Handbook for Mathematics Teaching Assistants

8/13/2019 Handbook for Mathematics Teaching Assistants

1/68

A Handbook for Mathematics Teaching Assistants

(Preliminary Edition)

Tom Rishel, Cornell Uniersity ! The MAA

"Contents"

#$ %ntrod&ction '%ntrod&ction

*$ Ty+es of TA Assignments Recitation, -ect&re, .rading 'Ty+es/*0of/*0TA/*0Assignments

1$ 2efore 3o& Teach A Checklist '2efore/*03o&/*0Teach

4$ 5ay 6ne '5ay/*06ne

7$ 8hat .oes 6n in Recitation9 '8hat/*0.oes/*06n/*0in/*0Recitation

:$ 8hat ;ho&ld be on a ;yllab&s9 '8hat/*0;ho&ld/*0be/*0on/*0a/*0;yllab&s

$ Coo+eratie -earning 'Coo+eratie/*0-earning

#0$ Technology 'Technology

##$ 8riting Assignments '8riting/*0Assignments

#*$ Making U+ E?ams and @&ies 'Making/*0U+/*0E?ams/*0and/*0@&ies

#1$ Using Cognitie Models to Make A++ro+riate Problems 'Using/*0Cognitie/*0Model(Bith Mary Ann Malinchak Rishel)

#4$ The Actie Classroom 'The/*0Actie/*0Classroom

#7$ 8hat 8as That @&estion Again9 '@&estion

#:$ Motiating ;t&dents 'Motiating/*0;t&dents

#$ .et Along Bith Colleag&es '.et/*0Along/*0Bith/*0Colleag&es

*0$ 8hat is a Professional9 '8hat/*0is/*0a/*0Professional

*#$ Teaching Methods for Dario&s Ty+es of Classrooms 'Teaching/*0Methods

**$ Problems of and Bith ;t&dents 'Problems


2/68

*1$ ;t&dent Ty+es 8ho is the A&dience9 ';t&dent/*0Ty+es

*4$ HoB to .et ired 'HoB/*0to/*0.et/*0ired

*7$ Adice to %nternational TAs '%nternational/*0TAs

*:$ ;illy ;t&ff$$$ ';illy/*0;t&ff

*$ Gobs, Gobs, Gobs 'Gobs

10$ -etters of Recommendation '-etters

1#$ Mathematical Talks 'Mathematical/*0Talks

1*$ 2ecoming a ac&lty Member '2ecoming/*0a/*0ac&lty/*0Member

11$ Uniersity and College .oernance '.oernance

14$ 8hat 5oes an Eal&ator Eal&ate9 '8hat/*05oes/*0an/*0Eal&ator/*0Eal&ate

17$ The Essence of .ood Teaching 'The/*0Essence/*0of/*0.ood/*0Teaching

1:$ Case ;t&dies 'Case/*0;t&dies

%ntrod&ction

This is a te?t abo&t teaching college mathematics$

My ieB is +ersonal, informed by oer forty years in higher ed&cation,oer thirty of them teaching in some form or another, and almost tBentyof those inoled Bith training and eal&ating teaching assistants and&nior fac&lty$ %f % seem to em+hasie firstIand secondI+erson narratiein my Briting, it is beca&se m&ch of this te?t has come, literally, fromdisc&ssion Bith yo&, the TA or &nior fac&lty member, abo&t the realBorld sit&ations Be are enco&ntering daily in o&r classrooms$

At most eery &nct&re in the te?t, % em+hasie n&ts and boltsconsiderations oer theory$ This is not beca&se % beliee that theorydoes not e?ist or is not im+ortant, b&t beca&se % think that good

teaching starts Bith seeming triialitiesIItalk lo&dly, Brite large,+re+are caref&lly, e?+lain a lot, be friendly$ 6nly after Be arefamiliar Bith s&ch sim+licities do Be begin to feel comfortable moinginto theories of learning$ This last is not to say that s&ch theoriesare neer &sef&l or im+ortantIIotherBise, Mary Ann Malinchak Rishel and% Bo&ld not hae Britten the long section on hoB &sing cognitie methodscan lead to better e?aminations, for instance$ HoBeer, % do think thatyo&, as a grad&ate TA or a yo&ng fac&lty member, Bill +rofit more andim+roe faster from short, sim+le, clear s&ggestions that hae immediateand obio&s im+act in yo&r dayItoIday classroom$ %f this im+roementleads yo& to decide that yo& Bant to think more dee+ly abo&t yo&r


3/68

c&rrent and f&t&re teaching, so m&ch the better$ ;end me eImail so Becan talk trishelJmaa$org 'mailtotrishelJmaa$org$

inally, let me address a ery common ieB abo&t the disci+line ofteachingK namely, as % Bas told again &st last Beek, Teaching canLt beta&ght$ 8ell, maybe, &st maybe, great teaching is lightning in abottle and canLt be e?+lained, b&t % claim em+hatically that goodteaching can be ta&ght$ 6f co&rse, % am biased in my ieB, if only

beca&se % hae s+ent the last tBenty years (ro&ghly) trying to achieethis aim$ 2&t, in fact, % beliee not only that teaching can be ta&ght,b&t that if mathematics is to +rogress, it m&st be ta&ght II to thebright yo&ng +eo+le Bho Bill carry it on after &s$ % ho+e that, by theend of this ol&me, yo& Bill agree Bith me$

;o, letLs sto+ talking and get to Bork$$$

Ret&rn to To+ 'Table/*0of/*0Contents

Ty+es of TA Assignments Recitation, -ect&re, .rading

Most teaching assignments for grad&ate st&dents fall into one of threecategories listed in the title of this section$

Probably the most common TA assignment in mathematics, and the one BithBhich the maority of the fac&lty began their careers, is that ofrecitation instr&ctor$ Those of yo& Bho hae receied an &ndergrad&atedegree from a large &niersity Bill be familiar Bith thelect&reIrecitation format a fac&lty member lect&res to a large class ofst&dents tBo or three times a Beek on an assigned to+ic from a te?tbook,after Bhich a grad&ate st&dent ansBers &estions abo&t the lect&re anddisc&sses assigned homeBork +roblems$ %n this format, the lect&rerdecides Bhich homeBork to assign, and often determines the str&ct&re ofthe recitation$ 2y this % mean he or she may say 5onLt do all the

+roblemsK &st the ones that are designated not to be t&rned in forgrading$ Alternatiely, the lect&rer may s&ggest that yo& begin eachrecitation Bith a co&+le of e?am+le +roblems$ .enerally, hoBeer, mostinstr&ctors Bill gie yo& little or no adice, e?ce+t to say somethinglike G&st do a standard recitation$ (or a sam+le standardrecitation, Bhateer that may be, see the later section, 8hat .oes 6nin Recitation '8hat/*0.oes/*06n/*0in/*0Recitation$)

Another common assignment for TAs is to be asked to lect&re$ ;choolsary as to Bhen in a grad&ate st&dentLs career this is to be doneK atsome instit&tions yo& are handed an algebra and trigonometry te?t andtold, .o teach this$ 5onLt mess &+N 6ther schools Bait for a year ortBo &ntil yo& hae had some less demanding assignments before they ask

yo& to +lan lessons, make &+ yo&r oBn e?ams, determine grading +olicy,and generally deal Bith the +roblems of teaching &ndermotiated freshmen(or Borse, &ndermotiated seniorsN) the oys of +recalc&l&s$

%t is +robably Borth +ointing o&t here that at some +oint in yo&rgrad&ate career yo& sho&ld +&rs&e a lect&ring assignment, for tBo basicreasons

#$ A grad&ate st&dent Bho has lect&red has a real adantage in the obmarket (see the section, Gobs, Gobs, Gobs 'Gobs)$*$ 2y lect&ring before yo& take a first fac&lty +osition, yo& remoe


4/68

some of the stress oer teaching that goes into the ten&reI+ress&re$

A third common TA assignment is that of grading, sometimes in anelementary co&rse, more often in an adanced &ndergrad&ate or een agrad&ate co&rse$ Many TAs describe s&ch assignments as easy orboring$ 8hile the assignments can be either or both, grading obs,hoBeer, can teach yo& hoB far yo& hae come since the days Bhen thisco&rsematerial Bas a real effort$ These assignments can also shoB yo&

hoB hard it is to teach others to Brite clear, concise ansBers and+roofs$ A third benefit to a grading ob is that yo& can &se it toreieB the material that may be asked on a grad&ate com+rehensiee?amination$ % Bill say more abo&t the &estions inoled in grading+a+ers later on in the section titled .rading %ss&es '.rading/*0%ss&es$

or noB, think abo&t

8hich ty+e of TA assignment a++eals to yo& most noB9 %s there one thatyo& might neer Bant to do9 5o yo& think that yo&r o+inions might changelater on in yo&r career, or are they set in stone9


2efore 3o& Teach A Checklist

" 5o yo& hae keys for yo&r office or yo&r classroom9 " Are the classrooms going to be o+en9 " 8ill yo& find chalk and erasers in the classroom9 " 8here is yo&r office9 8hat is yo&r office n&mber9 " 8hat is yo&r tele+hone n&mber9 3o&r email address9 " Can yo& get a desk co+y of the te?tbook for yo&r co&rse9 " Can yo& Brite in the margin of the te?tbook9 6r Bill yo& hae to ret&rn the book at the end of the term9 " 8here is the library9

" 8here are the restrooms9 " Can yo& get +encils and +a+er from the de+artment office9 or do yo& hae to b&y yo&r oBn9 " 8hat is the +olicy on making co+ies of e?ams for yo&r class9 " Are the co+y room and mail room accessible d&ring eenings and Beekends9 " 8here can yo& find the class sched&le so yo& knoB Bhere yo& are teaching9 " Can yo& get old syllabi for yo&r class9 HoB abo&t last year9s e?ams9 " Can yo& get an oerhead +roector and trans+arencies9 5o yo& een Bant these things9 HoB abo&t a +roector for calc&lators9 " HoB long is the semester9 %s the e?am sched&le made &+ in adance9 " HoB many st&dents might yo& e?+ect to see in yo&r class9

" HoB m&ch grading are yo& e?+ected to do9 " Can yo& get yo&r teaching sched&le changed easily9 " 8hat is a ty+ical Borkload for a neB TA9 " And, Bhere do yo& get yo&r +aycheck9


5ay 6ne

%t is fitting that % begin Briting this section noB, for today is the


5/68

first day of the second semester$ % hae &st Balked +ast a largelect&re hallK the instr&ctor is animatedK st&dents are listeningintently, Banting to knoB Bhat is coming$ or me, the irony here is that% hae +assed this room d&ring +ast semesters, often obsering seeralst&dents slee+ing or reading the cam+&s neBs$

