in which the greatest possible directional derivative would occur. Pretty standard stuff.

On an exam I asked my students to (a) compute the gradient of a function of two variables and evaluate it at a given point. No problem. In part (b) I asked them how large the directional derivative could be? Several students were thrown for a loss. They wanted to compute a specific directional derivative, but instead I was asking them for its maximum possible value. There was no way they could do what they wanted to do because I had not provided a direction, so they made one up. They had memorized the pattern in the quiz and insisted on replicating it exactly on the exam. Since I had, in effect, swapped (b) and (c), they were deeply perplexed and forged ahead with the moves they had learned by rote.

Embarrassing! It wasn't a very large number of students, but I had been hoping they had been weaned away from this tendency by the time they arrived in the calculus III class. I learned otherwise.

Brain damage!

Explaining students

Two of the greatest minds in pedagogy recently came together to ponder some of the profoundest educational conundrums of the era. Or, to put it more prosaically, I called up a former student of mine for a chat. I, of course, hold a prestigious tenured professorship at a California community college. He is a lecturer in English at an out-of-state university. No, we are not universally recognized as the leading experts in our respective fields, but we figure that's mostly the fault of other people. Whenever we talk, we quickly reach agreement in our perspectives and opinions. It immediately follows that the many deficiencies in modern education must stem mostly from a failure to sufficiently adopt our preferred policies and emulate our instructional practices. Just listen to us! It's really quite a pity that so straightforward a solution to so many problems continues to languish unrecognized.

However, we should accept the need for a modicum of caution. There is an unfortunate gap in our grasp of the educational enterprise. Upon comparing notes, PiD and I have come to the unhappy realization that our immense intellects have yet to figure out what makes our students go. (Or not go.) It's perplexing!

For example, I told my entire algebra class that our mastery of the quadratic formula meant that we would never again face a quadratic equation for which “no solution” was a satisfactory answer. Solutions would always exist, whether rational, irrational, or complex. Always! Yet on the next exam several of my students labeled some of the quadratic equations as “prime” and solemnly wrote “no solution” in the answer blank.

PiD advised his English composition class that rewrites were a fundamental component of composition and that course grades would rely much more on their diligence in rewriting and improving their essays than on generating sparkling first drafts. As the academic term progressed, several students asked him how to get better grades. “Have you submitted rewrites of all of your essays?” he asked. “We didn't know we had to do that!” they told him. “But the due dates for rewrites are on the syllabus and I send out e-mail reminders as the dates approach!” “Yeah, but we can't know those unless we look at the syllabus or check our e-mail. You should have told us in class.” “But I did tell you in class!” “Well, maybe. But did you check that we were in class that day? I'm too busy to come to class every day, you know.”

A student wrote me a note in response to a problem on the calculus final exam. The problem asked, “What is the area inside the circle r = 3 and outside the cardioid r = 2(1 – cos θ)?” My student wrote, “Failed because I forgot the eq. for a circle in polar coordinates.” Um. Did you notice? The problem said, “the circle r = 3”?

The great minds of the age crumple in defeat.

Perhaps I did not sufficiently recognize a learning opportunity of my own from decades ago, back when my intellect was forming and a famous educator was trying to teach me some vital lessons.  William H. Cosby, Jr., Ed.D. (1976, UMass, Amherst), discovered these clues during highly personalized field research on his own family. Perhaps our students, like Cosby's children, are led into irrational, disturbing behavior by brain damage. It would explain so much!

If only I had paid more attention back then.

Lesson unlearned

College crisis by the Bay

The example of the accreditation crisis at City College of San Francisco is being cast as an important lesson to those involved in higher education. I fear, however, that not everyone is learning the right lesson. Consider, for example, the unfortunate Rafael Mandelman, first elected to the CCSF board of trustees in November 2012. He joined a board in upheaval. The Accrediting Commission for Community and Junior colleges had rejected the college's self-study report and application for reaffirmation of accreditation. Instead, the ACCJC had issued a “show cause” decision at its June 2012 meeting, which meant that CCSF had one year to show why it should not be shut down. Five months were already gone when Mandelman was elected to his board seat. By the time he was sworn in as the board's newest member in January 2013, two more months had gone by and the deadline for CCSF's response to the ACCJC was looming.

On March 15, 2013, CCSF submitted its Show Cause Report to the accrediting commission in hopes of having made its case for the college's continuing existence. In June the ACCJC met and in July the commission revealed that it had voted to terminate the college. CCSF had neither resolved the deficiencies identified in the 2012 evaluation nor demonstrated sufficient progress toward alleviating them. Barring dramatic developments, the college would close after its spring 2014 semester.

Trustee Mandelman, of course, had minimal impact on these developments. Not only was he the board's junior member, the entire board had been subordinated to a special trustee selected by the statewide community college chancellor. The dysfunctionality of the board had been highlighted in Recommendation 14 of the ACCJC evaluation, so the board was not being trusted to devise its own solution; adult supervision had been imposed. Even that, however, had not been enough to save the school. Understandably frustrated, Mandelman expressed his outrage in an opinion piece published in the July 21, 2013, edition of the San Francisco Chronicle:

If the Accrediting Commission for Community and Junior Colleges is correct and City College has failed over the past year, there is plenty of blame to go around.

