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CAT(TS):COMPUTER ASSISTED TESTING (IN TECHNICAL SUBJECTS) May 23rd, 1991 Carl W. David Department of Chemistry University of Connecticut Storrs, Connecticut 06269-3060 TABLE OF CONTENTS _________________ INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1 A Polemic . . . . . . . . . . . . . . . . . . . . . . . 1 What are we going to do? Improve testing! . . . . . . . 3 Caveats . . . . . . . . . . . . . . . . . . . . . . . . 4 Why should I read this manuscript? . . . . . . . . . . 6 Acknowledgements . . . . . . . . . . . . . . . . . . . 7 IMPLEMENTATION . . . . . . . . . . . . . . . . . . . . . 7 PROCTORn . . . . . . . . . . . . . . . . . . . . . . . . 8 Purpose:To administer a computer assisted examination. 8 Implementation . . . . . . . . . . . . . . . . . . . . 8 Function. . . . . . . . . . . . . . . . . . . . . . . . 9 Philosophy of Browsing . . . . . . . . . . . . . . . 11 The Rest of this Book . . . . . . . . . . . . . . . . 11 UTILITIES . . . . . . . . . . . . . . . . . . . . . . . 12 UtilTest . . . . . . . . . . . . . . . . . . . . . . 13 Routines found in UTILITY.PAS and their use. . . . . 14 EVALUATING EXPRESSIONS . . . . . . . . . . . . . . . . 16 EVALTEST . . . . . . . . . . . . . . . . . . . . . . 18 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . 19 A First Test Question . . . . . . . . . . . . . . . . 19 A simple Calculus Question . . . . . . . . . . . . . 19 An Advanced Thermodynamics Question . . . . . . . . . 19 COMPUTER ASSISTED TESTING in technical subjects INTRODUCTION ____________ A POLEMIC _________ "The objective is to dramatically improve our schools by the year 2000. There is no higher priority for business than this. Without an educated populace we cannot have a strong economy." David T. Kearns, Chairman, Xerox Corp. Business Tokyo, March 1990, page 57 "across the political spectrum, officials and business leaders worry about American schoolchildren lagging behind Asian schoolchildren, about electronic markets ceded to the Japanese, about a self-indulgent corpo- rate culture that has thrived on short-term profits, about an American political system that has grown cyn- ical, slashing, and corrupt.... In education, the President promises that American Students will be the best in the world at math and science by the turn of the century. And the Nation Governors' Association, meeting in Washington last week echoed the goal. But some educators merely shake their heads, arguing that that is unlikely. Even as the the President praised the governors' interest in education, Congressional Democrats criticized the "tepid" 2% education spending increase proposed by the Administration which holds that increased outlays are not necessarily the key to education improvement." Maureen Dowd, New York Times, May 4, 1990, Section 4, page 1 THE PROBLEM Is there anyone left in this country who doubts that there is a problem in mathematics and science education? Parents, educators, business leaders, intellectuals, and even politicians all bemoan the failings of the education system which is going to leave us bereft of native born sci- entists, and dependent on the generosity of other nations' expatriates for our future survival. 1 "This year I am teaching math, and I can see why there is little physics in the inner-city schools. The stu- dents cannot do the mathematics" S. W. Brekke, Letter, Physics Today, Aug. 1986, pg 74. "A test of 47,000 College Freshman prompts call for continuance of remedial program. A third or more of the students entering New Jersey colleges have not ac- quired the verbal and mathematical skills they need to do college-level work, ..." New York Times, Nov. 23, 1979, pg 21. "Report after report has shown that American students are straggling near the tail end of all international math and science competitions. What should be done?" F. Hechinger, The New York Times, March 1, 1989, pg. B7. A SOLUTION? Having spent a lifetime in education, as a professor of chemistry on the one hand, and as a member of my local school board on the other, it has become apparent to me that reforming the educational system in situ is impossible. _______ Partly, this is because no teachers accept culpability and/or responsibility for their work. Even I, when faced with criticism that my students in freshman chemistry, when passed and sent on to organic, can not do stoichiometry, do not know what equilibrium means, can't tell an acid from a base, etc., etc., etc., exclaim:"I taught it. They "passed" the tests. What more is there?" If I am not responsible for the failings of my efforts once my students leave me (provided that I have not pandered to the local authorities and passed fools and charlatans), then I can not criticize teachers in the lower regions of the establishment when they also fail to teach material which I regard as necessary(1) . After a lifetime of reflection on the problem, and watch- ing the country fritter away a king's ransom for "research" and other frivolities in the educational infrastructure, af- ter seeing an enormous investment in computer hardware and software without any discernible gains, it becomes apparent that something is structurally wrong with the system, and conventional methods of fixing the system just won't work. ---------------- 1 Actually, this last sentence is, post hoc ergo propter _____________________ hoc, false. If the students haven't learned, one has no ___ proof that the teachers haven't taught! 