Making a recitation schedule Joseph Bow den THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES Making a RECITATION BOWOEN Making a Recitation Schedule BY JOSEPH BOWDEN, Ph. D. Professor of Mathematics in Adelphi College New York Joseph Bowden 24 Clifton Place, Brooklyn 1922 Copyright, 1922 BY JOSEPH BOWDCN THI CANAAN PHINTING CO. CANAAN. CONN. List of Illustrations Page Sequence card 6 Electiv blank 10 Courses arranged by teachers - 11 Courses arranged by departments 12 Clas list and conflict strip 14 Clas list table 17 Conflict table, partly made out - 23 Conflict table 26 Course sequence form of schedule 31 Unary form of schedule - - 34 Making a Recitation Schedule 1. The plan described in this little book makes the work of schedule mak- ing almost mechanical and thus does away with many of the worries gener- ally associated with such work. The plan is especially suitable for a small institution, but may be adapted to a large one, as wil be explaind later (42). For large institutions however other methods may be more convenient. 5 G MAKING A Sequences. 2. One of the first things for the schedule maker to do is to divide the hours that may be used for clas work into separate groups, prefer- ably so that no two hours of a group come on the same day. I wil call these groups sequences. The sequence card used for several years at Adelphi Col- lege is given below: Sequence Card AOEI.PHI C^OLUEOt V 9 Ml 1 10 11 u i 3 4 M / s- Jt 6 z 10 t / 3 4 5" 7 9 u w 2 3 * 6 ? 9' 10 n 1 S {, 7 10 II r X 3 t 7 ? 9 II 1 '1 ' ' ' 1 ' > 1 1 9 "I" RECITATION SCHEDULE 7 The letters in the left hand colum stand for the days of the school week; the numbers across the top of the table indicate the recitation hours. Sequence I comes at the hours indicated by the figure 1 inside the table, and so on. The vacant hour on Monday at 3 o'clock is left for the faculty meeting and glee club rehearsal, the hour on Thursday at II for the general college assembly. Each course is to be assignd to hours coming all at one sequence. If the courses ar all three hour courses, each sequence should contain three hours. If ther ar some one or two hour courses, they may each be assignd to one or two hours of a three hour sequence. If ther ar some courses of more than three hours, some of the sequences may be made up of the corresponding numbers of hours or such a course may be as- signd to more than one three hour se- quence. For the latter purpose it may be convenient, for example, to call a six hour course two courses and to assign one of these hypothetical two courses to 8 MAKING A one sequence and the other to another sequence. 3. Just as the hours ar groupt into a number of sequences, so it would be convenient if it wer possible to arrange the courses into the same number of groups, such that no two courses of the same group should hav any common member, teacher or pupil. This requirement is frequently im- possible to realize. Then we try to real- ize it as nearly as possible, that is, we try to arrange the courses into groups so that any two courses of the same group do not hav the same teacher and hav as few pupil members in common as possible. If the number of sequences available is large enuf, it is possible to fulfil the above ideal condition exactly, if in no other way, by having one sequence for each course. RECITATION SCHEDULE 9 A large number of sequences has the advantage, then, of removing conflicts, but the disadvantage of extending the hours of recitation into the late after- noon hours, if that is a disadvantage. A small number of sequences has the ad- vantage of closing the hours of recita- tion early in the day, but the disadvan- tage frequently of causing a large num- ber of conflicts, so that many students would hav to substitute for conflicting courses some courses that they do not wish or that ar not so wel suited to the ends they hav in view. Teachers' 4. The next thing, pos- Offers. sibly the first, for the pro- gram maker to do is to get from each teacher a list of the courses he offers for the next semester and a statement of any preferences he may hav for the hours of his courses. For this purpose the following form may be used: 10 MAKING A ElecNv Blank ADELPHI COLLEGE Will you please fill out Ike Jorm fruited telau and return to the office on or before COMMITTEE ON SCHEDULE MM COURSES FOR THE lit 2nd SEMESTER 191 -191 tin. Stt 111 n or cmsx :?* ii r-j I'M u- jrr l MAI nv H L M AK] INI H L M 1 I H L M | The H, L, M in this form stand res- pectivly for History and Filosofy, Lan- guages and Literatures, Mathematics and Siences, the three divisions into which the courses offerd in Adelphi Col- lege wer groupt, one of which divisions was chosen by each student as a major, another as an intermediate, and a third as a minor. RECITATION SCHEDULE 11 5. When these blanks ar returnd to the offis, they should be arranged alfa- betically according to the names of the teachers. In the upper left hand corner should be placed an abbreviation of the teacher's name, say the first one, two, or three letters of his last name, or some other symbol to represent the teacher. 