But I do not agree that City College has failed. There have been missteps, to be sure, but the facts do not support [California Community Colleges Chancellor Brice] Harris' portrayal of a recalcitrant institution resisting change. Rather, they show one that has moved quickly to bring itself into compliance with accreditation standards.

That real progress has been made over the last year is evidenced by the report of the accrediting commission's visiting team, which indicates that although work remains to be done, significant progress has been made in each of the 14 areas cited.

“Significant”? Perhaps. But obviously not deemed “sufficient” by the accrediting commission members. A dozen of the deficiencies had been previously identified in the ACCJC's 2006 evaluation of the college. Accreditation was reaffirmed, with a reasonable expectation of resolution of the problems by the time the 2012 cycle rolled around. Instead, the ACCJC found continued neglect and added two more deficiencies, producing the new baker's-dozen-plus-one recommendations. (In one of the more amusing responses to the lack of progress by CCSF, one of its exponents commented that it was never clear that CCSF could not just take it or leave it when it came to “recommendations.” But one should not take an Internet comment as representative of the college's understanding of the imperative nature of ACCJC recommendations.)

The list of recommendations constitutes a strong bill of indictment against CCSF, even when rendered in buzz-word summary form by the college itself in its Show Cause Report:

The College has focused its attention on responding to all 14 current Recommendations over the past nine months by:

• revising and focusing the College Mission Statement (ACCJC Recommendation 1);
• creating a more effective, integrated, data-informed planning process with the Mission Statement and Program Review as central mechanisms for decision making that promotes institutional effectiveness (ACCJC Recommendations 2 and 3);
• engaging in a comprehensive, College-wide effort to centralize the documentation, reporting, and assessment of SLOs [Student Learning Outcomes] that informs institutional planning (ACCJC Recommendations 2, 3, 4, 5, and 6);
• identifying and implementing changes to the delivery of student services to better promote student achievement and access by all students, regardless of location (ACCJC Recommendations 2, 3, and 5);
• developing more efficient administrative structures with greater authority and accountability (ACCJC Recommendation 7);
• improving the management of physical resources, including the development of a model to determine total cost of ownership (ACCJC Recommendations 2, 3, and 8);
• creating a comprehensive plan for equipment maintenance, upgrade, and replacement (ACCJC Recommendations 2, 3, and 9);
• improving the College’s financial stability, integrity, and reporting (ACCJC Recommendations 2, 3, 10, and 11);
• developing and implementing a new Participatory Governance system that is efficient, serves an advisory function, and promotes transparency (ACCJC Recommendations 12 and 13);
• and providing the Board of Trustees with opportunities to realize fully their appropriate role and responsibilities (ACCJC Recommendation 14).

No wonder that CCSF could not adequately address all of these deficiencies between the “show cause” ruling in June 2012 and the response submission in May 2013, especially given the shortcomings in the college's planning and administrative processes.

While CCSF remains accredited through the current academic year, the negative impact of the accreditation ruling is already evident. Student enrollment is dropping and open staff positions are difficult to fill. Trustee Mandelman is ready to place the blame:

What City College does not need are stern lectures or threats, from Brice Harris or the commission. What it needs now is time: time to continue to address the real problems the commission identified last year and the ones they missed; time, frankly, to recover from the damage that the commission has done.

Chancellor Harris's people have been in place during the past year attempting to bail out CCSF, but Mandelman does not appreciate Harris's frank acknowledgment of the college's shortcomings. Almost all of the deficiencies have been on the record for half a dozen years while the powers-that-be at CCSF took a mañana approach to addressing them, but now there is no tomorrow.

I might point out that Dr. Harris is probably the best advisor and overseer that CCSF could hope for. When he was chancellor of the four-college Los Rios district based in Sacramento, Harris steered all of his schools through three rounds of accreditation with no significant findings of deficiency and numerous commendations. It's worth listening to him.

I have yet to mention a side-issue which some people in the CCSF community may be contemplating with undue optimism. The ACCJC has long been regarded as more draconian than other regional accrediting agencies—and there's evidence to support the charge, especially given the higher rates at which the ACCJC imposes sanctions compared to other regional accreditation agencies. The U.S. Department of Education has slapped the ACCJC with its own list of deficiencies. The unduly optimistic are therefore celebrating the treatment of the gander in accordance to what it inflicted on various geese. 

In brief, the Department of Education cited the ACCJC for lack of clarity in providing institutions with due process and in appropriately constituting its evaluation teams. The commission's responses to these shortcomings should make future evaluation cycles a little more civilized. However, there was nothing in the Department of Education's recommendations (there's that word again!) to suggest that previous accreditation decisions were so flawed as to require review or revocation. CCSF has to play the cards it was dealt.

The college needs to acknowledge more frankly the stark reality of what occurred: Its problems do not stem from the arbitrary decision of a star chamber tribunal populated by faceless bureaucrats. In reality, an evaluation team of peers—staff, faculty, and managers from other community colleges—visited CCSF and found it wanting. The peers reported to the commissioners of the ACCJC—who are also peers recruited from the ranks of community college faculty and management—and the commissioners concurred with the findings of deficiency. Until your peers agree that you're doing a good job, you're probably not.

The twelfth hour

And even the eleventh hour is too late!

May flowers are supposed to follow April showers. Well, an even more reliable sequence is the arrival of plaintive e-mails after the publication of semester grades. Here's one from a student who missed a passing grade by half a percentage point. Yes, sometimes I round up an average score of 69.5 and assign a student a C, but only when that average includes a solid passing score on the comprehensive final. This poor student, however, did not pass the final.