5ay one of the semester is too im+ortant to throB aBay$ %f all Be do iscall the roll and dismiss the class, Bhat message are Be sending9 3et,

many instr&ctors do &st that$ % didnLt really think abo&t this class&ntil noB, maybe, or, 3o& donLt need to be any more serio&s abo&t thematerial than % hae been &st noB$

6n the first day of class, st&dents Bant to knoB hoB the co&rse Bill ber&n Bhat are the maor to+ics, Bhy is the material releant, and, ofco&rse, HoB Bill Be be graded9 %n light of these st&dent interests,Bhat can be done Bith day one9 Here are some s&ggestions

" Call the roll b&t donLt sto+ here$ " Hand o&t, read, and ansBer &estions abo&t the syllab&s$ " E?+lain hoB yo& intend to handle classes$ " 5isc&ss the n&ts and bolts of homeBork, e?ams and grading$ '

" 6ffer an oerieB of the co&rse$

FoB letLs disc&ss some as+ects of each of the categories aboe$

2y the seemingly sim+le act of calling the roll, yo& signal that yo&Bant to knoB the st&dents$ 3o& Bill get to knoB some names, and thatBill make the co&rse more +ersonalied$ This can lead to betterattendance, feBer +roblems like cheating (since the st&dents feel moreinested in the class, and since they knoB that yo& knoB Bho they are),and better co&rse eal&ations for yo& at the end of the co&rse$

Handing o&t a syllab&s is another common first day actiity$ %f yo& areneB to teaching, yo& Bill hae many &estions as to hoB to constr&ct

s&ch a syllab&s, some of Bhich can be ansBered in a later section, 8hat;ho&ld be on a ;yllab&s '8hat/*0;ho&ld/*0be/*0on/*0a/*0;yllab&s$

Many instr&ctors ass&me that st&dents Bill read Bhat is handed to themK% think this is incorrect$ Eery time % hand o&t a doc&ment, Bhether itbe a syllab&s or a homeBork assignment, % read it to the st&dents$ 2yreading thro&gh the syllab&s, % alloB st&dents to ask &estions that %may not hae ansBered clearly in my te?t, and % also ens&re that, Bithinreason, st&dents knoB Bhat is re&ired of them$ irstItime grad&atest&dents are often teaching firstItime &ndergrad&ates$ The&ndergrad&ates need to knoB hoB college o+erates ;ho&ld % bring myte?tbook to each class9 8ill yo& collect homeBork eery day9 5o yo&ansBer &estions d&ring class, or do Be Bait &ntil later9 5o yo& grade

on attendance9

More adanced st&dents Bill hae &estions, too$ Maybe they hae neerhad a mathematics co&rse in college, or more likely, they &st Bant toknoB Bhat the r&les are % hae lots of ob interieBs this semester$5o yo& re&ire attendance9 8ill yo& hae ansBer sheets in the library,the Bay they did last semester9 2y the Bay, there is nothing Brong Bithyo&r ansBering, % donLt knoBK %Lll check it o&t let yo& knoB ne?tclass$ G&st make s&re that yo& carry o&t yo&r +art of this bargain andgie them a definite ansBer at the ne?t class$ As to more s+ecificcomments abo&t hoB class is to be handled, Be Bill ret&rn to this to+ic


6/68

in the section, Ty+es of Assignments$ ;t&dents Bant to knoB Bhether andhoB often homeBork are going to be collected$ 8ill yo& grade each+roblem, or only some9 HoB Bill they knoB Bhich9 5o yo& hae an idea ofhoB yo&Lll assign grades to the homeBork9 or instance, Bill yo& &se an&merical system Bhere each +roblem is Borth, say, from ero to fie+oints9 %f yo& knoB Bhat system yo& or the co&rse leader is &sing, noBis a time yo& can tell the st&dents$

;imilarly, yo& can describe Bhen yo& Bill gie e?ams, and Bhether theyBill occ&r in class or in the eening$ 3o& can also describe Bhere thee?ams Bill be gien, for instance, in a large lect&re hall Bith 400st&dents, or in the classroom$ 3o& can also tell yo&r class that 3o&Bill hae ninety min&te e?ams, and % Bill shoB yo& some old e?ams forreieB$

Then yo& can e?+lain Bhat yo& knoB of the final e?am and grading+olicies$ %s the final c&m&latie9 5oes it hae the same length as theother e?ams9 5oes it co&nt for more +oints than the earlier e?ams9

There are other bits of information yo& also sho&ld gie The names ofthe te?ts for the co&rse, yo&r office ho&rs, and any s&++lemental te?ts

or materials yo& Bill &se$

FoB that yo& hae s+ent abo&t tBenty min&tes on the n&ts and bolts ofthe co&rse, it is time to t&rn yo&r attention to content$ 8hat are theto+ics yo&r st&dents Bill be learning9 HoB do those to+ics relate toother s&bects they may be st&dying9 %n Bhat Bays Bill the material be&sef&l in the real Borld9

-etLs be more s+ecific abo&t detailsK many of yo& Bill start teachingBith a first semester calc&l&s co&rse$ 3o& may Bant to say somethinglike this

Calc&l&s is &s&ally s+lit into tBo ty+es differential and integral$

5ifferential calc&l&s deals Bith instantaneo&s rates of change hoBthings change right noB, not oer si? years or ten miles (those areaerage rates of change), not oer si? seconds or si? oneIh&ndredth of asecond, b&t right noB, this instant$ 8e Bill be learning abo&t thisinstantaneo&s change this soIcalled deriatie, hoB to find it, hoB tomani+&late it, and hoB to &se it in +roblems from +hysics and chemistryto b&siness and economics$ or instance, if the instantaneo&s changetakes +lace oer time, then this deriatie is the elocity of theobect that is moing, and this conce+t is of s+ecial interest to+hysicists and engineersK it is one of their tools for e?+laining the+hysical Borld$ 8hen %saac FeBton Brote O ma, for instance, he Bassaying that forces are related to acceleration, and acceleration is aderiatie, a rate of change$

;cientists are not the only +eo+le interested in calc&l&s$ Economistsand b&siness +eo+le also &se the s&bectK for instance, the cost ofdoing b&siness changes essentially instantaneo&sly oer timeK thischange of cost is called marginal cost$ Monitoring marginal cost alloBsb&sinesses to track their changes today, not oer the last tBenty Beeksor tBenty months$

Then yo& might go on to e?+lain hoB taking a deriatie re&ires hainga f&nction to Bork BithK th&s yo& Bill begin Bith a reieB of somecontin&o&s and notIsoIcontin&o&s f&nctions$ After that, yo& can say that


7/68

yo& Bill go on to talk abo&t ario&s methods of taking deriaties ofmore and more inoled f&nctions, and then yo& Bill disc&ss somea++lications of deriaties, s&ch as hoB to ma?imie and minimie+rofits, say, or maybe elocities, or areas of land$

At this +oint, % Bill leae as an e?ercise for yo& can decide Bhat yo&might Bant to say abo&t integral andor differential e&ations$MeanBhile, letLs sh&t the door on this first day calc&l&s class, and

moe doBn the hall to the +recalc&l&s class, Bhere a more actiistdisc&ssion has beg&n

%nstr&ctor (%)$$$ and BeLll also talk abo&t f&nctions$ Maybe some ofyo& hae seen some f&nctions, like, say, +olynomials$ Can yo& name somef&nctions that are +olynomials9

TBo st&dents together (;#and ;*) ;# ;&re$ y O a?Qn b?QnI# $$$;* Unh maybe ?Q* 9

% 6$S$ y O ?Q* Borks$ %tLs a +olynomial$ Any others9

;# ?Q1 9

;* HoB abo&t y O ?Q* ? #9

%3es$ 8riting both +olynomials on the board$V Anything harder9

;1 HoB abo&t the s&are root of ?9

% 8riting y O ? O ?Q#* on the board$V That one doesnLt Bork$ 5oesanyone knoB Bhy9

;ilence$ ThenV

;# C& oneIhalf is Brong$

% .ood$ 6neIhalf doesnLt Bork as a +oBer, right9 % mean, y O (#*)?Q*is a +olynomial, right9 Pa&seV ;o, this #* +oints to the +oBer in?Q#* doesnLt BorkII% mean, itLs not LlegalL for being a +olynomial,altho&gh it is LlegalL for being some kind of f&nction, yes9 (This+ointsV is called a +oBer, by the Bay, and the other is a coefficientof the +olynomial$ 8eLll define these terms +retty caref&lly d&ring theco&rse$$$

A co&+le of min&tes later$V

% HoB abo&t some other kinds of f&nctions9 Hae any of yo& heard oftrig f&nctions9 Can yo& name some9

;# ;&re$ yO sin ?$

% 3e+, sine Borks$ 8eLll st&dy it, and the others, like cosine andtangent and Bhy theyLre all different from +olynomials$ L;ineLsL+ict&re, by the Bay,is, sin (?) right9 And, it comes &+ in s+ring and+&lley mechanisms, and electrical st&ff, and things like that, and$$$

-etLs ti+toe aBay noB, Be get the idea$

This last instr&ctor can teach &s a lot abo&t managing the classroom$


8/68

Fotice hoB she acce+ted the ansBer she needed to her first &estion,rather than going Bith the seemingly more com+lete res+onse from ;t&dent#, Bho obio&sly knoBs a good deal of the material she may be s+endingthe semester teaching to the others in the class$ ;he also did a goodob ada+ting to the incorrect ansBer y O ?Q#* s&ggested by ;t&dent 1$;he did so Bitho&t em+hasiing the st&dentLs Brong ansBerK in fact, shet&rned a common mistake into a learning e?+erience for the entire class$

There are many good +oints to the classroom disc&ssion Be hae &stBitnessed, b&t in the interests of kee+ing the disc&ssion short, letLs&st say the folloBing Most +eo+le say that teaching +recalc&l&s isboring, boring, boring, b&t this +artic&lar instr&ctor doesnLt make itseem so$

"E?ercises "

8hich of the tBo methodologies described aboe for a firstIdaydisc&ssion of co&rse material Bo&ld yo& be more comfortable Bith9 illin the details of Bhat yo& Bo&ld say to a first semester calc&l&s classabo&t the to+ics of integration and differentiation$ (3o&r ansBers maybe nothing, of co&rse, b&t yo& sho&ld then hae an e?+lanation based on

the syllab&s$)