6. From these blanks a list of all courses offerd should be made out in two torms, first arranged alfabetically ac- cording to the names of the teachers and second according to the names of departments or subjects, either in one alfabetical list or in as many as ther ar divisions. The following may be used: Courses Arranged lst 2 ^d |^y semester Teachers 1^2 -192 f 12 MAKING A Courses Arranged lst 2nd [^y semester Departments 1^2 -192 IV a. one f o-f Courses Posting 7. A list of all courses Courses. offerd should then be Students' posted, or printed and dis- Electivs. tributed among the stu- dents, for which purpose either of the latter forms, or a combination of them, may be used. From this list the stu- dents should make their selections, for reporting which the form used for the teachers' offers (4) may be used. RECITATION SCHEDULE 13 8. When the students' electiv blanks hav been handed in, they should be numberd, in the upper left hand corner, using say the numbers 1-50 for the seniors, 51-100 for the juniors, 101-200 for the sofomores, 201-300 for the fresh- men. If the members of the freshman clas ar not individually known, we may assign the number 201 to the whole freshman clas, or 201 and several fol- lowing numbers to represent several types of freshmen. Clas 9. After evident errors Lists. in these blanks hav been corrected by the schedule committee, the clas lists should be made from them. For this purpose the following form may be used: 11 MAKING A ?Cu\s LIST 8 5 AN> ^ o CoN/FLICT S ^ STRIP | E J 1 3 5 3 7 i^ ff ? /* 5 2 (o /J 7 /s ? ^i^-m of Nu.ru of StuJtHts Conflicts RECITATION SCHEDULE 15 In this form the small numbers in the left hand colum ar the students' serial numbers. For the sake of illustration I hav imagind a very small college with sixteen students. The large numbers at the right stand for eight courses which ar supposed to be offerd in our imagin- ary college. The use of these numbers wil be explaind later (18). The left hand margin when fild out as explaind below (11, 12) wil be a clas list; the right hand margin when properly fild out (21-26) wil be the conflict strip of the corresponding clas. 10. Either the students' names should be printed on the form after their serial numbers or the numbers and names should be printed on long strips of paper, using the same sized type and the same spacing as in the form. 11. In making the clas lists one of these clas list blanks is used for each clas. The name of the course is ritten at the top of each blank as indicated. The blanks ar arranged alfabetically accord- ing to the names of the classes and ar 16 MAKING A placed one on top of the other, the blank belonging to the first clas at the bottom, so that only the left hand mar- gins sho, except for the top one, which of course wil be entirely visible, and for the bottom one, of which the left hand colum of numbers should also be visible. The blanks wil be arranged more ac- curately in place if they ar laid on a drawing board upon which a line has previusly been drawn to correspond to one of the hevy black lines near the top of the clas list blank. As a blank is laid down, the hevy line on the strip should be mad to match the line on the board and the blank should then be secured in place by two thum tacks, one at the top and one at the bottom. 12. To make the clas lists a ruler is laid across the blanks from the middle of the first figure 1 to the middle of the second, the electivs of student number 1 ar red from his electiv blank, and a broken line is drawn in pencil as indi- cated in the following diagram, which supposes that student 1 elects courses Bi. 2, Eng. 2, Hist. 2, and Mus. 2 ; and so on for each student. RECITATION SCHEDULE 17 Gas List Table ^ i i o * i ^ $ N > XX) Rr U4 N -Q F; tjy x* -t~ O zr N "S re \ LO d ^ ^ v5 3 2 ?CusLisr| 5 "ND 4 I CONFLICT 1 STRIP 1 OB 06 S 5 i t e ^ J / z 3 V I 9 to // 11 /J /* / s /A L- / 2. 3 H s I 7 9 1 to II ti 13 /* /S If, / X i -^ 3 . 4 5 6 7 8- 5 Wuw SW 7 r 8 9 7 ? ? /Vcon of Nu.ifi.oj- Studfitts Conflicts In this table each horizontal line in- dicates the corresponding student's choice of courses and each colum repre- sents the clas list of the corresponding course. 18 MAKING A 13. The clas lists should now be copied by placing a clas list blank be- side each of these clas lists in turn and checking the corresponding numbers. 14. The copies should be given to the proper teachers for revision. When the revised lists ar returnd, the originals should be corrected and the lines re- drawn in ink, using preferably a ruling- pen and making broad lines. Sections. 