Professor is there any way possible to retake the final or to roll up  the .5 of the grade? The last half of the semester were very difficult for me, I have encountered family hardships and fell ill. I know it is not an excuse but it would mean the world to me as so much depends on it. I am truly sorry to put you in such a situation. I'm just lost and I'm pleading for some help. I'm just hoping you can assist me in my situation. Again thank you very much for your attention, I am glad to have a professor who is willing to lend a helping hand.

It's a poignant missive, but much too late. We do strive to provide reasonable accommodate for hardship cases, including deadline extensions or makeup exams when illnesses or other emergencies intrude into a student's academic program. We can't, however, do a darned thing about it after the fact. And, in his case, there had been no hint of any difficulties during the semester itself. Only now, when it was too late. I replied to his message.

It's an intriguing idea, but absolutely forbidden by the college rules. No mitigation or revision is permitted after semester grades are assigned. It’s a strict but necessary regulation. Otherwise we would face a constant onslaught of students seeking to improve their grades by post-semester work.

I tried to let him down gently, explaining that his best option was to retake the class immediately, thereby taking advantage of what he had learned while he still retained it. The summer session sections of the course were already fully booked, but I contacted one of the summer instructors and explained why my student was in need of last-minute enrollment in summer session. He consented to add my student, going above the enrollment limit, so I passed the word along.

Dr R has promised to let you into his summer session class. Be sure to show up on Day One!

My student, whose fall enrollment at the University of California appears to be contingent on his passing this class before he gets there, was relieved to learn he had an option to fulfill the requirements of his UC transfer agreement:

Thousand thanks Professor you just made my day, thank you so much!!! Again thank you !!!

A happy ending? That remains to be seen. But he's got a shot.

Brain pain

Lesson unlearned

My students were not happy with me and they weren't keeping it a secret. After a unit on scientific notation, I gave them a quiz containing a question they deemed terribly unfair:

The mass of a proton is 1.7 × 10^–27 kilograms. What is the total mass of 7.2 × 10³³ protons? (Write your answer in scientific notation and include the units.)

I was told, with exquisite care and patronizing precision, that it was wrong of me not to tell them which arithmetic operation was expected. Addition? Multiplication? Subtraction? Division? How dared I give them numbers without specific instructions!

With professional patience, I waited out their lengthy complaints. Then, without saying a word, I turned back to the chalkboard and wrote out a brand-new problem:

The mass of a nickel is 5 grams. What is the total mass of 6 nickels?

With frowns still on their faces, they blurted out, “Thirty grams!”

Another long silence as I waited for their reactions. The faces went neutral. One brave soul ventured a comment: “Were we supposed to know that?”

“Sure,” I replied. “All of you know that you multiply to solve problems like this. You just yelled out the answer to the nickel problem because it was so easy. What I'm trying to get across is that numbers written in scientific notation are still just numbers. You work with them just like you work with other numbers. You're letting your minds shut down because they look different, but you actually already know what to do.”

A smug expression is bad pedagogy, so I maintained a mild and neutral mien. I was quietly satisfied that I had gotten an important point across. My self-congratulation was just a little premature. (You'd think I would know better by now.)

A student in the back row grunted in dissatisfaction and posed a question in an irritated tone: “So on the next exam are you going to tell us what to do with the numbers?”

My spirits fell a notch.

“What do you think?” I asked.

I hope indeed that they do.

Self-diagnosis

This ought to hurt a little

It usually happens right after the first exam of the semester. Somewhere between one third to two thirds of the class is disappointed with the results. Nearly everyone expected an A or a B. Many are surprised they earned a C, D, or even an F. I give an assignment:

Send me an e-mail message by noon on Wednesday that contains two things:

1. A description of what you think went wrong on your exam and why you didn't score better.
2. A description of what you plan to do to deal with the problem(s) described in #1 and how you're going to do it.

Except for the few fatalists who signed up for the class in full expectation of miserable failure (why are they even there?), the students tend to take the assignment seriously. Interesting and often thoughtful responses come in:

I think part of my reason for scoring so low was I didn't thoroughly double check my work. I missed a good amount of points by not double checking that I knew answers to, or just wrote down wrong but still knew the right answer to.

An excellent observation. We have a long class period and I allow my students the entire time for the exam. They have ample opportunity to review and check their answers. Getting out the door before the class period is over is not a good priority.

I skipped the last two sections of the chapter so I didnt get enough practice with the word problems. I also made a lot of simple mistakes that could have been avoided if I would have checked my work carefully.

Self-knowledge. A beautiful thing. The next step is to actually do something about it.

I didn't push myself hard enough to finish all chapter homework. which would of help me master solving linear equations, inequalities and problem solving ect.

Indubitably. Hardly anyone succeeds without practice, and that's what the homework is for. Thanks for noticing.

I think my problem for the test was I didn't study enough.

Yes, I do recommend the practice of studying. Do please give it a try.

1. I think what was wrong with the exam and why I got such a low score was the fact that I barely got any sleep. 2. Study more, go to bed early, and be more prepared. Also I should try to understand certain problems more

Okay, I think you raise some good points. People do better on exams when they are well rested. However, I sense an element of denial. Of the last five class days, you missed three. See the problem?