8hat .oes 6n in Recitation9

6ne ty+ical format for a recitation is this The TA begins by asking ifthere are any &estions on the assigned homeBork +roblems$ A st&dentthen asks to see section :$*, n&mber #, and HoB abo&t n&mber 79 6thers ask for some+roblems from section :$1$ 6ne fairly &iet st&dent says, % Bonder ifyo& co&ld do an old +roblem from section :$#9 Then, for good meas&re,

another st&dent asks yo& to try one of the &estions from section :$4,the ne?t assignment, so Be can see hoB they are done$

3o&, as the +erson in charge, can field &estions in the order in Bhichthey occ&r, taking section :$*, n&mber #< before n&mber 7 from the samesection, say$ 6r, yo& can ask for a list of all the +roblems at thestart of class, collect them on the board, and do them in the order inBhich they occ&r in the te?tbook$ The adantage of the first method isthat yo& ansBer &estions in the order in Bhich they arrie$ Thedisadantage is that the st&dent Bho co&ldnLt do one of the easy+roblems may be totally at a loss as to Bhat yo& are talking abo&t Bhenyo& start off Bith the hardest +roblem in the section$ The second methodsoles the latter +roblem, b&t only at the risk of falling behind in

the material$ This is a +oint yo& may not consider too im+ortant, b&tst&dents alBays do$

A ia media for making the best of both methodologies is to collect the&estions as aboe$ Then tell the st&dents yo& Bill do the section :$4&estion if there is time at the end of class$ ;tarting Bith c&rrentmaterial, do tBo or three of the +roblems from section :$*, one or tBofrom section :$1, and then go back to the one from :$#$ inally, ifthere is time, yo& can s&ggest a hint to get +eo+le started on the :$4e?ercise, Bhich, after all, essentially no one has looked at b&t the onest&dent Bho asked$ %n this Bay, yo& em+hasie c&rrent material of most


9/68

interest to the maority of the class, Bhile at the same time shoBingthat yo& are Billing to deal Bith old and neB b&siness as time+ermits$ And, by giing &st a hint as to hoB to do the neB +roblem, yo&alloB the entire class the o++ort&nity to +&le o&t the secrets of that+artic&lar +roblem$

%t sho&ld be clear by noB that, since recitation consists mainly ofdisc&ssing homeBork +roblems, yo& sho&ld shoB &+ on time and be +re+ared

to disc&ss +ast and c&rrent assigned +roblems$ A shocking n&mber of TAsand instr&ctors try to Bing it often Bith &n+leasant conse&ences forthemseles, their st&dents, and for their end of term eal&ations$ ;o %Bill say this again, Bith em+hasis

A recitation instr&ctor Bill shoB &+ on time +re+ared to disc&ss +astand c&rrent homeBork +roblems$ Fo e?c&ses are acce+tableK this is +artof yo&r ob$

This means that yo& Bill read thro&gh all the +roblems the night beforerecitation, yo& Bill +erform the re&ired com+&tations (3es, the chainr&le is d&ll, and yo& hae &sed it so often before, b&t, &st Bhen yo&donLt +re+are a set of +roblems beca&se theyLre too easy, thatLs Bhen

yo&Lll get st&ck in front of yo&r class on the day before the e?am$),and yo& Bill get the ansBer in the back of the book, beca&se thatLsthe one the st&dents +rie so highly$

8hy do yo& Bant to +re+are metic&lo&sly Bhen yo& knoB this st&ff soBell9 2eca&se

Peo+le neer learn co&rse material as Bell as Bhen they hae to e?+lainit to others$ Een tho&gh yo& took and +assed this co&rse some yearsago, that doesnLt mean yo& canLt learn from a refresher$ After all, itBas si? years ago in high school that yo& took AP calc&l&s, right9Te?tbook a&thors loe to +&t little tricks into the e?ercises to kee+st&dents on their toesK these tricks can tri+ &+ &ns&s+ecting

instr&ctors, too$ 3o& are getting +aid to do these e?ercises$ Een a TABho has done this co&rse three times already needs to recall Bhere the+itfalls are +laced$

3o& can +robably add one or tBo more Bell +laced reasons to this list$Remember those reasons Bhen yo& decide to take a day off from +re+aring$

6ne final tho&ght on this to+ic Co&rse eal&ations bear o&t theim+ortance of instr&ctor +re+aration in st&dents estimations ofteaching$ Een those fac&lty Bho are described as boring and&nmotiating &s&ally receie oerall eal&ations in the 2Imin&s to2Inat&ral range if st&dents say that they can do the co&rseBork asshoBn by their being Bell +re+ared$

%n this section, % hae em+hasied the im+ortance of being +re+ared inteaching recitations$ Pre+aration is im+ortant, b&t it isnLt the onlything$ or more adanced adice, see the sections on The ActieClassroom 'The/*0Actie/*0Classroom and Motiating ;t&dents'Motiating/*0;t&dents$

"E?ercise "

Fame some of the to+ics yo& think % hae slighted or ignored in theaboe disc&ssion$ HoB essential do yo& think they are to good recitations9


10/68


8hat ;ho&ld be on a ;yllab&s9

;ome de+artments kee+ syllab&s files, Bhich +roide a maor im+et&s forinstit&tional, not to mention +ersonal, memory$ Een if s&ch a file is

not readily aailable, yo& can still find o&t Bho ta&ght yo&r co&rselast time, Bhat books they &sed, Bhich cha+ters they coered, hoB+leased they Bere Bith the o&tcome, and Bhat they tho&ght of thest&dents$ %n the &nlikely +ossibility that the +reio&s instr&ctors allhae retired or left toBn, yo& can get some hints and adice frommembers of the c&rric&l&m committee, or maybe een from the staff memberBho deals Bith the cam+&s bookstore$ %f all else fails, yo& can look atthe a++endi? of this te?t for some sam+le syllabi of randomly chosen&ndergrad&ate co&rses$

Eno&gh said abo&t hoB to find old syllabiK noB, Bhat sho&ld yo&rsdescribe9

irst, gie the name, n&mber and section of the co&rse$ Es+ecially ifm&lti+le sections are ta&ght, yo& Bant to identify yo&rs as s+ecificallyas +ossible$ Also Brite days, times and room n&mbers on the syllab&sKe$g$, M8 #0I#070, 104 8hite Hall$ P&t yo&r name on the syllab&s (some+refer Professor A$ 2$ C$ Gones others like 5$ ;mith), yo&r officen&mber and ho&rs if yo& knoB them$ %f yo& haenLt decided yo&r officeho&rs yet, +romise to Brite them on the board as soon as yo& do knoBthem, and "do so often oer the ne?t feB Beeks$"

%t is Borth saying here that % am alBays amaed b&t +robably sho&ld notbe at hoB little erbal information is +rocessed, and % am reminded ofthis fact oer and oer again thro&gho&t my career$ (% told thest&dents that that to+ic Bo&ld be coered on the e?am, b&t they didnLt

listen$)$

Fame the re&ired and recommended te?ts and readings, incl&ding editionn&mbers, s+ecifying Bhich te?ts are re&ired and Bhich are recommended$Then e?+lain Bhich cha+ters Bill be coered (ThomasIinney, Cha+ters#I


11/68

that information into the syllab&s, along Bith any other details yo& mayhae, s&ch as hoB long the e?ams Bill be and Bhere they Bill take +lace$

As far as grading is concerned, offer a general statement like,$$$three e&al e?ams, along Bith a com+rehensie final e?am co&ntingdo&ble alternatiely, oneIandIoneIhalf9V the al&e of the e?ams$HomeBork and class +artici+ation Bill also co&nt abo&t ten +ercent ofthe total grade$ %n this Bay, yo& offer the st&dents a frameBork, Bhile

at the same time alloBing yo&rself some leeBayII Bhat is class+artici+ation for instance, and hoB do yo& +ro+ose to meas&re it9 3et,itLs logical to s&ggest that s&ch +artici+ation is Borth something, andyo& do Bant to hae a mechanism for reBarding st&dents Bho make an e?traeffort$

At this +oint, syllabi often dierge, de+ending on co&rse, material andstyle$ or instance, % hae seen a feBII ery feB, act&ally II fac&lty+&t a short descri+tion of their academic credentials in the syllab&s$6thers, es+ecially those Bho are teaching in a fairly nontraditionalBay, Bill feel the need to describe the classroom sit&ation as they seeit ha++ening$ or instance, they might describe hoB their+roectIoriented calc&l&s sections Bill Bork, Bhat kinds of Briting

assignments they Bill offer in their geometry class, or hoB they Billhandle gro&+ Bork in their +recalc&l&s class$

Regardless of Bhat yo& +&t into yo&r syllab&s, it Bo&ld be Bell toremember that this doc&ment takes on the character of a contract Biththe st&dentsK yo& are telling them Bhat yo& +lan to do, and in t&rn Bhatyo& e?+ect them from them$ Th&s it behooes yo& to take a little careBith Bhat yo& Brite$ 3o& might consider +assing it by an older, Biserfac&lty member for a++roal$

Co&rses often re&ire &n+lanned or &ne?+ected changes in midstream$ Mostof these are acce+table to st&dents$ 6n occasion, hoBeer, somead&stments yo& &nderstand to be minimal or benign Bill elicit an

&ne?+ected o&tb&rst 8hy are yo& canceling e?am three9 % Bas co&nting onthat one to boost my gradeN 3o& canLt do this &nless the entire classagrees, yo& knoBN And then, heaen forbid, if yo& decide to take aote on the &estion, those st&dents Bith higher grades +l&s those Bho&st donLt Bant to take an e?am along Bith those Bho &st Bant to getthe co&rse oer Bith Bill sim+ly o&tote the three really angry ones BhoBant the e?am$ The &ltimate o&tcome is that yo& end &+ giing an e?amyo& ho+ed not to gie, Bhile yo& hae lost the res+ect of, and a&thorityoer, yo&r st&dents$

Fo one can aoid all diffic&lties or see all the +ossible +roblems abo&tto a++ear$ HoBeer, yo& need to think caref&lly abo&t yo&r syllab&sbefore yo& start the semester$ That and getting in+&t from colleag&es is

a strategy that Bill make for a more coordinated co&rse$ The o&tcome ofs&ch +lanning Bill then be better for yo& and for the st&dents, and Billmake yo&r co&rse less Bork in the long r&n$

"E?ercises"

8hat goes into yo&r co&rse9 8hat Bo&ld yo& add to the aboe syllab&s9 %sthere anything that yo& think sho&ld be s&btracted from the syllab&s,and if so, Bhy9 HoB Bo&ld yo& resole the +roblem disc&ssed in thissection of the st&dent Bho Bants to take the third e?am9 %s he being&nfair9 Are yo& Brong for s&ggesting that the e?am be dro++ed9