15. It may now be de- cided which courses should not be given and which classes divided into sections. The actual division into sections may be made now, according to any plan, or it may be left to be determind by the stu- dents' cards, each student being put into that section which suits his card best. The latter plan wil frequently be found more convenient. The number of laboratory sections may also be decided upon. RECITATION SCHEDULE 19 Numbering 16. If the division into Classes. recitation and laboratory sections is made now, ther should be assignd to each recitation section and to each laboratory section a clas list and conflict strip. The classes and sections should also be numberd in series. For example, if Fysics 1 has two recitation sections and two laboratory sections, these sections may be numberd 71, 72, 73, 74. If the division into sections is left to be made later, one serial number should be assignd to each clas, but no extra numbers for the sections. 17. We may also assign numbers to courses which for varius reasons, as smallness of classes, it is believd wil not be given. Sometimes it is finally de- cided to giv such courses. In such case, if a number had not been assignd, we might be obliged to use decimal frac- tions, or letters, for interpolation, in order to hav the courses numberd in the proper order. 20 MAKING A 18. The assignd numbers should be enterd, in red ink, above the correspon- ding numbers in the lists of courses men- tiond in 6. They should also be en- terd, in red ink, in three places on each clas list and conflict strip, in the two places indicated near the heds of the two colums on the left and right and also in the square to the right of the corresponding black number at the right. 19. The strips belonging to courses which it is believd wil not be given may now be laid aside, to be used later, if it is decided to giv these courses. Conflicts. 20. We ar now redy to investigate conflicts. Two classes ar said to conflict if they hav either the same teacher or one or more pupils in common. Two such classes cannot be placed at the same sequence unless, in case the teacher causes the conflict, an- other teacher is assignd to one of the classes, or, in case the conflict is due to common pupils, these pupils choose be- tween the two courses. RECITATION SCHEDULE 21 21. Arrange the clas lists again as in the table of 12. Take the first clas list from the bottom of the pile and lay it alongside of each other clas list in turn. It is then easily seen whether clas 1 and any other clas, say clas 2, hav any pupils in common, and, if so, how many, and which ones. If they hav none, rite an "0" with ink in the blank conflict strip of the first clas in the square opposit 2. If they hav more common members than the greatest number of conflicts that would be allowd, say 5, rite a check mark " V" with ink in the square. If they hav less than 5 common mem- bers, we may follow either one of two plans. We may rite in the square with pencil the number of common members, or we may rite with ink the ordinal num- bers of the common members. The lat- ter plan takes more time, but wil fre- quently save time in the later work, since we frequently want to kno not only how many common members two classes hav, but who these conflicting members ar. 22 MAKING A In this way all the squares of the blank conflict strip of clas 1 wil be fiki, starting with the square opposit 2. In the same way all the squares of the second blank conflict strip, starting with the square opposit 3, may be fild. And so on. 22. Of course, if two classes hav the same members, their conflicts with the other classes wil be the same. It wil not therfor be necessary to compare them both with the other classes. The squares of the second's blank conflict strip may be fild by copying from the first's strip. 23. As the blanks ar fild out, lay them in a pile with the first at the top and the conflict strips showing, as indi- cated on the next page: RECITATION SCHEDULE 23 Conflict Table Partly made out **. PQ fClASLlST | i3 <~> ^ AND ^ 1 CONFLICT | ^ STRIP ^ oC oq s PQ *^ * Ul <^ Ul >K *^ ^) IT: rj 4~ \n ir v> 3 ^ s ^ 2 / j J / i 3 2 ^T ^ 7 F / A 3 f / / ^ ^ s~ 6 7 9 "? 10 // 13. /3 / v / X /< 3 3 s 3 f i e * S 7 3. 3 A S 6 2 S s i o ^ 7 4 4 >~ j 5" j 7 ^ s 3 3 K V * o ? ? Vum o/ Num.^f Sfudewrs Co7if]/rts 24 MAKING A 24. We may now very easily enter in this table the conflicts due to teachers. If teacher A has courses 1, 2, 3, 4, an "A" should be enterd in squares 2, 3, 4 on blank 1, in squares 3, 4 on blank 2. and square 4 on blank 3. Similarly for the other teachers. 