Plus or minus

Rather missing the point 

One of my favorite negative reviews on RateMyProfessors.com is the following:

I don't understand why people say he is a good instructor. Many students in his class struggle to get a good grade. yes he is clear but his tests are extremely difficult. And expect a ton of repetitive homework assignments.

Let's deconstruct my student's complaint piece by piece:

Many students in his class struggle to get a good grade.

Yes? You mean they don't get good grades automatically? The student in question was enrolled in a calculus class. Such classes are notorious for easy grades, right? Yeah, right. More to the point: In a typical college class you can expect a distribution of grades, most of which are C's. Not what I would call “a good grade.” Good grades are A's and B's, earned only by those students who put in the effort.

[E]xpect a ton of repetitive homework assignments.

I checked. The syllabus contained homework assignments for each section with, typically, 12 to 20 problems. There were 33 sections that we covered, so students were expected to solve approximately 500 problems over the course of a 16-week semester, or a little over 30 exercises per week. (My bleeding heart weeps for them.)

Funny thing: There is a remarkably high correlation between doing the homework and getting one of those good grades. There were thirty students in the class. I note that only one student in the top half of homework performance was not earning an A or a B (and that one student was pulling a solid C). Of the fifteen students in the bottom half of homework performance, only four had “good” grades (three B's and one A [there's one in every crowd]). Conclusion: Do the work, get a good grade.

[H]is tests are extremely difficult.

Evidently not the case for those who work at it by doing the “repetitive” assignments. (Average scores were actually in the low eighties.)

yes he is clear

Thank you very much. Clarity is something I strive for and I am pleased that you noticed.

I don't understand why people say he is a good instructor.

Indeed you don't.

Must be present to win

A cry for help

One of my students—let's call him “Dick”—sent me a distressed e-mail. He was not doing well in class and was hoping for some wise words of guidance from his teacher. His semi-coherent message ran thus:

hey Dr.Z dick here,
hey i wanted to run over a little bit of questions, 1.please tell me if there is anything you can pinpoint from my work that i can work on to develope the grasp of this sections.i do not want to fail and sometimes i feel i can grasp it then sometimes i fail it.i do not want to fail this class i meet with tutors every week twice and home tutors and i can do decent but cannot prove my worth on every other test.im using the dropin ctr efficiently...any help you can recommend i do not want to lose my financial aid as it is viable to my continued succession.i can retake the course next semester as a retry but do not want to receive a W as it may discontinue my aid as well..
dick,

I often reply immediately to such messages, both to reassure the student and to prevent them from getting lost in the in-box maelstrom. Students benefit most from timely feedback. This time, though, I sat on my hands and just stared. And stared. And walked away from the computer.

Dick was in class the next day. I asked him to see me at the end of the period. He dutifully approached me as his classmates filed out of the room.

“I got your message, Dick, but I have to say I'm puzzled. Isn't it obvious what you need to do?”

“Huh? I'm trying everything I can, Dr. Z!”

“Even attending class? You routinely miss one class session per week and you often skip two. I'm less impressed about the frequency with which you meet with tutors if you don't attend actual class sessions.”

“Well, uh, sometimes I can't make it.”

“So it seems. But if you can't attend class, you can't reasonably expect to pass it. And where is the work you're doing with your tutors? I didn't see any homework from you for the last two chapters. So far, in fact, you've missed about thirty percent of the homework and quizzes. You'd barely be passing if you got perfect scores on the remaining seventy percent, but you're nowhere close to that.”

Dick had nothing to say, but he was nice enough to look embarrassed.

“Dick, I was astonished by your message, especially since it should be perfectly obvious that you desperately need to come to class and pay attention to the lessons. You can't skip out on a third of our sessions and survive. Few students could get away with that. I need to see you in class, on time, every day for the rest of the semester. That's my advice.”

He nodded his head. He even showed up the next day. Two days in a row. That's good! I wait to see if he makes it to three, which has occurred before—but rarely.

One thing sticks in my mind, though. Dick was clearly surprised—startled, even—at my advice. The notion of actually coming to class regularly had never occurred to him.

Too cool for school

No royal road to algebra

Although its hours have been trimmed by the current state budget crisis, my college's Tutoring Center continues to serve as a lifeline for many of our students. Each semester, therefore, I make a point of ensuring that my math students are aware of the facility's existence. I don't just tell them, I show them. Thus it was once again that, during the second week of the semester, I gathered up the entire class and took them on a “field trip.”

It puzzled my students when I announced it, of course. I told them to leave their books and papers behind in the classroom, which I would lock behind them. We would take a few minutes to stroll down the sidewalk to the Tutoring Center, which was only a couple of buildings over. Short field trip. Once I mentioned where we were going, some students nodded their heads in comprehension, grasping my purpose. Other students, however, had a different reaction.

One came up to me, backpack in hand, clearly ready to make a break for it.

“Is this required?” he inquired.

“We're all going to the Tutoring Center,” I said, in oblique response.

“Yeah, but do we have to? Is it an assignment?” He was nothing if not persistent.

“We're all going to the Tutoring Center and we'll be back in a few minutes to start on the next topic,” I said, demonstrating a charming obtuseness.

I don't think my student was charmed. He got to the point.

“Does this affect our grade? Are we getting participation points?” he asked.

I looked right at him, allowing my surprise to show.

“‘Participation points’? In a college class?”