12/68

-esson Planning ;&rialist Tactics

;&++ose yo& came to toBn on Th&rsdayK it Bas yo&r first time at thecollege$ ;&++ose f&rther that classes begin on Monday, that yo& hae tomoe into yo&r neB a+artment, register for classes, Bait for the cableto be connected, and oh yes yo& hae to start teaching yo&r ery first

class on Monday morning$ or Bhat to do on 5ay 6ne, of co&rse, yo& canlook back to that section in these notes$ 6f co&rse, that doesnLt letyo& off the hook that easily, beca&se yo& are st&ck trying to b&ild asyllab&s$ And then, once yo& hae gien the st&dents a generalintrod&ction to the co&rse, yo& Bill hae to start making &+ lesson+lans$ &rther, yo& BonLt &st hae lesson +lans for T&esday (or, ifyo&Lre l&cky, 8ednesday) yo& hae to +lan an entire semesterLs Borth$

%n this section, letLs consider the most basic as+ects of lect&ring$-ater, in sections called The Actie Classroom'The/*0Actie/*0Classroom, and Motiating ;t&dents'Motiating/*0;t&dents, Be Bill look at more refined as+ects of makings&ch +lans$

6nce, some years ago Bhen % Bas a grad&ate st&dent teaching a nightco&rse in thirdIsemester calc&l&s, % got the tBentyIfo&r ho&r fl& abo&tan ho&r before class started$ My office mate, being a ery kind +erson,offered to s&bstit&te for me$ G&st tell me Bhich section yo& Beres&++osed to do, he said$

The ne?t day, after % had s&fficiently recoered, % asked my officematehoB things had gone$ ine, he re+lied, and Bent on to tell me hoB farhe had gotten in the material$ 2&t hoB did yo& +re+are9 % asked$Easy$ % Bent in to class, anno&nced that % Bas s&bstit&ting for yo&,asked to borroB a co+y of the te?t, and gae the st&dents a fie min&tebreak Bhile % looked oer the a&thorLs a++roach to the material$ Then %

made &+ three e?am+les of arying diffic&lty, and % Bent Bith it$ 2y theBay, hoB are yo& feeling9

;o there it isK a basic +lan for lesson +lans (a +lan for +lans),co&rtesy of my officemate$

;tart by finding o&t Bhat todayLs to+ic is s&++osed to be$

Per&se the te?t to see hoB the a&thor a++roaches the to+icK this hel+syo& +resere the same notation as the te?t, among other things$

Pre+are an int&itie e?+lanation (a he&ristic arg&ment) as to Bhy theto+ic is im+ortant, &sef&l, and releant$

Fe?t, +re+are a feB homeBorkIstyle +roblems of increasing diffic&lty toill&strate to the st&dents the main conce+ts of the section of the te?t$

Allot remaining class time to ansBering &estions or doing old homeBork+roblems$

6f co&rse, this methodology doesnLt sole all +roblems$ %f it did,teaching Bo&ld be triial$ ;o, letLs disc&ss some of the iss&es raisedin the aboe o&tline more f&lly$


13/68

6ne com+laint often oiced is 2&t % donLt like the Bay the a&thor doesthis section$ 8hy sho&ld % enco&rage bad mathematics9

air eno&gh$ Een tho&gh Be may not hae had a choice in the te?tbook,the st&dents Bill still be &sing it for e?+lanations, e?ercises andhomeBork$ 8e can offer alternatie +roofs or better methods, b&t if thest&dents are getting their homeBork from the te?t, they Bo&ld rather nothae to kee+ translating from o&r lang&age and symbolism to the

a&thorLs$ Th&s, Be oBe it to the st&dents to at least say, HereLs hoBthe a&thor a++roaches$$$ An easier more common, better, more &sef&l,more so+histicatedV Bay is as folloBs$ 6n the homeBork and tests, &seBhicheer method yo& like best$ % donLt care as long as yo& get theright ansBer and can e?+lain yo&r method$

Another common obection is that Be sho&ld not &se he&ristic arg&mentrather than an honest, direct, com+lete +roof$

This s&ggestion may sim+ly be a f&nction of a&dience leel (disc&ssedmore f&lly in the section ;t&dent Ty+es ';t&dent/*0Ty+es)$ Clearly, ifyo& are teaching the intermediate al&e theorem in real analysis orto+ology, yo& Bill Bant to consider the roles com+actness ands

connectedness +lay in the disc&ssion$ 2&t, for a freshman English orbiology maor, some +ict&res of contin&o&s and discontin&o&s f&nctionsthat hae +ositie yIal&es at ? O # and negatie yIal&es Bhen ? O 1Bill be m&ch more conincing than an &nintelligible, &nmotiated formal+roof$

This last is also not to say that yo& canLt be l&cky and draB a class ofeager st&dents in an enriched calc&l&s +rogram for +otential mathematicsmaors b&t noB Be are back to the ;t&dent Ty+es &estion$

A third obection is, 8hy do e?am+les9 TheyLre right there in the book$

3o&Lre rightK there are Borked o&t e?am+les in the te?tbook$ 2&t, first

of all, many, if not most, st&dents donWt read the book$ ;econd, noteery detail of the e?am+les is s+elled o&t in the a&thorLs e?+osition$&rther, it isnLt alBays necessary to choose the e?am+les in the te?tKmany instr&ctors % knoB donLt choose the a&thorLs e?ercises$ %nstead,they o+t for a feB +roblems near the assigned homeBork +roblems,telling the st&dents, %f yo& &nderstand hoB to do these e?am+les %LmshoBing yo&, yo&Lll hae a great start on tonightLs assignment$ The&nderlying message is the great motiator %tLs Borth Batching me dothese +roblems, beca&se theyLre like the ones yo&Lll be trying soon$

6ne more obection to the +ro+osed lesson +lan is often bro&ght &+ %sthe s&ggested allotment of time for a lect&re correct9 That is, hoB canyo& leae so m&ch time for &estions and homeBork9 5onLt yo& need all

that class time to e?+lain the details of the c&rrent to+ic9

This, too, is a reasonable obection$ 5ifferent instr&ctors find thatthey take different amo&nts of time to e?+lain details of a lesson$;till, % try to find Bays to leae time for st&dent &estionsKotherBise, hoB do % knoB Bhether they are absorbing the material % claimto be teaching them9 The best Bay to find o&t if my lect&re is beingreceied is to gie the st&dents a chance to tell me Bhat is stillbothering them$ % Bill ret&rn to this to+ic again in the ActieClassroom 'The/*0Actie/*0Classroomsection$


14/68


.rading %ss&es

%t goes Bitho&t saying that grading can bring on +roblems$ Many st&dentsseem to feel as if they start o&t Bith #00/, and Be fac&ltyV m&st&stify the remoal of each indiid&al +oint$ At the same time, fac&lty

sometimes take the e?act o++osite a++roach$

.rading is best treated as a learning sit&ation for all concerned$ Theinstr&ctor learns hoB Bell he or she has ta&ght the material anddesigned the e?am, Bhile the st&dent learns hoB Bell he or she hasabsorbed the co&rse information and st&died for the e?am$

%n mathematics, yo& Bill &s&ally be grading homeBork, &ies ore?aminations$ 6ther +ossibilities are that yo& may grade Britingassignments or class +roects and, of co&rse, yo& Bill be inoled inassigning final grades$

HomeBork is generally the easiest to gradeK the assigned +roblems are

&s&ally Bell Britten o&t in the te?t, and the sol&tion method is fairlyclear$

A common, b&t not &niersal, techni&e for grading homeBork is to assigneach +roblem a fi?ed n&mber of +oints$ ;ome graders &se a tBoI+ointsystem, 0 for a Brong ansBer, # for 6S b&t not com+lete, * forf&lly correct$ After &sing this methodology once or tBice, most gradersfind that it doesnLt hae eno&gh +oints to +ro+erly disting&ish amongthe ariety of +ossible errors that a gro&+ of st&dents can make$;t&dents also tend to sense the same +roblem$ Their com+laint abo&t thegrading is &s&ally to say something like, % only got one n&mber Brong,and all % got Bas a #$

A ero to fie scale is +robably better

0II didnLt een try the +roblem,

#II tried, b&t not een close, * and 1II ario&s leels ofsomeBhat alid b&t mistaken attem+ts,4II correct ansBer b&t Bith some minor errors,7II the correct ansBer Bith details s+elled o&t$

Fote the last comment 6nly the correct ansBer Bith details merits f&llcredit$ There Bill be +oints early in the semester Bhen st&dents Billask yo& to reconsider grades beca&se they got the right ansBer Bitho&tshoBing any s&++orting eidence as to hoB they did so$ 3o& can &se this

as an o++ort&nity to instill good habits into the st&dents$ E?+lain tothe &estioner that he has lost one +oint on this +artic&lar assignmentfor not clearly describing the Bay he Bent abo&t soling the +roblem$This is m&ch easier than trying to conince the same st&dent that hesho&ld hae lost tBele +oints o&t of tBenty for the same a++roach to a+roblem on the second e?am$

This last +aragra+h +oints o&t a good general +rinci+le, both forst&dents and assistants$ HomeBork time sho&ld be &sed to instill goodhabits$ or the st&dent, this means Briting correct, clear, com+letesol&tions$ or the instr&ctor, look to make &niform, defensible grading


15/68

Bith &sef&l comments$

FeB TAs often ask hoB long comments on +a+ers sho&ld be$ My res+onse is&s&ally Fot long at all$ % say this beca&se it is fairly common forneBer TAs to contin&e the sol&tion to the +roblem in the margin of eachst&dentLs +a+er e?actly from the +oint at Bhich the first errorocc&rred$ ;t&dents often donLt read these commentsK sometimes they doread them, b&t still donLt &nderstand Bhat they did Brong$

There are a least tBo Bays to red&ce the amo&nt of commenting yo& needto do on homeBork$ 6ne Bay is to sim+ly +&t an X mark at the +laceBhere the first error occ&rs, and then after all the +a+ers hae beengraded, Brite &+ sol&tion sets of the most commonly mis&nderstood+roblems for all the st&dents$ A second Bay is to start or finish thene?t class Bith a co&+le of homeBork +roblems lots of +eo+le seemed tohae diffic&lty Bith$

@&i grading is not dissimilar to that of homeBork$ 3o& can &se asimilar +oint scheme, and again yo& can sae some grading time by+&tting the ansBers on the board Bhen yo& hand back the &i$ 6nedifference that sometimes occ&rs, hoBeer, is that if yo& are the one