2 In fact, heresy, heresy, pouring money into the system won't cure its ills. The New York Times reports: "U.S. PANEL FAULTS UNIFORM TESTING --- Fairness and Accountability Are at Issue, Especially in Multiple Choice Format. report urged changes in standardized tests themselves and in the ways they are used, be- cause current tests are often misleading or unfair and because the nation's changing work force. report said too many tests emphasizing'lower thinking skills' were consuming too much classroom time and school money." May 24, 1990, New York Times If one agrees that multiple choice testing is harming the total educational system, and if one feels that national testing and accountability is important for nudging the sys- tem into improvements, then it is clear that improving test- ing is the sine qua non for consideration. ____________ In what direction then should we turn for testing? In TECHNICAL testing, it is clear that we need to turn away from multiple choice methods and toward truly objective methods of assessment. We need to increase the pressure on students to retain knowledge. We need to ignore the following: "New York State's Education Commissioner said today that the state's public schools should adopt a far broader measure than standardized tests in assessing student performance." Sam Howe VerHovek New York Times, May 23, 1990. The challenge is there. The gauntlet has been thrown. "No more awards for predicting rain. Only for building arks." COMAC, Summer 1990, Solomon Garfunkel, page 2 as re-quoted from Business Week, Spring 1990 WHAT ARE WE GOING TO DO? IMPROVE TESTING! _________________________________________ After jousting with educators over what is and isn't taught, what is and isn't learned, etc., etc., ad nauseam, __________ one comes to the conclusion that no one knows what is being truly learned. The tests which we employ locally are defec- tive, and those used nationally are worse. Measuring what is going on is the first step in correcting what is uni- versally perceived as a major problem in America. To improve testing we need to: 3 1. eliminate multiple choice testing, which warps the way test takers think, 2. require that students maintain the earlier learned skills needed at the current level (precursor material), 3. eliminate or curtail partial credit on poorly worked problems, 4. demand that the word "mastery" be meaningful, i.e., that students command that part of the material which is cen- tral to continuing on. In this book I present the codes and programs required to implement Computer Assisted Testing, in which students are: 1. held responsible for earlier, precursor material, 2. held to a performance level which clearly demonstrates mastery of material without recourse to partial credit, 3. and results in grades which are meaningful. Computer Assisted Testing allows the teacher to construct examinations which are graded in real time by computer. When a student makes a mistake, the teacher can have previ- ously decided to offer help on this question, and this help can be offered uniformly and fairly (even handed) to all students who make a similar error. This help, programmed into the computer, is available in a fairer manner than the help obtained when the teacher approaches the desk of a stu- dent with a problem during an examination, and the student artfully wheedles some hint from the teacher. Alterna- tively, the teacher could have decided not to offer help other than the information that the student has made an er- ror. Even this information can be helpful to a student. If a student truly can't do the work (can't complete the problem), then at some point the student will have to give up. There can be no self deception, no fooling oneself when it comes to passing or not passing Computer Assisted Tests. If you finish, you demonstrated that you knew the material. If you don't finish, you know that something is wrong! ___ CAVEATS _______ My intention is to give you, the reader, the tools for creating Computer Assisted Tests in an MS-DOS environment. These tools consist of programs which themselves will gener- ate programs. The tests we are creating ARE programs which run under MS-DOS (the operating system). It is important to understand that the customization of tests, both the questions themselves, and the help schemata employed, depend on the teacher (you) deciding upon various things such as levels of help, phraseology of questions and 4 help statements, etc., etc., etc.. Therefore, as you adopt Computer Assisted Testing, you will also be adopting a method of working which involves creating not only tests, but programs WHICH ARE tests! The investment made by you in creating each test question will be partially repaid by be- ing able to virtually clone that question into