25. The blanks now constitute as laid together half of the conflict table. Since the conflicts of one clas with a second ar the same as those of the sec- ond with the first, this table should be symmetrical about the principal diagon- al, the line of red figures running from the upper left hand corner to the lower right hand corner. The blank squares of the first ro may therfor be fild by turning the first conflict strip around thru a right angle and laying its squares alongside of the first ro of squares. The blank squares of the second ro may similarly be fild by using the second conflict strip, and so on. RECITATION SCHEDULE 25 26. The number of different courses that each course conflicts with should now be counted up and enterd in the square at the bottom of the correspond- ing conflict strip. These numbers may be cald the conflict coefficients. A course whose conflict coefficient is large is in general harder to arrange for on the schedule than one whose coefficient is small. The courses with largest coeffi- cients should therfor be provided for first. 27. If the conflict strips ar now again arranged as in 23, altho this is not necessary for our purpose, they wil form the completed conflict table, which wil look as follows: 26 MAKING A Conflict Table \CLXS LIST 8 1 ^ AND o x I CONFLICT ^ ^ ^ H X N ^ pq STRIP 4 CO S 3 iS M. 52 2T I / '' i ^ / ^ 3 y 5 r 7 8" X / / D 3 4 7 i * 5- 3 _ I) JL X. 3 JL * * * 3 .T i 3 a 5" 3 M j ^ r A 7 * . ff 7- i JL T 4 4. 3 " /O s r X 3 < 5" (7 r // /z 1 a. r 5" x 6 j * / J /* 7 7 / r _ A4 c>* / 6 o r ^ J r ^ V O o f V,-. of - Hut Stu-dtntj Con/M of cts 7 7 7 7 7 7 7 7 i RECITATION SCHEDULE 27 28. It may be wise now to make a vertical list of the courses on one sheet of paper, arranging the courses accord- ing to the magnitude of their conflict coefficients. Assigning 29. The object now is Courses to arrange the courses in to groups, such that the Sequences, courses of each group do not conflict with each other, or conflict as little as possible, and to assign these groups to separate sequences. All of our previus work has been done in order to make this work as easy as possible. Probably the best plan is to cut the conflict strips from the completed clas list and conflict strips. Place the clas lists aside. If the division into sections has been left to be determind by the students' cards (15), the conflict strip belonging to a clas which is to hav sections should now be assignd to recitation section 1 and another conflict strip should be made out for each other recitation sec- tion and laboratory section by copying from this strip. 28 MAKING A The conflict strips should be placed side by side on a table, arranged ac- cording to the magnitude of their con- flict coefficients. Now take as many blank clas list and conflict strips as ther ar sequences and from each of these cut out the strip con- taining the list of course numbers. Number these strips to correspond to the sequences, say from 1 to 12. We wil call these strips, so numberd, the sequence gides. Spred the sequence gides out on a table, leaving spaces be- tween .to represent the sequences. 30. We may next assign certain courses or sections arbitrarily to the se- quences, not more than one to each, these courses or sections being ones which for varius reasons it seems should be set at definit places on the program. The corresponding conflict strips should be placed beside the proper sequence gides. 31. Now take up the conflict strip belonging to that one of the unassignd RECITATION SCHEDULE 29 courses or sections whose conflict coeffi- cient is greatest or one of the greatest. Say this is course 9. By running the eye along the 9th ro of squares on the strips belonging to the courses alredy assignd it can generally be easily seen at which sequence course 9 should be placed to cause the least number of conflicts. Place this conflict strip in the space representing this sequence. If ther ar several equally available sequences, it is usually best to put the course at the sequence coming earliest in the day. Or this course can be left to be assignd after the course having the next highest conflict coefficient. We may continue in the same way until all the courses and sections hav been assignd to sequences, the conflict strips for each sequence being arranged in numerical order. 32. If it happens that about the same number of conflicts wil be caused by assigning a course to either of two different sequences, it may be advisable to consider who ar the students that 30 MAKING A cause the conflicts. One student may find it easy to change his electivs, an- other may find it hard. If the conflict table was made accord- ing to the first plan mentiond in 21, it wil now be advisable to reconstruct a part of it according to the second plan. Suppose that courses 2, 4, 5, and 7 ar alredy assignd to a certain sequence and we wish to find what conflicts wil be caused by putting course 6 at this sequence. We compare clas list 6 again with clas lists 2, 4, 5, and 7 and rite with ink the ordinal numbers of the students causing the conflicts in the correspond- ing squares of the conflict strips 6, 2, 4, 5, 7 in place of the numbers originally put in these squares. 