Briting the &i, yo& may occasionally find that yo&r &estion isina++ro+riate$ Een if yo& are not Briting the &i, b&t sim+ly(remember, nothing is eer sim+le) choosing a +roblem from the te?t, yo&may choose one that re&ires a +iece of information that yo& act&allydidnLt lect&re on$ %n that case, common sense sho&ld take +recedenceoer +&re grading iss&es$ 5id yo& ask a &estion st&dents co&ldnLtansBer Bith c&rrent methodology, say9 Then maybe yo& sho&ld gieeeryone f&ll credit for their aliant efforts, Bith e?tra credit forthe one or tBo Bho may hae act&ally knoBn hoB to sole the +roblem$

E?am grading is also in many Bays like homeBork, altho&gh in this casecaref&l +re+aration before grading can sae m&ch time$ There seem to betBo models of mathematics e?ams Those that are gien to classes of &+

to thirty st&dents, and those for fie tho&sand (8ell, maybe fieh&ndred)$ %n the first case, yo& end &+ grading all +roblems on all thest&dent +a+ers$ %n the second, yo& tend to grade only one +roblem b&tyo& m&st grade &ntil yo& dro+, and then get &+ and grade some more$

Uniformity Bith fairness and s+eed are keys to grading e?ams$ Fothing ismore disconcerting than finding at 1 a$m$ that yo& hae graded 14 anyBay, do yo& hae to carry a+ass+ort all the time, Bhere do yo& find ramen noodles, hoB m&ch moneydo yo& really need to lie on in the ;tates, etc$

% am ery sym+athetic Bith yo&r +roblemsII% lied thro&gh this samee?+erience, not once, b&t tBiceIIb&t here % Bill concentrate on theteaching as+ects of yo&r sit&ation$ irst, % Bill address the &estionof hoB to get thro&gh the first feB days in the classroom in the United;tates, and then % Bill talk briefly abo&t the c&lt&ral as+ects of


43/68

teaching in a foreign co&ntry$

"A irst TA AssignmentII8hat to 5o, HoB to Co+e"

irst, it is all right to be nero&sK % Bo&ld be s&r+rised if yo&BerenLt$ All neB TAsIIat least, all the ones Bho care abo&t the ob andBant to do BellIIare nero&s$ G&st remember that, altho&gh yo& may nothae ta&ght before, at least in the United ;tates, yo& hae been

recognied as an intelligent h&man being by those Bho chose yo& to be agrad&ate st&dent$ They did not select yo& for fail&reK instead, yo& haebeen recognied for yo&r +otential for s&ccess$ 6ne of the earlymeas&res of this +otential is the n&mber and &ality of the &estionsyo& ask$

;ome &estions to consider abo&t yo&r TA assignment

Can yo& s+end the first semester or tBo grading in a more adanced classrather than haing to stand in front of a gro&+ of freshman calc&l&sst&dents9 %f so, yo& Bill hae an o++ort&nity to take some Englishlang&age classes and Batch some (terrible) teleision to get thelang&age doBn better$ 3o& can also hae a co&+le of office ho&rs to do

some oneItoIone t&toring to increase yo&r lang&age abilities$

%s it +ossible to get a class that is an easy ob, not necessarily inthe sense of material sim+ler to &nderstand, b&t in the sense ofmaterial easier to e?+lain to st&dents9 2y this % mean st&dents ino&rier series, for instance, hae feBer mis&nderstandings than those ina s&++osedly triial freshman algebra classK th&s o&rier series,altho&gh harder to &nderstand, can be easier to teach$

%f a grading assignment or an easy ob is not +ossible, there are stillBays in Bhich yo& can hel+ yo&rself get thro&gh the semester Bith yo&rsanity, and yo&r dignity, intact$

ind yo&rself tBo mentors yo& think yo& can tr&stK one from yo&r homeco&ntry (if +ossible), and another from the United ;tates$ Ask them toadise yo&, in a semiformal Bay$ Then, before yo&r first class, afteryo& hae done the first homeBork assignment, hae a mock class Bith (atleast) the U$;$ mentor$ %n this mock class, go to a board and do some+roblems as yo& Bo&ld in the first dayLs class$ Concentrate on+ron&nciationIIes+ecially of diffic&lt Bords like contin&ity andtheorem that Bill a++ear in a mathematical conte?t II Brite a lot onthe board, and ask for adice$ ;ee hoB Bell yo& &nderstand the comments,&estions and adice that the mentor is giing yo&$

Fe?t, go to yo&r co&ntryman and ask some &estions abo&t Bhat yo& sho&lde?+ect the st&dents to be like$ This is information that yo&r co&ntryman

Bill &nderstand, b&t the U$;$ TA, haing lied and ta&ght only in the;tates, Bill not$ (% Bill hae more to say abo&t c&lt&ral &estionslater in this section$)

Then go to yo&r first class$ As +art of yo&r introd&ction, e?+lain tothe st&dents that yo& are from another co&ntry and neB to teaching$ Tellthem that, to hel+ them and yo&rself, yo& Bill be trying to s+eaksloBly, that yo& intend to Brite a lot on the board, and that yo& Bo&lda++reciate it if the st&dents Bo&ld hel+ correct yo&r +ron&nciation$8hen someone asks yo& a &estion, if yo& sim+ly do not &nderstand it,ask the other st&dents for hel+ in re+hrasing it$ %f someone says that a


44/68


45/68

My +oint in telling this story is not to claim that a +artic&lar methodof instr&ction is better or Borse than another (altho&gh % do e?+resssome o+inions as to the efficacy of interactie methods elseBhere inthese notes), b&t rather to shoB hoB different s&ch methods can be$

%n the ;tates, most st&dents Bill hae come from high schools Bhere theyBere enco&raged to ask &estions in class, sometimes merely by

interr&+ting the teacherK and Bhere they Bere often re&ired to Bork insmall gro&+s in rather noisy classroom settings$ Th&s, if yo& hae comefrom an atmos+here like the one % described seeing in Ga+an, yo& may beshocked by Bhat yo& think is insolent behaior on the +art of yo&rAmerican st&dents$ 6ccasionally % feel as if % sho&ld a+ologie for someof Bhat % see in the U$;$ classroomK at the same time, % can &nderstandhoB o&r st&dents can +rofit from being able to ask a &estion Bhen theyBant toIIBithin reason$

As &s&al, % hae some s&ggestions$ %f yo& find, as % do, that st&dentssho&ld be able to ask &estions, b&t in a more mannerly Bay than by &styelling o&t, ThatLs not rightN The ansBer sho&ld be fie, then %+ro+ose that yo& tell them on day one that % am o+en to &estions$ 2&t,

+lease raise yo&r hand, so that % knoB Bho is asking the &estion, andso that % can finish my tho&ght before ansBering yo&$ (or mores&ggestions as to hoB to make yo&r classroom more actie, look at s&chsections as The Actie Classroom 'The/*0Actie/*0Classroom andMotiating ;t&dents 'Motiating/*0;t&dents$) %f, on the other hand,yo& beliee that st&dents sho&ld hear Bhat yo& hae to say before theystart asking &estions, ask them to hold their &estions &ntil yo& haef&lly e?+lained the to+ic, the e?am+le or the e?ercise yo& are Borkingon$ %n short, remember that the c&lt&re may not be yo&rs, b&t theclassroom is yo&rs, and it is yo&r right to decide, Bithin reason,Bhat is the best Bay for yo& to get the material across$

A short list of tho&ghts abo&t teaching and liing in an alien c&lt&re

" Altho&gh it is &s&ally easier to lie Bith, room Bith, and deal Bith +eo+le from yo&r oBn co&ntry and c&lt&re, yo& Bill find yo&rself learning so m&ch more if yo& make the effort to s+end a fair amo&nt of time as yo& can in the natie c&lt&re$

" There are a n&mber of adantages to TAing in the U$;$ 3o& Bill learn the lang&age, Bhich can hel+ yo& in yo&r st&dies as Bell as in yo& teaching$ &rther, if yo& decide to stay in the ;tates after grad&ation, yo& Bill need all the lang&age skills yo& can get for yo&r ob$

" %f yo& go back to yo&r home co&ntry, yo&r knoBledge of English

Bill also be hel+f&l there in yo&r ob and yo&r research$

" %f yo& find that some classroom sit&ations are bothering yo&, talk them oer Bith yo&r mentor from yo&r oBn co&ntry$ The +roblem may t&rn o&t to be easily solable, or it may really reflect some c&lt&ral differences$ %n either case, yo& can get adice on dealing Bith the sit&ation$

" 3o& do not hae to acce+t Bhat yo& +erceie to be im+ro+er behaior on the +art of yo&r class$ %f yo& find the st&dents acting in a Bay yo& think is &nacce+table, talk it oer Bith yo&r


46/68

U$;$ mentor$ %n this Bay, yo& can gain some al&able insight into hoB standards ary betBeen yo&r oBn c&lt&re and the one in the United ;tates$

" And finally, enoy yo&r teaching e?+erience$ DieB it as an o++ort&nity to learn abo&t another c&lt&re$ Try to deelo+ a classroom atmos+here that is in kee+ing Bith yo&r +ersonality, Bhile at the same time is rela?ed$ 8hy not hae some f&n Bhile yo&

are getting a degree9


;ome ;illy ;t&ff$$$

This section reca+it&lates some of the material from the earlierChecklist section, b&t in a bit more detail$V

Eeryone Bho starts a neB ob Balks into a +lace that has a life of itsoBnK there is all sorts of silly st&ff too small to consider, and atthe same time too im+ortant not to consider$ And, if yo& ignore all the

little details beloB, a lot of +eo+le Bill get annoyed Bith yo&$

or instance, Bhere are the bathrooms located in yo&r neB b&ilding9 %fyo& c&t yo&r finger, can yo& get a bandage9

8here do yo& get keys to the b&ildings and offices9 5o yo& hae to +ay ade+osit for the keys9

8here do yo& get chalk and erasers9 Carry an e?tra +iece of chalk to theclassroom$ (% knoB an instr&ctor Bho once &sed his shirt to erase theboardK his st&dents neer forgot$)

ind o&t the methods and r&les of &sing the co+y machines$ HoB many

co+ies may be made for yo&r class9 Can yo& make +ersonal co+ies for afee9 8o&ldnLt it be nice if yo& didnLt hae to bother the staff eachtime the machine r&ns o&t of +a+er9

Ask Bhere and Bhen yo& get yo&r +aycheck$ 8hen is the first +ayday9 Thelast9

-earn hoB to search for and check o&t books at the library$ (%Lll betthe librarians knoB, and they might een hel+ yo&$)

ind o&t Bhether yo&r keys to the b&ilding Bork on eenings and Beekends$

8ho decides Bhere yo&r desk is located9

8hat are the r&les abo&t te?tbooks9 5o they hae to be ret&rned at theend of the semester9 Can yo& go ahead and Brite all yo&r notes in themargins9