many other similar questions with minimal effort. Further, preserving the questions on disk in a library will allow you at some future date to create similar tests easily by assembling pre-tested questions into packages as needed. Also, the test questions, once obsolete for some reason, can be re- leased to your students for use as study material. All this will be explained later. There is one over-riding decision which I am making for you, which you should accept now (or put this book down). That is, I have chosen to work in Turbo Pascal (from Borland). There are lots of other choices, but this one provides tons of tools for program development, lots of knowledgeable consultants, and is very, very inexpensive in keeping with Borland's philosophy. If you choose to use the system of examinations that I am providing, then you need not learn Turbo Pascal, and you need not ever be involved in changing the format of test questions. HOWEVER, the chances are that you will not be happy with the choices that I have made in terms of how to structure questions, help, etc.. THEREFORE you will have to be willing to take my questions and change them, i.e., re- program them. This will entail learning Turbo Pascal! In any event, you will need to purchase Turbo Pascal version 6.0. You will not need to learn TP6.0 unless you want to perform surgery on questions once you have created them us- ing the procedures included here, i.e., you find that your taste and mine differ(vide infra). To summarize, you must __________ purchase Turbo Pascal Version 6.0! You need not learn it unless you choose, but you must make the program TPC.EXE available to the Computer Assisted Testing programs which you will use to create test questions and examinations. Further good advice is to use a computer with a hard disk. We are going to be creating programs which must be compiled before they are in a form useful for students. Al- though all of this will be set up to run fairly automat- ically, the fact is that once you get started, you will rapidly generate an enormous number of files of test questions. If you attempt to keep these on floppy disks, you will be in big trouble. Therefore, I recommend that at least for you personally, for development purposes, have a PC with a hard disk (the bigger the better). That is not to say that you shouldn't back up your test question files to floppy disk. You should, religiously! But going to a floppy based archive for a question is not pleasant, while having thousands of questions at hand, possibly divided into 5 directories according to subject or sequence number, or something, will be very, very handy. On the other hand, please do not ask your school to equip the examination PC's with hard disks. They should be plain vanilla items, with one and only one floppy disk drive and ________________ 640K of core (i.e., bare bones)! Do not get sophisticated here and network them! Whether we like it or not, some stu- dents will try and steal questions, and it is important to make it as hard as possible to accomplish this task, vide ____ infra. _____ WHY SHOULD I READ THIS MANUSCRIPT? __________________________________ It is true that the diskette contained with this manu- script has on it a program which will allow you, by means of filling in blanks and choosing from menus, to create tests which are "ready to go". In essence, you can treat the en- tire business as a black box in which you pay no attention what so ever to the details, and create tests immediately. But this would deprive you of several important advan- tages. First, there are times when you teach certain spe- cific methods for solving problems, in which the student, generally, follows your method and arrives at an answer. For such highly structured methods, there is no general method of testing, and you will be required to come up with a PASCAL scheme which carries the student through the vari- ous steps one at a time IF YOU CHOOSE TO GIVE THE STUDENT GUIDED HELP IN THIS STRUCTURED METHOD. That is, if the stu- dent, using pencil and paper, does not come up with the cor- rect answer, and you, in writing the test decide to offer help, then you can give STRUCTURED help if you can program it yourself in PASCAL, but are stuck with unstructured help if you can not program it yourself in PASCAL. Therefore, reading the book, and understanding the various PROCEDURES and FUNCTIONS which are given to you (put at your disposal), will open a wider universe of testing possibilities for you. Secondly, and of lesser importance, once a test has been created, it is useful to be able to clone that test without going through all the menus and such which the test genera- tor program will force upon you. Therefore, for cloning purposes, knowing some PASCAL, some editing, etc., is worth- while. Finally, as with any tool, understanding its inner workings makes you more comfortable in using it, especially when something unexpected happens. Since no programs are perfect, you can expect glitches and bugs to appear; being knowledgeable will help you in stamping them out. 6 ACKNOWLEDGEMENTS ________________ All the code that is going to