A central precept of Physics Boards concerning homework assistance is to not present options on demand however to information college students alongside a path to the reply.  The rationale behind this precept is articulated within the acquainted saying, “For those who give a hungry man a fish, you feed him for a day; when you educate him methods to fish, you feed him for a lifetime.”  That mentioned, I’ll quote one other acquainted saying, “You may lead a horse to water, however you possibly can’t make him drink.”  Then I’ll mix the 2 into “You may educate a hungry man methods to fish and lead him to the water, however you possibly can’t make him fish.”

This mélange epitomizes a conclusion I reached after many years of educating minds, some hungry some not, methods to assume. How I reached this conclusion and the way I finally got here to phrases with it are the topic of this text.

The seeds

After I started graduate faculty, my duties included serving to with grading hourly exams in giant lessons (150-200 college students).  Right here is the examination query that began all of it.

An electron of cost ##-e## enters with velocity ##v## a area of uniform magnetic area ##B## directed into the web page.  It exits at a proper angle from its authentic route (see determine). Discover the work that the magnetic pressure does on the electron from entry to exit.

(A) ##~evBdfrac{pi R}{2}##

(B) ##~-evBdfrac{pi R}{2}##

(C) ##~evBsqrt{2}R##

(D) ##~##  Zero.

Surprisingly few college students, perhaps a handful or two, gave the proper reply (D).  Most college students selected (A) or (B) constantly with the dreaded generalization “work is pressure occasions distance.” I used to be astonished as a result of the professor in command of the course had a sterling educating status. Certainly, he should have taught it proper.

A number of years later, as a postdoc, I volunteered to team-teach a course on Fashionable Physics with the intention to achieve demonstrable educating expertise earlier than making use of for a “actual” job.  The course was break up into two 30-student sections with a standard syllabus set by my teammate professor. The small print of implementing the syllabus for my part had been left as much as me and included authoring the hourly checks.

Shortly earlier than the winter vacation break, I gave a scheduled quick hourly take a look at.  My directions had been “Choose any two (emphasis within the authentic) of the next three statements, reply “True” or “False” and  justify your reply.”  To ensure they obtained it, I learn aloud the directions earlier than handing out the questions.  The primary assertion was associated to the Bohr mannequin and the second to Compton scattering.

The third assertion was “It’s enjoyable to trip on a one-horse open sleigh.”  It was my vacation reward to the category and I awarded full credit score to all solutions and justifications.  Nonetheless, about 1/3 of the scholars declined my provide and labored on the primary two questions.  One among them informed me that she answered the primary two questions “simply in case” as a result of she didn’t consider I meant it.  I noticed a component of mistrust stemming, maybe, from an ingrained notion that college students and instructors are adversaries.  I used to be chagrined with the tip end result and by no means contemplated “items” of this type once more.

The germination of an thought

Quick ahead a decade. In my “actual” job as a college assistant professor, my flip got here to show calculus-based introductory E&M to a big class.  After we obtained to “Movement of Charged Particles in Magnetic Fields,” I took further care to level out that the Lorentz pressure is at all times perpendicular to the speed and, due to this fact, to the trail, that it does no work and that kinetic vitality is conserved.  For good measure, I confirmed how the work-energy theorem suits in. Lastly, I concluded with “and if somebody asks you to search out the work accomplished by the magnetic pressure on the charged particle, don’t be fooled.  The one right reply is zero.”  Because the reader may need guessed, I had determined at the moment to be the “somebody”  and put the query on the ultimate examination.

Upon grading the finals, I used to be distressed to see that solely a couple of quarter of the solutions had been right.  I went to see David, a veteran of the ditch wars in opposition to ignorance, who was my unofficial mentor. I defined what occurred and vented my frustration: however I informed them!  He mentioned, “Telling them is meaningless to plenty of college students.” Then he associated a narrative of his personal.  After a dismal efficiency of his college students on a homework downside in his Intermediate Mechanics class, he introduced that he would put the identical downside on the ultimate. Properly, you guessed it, solely a handful of his college students studied the issue and improved their efficiency. He concluded his story by saying, “Even when you inform them, there’ll at all times be some who received’t consider you.”  Flashback to the coed who rejected my vacation reward.