8here do yo& t&rn in grades at the end of the semester9

%f yo& are giing eening or ;at&rday reieB sessions or e?ams, are therooms generally o+en9 5o yo& hae to resere the room9 rom Bhom9

Are there syllab&s files9 6r files of old e?ams9 8ho can &se them9


47/68

5o yo& hae to +ay for yo&r oBn +encils and +a+er9 HoB abo&ttrans+arency sheets if yo& &se an oerhead9

8hat do all the staff members do9 HoB m&ch of it concerns yo&9

8hat are the general r&les abo&t hoB m&ch time yo& sho&ld be s+ending onyo&r teaching9 HoB many office ho&rs are considered a++ro+riate9

8hen st&dents ask yo& adising &estions yo& donLt knoB the ansBer to,to Bhom sho&ld yo& send them9

8ho is yo&r immediate s&+erisor, and hoB often sho&ld yo& re+ort to himor her, if at all9

5o yo& hae to go to the calc&l&s lect&re yo&Le been assigned to TA for9

8hat is e?+ected of yo& at acation time9 Can yo& go home d&ring st&dyBeek, say, or d&ring that +art of e?am Beek before yo&r class takes itsfinal9 6r Bill the co&rse oerseer get angry beca&se yo& arenLtaailable for office ho&rs and to hel+ Bith the make&+ of the e?am9

Hey, thereLs lots of silly st&ff yo& hae to ask abo&tN %Lll bet yo&can think of ten &estions % missedN And eery school is differentKdonWt ass&me that Bhat yo& did Bhen yo& TAed as an &ndergrad&ate or Bhenyo& Bere Borking on that masterLs degree Bill a++ly noB$


$$$And Fot ;o ;illy ;t&ff

There is bo&nd to come a time Bhen yo& hae a disagreement Bith yo&rco&rse leader$ % can think of many Bays in Bhich this can come abo&tK

for noB, % Bill disc&ss tBo hy+othetical sit&ations$

%n the first case, yo& find that Professor 5imble, the lect&rer incalc&l&s this semester, seems to be haing an inordinately diffic&lttime e?+laining the te?t to the st&dents$ He is a former teaching aBardBinner at yo&r instit&tion, .rand U$, b&t his eyesight, hearing and mostim+ortantly his memory seem to be failing him$ All of this is ca&singthe st&dents a great deal of consternation, and costing yo& and theother TAs a great deal of time$ ;t&dents are coming to yo& foradditional lect&res and they are bombarding yo& and the other TAs Bithlots of &estions o&tside of class$ 8hen yo& dem&r oer e?tra eeningsessions, they res+ond, 2&t Be need yo&IIProfessor 5imble &stdoesnLt make senseN MeanBhile, yo& are in the last f&ll year of yo&r

schoolingK yo&Lre Briting yo&r thesis, trying to finish &+ a +a+er for+&blication, and looking for a ob$ 3o& donLt need the added stress ofbasically teaching calc&l&s to freshmen for a grad&ate st&dentLs salary$

;o Bhat do yo& do9 8ell, one sol&tion Bo&ld be to make yo&r feelingsknoBn to all$ Com+lain to the st&dents, to yo&r thesis adisor, to otherTAs, to the chair, to the deanN 3o& co&ld also ref&se to gie thest&dents e?tra hel+K After all, % didnLt create this +roblem$ 3o&co&ld een call and tell yo&r family$ This Bo&ld certainly get yo&r+osition acrossK een Professor 5imble Bo&ld +robably find o&t, hishearing +roblems notBithstanding$


48/68

8hat Bill be the effect of yo&r com+laints9 8ell, the st&dents Bill knoBhoB yo& feel$ 2&t, if yo& donLt offer them some hel+, they BonLt see yo&as +art of the sol&tion, &st another obstacle in the Bay to theirlearning calc&l&s$

3o&r thesis adisor Bill see yo& as a yo&ng researcher Bho doesnLt&nderstand the +rofessional c&lt&re, Bho Bill mat&re eent&ally, maybe

after yo& get to yo&r first real ob$ He or she BonLt say this to yo&directly, of co&rse, b&t yo&Lll hear abo&t it later thro&gh the gra+eine$

The other TAs Bill think that yo&Lre a +rima donna, that yo&Lre moreBorried abo&t yo&r thesis and yo&r career than abo&t yo&r felloB TAs oryo&r st&dents$

The chair Bill try to e?+lain to yo& abo&t Professor 5imble$ 3o& haeto &nderstand, heLs getting old$ 8e knoB abo&t the +roblem, and maybe byne?t year Be can do something, b&t right noB, BeWre in the middle of theterm, and right noB it Bo&ld be really &nfort&nate to +&ll him o&t ofclass$ 2&t thanks for the information$ 3eah, s&reNV

MeanBhile, the 5eanLs +osition Bill be 8hy doesnLt he kee+ this at thede+artment leel9 ThatLs Bhat a chair is for$

And +oor Professor 5imbleK heLll feel saddened, s&r+rised, shy,conf&sed, im+ro+erly maligned$ Personally ins&lted$

8ell, sol&tion one didnLt Bork too Bell$ %s there another9

-etLs back &+$ 8hatLs Brong Bith giing the st&dents a once a BeekreieB session9 3o& co&ld trade off Bith tBo or three of the otherTAs, so that yo& only hae to cond&ct one of these sessions once a Beek$Then, if yo& &ietly go to the chair (not the deanK kee+ it at thede+artment leel) to e?+lain the sit&ation, he or she Bill be gratef&l

for yo&r e?tra Bork, and may een be able to com+ensate yo& and yo&rfelloB TAs, if only Bith a red&ced load in the ne?t semester$

%f yo&r adisor asks Bhy yo& arenLt getting o&t that tBelfth draft ofyo&r oint +a+er, yo& can e?+lain the details$ He Bill then tell othermembers of the de+artment, and more im+ortantly, Bill Brite in hisrecommendation letter to other schools that yo& are a mat&re yo&ngmathematician Bho Billingly took on e?tra d&ties to sole a smallteaching +roblem Be had here at .rand U$ This Bill make yo& so&nd likesomeone another school Bo&ld be ha++y to hae in the ten&reIstream+osition it is adertising$

3o& Bill hae +resered yo&r good relations Bith yo&r felloB TAs e?ce+t

for that one +erson Bho ref&sed to hel+ yo& and Professor 5imble Billfinish &+ his ill&strio&s career Bith his honor intact$

FoB to the second sticky sit&ation Haing s&ried Professor 5imble,yo& are gien Bhat the chair considers an easy assignment$ Again, yo&Bill hae a section of calc&l&s, b&t this time itLs Bith ProfessorAggress$ rom the gitIgo, the good +rofessor is after st&dents$ Arethey all as d&mb as they seem9 is the first &estion he asks yo&$ Hecalls yo&r homeBork grading into &estionK 3o&Lre too easy on them, andyo& didnLt grade n&mber fifteen +ro+erly he tells yo& in front of agro&+ of TAs and fac&lty in the de+artment lo&nge$ Then he ins&lts other


49/68

fac&lty in front of yo&, and yo& hear from yo&r officemate that he issaying some &nkind things abo&t yo& to them$ &rther, Professor Aggressgies really diffic&lt e?ams (the st&dents say that theyLreim+ossible), and Bants to hae no c&re$ As far as %Lm concerned, ifthey canLt get a L:0L on this e?am, they &st sho&ldnLt be takingmathematics$

6k, yo& s&ried L6le 5imble, so yo& sho&ld be +rofessional eno&gh by

noB to knoB that it Bill do no good to sim+ly scream at ProfessorAggress$ After all, sho&ting and being ins&lting is his stock in tradeKheLs been at it for the last thirtyIsi? years$ HoB abo&t trying to thinklike a +rofessional, instead9

irst of all, ask yo&rself if yo& really did grade n&mber fifteenincorrectly$ %f so, a+ologie and offer to do it oer$ Then, Bhen thene?t e?am comes aro&nd, Bhen yo& make &+ yo&r grading key, ask ProfessorAggress if yo& can shoB it to him to see if it looks like Bhat he Bants$

8hen the st&dents come to com+lain to yo& abo&t Professor AggressLattit&de, do not talk badly abo&t him$ 3o& and the entire de+artment maycom+letely agree Bith their com+laints, b&t Bhateer yo& say Bill not

change the sit&ation one iota$ &rther, if it gets back to the+rofessor, it Bill only end &+ ca&sing yo& to be castigated by the chairor someone else in a&thority$

%nstead, concentrate on making an effort to kee+ the e?ams and gradingscheme as reasonable as +ossible$ To hel+ the st&dents, look back at thefirst e?am to see Bhether the +roblems Bere sim+ly chosen from among thereally hard ones, or Bhether they Bere totally o&t of line$ %f theformer is the case, occasionally &se class time to disc&ss Bith thest&dents some of the later +roblems in each section$ %f itLs the latter,maybe, after yo&Le done yo&r best to get into Professor AggressL goodgraces, yo& might be able to s&ggest some +ossible +roblems for thelater e?ams ones that the st&dents hae some chance of Borking$

Remember, thereLs a h&ge difference betBeen liking a +erson andBorking Bith that +erson$ 3o& do not hae to sit in the coffee roomand defend Professor AggressL attit&des$ %n +oint of fact, the+rofessorLs insolence seems to be coming from some dee+ seated +roblemthat no one in the de+artment is likely to be able to sole$ 2&t, thatisnLt yo&r ob yo&r goal is sim+ly to be an honest, straightforBard,+rofessional +erson$

6f co&rse, one of the ironies of this sit&ation is that, if yo& reallyare +rofessional, co&rteo&s, hel+f&l to the st&dents, and sensitie toProfessor AggressL attit&des, he may &st ask to hae yo& as a TA againthe ne?t semester$ This is one of the diffic&lties yo& Bill hae to

g&ard againstK on the other hand, yo& hae done s&ch a great ob, that %certainly donLt need to tell yo& hoB to handle this +roblem$

"The Perry Model"

8illiam Perry *0V +&blished a theory of st&dent deelo+ment that hasbeen ery infl&ential in higher ed&cation$ The basic model has beenmodified in ario&s Bays$ 2elenky, et al *V hae reised them to fitgender differences, and C&ler and Hackos #0V hae done the same forthe engineering disci+lines$


50/68

Perry9s original model consisted of nine stages of deelo+ment$ % Billdescribe a sim+lified (some might say oersim+lified) fo&rIstage modeland briefly disc&ss +ossible im+lications for mathematics