He fell silent but unrepentant. He wanted points if he was going to go to the Tutoring Center with his classmates. It was finally obvious I wasn't giving any. He trailed along behind the rest of the group and I expected him to lag increasingly until he took a “wrong turn” and vanished toward the parking lot.  I was thus mildly surprised and pleased to see that instead he stuck it out and hung at the periphery of the group as I introduced them to the instructional assistant who managed the math tutors in the Center and walked everyone over to the area where drop-in tutoring occurred. Now that my students had been physically present in the facility and had met the key personnel, I figured it was much more likely that they would feel comfortable about returning to it when they needed help.

We returned to our classroom and launched into the lesson for the second half of the class period. The point-grubbing student sat quietly in the back, apparently ruing his decision not to skip out. At least I assume so, since in the next few days he developed a habit of nonattendance or early departure. When our first exam came along, he achieved the class's low score, missing a D by several points. (In fact, his score in the thirties might reasonably be characterized as an F-minus-minus.) He had never come to my office hours and he had never darkened the door of the Tutoring Center again.

I guess he really needed those participation points.

Fill in the blanks

Template tests

I was flummoxed. Under normal circumstances, algebra students abandon the complete-the-square technique for solving quadratic equations as soon as they meet the quadratic formula. It is by a significant margin the least-favored of the solution techniques, trailing badly after formula and factoring.

Why, therefore, were so many of my students diligently completing the square when they didn't have to? Even worse, they were doing it on an exam problem, when time is at a premium. Worst of all, they were completing the square to solve a quadratic equation where its use was clearly contraindicated! I was at a loss.

As you may know, the solution of the quadratic equation is the great pinnacle and climax of your traditional introductory algebra class. The end of the semester wraps up with the astonishing revelation that one can now solve any quadratic equation. No exceptions! Such universality is rare, and I try to engender a little appreciation in my students for so powerful a conclusion, the big finish of Algebra 1.

Of course, I also try to get them to approach quadratic equations thoughtfully and methodically. First of all, does the equation factor easily? Then go for it! Is it (or does it appear to be) prime? Then one can apply the never-failing quadratic formula or—in certain specific cases—resort to completing the square. The specific case, naturally, is one in which the quadratic polynomial in question is monic (has a lead coefficient of one) and possesses a first-degree coefficient that is even (making it easy to take half of it and square the result, as required for completing the square).

Otherwise, don't even think of completing the square.

The problem that was puzzling me was monic, all right, but its middle term had an odd coefficient, making it a quite unsuitable candidate for square completion. Why, then, did so many of my students plow right in and start juggling fractions and slogging through more and more complicated expressions? They didn't know and couldn't tell me why they had done it.

The reason finally came to light while I was paging through my collection of quiz keys. I paused to consider the quiz containing the combined-work problem (or “joint effort”—computing the time a job takes if two or more people pitch in and you know how long it takes each person to do the job alone). This was exactly the kind of problem that had caused so much square-completion grief on the exam.

I noticed that I had solved the resulting quadratic equation on the quiz's solution key by completing the square. The polynomial had been monic with an even linear coefficient, so completing the square gave a quick and easy solution ...

... and my students had learned the lesson that combined-work problems are solved by completing the square! After all, the teacher had demonstrated this in a quiz solution key that he had posted on the course website. Did he not constantly encourage them to emulate his example? Follow his lead? Write solutions like he did? Indeed! Indubitably!

Damn.

They learned a lesson I wasn't teaching. They had studied my solution to a particular combined-work problem and then followed it slavishly when next they encountered a problem of the same type—even though the resulting quadratic equation had different characteristics and argued for a different solution technique.

I failed to banish the template problem. My fault!

You know what a “template problem” is, don't you? I'm sure you do. Lots of books are full of them. It occurs when a section of the text presents a carefully worked-out problem in Example 1, you turn to the homework section, and Exercises 1 through n follow the prompt “See Example 1.” And then all of the problems are exactly like Example 1 except that the numbers got tweaked a little. Or maybe Example 1 was a word problem about Sally and Exercise 1 is about Sam. Trivial changes. You can copy the solution of Example 1 as a template and go through filling in the old numbers with the new numbers.

Hardly any thought necessary.

I don't want to be too harsh. Routine drill problems are useful for building basic skills. They are, however, too bland for a steady diet and do not do much (if anything) for building conceptual understanding. Students, however, often prize them for their dull predictability and lack of challenge. They even ask for more, as when they beg for a “practice test” before a big exam. The most favored practice tests are those full of templates for the real thing. Woe betide the instructor who gives in to the pleas for a practice test and then changes the problems too much in the actual exam! Students will feel betrayed.

I refuse to give practice tests. I decline to channel my students' attention too narrowly to specific kinds of problems solved in specific kinds of ways. I want them to consider each problem independently, with a minimum of prompting, examining their knowledge of solution tools and picking the most appropriate one to apply.

The complete-the-square affair demonstrates, I'm afraid, that I have discouraged template thinking less than I had hoped. Perhaps I should ask my colleagues how they avoid it and then do exactly what they do....

Professor Google

Live and interactive!