be shown and discussed in this book and included on the distribution diskette(s) is either original coding (by me) or public domain coding re- leased to the general public. I will specifically acknowl- edge the authorship of coding when I know it, so that these persons can feel some pride of authorship. This code "bor- rowed" from others has been (often) substantially altered by me. The central algorithm for evaluating expressions was sig- nificantly enhanced by my wife, Elaine David, who discovered that using bakwards paired brackets could help one locate appropriate places for the multiplication sign (*), i.e., we find juxtapositions of items without an intervening opera- tor, place a )( pair between the items, and expand )( to )*( vide infra. I also wish to acknowledge the support of Professor Maryanski, Associate Vice President of the University of Connecticut, who supported this work with a starter grant which enabled me to purchase the PC upon which all this work was done. Finally, I wish to note that not one federal funding agency was willing to support this work, that every referee that read my entreaties failed me, and that I have been forced therefore to abandon this project. IMPLEMENTATION ______________ What follows is a structured (logically, I hope) dis- cussion of the Computer Assisted Scheme I have created. The student, when handed a diskette, places that diskette in the A: drive of an MS-DOS machine, and types in PROCTOR4 for a 4 question exam (the student has been told how many questions, 2 thru 9, to expect). 7 PROCTORN ________ PURPOSE:TO ADMINISTER A COMPUTER ASSISTED EXAMINATION. ______________________________________________________ This main (driver) procedure performs the following functions: 1. Initialization of variables 2. Read student diskette and determine if student is start- ing or continuing an examination 3. Loop over remaining questions: a. Read next question from diskette (overlay). It is the responsibility of each question to perform the following functions: 1) If this is a re-run of a question, read the save file (*.SAV) otherwise, create the question and create the save file (*.SAV). 2) Present question to student. 3) If desired, echo question to a disk file (*.$$$) 4) Accept student responses, judge them, act on that judgement 5) If desired, echo all student responses to a disk file. b. At the end of each question, when the student has "gotten it right", record that fact, along with other pertinent data, such as whether or not the student needed help and if so, whether or not the student needs to solve a similar (cloned?) problem 4. If done with prescribed number of questions, exit from PROCTOR else go back and continue to the next question. IMPLEMENTATION ______________ In order to implement the above, I have written each question as an OVERLAY, running under a master program (PROCTOR), so that exiting from the overlay without aborting means that the question has been answered or skipped (al- though possibly after help has been given). +-------------------+ | PROCTOR | +----+--------------+ | | +---------+---------+---------+ | | | | +-------+ +-------+ +-------+ +-------+ | Q1 | | Q2 | | Q3 | | Q4 | +-------+ +-------+ +-------+ +-------+ 8 The driving program presents unanswered questions in order. At each return, the main program updates the grade book (perhaps with information passed back from the overlaid question), and then goes on to overlay the next question. To leave the examination the student either completes all the questions correctly (with or without help) or chooses to leave the examination in the middle (choosing the F6 option vide infra of quitting the examination). In either case, provided no tampering has occurred, the diskette which the student hands back to the monitor (or teacher) contains a record of what has transpired, as well as re-start material so that if the student needs to come back an complete a question, the same numbers will be used in the second pres- entation (even if they were chosen at random initially). FUNCTION. _________ We now expand on the various functions of PROCTOR as noted above (features marked 'future' are to be implemented): 1. Initialization a. Set counters, assuming that this is a start of exam- ination, not a continuation of a previous examina- tion. b. (future) Check that program has been loaded at proper point, i.e., that no TSR has been loaded which could allow student to interrupt the testing procedure for improper reasons. c. Obtain the students password(2) ---------------- 2 Just as I am writing this (May, 1990), word comes that several students were canvassing in our dormitories, of- fering to take a Chemistry final examination for money. Several were caught, but the important fact is that many students remain, as ever, interested in the easy way out. It pays us to implement guardian schemes to pro- tect the honest student from the sleazy ones. To do this, we UUENCODE the grade book on the student's disk and then when the student starts work, we use the PROCTOR program to UUDECODE the grade file that is in- cluded on the diskette. Since UUENCODE and UUDECODE Pascal source code in the public domain is available, it is technically possible to incorporate this feature into our schemes. Since the test questions themselves are in compiled form vide infra nothing on the student disk is __________ human readable, and the driver program can't be executed 9 d. Read (and decode) the existing grade file. 2. Is this a resumption? If this is a resumption, then check which questions have already been done correctly, and mark them in such a way that they are not presented to the student. 