However, I stubbornly discounted David’s recommendation.  When “Movement of Charged Particles in Magnetic Fields” got here across the subsequent yr, I used to be ready.  I began with the presentation from the yr earlier than.  Nevertheless, since that alone didn’t work, I labored out the query on the board and defined why the reply is (D).  Then I overtly informed them. I mentioned, “I defined all this to final yr’s class, however solely 1 / 4 obtained it proper on the ultimate.  Don’t be like them.  For those who see this once more, do not forget that uniform magnetic fields do zero work.”  I bear in mind my voice wavering as a result of a part of me was questioning whether or not I’m giving freely an excessive amount of.

Judgment day got here and went with minimal enchancment. The fraction of right solutions rose from one-quarter to one-third.  I went again to David with my second however I informed them account.  He listened silently with a “and I informed you” smirk on his face.

For those who can’t beat them, be part of them

Chastened by the expertise, I turned satisfied that telling them is important to show however not attain college students.  Main them to the fountain of data isn’t a assure that they’d drink.  That was my “aha” second.  Since it’s tough to provide away even one query, I reasoned, why not give all of them away? Thus, the booklet got here into being.

The booklet

The booklet was a compendium of about 120 homework-style however non-textbook issues from materials lined all through the course. I printed it on the internet for all to see.  On the primary day of lessons, I introduced that every of the three hourly exams plus the ultimate will include randomly chosen issues from the booklet.  No tips, no gimmicks, no guessing, no hidden traps.  All issues had numerical variables with numerical solutions in order that college students might examine and confirm their work. Nevertheless, questions on exams will seem with the numbers eliminated.  College students must derive the solutions in symbolic kind and present their derivations.  The booklet sections that might be truthful sport for every examination and my workplace hours for offering assist had been included.  The Appendix exhibits two pattern issues from sections “Coulomb’s Legislation” and “Particles, Magnetic Fields & Currents”.

How did it work?

In idea

Ideally, a scholar will try all the issues applicable to a specific examination earlier than the occasion. The makes an attempt ought to be concurrent with the associated homework to permit adequate time for asking questions.  I additionally inspired the formation of examine teams through which the scholars might work collectively and assist one another.  I figured that perhaps the horses that don’t need to drink would possibly study from those who do.  Additionally, by eradicating the numbers within the examination model, I hoped that college students would summary and bear in mind a strategic and conceptual strategy for every downside and convey that to the examination.

I used to be not apprehensive that I gave an excessive amount of away for 2 causes: (a) David taught me that it’s not attainable to provide an excessive amount of away; (b) in my thoughts, any scholar, who is ready to reproduce the algebraic options to fastidiously crafted issues, has achieved the objectives of the course. I couldn’t count on extra.

In follow

First the dangerous information.  Scholar site visitors in my workplace was the identical relative to the pre-booklet days. Solely the main focus of the visits modified from serving to with tough homework issues to serving to with booklet issues.  Some college students waited till the final second after which crammed.  Others performed the lottery and studied solely the issues they guessed I might placed on the take a look at.  They didn’t consider me that the choice could be random.  Some felt that since they “knew” what will probably be on the examination, they may wing it with out understanding the issues.  Briefly,  the introduction of the booklet didn’t noticeably affect scholar habits or their efficiency on exams.  One would possibly assume that every one of them would soar on the alternative of understanding what could be on the examination. Not so.  Motivated horses drank, unmotivated ones didn’t.

Now for the excellent news.  The booklet turned out to be a win-win scenario. For the scholars, it mitigated the worry and psychological paralysis that afflict plenty of college students earlier than and through exams. An oft-heard lament was, “I believed I understood the fabric, I did all of the homework, however after I got here to the examination I freaked out.” With the booklet, the anxiety-producing unknowns, e.g. degree of problem, the character of the questions, the place one ought to pay attention one’s efforts, whether or not one has adequate preparation, and so on. turned knowns.  The booklet positioned the duty of the coed’s efficiency squarely upon themselves to the place it belongs.