This is not a rant about students relying on things like Google and Wikipedia for their schoolwork. It's not that at all. It is instead a rumination about the tendency of some students—at least one in particular—to rely on an information-at-your-fingertips approach to education. The student I have in mind appears to have lost—to a remarkable degree—the trait of self-reliance. Let's call this student “Shawn.” He took my algebra class. He took it twice, having flunked it the first time. In both semesters I was treated to Shawn's pop-up arm, which waved for my attention at the least provocation. As a highly interactive instructor, I welcome student questions and want them to feel that their queries are welcome. Shawn, however, was trying my patience (along with that of his classmates).

It took me a while to figure out what was going on. Ever in the moment, Shawn had abandoned thinking. If something—anything—gave him pause, his arm shot up. He wanted immediate clarification from the instructor in preference to actually thinking about it himself. Somewhere along the line he had discovered that the path of least resistance involved asking the professor.

Back in the old days before the World Wide Web and Google, I sometimes fussed for hours (or even days), wracking my brain trying to recover some odd bit of information. I'd pull books off the shelf and page through them. Did I read it in this one? Should I dig out the encyclopedia? Did a friend mention it to me in conversation? Should I try calling him? (Which one?) As you may have heard, we call these the “good old days.” I confess, however, that the Internet and Google have become two of my most cherished friends. Facts and factoids are at my fingertips and I discover or rediscover things with alacrity and pleasure.

Shawn doesn't have Google in the classroom. He has me: Professor Instant Gratification. (I had a lesson to learn as much as Shawn did.)

The starkest example of Shawn's abandonment of thinking arose during a lesson on nonlinear systems of equations. I had created an elementary introductory problem involving a parabola and a line, writing their equations on the board and telling the students we were going to discover the points where their graphs crossed each other. The computations were straightforward (amazing, isn't it, how simple the answers are for Example 1?). Then I told the students we were going to examine the plausibility of our solutions by graphing the two curves and considering their appearance.

I plotted two points (the axis intercepts!) that satisfied the linear equation and sketched the line. Shawn was keeping his peace and presumably keeping pace. The quadratic equation was a little more challenging to graph, but it was still pretty elementary, so I created a short table of values to find some points that would help us sketch the parabola. In rapid succession, I plugged in x = 0, x = 1, and x = 2.

Up went Shawn's hand.

“Yes, Shawn?”

“How did you compute those values?”

“The values in the table?”

“Yeah. Where did those come from?”

Mind you, we had done the parabola to death in the previous chapter. We had graphed vertical parabolas and horizontal parabolas. We had found their axis intercepts with the quadratic formula (if necessary). Several old quizzes and the most recent exam had featured the parabola most prominently. All of the students, including Shawn, had had multiple exposures to the mundane task of plotting a parabola. He had had even more examples of plugging in conveniently chosen numbers to evaluate algebra expressions for graphing. Shawn's question was extraordinarily lame.

“Shawn, I want you to think about that.”

“What?”

“I want you to think about that. I'm finding points that lie on the graph of a parabola, picking x's and computing y's. You've done that yourself, right?”

“Lots of times.”

“Okay. Do it now.”

Long pause.

“Oh,” he said.

“Right,” I said, hoping that he was indeed right in what he was thinking.

It was not easy, but “think about it” became a standard response to many of Shawn's too-quick questions. By degrees, he eventually became more self-reliant instead of instantaneously asking the professor. He never learned to postpone gratification to quite the degree I would have liked, but he got a little better. He stopped asking questions without thinking and I stopped answering so automatically.

And Shawn's classmates got more rest for their eye-rolling muscles.

It figures

Or perhaps it doesn't

I'm still disappointed when it occurs, but I'm no longer surprised. Sometimes, such as when I give an exam on the last day before spring break, I send out a grade update via e-mail so that my students don't have to wait till school resumes to find out their status in the class. My report, which pops up in student e-mail, presents the latest grade distribution in descending order. The closer to the top you find your secret student ID number, the better off you are.

I also provide the weighted components that go into computing each semester score (and grade): homework, quizzes, and exams. I present averages rather than individual scores, and therein lies the rub. Students write back when they receive the grade report and ask, “What was my score on Exam 5?”

Let us consider this. What does the student have in hand?

The student has his average exam score: the grades on Exams 1 through 5 all added together and divided by 5. The student has his old exams, numbers 1 through 4.

How on earth is an algebra student supposed to figure out the unknown value of his score on Exam 5? It is a puzzlement, is it not? If only they had a better teacher, perhaps they could do it for themselves, but I'm afraid the classroom door is a portal to real life, beyond which nothing in the classroom has any relevance. It's not as though the stuff I teach them can actually be used for anything! (Not even for classroom-related applications!)

I recently responded to an inquiry from a student who was earning a B:

Didn’t you realize you could have computed it yourself? You have your average exam score from the grade distribution I sent out. Multiply your average exam score by 5 and then subtract your scores from Exams 1 through 4. What’s left is your Exam 5 score.

He gave me a cheery reply:

I should of know but thanks I'll make sure I put that in my notes.

I'm thinking of forwarding that to his English teacher.

Dates in conflict

Personal priorities and education

“Rob” was a good student, so I was unaccustomed to having him linger after class to ask questions. To make things even more unusual, Rob insisted on waiting till everyone else was gone from the room. Evidently he did not want any classmates to overhear his question. Rather tentatively, he voiced his query:

“Is it okay if I take our next exam a day early? On Thursday instead of Friday?”

Oh, no problem. I can answer that question easily: No.