The fo&r stages of st&dent deelo+ment are

2asic d&ality,M&lti+licity,

Relatiism, andCommitment$

%n basic d&ality, the Borld is s+lit in tBoK the only +ossibilities areright or Brong$ %n this mode, st&dents see their instr&ctors asa&thority fig&res Bho hae all the ansBers$ %nstr&ctors Bho do notinstill the correct ansBers, Bho are o+en to disc&ssion, are merelybad teachers Bho are +laying tricks on the st&dents$

The ne?t stage of deelo+ment, m&lti+licity, is, in PerryLs model,act&ally three stages$ %n the main, m&lti+licity means here that thest&dent noB beliees that itLs all a game$ At first, the st&dents ares&re that there is still a right ansBer and that the instr&ctor is &st

making them +lay along &ntil the correct res+onse is fo&nd$ -ater in them&lti+licity +hase, the st&dents may decide that the instr&ctor doesn9tknoB the ansBer eitherK He canLt be any good as a teacher beca&se hedoesnLt een knoB Bhat Be knoB$ -ater yet, the st&dents may decide tobeliee that anyone may hae their oBn o+inion$

rom this stage, st&dents then &m+ to the +osition of relatiism, Bhereanything goesIIall +ositions are e&ally alid$ Fo one can arg&eagainst my o&tlandish +osition (hoBeer badly reasoned), beca&se thereis no absol&te right or Brong$

%n the final stage, commitment, st&dents take into acco&nt +ositie andnegatie as+ects of decisions they are considering, and then make

balanced &dgements as to hoB to folloB$ %n PerryLs nineIstage model, hes+lits this +rocess into +arts that de+end on the de+th of the commitment$

The im+lications of the Perry model for mathematics and its teaching areim+ortant$ % Bill disc&ss &st a one

;t&dents Bho are in the basic d&ality and m&lti+licity +hases of groBthsometimes say that they like mathematics beca&se in math all theansBers are knoBn$ They often &se mathematics and science as models ofcorrect BorldieBs Bhen they are challenged on some +oint in asociology or English class, say$ 8hen these st&dents find o&t thatambig&o&s ass&m+tions are also made in theorems, they can becomedisill&sioned Bith mathematics itself or the Bay itLs being ta&ght$

Their s&bse&ent +roblems Bith ability to +roe theorems can th&s+ossibly be embedded in their ieB of ed&cation itself, and not sim+lyin their ref&sal to get the theoremI+roof conce+t$ 6ne +ossibleim+lication of this last, if tr&e, may be that co&rses in +roof theoryfor so+homores m&st be constr&cted to take into acco&nt the &estion ofst&dents belief str&ct&res$

2&t % am deling too far into a theory of learning for a te?t at thisleel$ The im+lications of the Perry model are intrig&ing, hoBeer, andyo& may Bish to +&rs&e them f&rther$


51/68


The ;emester in ie Min&tes

"A&g&st *th or 10th"Meet yo&r classes for the first time$ Take roll$ Half the class is noton the roll sheet, the other half isnLt in the classroom$ ;t&dents asklots of &estions only ansBerable if yo&Le been at yo&r instit&tion forfo&rteen years

%s this the right class for me9Are yo& gonna do transcendental f&nctions9HoB do % transfer o&t of here9

8ill yo& sign my sched&le95id % b&y the right book for this co&rse98here do % go to change my registration9% canLt make the final e?am at the sched&led time$ Can % hae a make&+9

Possible ansBers Maybe$ -etLs talk abo&t that after class$ % d&nnoKask me again ne?t time$ .o to (the a++ro+riate) office$ Fot at thisschool$ Maybe$ 6&r book is$$$ .o to (the a++ro+riate) office$ 8ehae some time to fig&re that one o&t, donLt Be9V

"8eek TBo"TBo neB st&dents arrie$ They Bant yo& to t&tor them on Bhat they missed$

A third st&dent kee+s coming to yo&r office for at least an ho&r eeryday for hel+ Bith his homeBork$ MeanBhile, yo&r oBn first big homeBorkset in analysis is d&e tomorroB$

"8eek ie E?am 6ne"Th&rsday night is the first e?am in calc&l&s$ 3o& hae to do an e?trahel+ session on T&esday night, < &ntil > +$m$, for yo&r and tBo otherTALs sections$

ifteen min&tes into the e?am itself, yo& realie that +roctoring is oneof the tBo or three most boring things yo& hae eer done in yo&r life$

3o& s+end the ne?t tBo min&tes calc&lating in yo&r head hoB many times

the lect&rer m&st hae done this in his or her lifetime$

After the e?am is oer, yo& s+end the ne?t tBo days grading oer fieh&ndred co+ies of one +roblem$

"8eek ;i?"3o& try to catch &+ on the class Bork for yo&r oBn co&rses, b&t yo&rst&dents kee+ coming to yo& o&tside office ho&rs for regrades on ario&s+roblems from the first e?am$

"8eek ;een"


52/68

3o& get behind in yo&r oBn Bork, so yo& decide to try a neB teachingstrategy called shoBing &+ &n+re+ared$ That goes so badly that yo&decide neer to try that again$

"8eek Eight"6ne of yo&r st&dents asks Bhen yo& are teaching ne?t semester, beca&sehe Bants to get yo& again$ 3o& canLt say Bhy, b&t this makes yo& feelreally good for the rest of the day$

"8eek Fine E?am TBo"This Beek is like Beek fie, the e?am one Beek$ %t Bo&ld hae gonebetter, b&t yo& hae an analysis midterm of yo&r oBn the day before yo&rst&dentsL test, and a h&ge algebra +roblem set d&e tBo days after thecalc&l&s e?am$ %nstead of grading for tBele ho&rs, it only takes yo&ten$ And, the n&mbers of regrades goes Bay doBn$ 2&t itLs still Bay toom&ch Bork$

"Thanksgiing"Attendance goes doBn drasticallyK st&dents head home een tho&gh thereLsan e?am the Beek they ret&rn$ -ater, they Bill say on the co&rseeal&ations that yo& and the lect&rer didnLt motiate them in the co&rse$

"8eek Thirteen E?am Three";t&dents are an?io&s and s&rly beca&se they didnLt get eno&gh time tost&dy$ The fact that this BeekLs e?am Bas anno&nced in A&g&st doesnWtseem to matter, nor does the fact that they did ski+ si? classes in thelast tBo Beeks$ 2&t itLs yo&r fa&lt that they didnLt knoB eno&gh abo&ttri+le integrals$

"8eek o&rteen"2reak before finals$ ;t&dents yo& haenLt seen for seen Beeks shoB &+for reieB sessions$ AfterBards, tBo come to ask yo&, 8hat can % do to+ass this co&rse9 3o& read yo&r co&rse eal&ations$ 3o& tho&ght yo&knocked yo&rself o&t hel+ing st&dentsK they say yo&Lre aerage, e?ce+t

for the category of organiation, Bhere yo& are beloB aerage$

"5ecember #7th"-ike Beek fie, b&t m&ch, m&ch Borse$ 3o& hae tBo take home e?ams ofyo&r oBn to hand in, +l&s one inIclass final on the day after yo&rst&dentsL finalIIand yo& hae to grade oer fie h&ndred +a+ers again$

"5ecember *0th"3o& hae a grading meeting Bith all the TAs and the lect&rer$ 6ne TAforgets his grade bookK yo& hae to Bait fortyIfie min&tes to calc&latethe class median$ Then yo& discoer that fie of yo&r st&dents are fromone to fo&r +oints beloB the c&toff for an A$ &rther, tBo of yo&r classattendees are not on the roll sheets, Bhile tBo other st&dents yo& hae

neer heard of are$

"5ecember *#st"As yo& t&rn in yo&r last take home in algebra, yo&r most annoyingst&dent Balks &+ to yo& and demands to meet Bith yo& today abo&t thefact that he got a 2, Bhen % obio&sly desered an AI, at leastN

"Gan&ary *nd"8hile Batching a football game, yo& s&ddenly realie, % did itN And itBasnLt that bad$ And, % co&ld do it again$ 2&t not &st yet$


53/68


Gobs, Gobs, Gobs

Maybe yo& haenLt heard, b&t there arenLt any ten&red TAs$ Th&s, todayis a good day to start looking for a ob$

.o to a Bord +rocessor$ P&t together a res&me$ 6f co&rse, yo&r name,address and all the standard categories are on it$ %f yo& are a neB TA,yo& Bill +robably hae lots of Bhite s+ace Bhere yo&r teaching,research and +rofessional actiities sho&ld be$ This Bhite s+ace isBhat yo& need to fill &+ oer the ne?t feB yearsK and, if yo& are anolder TA, yo& sho&ld hae done so already$

;o, &nder teaching, yo& sho&ld try to get as aried a backgro&nd as+ossible$ 5onLt alBays TA in the engineering calc&l&s section, een ifyo& like that best$ HoB is it yo& knoB yo& Bon9t like the b&sinessst&dents instead9

Ask to teach yo&r oBn section of some co&rse, then +&t together a small

+ortfolio Bith a co&+le of yo&r lesson +lans and all the &ies ande?ams$ P&t co+ies of yo&r good (they are good, right9) co&rseeal&ations in that +ortfolio, along Bith any nice eImails or lettersfrom st&dents$

.rade an adanced co&rse in yo&r area rather than teaching all the time$Ask to gie a lect&re or tBo in the co&rse, then +&t that on yo&r res&me$

8rite a teaching statement to +&t into yo&r +ortfolio$ 3o& Bill needs&ch a statement later on, Bhen yo& go &+ for ten&re, so noB is a goodtime to start to hone one$

%n the research category, once yo& hae reached the third year, yo&

Bill +robably hae +icked o&t a s+ecialty$ 3o& can then Brite a shortdescri+tion of yo&r to+ic for the res&me$ At the same time, yo& sho&ldBrite a co&+le of +ages for the +ortfolio on the recent history of yo&rto+ic, Bhat the im+ortant theorems are, Bho is Borking in the area, andBhere yo&r thesis to+ic sits relatie to the Bork of others in the field$

%f yo& are in yo&r first or second year and haenLt done any researchyet, maybe yo& can describe an REU +a+er yo& Brote or yo&r &ndergrad&atethesis at yo&r +reio&s school$

%n terms of +rofessional actiities, yo& can list any talks yo& haegien$ %f yo& hae neer gien talks, noB is the time to start +lanningto do so$ 3o& hae the +ossibility, from yo&r first year in grad&ate

school, to s+eak to the Math Cl&b or the grad&ate st&dent seminar$ 3o&can also call &+ yo& old +rofessors at yo&r &ndergrad&ate college andask them if theyLd like yo& to s+eak at their seminar the ne?t timeyo&Wre in toBn$

3o& sho&ld also oin the AM; and the MAA$ 5oing so shoBs that yo& hae areal, +rofessional interest in mathematics, both as a research area andin its teaching as+ects$