3. Process the current question The depth of analysis of errors, and the depth of error handling is a function of the purpose of the examination. For pre-college stu- dents, in which examinations are related closely to re- mediation, the depth should be greater than for college students. College students most likely should only be aided slightly, with the intention of inducing them to find their own errors. Thus, for college students, the following sequence need not descend more than one level ---------------- without the password! (I realize how ineffectual the scheme I have outlined is, and in a future implementa- tion, I assume that a full password protection scheme will be created.) To create the initial grade file, use program INITGRAD vide infra Thus the files on the diskette are __________ printable but not understandable, and a password then protects the contents of the disk from being de-crypted by unauthorized persons. I suggest that the teacher use a once only password scheme, and that the student get her password when she surrenders her identification to the test monitor. Once used, I suggest that the pass- word be destroyed, so that the next time this student gets a diskette with an examination on it, there is a new password in place. I accept that the overhead, the human wear and tear of implementing this is unpleasant, but I feel it is necessary and can be circumvented by persons who feel it is unnecessary; just issue a blanket password, and use it everywhere and every time (PASSWORD is a famous choice for the universal password). If UUENCODing is not sufficient, then a higher order coding scheme will be required, but at the outset, we use this simple scheme. Our assumption is that students will be monitored so that no disks are removed from the examination room (for leisurely inspection/hacking) and that no one brings a disk in with a copy of either UUDECODE or UUENCODE. Teachers are of course required to maintain vigilance, since students will often leave no stone unturned in order to pass a course. One last note, students who remove diskettes from their machines during a test, attempt some hacking, and who then re-start their tests with purloined results will generate PASCAL runtime errors! 10 into help schemes, while for lower level students, the depth of help (and diagnosis) might be larger. a. Clear the Screen, write the question to the top of the screen, put up the standard menu (calculator, answer, help, quit). b. Accept the answer given by the student, compare to the right answer. If student answer equals right answer, update grade book, exit loop to next ques- tion item. If student answer is wrong (and the stu- dent asks for help), then check if it is in repertoire of answers which instructor wishes to of- fer aid for; if so, give the help, record that help has been given. Return for student answer. 4. Update grade file, i.e., encrypt the current grade file, UUENCODE it into printable form, and write it to disk. 5. If student needed help during this last question, deter- mine from strategy whether to offer another, diminish grade, etc. etc. etc.. 6. Start up next question or, if at end of exam, halt proc- essing. PHILOSOPHY OF BROWSING ______________________ Should students be able to read all the questions on an examination and choose the order in which they are going to work? This question is central to the organization of the driver program. It implies that if students have access to a diskette and choose to quit the examination, their exam- ination will have to be changed (possibly only by cloning) so that when they return they are not at an advantage rela- tive to those who stayed. Perhaps a grade penalty must be exacted for any student who leaves and returns. We will of- fer these options to teachers later in the process. For the current system, browsing is not allowed. The current PROCTOR program goes through the questions in order, once, and then exits. Students who wish to can re-start the pro- gram, whereupon they are offered a second chance to attempt problems which have not yet been done. An alternative scheme certainly can be invented. THE REST OF THIS BOOK _____________________ To process a single question, we require various utili- ties for writing the question out, accepting answers, etc.. To start this book, we present our utilities with explana- tions below. Once the utilities are out of the way, we will present a set of questions, in ascending order of diffi- culty. Then we will present the utility programs for creat- 11 ing test questions and tests (made up of those questions), libraries, etc.. It is apparent, to