I was, however, nice enough to give Rob a reason:

“Sorry, that's not possible. The exam doesn't even exist until the night before. I don't finish writing it till we've had our review session.”

In fact, I sometimes tweak an exam after I find out what students have questions about. If we spend a lot of time on a particular topic, I want to be sure that the topic is not neglected on the exam. For example, if my students want to work especially intensely on mixture problems, then I'm more likely to choose a problem of that type to include among the various application exercises on the exam. (And—I admit it—I don't worry too much about the likelihood that this slightly disadvantages the students who choose to skip the review session.)

Furthermore, I dislike the very notion of giving exams early. The student who gets special treatment by getting the exam in advance is obviously subject to the temptation to leak information to friends in the class. The less opportunity for that, the better.

Rob seemed to be surprised by my answer. Perhaps he had had instructors in the past who wrote all of their exams at the beginning of the semester. Not me. I'm much more adaptive than that. Or less farseeing.

Rob was also dismayed by my answer.

“It's not really my fault, Dr. Z. I got tickets to a concert before the semester started, and I wasn't expecting to enroll in a class that met on Fridays.”

“Nevertheless, that's what you did, Rob. The conflict is of your own making. You have a conflict between our exam date and the concert date. I don't have a good way to accommodate that and it's not my problem to resolve it anyway.”

“Well, could I take the exam later? Would that be okay?”

“Sorry, Rob. Think about it. I post the solution key on-line right after the exam. I'd have to withhold it from your classmates all weekend and leave them in suspense so that you could be accommodated. They wouldn't get the answers until Monday, until after you've taken the exam.”

Rob hesitated a moment.

“Oh, I was meaning to tell you. I'm going to be out on Monday, too.”

The conversation ended soon after that.

Past your eyes

The writer as researcher

I can't help myself. I read prefaces and acknowledgments in books. It fascinates me when the author thanks the people who helped him dredge up the arcana that enriched his writing or when he cites source material that might reward further reading. I want to know where the amazing detail or fascinating inside information came from.

Of course, sometimes it's fake. One of my old college chums pointed out a passage in a bestselling novel that described in loving detail the wardroom of the aircraft carrier John F. Kennedy. The minutiae gave weight and verisimilitude to the scene set therein. But my friend scoffed.

“I've been there. It's nothing like that! The author just made it up.”

I guess it was even more a work of fiction than I realized at the time.

On another occasion I asked a bestselling author about his use of apparently real California neighborhoods. I asked him if he was depicting real-world venues or products of his imagination. He stated that every scene was set in a place he knew personally, and that he either scouted out locales in person or used neighborhoods in which he had lived or often visited.

This question came up as my publisher obtained pre-publication reviews of my manuscript. One reviewer sent in a single-spaced three-page commentary that warmed the cockles of my heart with its praise. Of course, the reviewer also suggested some judicious cuts in the manuscript, which I dutifully embraced, but most of my attention was focused on his more positive observations:

One suspects the author's encyclopedic knowledge of dairy farming comes not only from personal experience, but even more of it must come from serious research.

Um ... no. Research? What's that?

I lived on a dairy farm for twenty years. All of the utterly (udderly?) persuasive detail that so impressed my reviewer was based on simple experience—stuff that passed before my eyes. I would have known even more good stuff had I not been so willing to defer to my eager younger brother when there was work to be done. If he was willing to volunteer, then I was willing to sit behind the haystack with a book.

Every tool or machine employed in the sowing, raising or harvesting of crops is described in loving, complex detail, as is the nurture, handling and transportation of the cows themselves. One chapter entitled “Green Cotton,” for example, could be used as a primer for anyone interested in the cultivation of that particular crop.

This may astonish you, but my editors and I did not choose to quote this on the cover of the book. Nor did we use the line where he praised my “abstruse knowledge.” Hey, bookstore browsers! Want to read a rapturous ode to farm equipment, crop rotation, and animal husbandry?

The movie rights are as good as sold!

Still, the reviewer was exceedingly kind in his comments about my grasp of farm arcana, which I tell you in all honesty is nothing remarkable. Here's the “abstruse knowledge” comment in context, where you can see the reviewer's generous and kind appraisal:

The author’s abstruse knowledge, however, is never employed gratuitously, but invariably to establish some point of character (as in the above instance, the incompetent Candido’s attempts to “cut corners” which invariably end in disaster) or to advance the plot, as is the case of the elaborate description of the marvelously complicated—and dangerous—machine used to harvest alfalfa which causes the young Trey’s life-changing accident. This information is presented with such consummate authority the reader never for an instance questions its accuracy.

So there! I is an expert!

The reviewer shares my Portuguese heritage, which is certainly one of the reasons he was asked to review my novel in manuscript form. He appreciated my efforts to capture and convey the cultural tangles that arose as the novel's immigrant protagonists put down new roots in the New World and are gradually transformed into Americans. He also thought that I was mostly successful in presenting the travails of the main characters.

The plot is long and complex, the cast of characters large, and since one of the joys of reading is to meet them on one’s own terms, they are best left for readers themselves to discover. They are a lively and varied bunch and the author delineates them with considerable verve, humor and intelligence. You will enjoy getting to know them.