Another +rofessional actiity that is more im+ortant than yo& may thinkat first is to go to MAA and AM; sectional and regional meetings$ These


54/68

are &s&ally Bithin a co&+le h&ndred miles of yo&r home instit&tion, andthey gie yo& a decent idea of Bhat the c&rrent teaching iss&es and hotresearch to+ics are$


-etters of Recommendation

The first time yo& are asked for a letter of recommendation, yo& Bill+robably be s&r+rised$ As the s&r+rise Bears off, yo& Bill e?+erience asinking realiation that yo& hae no idea Bhat to Brite$

%f yo& really donLt knoB the st&dent, of if yo& cannot Brite a generally+ositie letter, yo& may s&ggest that he or she might Bant to findsomeone Bho knoBs them better and can Brite a more s+ecific letter$

6n the other hand, if yo& do remember the st&dent and can Brite a+ositie letter abo&t his or her +otential, by all means do so$ Here9s hoB

irst, note that yo& are being asked for a +rofessional assessment, so

Brite as caref&l a letter as yo& can$ To hel+ yo&rself and thecandidate, find o&t Bhat the +osition is he or she is a++lying for, andBhat the reason is for his or her needing the letter$ %s it for a s&mmerob, maybe9 6r is the st&dent transferring to another instit&tion, ormaybe asking for a letter to a grad&ate or +rofessional school, or for ascholarshi+9 Each +osition s&ggests the &alities the a++licant Bill beasked to shoB, and Bill th&s affect the letter yo& Brite$ Ask for ares&me, and ask the st&dent his or her reason for interest in the+osition$ A descri+tion of the ob can also be hel+f&lK get one from thest&dent if yo& can$

;tart yo&r letter Bith ;t&dentV has asked me for a letter ofrecommendation for yo&r obV$

Then % hae knoBn st&dentV since dateV in ca+acityV$

Fe?t My s+ecific comments as to Bhat % saB$$$ Here yo& can addresss&ch iss&es as came to class, asked good &estions, got a goodgrades, Borked Bell Bith others, and the like$

FoB address the &alities described in the ob descri+tion as beingdesirable motiated, selfIstarter, team +layer, etc$, fit here$%f yo& donLt knoB Bhat &alities the school or com+any is looking for,try to int&it Bhat the f&t&re em+loyer Bo&ld Bant$

inish Bith a comment as to the st&dentLs +otential$

See+ a co+y of the letter, by the Bay$ The st&dent may Bell be back Bithanother a++lication in hand$ And, the em+loyer may call yo& for a folloB&+ comment$ 5id yo& really mean Bhat yo& Brote9


Mathematical Talks

.enerally, yo& Bill be asked for one of tBo ty+es of mathematical talks


55/68

d&ring yo&r time as a grad&ate st&dent the long talk, of abo&t anho&rIIand the short one, abo&t ten to tBenty min&tes$ The long talkalso s+lits into tBo researchIrelated, and e?+ository$

2eliee it or not, of the three ty+es, the researchIrelated one is theeasiest to gie$ This is mainly beca&se, first of all, yo& Bo&ldnLt beasked to, nor Bo&ld yo& acce+t, an initation to s+eak abo&t yo&rresearch &nless yo& Bere actiely doing some$ &rther, noB that yo& are

act&ally doing research, yo& are someBhat of an e?+ert at the to+ic$Th&s, describing the history, stating the main theorems, disc&ssing aco&+le of releant e?am+les, stating and he&ristically +roing yo&rsand othersL res&lts, and listing some o+en +roblems sho&ld all be no+roblem for yo&$ The hardest +art of s&ch a talk is making s&re yo& kee+it interesting for the listener 8hat makes the +roblem significant9 HoBcan yo& make the a&dience care9 8hat kinds of e?am+les Bill gie &s afeeling that Be &nderstand the broad o&tline of the to+ic9 8hat othere?am+les or res&lts Bill indicate the de+th or +oBer of the +roblem9

P&tting s&ch a research talk together is &sef&l for yo& beca&se it Billoffer yo& insight into yo&r oBn Bork$ &rther, yo& Bill need to haes&ch a talk for Bhen yo& go onto the ob market, so noB is the best

time to start +re+aring it$

A good e?+ository talk is not really hard to +&t togetherK it &sttakes time$ 8hat is a good to+ic for &ndergrad&ates that isnLt &s&allycoered in the traditional c&rric&l&m9 ;&aring the circle, say9Fonstandard analysis9 Fonorientable s&rfaces9 Cry+togra+hy9 HoB abo&tThree neB &ses for matrices9 6r, The statistics of baseball9 Allthese, and more, hae been disc&ssed in books and +a+ers that yo& canrefer to, and b&ild from$ These make good talks for sectional meetingsof the Mathematical Association of America, or to grad&ate st&dentseminars and collo&ia, or to st&dents at the colleges at Bhich yo& areinterieBing for a ob$

As Bith the research talk, the e?+ository talk sho&ld be coherent andinteresting$ Here, hoBeer, yo& sho&ld em+hasie the history, e?am+lesand o+en &estions of the to+ic, rather than +recise definitions, +roofsand other dirty detailsIInot that these arenLt im+ortant, b&t theinterested listener can look them &+ later$

The short talk, Bhich % Bill call the tenImin&te talk, is the mostdiffic&lt, een tho&gh most neo+hytes think it is the easiest$ Thereason it is diffic&lt is clear Bhen yo& think abo&t it there is erylittle time in Bhich to say anything im+ortant or &sef&l$ Many +eo+lereason, ;ince they arenLt giing me any time to say anythingmeaningf&l, %Lll &st LBing itL$ This is a big mistakeK most yo&ngmathematicians end &+ haing to gie short talks, and the Borth of their

Bork is ga&ged by the &ality of their +resentation$ (My first talk Bason the last day of a national meeting$ % had an a&dience of three the+reio&s s+eaker, the ne?t s+eaker, and A$H$ ;tone$ ;tone took notes onmy talk$)

;o, hoB do yo& gie a &ality tenImin&te talk9 ;tart by thinkingbackBards 8hatLs the most im+ortant +oint yo& need to make9 Make s&rethat +oint comes in the talk someBhere toBard the end$ 6ften +eo+le Billthink, %tLs that neB theorem of mine thatLs the really e?citing thing,b&t are yo& s&re of that9 ;o often, the a&dience thinks that itLscorollaries or e?am+les that come from the theorem that are im+ortant,


56/68

or maybe the &estions that get ansBered or donLt get ansBered that arereally the reason for the talk$

;o noB yo& knoB Bhere yo&r talk is headingK Bhat do yo& need to getthere9 %s there a definition yo& need for com+rehension9 Then +&t it in$;imilarly, an ill&stratie e?am+le Bill &s&ally gie the a&dience moresense of the to+ic than +roofs$ Also, make s&re yo& indicate Bhy theto+ic is im+ortantK Bhose theorem are yo& e?tending9 8hat &estion are

yo& ansBering9 And Bhat neB &estions hae yo& &ncoered9 8hat are yo&going to try to +roe ne?t, and do yo& Bant to tell the a&dience this9(After all, yo& may Bant more time to get yo&r oBn +roof$)

6f co&rse, in ten min&tes yo& BonLt hae time to +roe thingsIIat most,yo&Lll hae time for a statement or tBo of int&itionIIand then, &s&allyonly in res+onse to a &estion from the a&dience$

;o yo&r talk starts %n #>=


57/68


2ecoming a ac&lty Member

or yo& as grad&ate st&dent, the +ros+ect of getting a fac&lty +ositionat a college or &niersity may seem like entry into +aradise, and to an

e?tent it is$ 2&t, before yo& decide that being a fac&lty member is allBonderf&l, let me e?+lain some of the neB challenges yo& Bill enco&nter$

The relief yo& Bill feel from haing fo&nd a ob Bill be almostimmediately s&++lanted by a sense of aloneness, insec&rity and aoidance$

8hen yo& Bere a grad&ate st&dent, yo& had a cohort of other nQth yearsBho Bere going thro&gh ro&ghly the same cr&cible yo& Bere$ FoB, hoBeer,the other +erson Bho Bas hired at the same time as yo& may Bell see himIor herself as ying for the lone ten&re slot$ 3o&r conersations Billbecome g&arded, if they e?ist at all$ The older fac&lty, at the sametime, Bill seem distant$ Maybe itLs beca&se they hae their oBn +roblemsto contend Bith, maybe they really are &st &iet, and maybe it

really is beca&se yo& re+laced the +erson they Banted to hae hired$ %nany eent, yo& may be s+ending a lot of comm&ting time in the morningsand eenings trying to +sych o&t other +eo+leLs motiations$

%t hel+s to kee+ telling yo&rself that the instit&tion yo& are going tohas already made a real inestment in yo&IIthey do Bant yo& to s&cceed,een if it doesnLt seem so at times$ Try to ignore Bhat seem to besn&bs, kee+ to the track of doing BhatLs best for yo&r st&dents and formathematics, and sae yo&r disagreements for e?tremely significantiss&es, Bhateer those may be$ Try to b&ild a coterie of colleag&es BithBhom yo& can Bork, share ideas, talk abo&t mathematics, andIImostim+ortantlyIIgo to l&nch or to the gym$

;+eaking of inestments, yo& Bill +robably think that the fact that yo&are noB earning abo&t three times Bhat yo& made as a TA makes yo& rich$8ell, not as m&ch as yo& tho&ght, beca&se yo&r ded&ctions from incomefor ta?es and social sec&rity, for yo&r medical benefits, for yo&rretirement (forty years hence), and maybe een for yo&r cam+&s +arking+lace, Bill +robably take abo&t forty +ercent of that +aycheck$ Thatleaes yo& Bith almost do&ble Bhat yo& had as a TA$ 2&t BaitIIyo& forgotthat yo& &sed to lie in collegetoBn Bith fo&r roommates, and thatLsgoing to change, too$ Fot to mention the car yo&Lll b&y to fill &+ the+arking +lace yo&Lre +aying for, right9

;ince yo& are neB to the instit&tion, yo& BonLt knoB (and sometimes yo&BonLt res+ect) the cam+&s c&lt&re$ %f yo& are caref&l and +olitic, yo&

Bill hae an o++ort&nity to redirect the c&lt&reIIBithin reason$ 2&tfirst, yo& m&st b&ild the confidence of others

3o& m&st listen first, before offering adice,3o& m&st make realistic s&ggestions that come o&t of the c&rrent modesof o+eration, and3o& m&st be Billing to acce+t criticism or correction$

R

Documents

Handbook for Mathematics Teaching Assistants