me, that the level of equation proc- essing that we can accomplish with the scheme I will outline here is quite limited. Had I gotten external support for programmer help, I would have reprogrammed the entire system using graphics, so that I could employ a more sophisticated equation processor, but alas, that is not to be. The following code is placed in the public domain. You may read it, copy it, modify it, spurn it. Any code which I have taken from other public domain sources are noted as such. You should be aware that there are commercial and shareware products which could be used instead of ours, which would be more efficient. However, in the spirit of "giving it away", the code included here is free. Including commercial units by experts will substantially improve your examinations. No claim for finality (closure or completeness) is made here. The material included is the first step on a long road which will never end. One last disclaimer- no attempt at elegance or sophisti- cation has been made in creating these codes. Rather, sim- plicity, transparency of understanding, etc., have been accentuated. Professional programmers scoffing at the code should remember that speed is not of the essence here, and that therefore, what counts is the ultimate user who may be a beginning programmer. Some day, when the system is more fully implemented, I assume that users will come on line who are not programmers at all, and for whom this is all a "black box". For those people, improvements in the sophis- tication of the code makes sense, since they will never read it anyway. But at the outset, where I am assuming that the reader is either a Pascal programmer or is willing to learn Pascal programming, there is no need to concern oneself with anything other than clarity. To paraphrase Einstein: "... matters of taste are left to the tailor ...". UTILITIES _________ For those unused to Turbo Pascal, and who are learning it here simultaneously, we offer the utilities in a unit (which we can modify later as we find other needs). The diskette contains the code in a form ready for use with Turbo Pascal. Therefore, you can compile this unit directly, setting the destination to disk, creating a UTILITY.TPU file. The .TPU file is going to be loaded each time the proctor program is 12 loaded, making the contents of this unit available to you for use(3) If you are reading this chapter, then you are either knowledgeable in Turbo Pascal programming, or you are learn- ing it. In either case, you should be aware that the fol- lowing manuscript text is not definitive, since as bugs are noted in utilities, I have gone in and corrected them. The composition of this manuscript, on the other hand, is an on- going process which may or may not reflect the latest changes of the files. Therefore, when in doubt, check the distribution disks to see the actual code. For the novice, you should first learn elementary edit- ing, using the WordStar like commands that Turbo Pascal uses. I have included an editor of this type (freeware) for your use in case you do not like using the Turbo Editor (it takes some time to load, since it loads both compiler (linker, etc.) and editor. Please feel free to edit back up copies of programs included here, with the intent of improv- ing them. I assume that you have Turbo Pascal 5.5 or 6.0. UTILTEST ________ UTILTEST.PAS, is a utility test program which allows you to check that the utilities are working properly before you commit to using them. It is included on the distribution diskette. When you compile and execute the program, it will load the UTILITY.TPU file from the diskette (unless you used TPUMOVER to move UTILITY.TPU into the TURBO.TPL file). You should exercise the UTILITY.TPU unit extensively, until you are satisfied that it will serve our purposes. ---------------- 3 In fact, since it is going to be used so often, it makes sense to include this in the TURBO.TPL file, which is loaded each time the Turbo Pascal compiler is loaded. To do this, compile UTILITY.PAS to disk, creating a file UTILITY.TPU. Next, from the DOS prompt execute TPUMOVER with the arguments TURBO.TPL and UTILITY.TPU, i.e. : TPUMOVER TURBO.TPL UTILITY.TPU whereupon you will enter the mover program which will allow you to move UTILITY.TPU into TURBO.TPL. THe ad- vantage of doing this is that UTILITY.TPU will then al- ways be available to you no matter what. The disadvantage is that you will decrease the size of other programs you are creating, since UTILITY.TPU will always be in memory. 13 ROUTINES FOUND IN UTILITY.PAS AND THEIR USE. ____________________________________________ Since the computer assisted testing system is evolving, the printed documentation which you are currently reading need not correspond exactly to the current contents of the actual distribution diskettes. Within reason, every attempt has been made to upgrade the documentation as changes are made in the various units, but slight differences between this documentation and the diskette's version should be ac- cepted. The diskette takes preference over the documenta- tion! What follows is an English description of the included utility routines: 1. Noise(WhatSounds:Sounds) ________________________ Noise is a program which will give various sounds ac- cording to the kind of argument passed, i.e., Good, Bad, FinishedGood, FinishedBad, Acknowledge, Cont. Each of these sounds consists of a duration, frequency and repe- tition pattern. They have no intrinsic meaning, and can be altered easily. 