The reviewer also gave me some fatherly advice about improving the novel's dialogue. I tend to use direct address quite often, with the use of proper names intended to avoid any ambiguity about who is speaking to whom. In real life, however, people seldom do this, so my conversations were a bit “wooden” in places. (On the other hand, no one ever had to go back several lines to go even-odd-even-odd to figure out who is talking.) I performed the reviewer's recommended excisions and similarly smoothed my dialogue. Of course, I didn't feel obligated to take all of his advice:

Your style is generally clean, straightforward, simple and direct, not much given to metaphor, which, unless it comes naturally, should generally be avoided. Nor do you, fortunately, attempt to wax lyrical. [You are, however, occasionally given to showing off your vocabulary.]

Yep, no waxing lyrical here! But as for showing off vocabulary? Indubitably!

And he finished by calling my book “excellent”! Coming to a bookstore near you this summer.

An angelic experience

Learning on the wing

Like a moth to a flame (or an archangel to a young Jewish virgin), I was drawn irresistibly to the opportunity to attend a faculty training event on the existence of angels. When it first came to my attention, I was initially struck by how inappropriate it seemed as a topic for a professional development activity. While not quite as bad as giving nurses continuing education credit for attending a Catholic indoctrination session, the angel seminar simply seemed irrelevant and beside the point. Where was scholarship in this? What useful lessons might I learn?

The presenter was TM, a young woman who holds a doctorate from the California Institute of Integrated Studies. She is an alumna of the CIIS program in Philosophy, Cosmology, and Consciousness, but I suspect “cosmology” in this context has very little to do with what science-types consider to be cosmology. That's just a guess, of course. You can visit the program webpage and consider the course content for yourself.

To give credit where it's due, Dr. TM declared in her opening remarks that she did not expect attendees to change their opinion about the existence (or non-existence) of angels as a result of her 90-minute presentation. That demonstrated TM's connection to reality, recognizing that the material she would present lacked the evidentiary weight necessary to persuade non-believers. Among the two dozen attendees were several who nodded their heads in sad acknowledgment that some people just aren't open-minded enough to embrace the reality of God's messengers. Others, like me, sat still, resisting the impulse to roll our eyes. It was prudent of TM to allow for our skeptical presence. We were, however, very well behaved throughout the event.

TM was much enamored of Carl Jung's notion of synchronicity, a concept I have never been able to take seriously. As TM explained, a synchronicity occurs when a strong interior impulse, condition, or sensation is reinforced by an exterior manifestation that generates a transformative moment of understanding. Jung's own favorite example, according to TM, was the appearance of a beetle at the window during a psychotherapy session with a female patient who was telling him about a dream about a golden Egyptian scarab. Since the beetle at the window was the nearest local analog to Egypt's golden scarab, Jung deemed it a synchronicity—an acausal simultaneity between his patient's inner life and the external world. (J. B. S. Haldane might have preferred to regard it as a manifestation of God's inordinate fondness for beetles, having scattered hundreds of thousands of species of beetle throughout the world.)

As TM hastened to explain, “Synchronicities are not just happy coincidences!” In response, one of my neighbors muttered, “No. Synchronicities are happy coincidences which people invest with heavy significance.” Only the closest people heard the riposte, but a couple of us nodded. (I was one of them.)

So, where were angels in all of this? As you might suspect, angels are implicated in synchronicities, especially when they manifest as exterior confirmations (i.e., as if they exist in the physical world) of interior emotions or yearnings. The archetypal example is The Annunciation. TM asked the attendees if anyone recognized this special event. I helpfully raised my hand and offered a description: “That's the event reported in the Bible of the archangel Gabriel appearing to Mary and announcing that she was to bear a son who would be the savior.” TM beamed at me and added some details. First of all, the yearning of the Jews for the coming of their messiah would be manifested in the hopes of young Jewish maidens to become the savior's bearer. Second, it didn't matter whether Mary was pregnant or not when Gabriel made his announcement. Either way, Mary would have a deep interior desire or anticipation that was acausally linked with the archangel's appearance.

TM was particularly interested in the parallels between synchronicities and annunciations. The incident with Mary and Gabriel is the most famous, but angels were also reported to have advised Joseph not to divorce Mary and later to flee to Egypt to avoid Herod's slaughter of the innocents. In her dissertation research, TM made the case that annunciations in religious history (by no means limited to Judeo-Christian sources) were anticipations of Jung's theory of synchronicity and fit well into the Jungian model. Furthermore, the parallels remain even if the angels did not actually exist. (Surprise!) That's because it's not strictly required that the coincidental confirmation of the interior sensation be an actual event in the physical world. The angels could, in fact, be confirmatory figments of the imagination.

At this point, I got to learn something—and by this I do not mean that I learned there's a lot of silliness in this field. After all, who should be surprised that there are parallels between supposedly different forms of delusion? No, in this case I learned a bit of Bible lore that I had not heard before, and which I found interesting and intriguing. According to TM, Gabriel does not appear in the earliest Bible texts. His role is magnified by redactors who found fault with Mary's inner conviction that she was indeed fated to become the mother of the messiah. If this is correct, then Mary's synchronicity was a progression from “I want to bear the messiah” to “I will bear the messiah.” That's pretty thin gruel. Having an archangel with a name showing up to put his stamp of approval on Mary's inner yearning makes the story much more satisfying.

A few of us got fidgety near the end of the event as some of the attendees hastened to offer personal examples of synchronicities. My inner yearning for it all to end was confirmed by the external manifestation of a yawn, but I'm afraid it lacked the acausal quality that would have classified it as a synchronicity.