Because of this, the booklet’s profit to me was peace of thoughts. It eliminated the justifications that college students use to shift the duty for his or her poor efficiency away from themselves: “The examination issues had been nothing just like the homework”; “we didn’t cowl this in school”; “I didn’t perceive this once we lined it in school”; “the examination was too difficult”; “the examination was too onerous”; “you didn’t educate us methods to resolve this type of downside” and so forth.

Nevertheless, the actual winners had been the motivated college students (about 20%) who took the booklet to coronary heart.  For them, it labored as I meant.  They handled the booklet issues as self-assigned homework. They got here to workplace hours with questions on a weekly foundation usually as groups working collectively.

The booklet additionally labored wonders with college students who did poorly however cared sufficient to come back and ask me how they may enhance their efficiency. Most of them had been last-minute crammers with poor time-management abilities. For them, I constructed timetables to prepare what to finish by what date and left it as much as them. The following vital group consisted of scholars with shaky math or physics problem-solving abilities. For them, I added a second set of timetables with to-learn lists.

No matter capacity, all motivated college students realized I didn’t design exams to reveal their ignorance however to consolidate their studying. That was a giant win for them and me.

Crafting the booklet

The booklet issues have not more than two sequential steps within the derivation and usually are not multipart issues.  Every query brings collectively ideas or abilities that college students ought to have acquired in another a part of the course or course conditions. As soon as solved numerically, the development of the questions makes the transition from numerical to symbolic kind clear.  Moreover, the questions don’t require greater than two sequential steps and the answer methods are one-liners.

For instance, questions 1.6 and 1.7, which can’t seem collectively on the identical examination, mix electrostatics and free physique diagrams. The technique in each is “Draw an FBD for the highest (or backside) bead” and say that the web pressure on the chosen bead is zero.”  The trick (if there may be one) is to comprehend that, regardless that the highest bead is free to maneuver, the string has to help the burden of each beads.

In query 6.5 the technique is “Specific the magnitude of every wire’s contribution to the B-field by way of the radius of the circle and the suitable trig capabilities and set the 2 magnitudes equal.”  The query brings collectively the magnetic area of an infinite wire, superposition, and the right-hand rule. It additionally requires one to recollect the id ##sin(apm b)=sin acos bpmcos a sin b.##

Afterthoughts

The customary understanding between teacher and college students is, “I’m going to show you after which I’ll study you to find out what you could have realized and what you are able to do.”  That’s OK in precept, nevertheless, there may be usually a niche separating the tip of educating from the start of studying. When college students carry out poorly, instructors are likely to blame the scholars for not studying and college students are likely to blame the instructors for not educating.  Nonetheless, each side declare to have accomplished their greatest.

This hole turned painfully obvious to me with the electron-in-a-magnetic area query which I now remorse asking.  It was a repeated measurement of what 2/3 (at greatest) of the scholars can’t do, not what they can do.   There isn’t any data to find out what college students can’t do, instructors already understand it.  The booklet shrunk the hole between educating and studying.  It outlined a boundary between the 2 with a transparent message: “Here’s what I count on you to have the ability to do. Let’s each see how properly you are able to do it.  If there’s something that you simply can’t perceive or do, ask me earlier than you might be examined.”  To fish or to not fish, that’s the query.

Appendix

In multipart booklet questions, reminiscent of those under, every half is standalone and doesn’t require fixing one other half first. So far as the random quantity generator is anxious, every numbered half is a separate query, however questions sharing a descriptive assertion don’t seem collectively on the identical examination, e.g. 1.6 or 1.7 however by no means 1.6 and 1.7.  Variables on the examination would not have numerical values; their symbols are left in place for college students to make use of as given portions.