33. When a clas is assignd to a se- quence, corresponding entries should be made, in pencil, in the course sequence form of schedule, the sequence room schedule, and on the teacher's hour time card. The form for the last of these may be the same as that given for tho sequence RECITATION SCHEDULE 31 card in 2. A form for the first is given below. In the interior squares should be placed the numbers of the courses coming at the varius sequences. Course Sequence lst TOrm Of semester Schedule 1^2 -192 / 2. 3 V <- 7 s- ? /o // U Ast Bi Ch Dr EC Ed Eng Fil F,s Fr CM Ger Gfk His^ It Lat Ma^ Mus Psy So 32 MAKING A 34. The sequence room schedule differs from the course sequence form of schedule in having inserted in the squares of the left hand margin the numbers of the rooms insted of the names of departments. In the interior squares should be placed the names of the teachers (or classes) occupying the varius rooms at the varius sequences. 35. After all courses hav been as- signd to places it wil frequently be found that certain courses hav more conflicts than when first assignd to places. The conflicts hav been heaping up as the time table grew. It wil be wise to consider each course over again, to see if, by changing its assignment, the number of conflicts cannot be re- duced. Frequently, when one course has its assignment changed, an opening is made by which we may improve the assignment of another course. The opening, if any, is of course in the se- quence from which the first course has been removed. While making these changes, also, the teachers' cards should RECITATION SCHEDULE 33 be studied, to see if they cannot be im- proved. 36. It wil be wise now to enter the electivs chosen by the students in the sequence strips at the bottoms of their electiv blanks. If these electiv blanks ar arranged one above another leaving the sequence strips exposed, it wil some- times be evident that one clas, senior, junior, sofomore, or freshman, has been favord more than the others with early hours. Sometimes a change can be made so as to remove the inequality. Sequence 37. These sequence Time time cards of the students Cards. may also be used in inves- tigating what course a student had bet- ter be advised to take in place of one of two conflicting courses. 38. They may also be used, with the sequence time card of the teacher, to determin the best place for some new course which it may hav been decided to giv. 34 MAKING A Forms 39. The time table is of now complete and exists Schedule in several forms. It may also be put into several other forms con- venient for use, one of which follows: Unary Torm of Schedule . semester 192 -192 H/ST *ND VlL LANG *m>L\r MAfHAN&Sl Conr*f *? Ttfr- 7?>rt Coarse Sf Tdr t^m Course St? ntr Rwi 40. From the schedule in the above form it may be wise to pick out the courses open to freshmen and with these make a freshman schedule in the same form. 41. Sometimes tables showing what courses come at the varius hours of the week and what teachers occupy the varius rooms at the varius hours of the week ar useful. These of course can be compiled from the other tables. RECITATION SCHEDULE 35 Large 42. The plan describ- Institutions. ed in this book would be unwieldy for a large institution. But it might be applied by artificially divid- ing the large institution into several small ones. The time table might be made up first for a certain group of students, say those whose chief work is in sience. Then another group of students would be considerd, the courses that they hav in common with the first group being considerd as fixt in place. The first group to be considerd might be the senior clas, the second the junior clas, etc. 43. The work may also sometimes be simplified by considering insted of individual students groups of students whose work is the same. A single num- ber could represent such a group. Examination 44. It wil be evident Schedule, that the same method may be applied to making an examina- tion schedule, or the examination sche- dule can be made up from the recitation schedule. INDEX Article Adjusting schedule - 31 Assigning courses to sequences 29-32 Clas list and conflict strip 9 Clas lists 9, 11, 12 Clas list table 12 Conflict coefficients 26 Conflicts - 20 Conflict strips - 9, 21-27 Conflict table 27 Copying clas lists 13 Correcting errors in electiv blanks 9 Course sequence form of schedule 33 Courses arranged by departments - - 6 " " " teachers - 6 " to be divided into sections - 15 " " " omitted 16 Electiv blanks - Examination schedule 44 Freshman " Hour time cards Laboratory sections Method applied to large institution 42 Numbering classes 16 " students' electiv blanks Posting list of courses 7 Revising clas lists 14 Sequences Sequence gides " room schedule " strips " time cards Students' electivs Teachers' offers Unary form of schedule 39 This book is DUE on the last date stamped bel *\ -291973 27 _ EIVED AUG28197: RECEIV MAY 21 7 8m-2, '45(8282) ED LIB. I LITHOMOUNT PAMPHLET BINDER Manufactured by \ 6AYLORD BROS, li Syracuse, N. Y. Stockton, Calif. UCLA-ED/PSYCH Library LB 1038 B67m A 000 974 700 7 Edv.cr.ticn Library LB 1058 B67m