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, “Should you give a hungry man a fish, you feed him for a day; should you educate him fish, you feed him for a lifetime.” That mentioned, I’ll quote one other acquainted saying, “You possibly can lead a horse to water, however you possibly can’t make him drink.” Then I’ll mix the 2 into “You possibly can educate a hungry man fish and lead him to the water, however you possibly can’t make him fish.”
This mélange epitomizes a conclusion I reached after a long time of educating minds, some hungry some not, suppose. How I reached this conclusion and the way I ultimately got here to phrases with it are the topic of this text.
The seeds
After I started graduate college, 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 subject ##B## directed into the web page. It exits at a proper angle from its authentic route (see determine). Discover the work that the magnetic power 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 right reply (D). Most college students selected (A) or (B) persistently with the dreaded generalization “work is power instances distance.” I used to be astonished as a result of the professor in control of the course had a sterling educating repute. Absolutely, he will need to have taught it proper.
A number of years later, as a postdoc, I volunteered to team-teach a course on Trendy Physics with a purpose to acquire 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 have been left as much as me and included authoring the hourly assessments.
Shortly earlier than the winter vacation break, I gave a scheduled brief hourly take a look at. My directions have 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 journey 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 supply and labored on the primary two questions. Certainly one of 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 top end result and by no means contemplated “items” of this sort once more.
The germination of an concept
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 additional care to level out that the Lorentz power is all the time perpendicular to the rate 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 matches in. Lastly, I concluded with “and if somebody asks you to seek out the work finished by the magnetic power 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 few quarter of the solutions have 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 numerous college students.” Then he associated a narrative of his personal. After a dismal efficiency of his college students on a homework drawback in his Intermediate Mechanics class, he introduced that he would put the identical drawback on the ultimate. Effectively, you guessed it, solely a handful of his college students studied the issue and improved their efficiency. He concluded his story by saying, “Even should you inform them, there’ll all the time be some who gained’t consider you.” Flashback to the scholar 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 12 months, I used to be ready. I began with the presentation from the 12 months 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 12 months’s class, however solely 1 / 4 obtained it proper on the ultimate. Don’t be like them. Should you see this once more, do not forget that uniform magnetic fields do zero work.” I keep in mind my voice wavering as a result of a part of me was questioning whether or not I’m gifting away 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.
Should you can’t beat them, be a part of them
Chastened by the expertise, I grew to become satisfied that telling them is important to show however not attain college students. Main them to the fountain of information isn’t a assure that they might drink. That was my “aha” second. Since it’s troublesome to present 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 coated all through the course. I printed it on the net 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 methods, no gimmicks, no guessing, no hidden traps. All issues had numerical variables with numerical solutions in order that college students may verify and confirm their work. Nevertheless, questions on exams will seem with the numbers eliminated. College students should derive the solutions in symbolic kind and present their derivations. The booklet sections that may be truthful sport for every examination and my workplace hours for offering assist have been included. The Appendix reveals two pattern issues from sections “Coulomb’s Legislation” and “Particles, Magnetic Fields & Currents”.
How did it work?
In idea
Ideally, a pupil will try all the issues acceptable to a specific examination earlier than the occasion. The makes an attempt needs to be concurrent with the associated homework to permit ample time for asking questions. I additionally inspired the formation of research teams during which the scholars may work collectively and assist one another. I figured that perhaps the horses that don’t wish to drink would possibly be taught from those who do. Additionally, by eradicating the numbers within the examination model, I hoped that college students would summary and keep in mind a strategic and conceptual method for every drawback and convey that to the examination.
I used to be not nervous that I gave an excessive amount of away for 2 causes: (a) David taught me that it’s not doable to present an excessive amount of away; (b) in my thoughts, any pupil, who is ready to reproduce the algebraic options to rigorously crafted issues, has completed the targets of the course. I couldn’t count on extra.
In apply
First the dangerous information. Scholar site visitors in my workplace was the identical relative to the pre-booklet days. Solely the main target of the visits modified from serving to with troublesome 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 shall be on the examination, they may wing it with out figuring out the issues. Briefly, the introduction of the booklet didn’t noticeably affect pupil habits or their efficiency on exams. One would possibly suppose that every one of them would soar on the alternative of figuring out 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 state of affairs. For the scholars, it mitigated the worry and psychological paralysis that afflict numerous college students earlier than and through exams. An oft-heard lament was, “I assumed I understood the fabric, I did all of the homework, however once I got here to the examination I freaked out.” With the booklet, the anxiety-producing unknowns, e.g. degree of issue, the character of the questions, the place one ought to pay attention one’s efforts, whether or not one has ample preparation, and many others. grew to become knowns. The booklet positioned the accountability of the scholar’s efficiency squarely upon themselves to the place it belongs.
In consequence, the booklet’s profit to me was peace of thoughts. It eliminated the justifications that college students use to shift the accountability for his or her poor efficiency away from themselves: “The examination issues have been nothing just like the homework”; “we didn’t cowl this in school”; “I didn’t perceive this after we coated it in school”; “the examination was too tough”; “the examination was too onerous”; “you didn’t educate us resolve this type of drawback” and so forth.
Nevertheless, the true winners have been the motivated college students (about 20%) who took the booklet to coronary heart. For them, it labored as I supposed. They handled the booklet issues as self-assigned homework. They got here to workplace hours with questions on a weekly foundation typically as groups working collectively.
The booklet additionally labored wonders with college students who did poorly however cared sufficient to return and ask me how they may enhance their efficiency. Most of them have been last-minute crammers with poor time-management abilities. For them, I constructed timetables to arrange 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 means, all motivated college students realized I didn’t design exams to show 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 should 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 stipulations. 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 power on the chosen bead is zero.” The trick (if there’s one) is to comprehend that, despite the fact that the highest bead is free to maneuver, the string has to help the load of each beads.
In query 6.5 the technique is “Categorical 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 subject 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 have got discovered and what you are able to do.” That’s OK in precept, nonetheless, there’s typically a spot separating the top of educating from the start of studying. When college students carry out poorly, instructors are inclined to blame the scholars for not studying and college students are inclined to blame the instructors for not educating. Nonetheless, each side declare to have finished their greatest.
This hole grew to become painfully obvious to me with the electron-in-a-magnetic subject 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 is no such thing as a info to find out what college students can’t do, instructors already realize 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 effectively you are able to do it. If there’s something that you just 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, akin to those under, every half is standalone and doesn’t require fixing one other half first. So far as the random quantity generator is worried, 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 do not need numerical values; their symbols are left in place for college kids to make use of as given portions.