2. Read_Key ________ Contrary to most of the other procedures in this file, Read_Key is a function. This function serves two purposes. First, it obtains characters, function keys as well as normal characters, and second, it sets the global variable Escape_Struck true or false depending on whether or not the user has struck the ESCape key. 3. Our_Write(X,Y,s); _________________ Our_Write is a procedure which takes over a line starting at the point X,Y and writes a string (s). Af- ter writing the string, Our_Write clears the rest of the line! 4. YesNo(X,Y,s); _____________ Function YesNo prints a prompt (s) at the pont (X,Y) and then ways for a value in the set 'y','n','N','Y'. Yes returns True, No returns false. 5. Pause(X,Y,s); _____________ Pause prints a prompt (s) at the pont (X,Y) and then waits for any keystroke from the keyboard. 6. CheckBrackets(Str,Err,Err_Message) __________________________________ 14 CheckBrackets counts the number of left and right brackets in an algebraic expression and returns a mes- sage about that count. If the expression is well formed, the count should be zero and the procedure should return an Err of zero and an Err_Message of 'O.K.'. Either can then be used for future reference. 7. Remove_Double_Blanks(Str) _________________________ This procedure takes a string and shrinks it by re- placing all multiple blanks with a single blank, suit- able for printing. 8. Remove_all_blanks(Str); _______________________ As implied by the name, this procedure changes a string with blanks into one without any blanks by squeezing the string. This is required so that there will be no blanks in equations, even if the student typed some in to improve readability. In case extra blanks crept in to a string during substitutions, this procedure will remove them! 9. Trim_fore_aft(Str); ___________________ This procedure removes leading and trailing blanks, but leaves internal blanks alone. 10. PoseQuestion(Y,question); _________________________ This procedure writes the text (question) out, start- ing in column one of line Y. The line is broken at a blank, no words are artificially split up. 11. Read_Equation(X,Y, __________________ L{length}, __________ s{returned string}, ___________________ char_set); __________ This procedure reads an equation, accepting numbers, algebraic symbols, the period, and all the chars in the char_set, which allows for functions and the current variable. 12. Read_Float_Masked(X,Y,L _______________________ {number of places to right of decimal _____________________________________ point}, _______ Prompt (text of prompt message), ________________________________ Print_Prompt {show old value? ______________________________ (Boolean)}, ___________ W {resultant value/or original one, ____________________________________ real}) ______ 15 This procedure prompts at (X,Y) for an answer of the form +x.yyyE+zz where L is the number of y's in the x.yyy form, i.e., 3 here. If Print_Prompt is true, the old value of W is printed inside the prompt, otherwise it is not show. 13. Read_Fixed_Masked(X,Y, ______________________ Left,LRight {number of places to left _____________________________________ & right of decimal point}, __________________________ Prompt {text of prompt message}, ________________________________ Print_Prompt {show old value? ______________________________ (Boolean)}, ___________ W {resultant value/or original one, ____________________________________ real}) ______ This procedure prompts at (X,Y) for an answer of the form +xxx.yy where Left is the number of x's in the xxx.yy in the form, i.e., 3 here, and LRight is the num- ber of y's. If Print_Prompt is true, the old value of W is printed inside the prompt, otherwise it is not show. 14. Read_Integer_Masked(X,Y, ________________________ L, {number of digits}, ______________________ Prompt {text of prompt message}, ________________________________ Print_Prompt {show old value? ______________________________ (Boolean)}, ___________ IW {resultant value/or original one, _____________________________________ integer}) _________ This procedure prompts at (X,Y) for an answer of the form +yyy where L is the number of y's in the yyy form, i.e., 3 here. If Print_Prompt is true, the old value of IW is printed inside the prompt, otherwise it is not show. EVALUATING EXPRESSIONS ______________________ The single most important difference between Computer As- sisted Testing and all other kinds of testing (not including oral examinations) is that Computer Assisted Testing can be used to ascertain whether or not a students formula is cor- rect. Thus, when a student gets a wrong numerical answer, the computer can ask for the formula (or expression) used to obtain this (incorrect) answer and ascertain whether or not the expression itself was correct (relative to the known right answer). Where in hand grading you might not see the equation (tired, bored, angry (?)), the computer tirelessly handles each students responses equitably and uniformly. So, our problem is, how do we get the computer to understand formulas? 16 Assume that the student gives an answer 'x+4' and the computer is looking for the formula which you wrote as '4+x'. Clearly, if we subsitute THE SAME random number into each of these expressions we will get the same answer! Assume that we have an expression 4-1.01x and the student enters -1.01x+4 Assume that the random number generator creates for its next returned value the number 0.01234. -1.01*0.01234 + 4 = 4 - 1.01*0.01234 so you can see that substituting the random number into the "correct" and the "student" equations results in a numerical equality. We are sure that the two forms are equal. If we doubt it, do the process again with a different random num- ber. Since the equations are both linear, it is impossible that the equality could hold at two different values of 'x', and therefore we are assured that the forms are equivalent. We will also get the same answer if the student is play- ing games and entered '2+2+x', and '(x+2)+2', etc., etc., etc.. In other words, no matter what the student offers (lexicographically), we can cope provided that the students response evaluates to the 'correct' value. If the student offered '4.1+x', then provided we set our tolerance level for numerical equality low enough, we can distinguish between this response and the desired one. We will use a statement: IF ABS(student_value - our_value) <= tolerance THEN ___________________________________________________ as our central scheme for deciding whether or not the stu- dents answer is correct, i.e., agrees with what we expect. So, summarizing, we see that to tell if two expressions are the same: 1. make sure that both equations have the variable present 2. substitute a random number into each expression and pass the resultant purely numeric expressions to Evaluate. They should return the same value, but to be sure that there is no possibility that slight numerical errors, such as having a different number of significant fig- ures, we use the following: ABS(student value - known value) <= tolerance _____________________________________________ to make sure that the two are identical. We will also use this scheme to find out what the student did wrong, since we will include in our help sections equations for common errors which can be compared to student responses, with the idea that if we can ascertain the nature of their error from a table of common errors, then we can CHOOSE OR NOT to offer them some help. 17 To begin, we need to be able to evaluate numerically based algebraic expressions (without variables). EVAL3.PAS is the latest version of the parsing scheme. This material is adapted from the Borland code which was included in vari- ous earlier versions of Turbo Pascal. EVALTEST ________ On the distribution diskette is a program called EVALTEST.PAS which checks that the EVAL3.TPU module works. This program allows you to input calculator like expressions such as 1. 1 + 2 2. 2*3+4 3. 2*(3+4) 4. 2*(3+4)/2.1 with the evaluated value spit back. After reading the EVAL3.PAS code, you will see that several functions, e.g., cosine, log, etc., are also useable in EVAL3. The second part of EVALTEST checks for expressions. This uses CHECKANS (vide infra) to check that two single variable expressions are equal. Try entering: 1. 3x 2. 2x+x to see whether or not these two expressions are equal. EVALTEST will evaluate numerical expressions until the first question mark ("?") is entered, and then it will evaluate single variable expressions until a second question mark is entered at the correct prompt. This is (adjusted) copyrighted code, owned by Borland and declared in the public domain for non-profit use. For simple numeric input problems, we are done. EVAL3 can be used directly to evaluate expressions such as "3*4+2.1". If our tests only involved numerical answers, this would be the end of it. In fact, MQ03, the MAKEQUEStion program included on the distribution diskette assumes that this is the most that you are going to do, e.g., employ questions with solely numeric answers. 18 EXAMPLES ________ The examples indicated below are creations of the MQ pro- gram. The .IN1 files can be found on the distribution diskette. A FIRST TEST QUESTION _____________________ INITQUES.IN1 is the output of the MAKEQUES program, and creates a simple algebra problem. You will see that it in- volves the simultaneous purchase of two kinds of nuts (how a propos). This file is included by the Turbo Pascal compiler when you are compiling PROTOTYP.PAS, since that program con- tains a statement '{$I INITQUES.IN1}'. A SIMPLE CALCULUS QUESTION __________________________ Here is a simple calculus question, INTEG1.IN1. There are several other INTEGn.IN1 files included in the distrib- ution. AN ADVANCED THERMODYNAMICS QUESTION ___________________________________ This last example is a theoretical flame temperature problem. 19