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*Tue Apr 15 04:41:17 2008 UTC*
(11 years, 10 months ago)
by *gage*

File size: 12019 byte(s)

File size: 12019 byte(s)

Edited the first three paragraphs describing why math objects are used. (I also copied these paragraphs into the wiki itself in the "introduction to math objects" page.)

1 =head1 MathObjects-based Answer Checkers 2 3 MathObjects are designed to be used in two ways. First, you can use it 4 within your perl code when writing problems as a means of making it 5 easier to handle formulas, and in particular, to be able to use a single 6 object to produce numeric values, TeX output and answer strings from a 7 single formula entry. This avoids having to type a function three 8 different ways (which makes maintaining a problem much harder). Since 9 MathObjects also included vector and complex arthimetic, it is easier to 10 work with these types of values as well. 11 12 Secondly using MathObjects improves the processing of student input. 13 This is accomplished through special answer checkers that are part of 14 the Parser package (rather than the traditional WeBWorK answer 15 checkers). Each of these checkers has error checking customized to the 16 type of input expected from the student and can provide helpful feedback 17 if the syntax of the student's entry is incorrect. 18 19 Checkers are available for each of the types of values that the parser 20 can produce (numbers, complex numbers, infinities, points, vectors, 21 intervals, unions, formulas, lists of numbers, lists of points, lists of 22 intervals, lists of formulas returning numbers, lists of formulas 23 returning points, and so on). 24 25 To use one of these checkers, simply call the ->cmp method of the 26 object that represents the correct answer. For example: 27 28 $n = Real(sqrt(2)); 29 ANS($n->cmp); 30 31 will produce an answer checker that matches the square root of two. 32 Similarly, 33 34 ANS(Vector(1,2,3)->cmp); 35 36 matches the vector <1,2,3> (or any computation that produces it, e.g., 37 i+2j+3k, or <4,4,4>-<3,2,1>), while 38 39 ANS(Interval("(-inf,3]")->cmp); 40 41 matches the given interval. Other examples include: 42 43 ANS(Infinity->cmp); 44 ANS(String('NONE')->cmp); 45 ANS(Union("(-inf,$a) U ($a,inf)")->cmp); 46 47 and so on. 48 49 Formulas are handled in the same way: 50 51 ANS(Formula("x+1")->cmp); 52 53 $a = random(-5,5,1); $b = random(-5,5,1); $x = random(-5,5,1); 54 $f = Formula("x^2 + $a x + $b")->reduce; 55 ANS($f->cmp); 56 ANS($f->eval(x=>$x)->cmp); 57 58 $x = Formula('x'); 59 ANS((1+$a*$x)->cmp); 60 61 Context("Vector")->variables->are(t=>'Real'); 62 $v = Formula("<t,t^2,t^3>"); $t = random(-5,5,1); 63 ANS($v->cmp); 64 ANS($v->eval(t=>$t)->cmp); 65 66 and so on. 67 68 Lists of items can be checked as easily: 69 70 ANS(List(1,-1,0)->cmp); 71 ANS(List(Point($a,$b),Point($a,-$b))->cmp); 72 ANS(List(Vector(1,0,0),Vector(0,1,1))->cmp); 73 ANS(Compute("(-inf,2),(4,5)")->cmp); # easy way to get list of intervals 74 ANS(Formula("x, x+1, x^2-1")->cmp); 75 ANS(Formula("<x,2x>,<x,-2x>,<0,x>")->cmp); 76 ANS(List('NONE')->cmp); 77 78 and so on. The last example may seem strange, as you could have used 79 ANS(String('NONE')->cmp), but there is a reason for using this type 80 of construction. You might be asking for one or more numbers (or 81 points, or whatever) or the word 'NONE' of there are no numbers (or 82 points). If you used String('NONE')->cmp, the student would get an 83 error message about a type mismatch if he entered a list of numbers, 84 but with List('NONE')->cmp, he will get appropriate error messages for 85 the wrong entries in the list. 86 87 It is often appropriate to use the list checker in this way even when 88 the correct answer is a single value, if the student might type a list 89 of answers. 90 91 On the other hand, using the list checker has its disadvantages. For 92 example, if you use 93 94 ANS(Interval("(-inf,3]")->cmp); 95 96 and the student enters (-inf,3), she will get a message indicating 97 that the type of interval is incorrect, while that would not be the 98 case if 99 100 ANS(List(Interval("(-inf,3]"))->cmp); 101 102 were used. (This is because the student doesn't know how many 103 intervals there are, so saying that the type of interval is wrong 104 would inform her that there is only one.) 105 106 The rule of thumb is: the individual checkers can give more detailed 107 information about what is wrong with the student's answer; the list 108 checker allows a wider range of answers to be given without giving 109 away how many answers there are. If the student knows there's only 110 one, use the individual checker; if there may or may not be more than 111 one, use the list checker. 112 113 Note that you can form lists of formulas as well. The following all 114 produce the same answer checker: 115 116 ANS(List(Formula("x+1"),Formula("x-1"))->cmp); 117 118 ANS(Formula("x+1,x-1")->cmp); # easier 119 120 $f = Formula("x+1"); $g = Formula("x-1"); 121 ANS(List($f,$g)->cmp); 122 123 $x = Formula('x'); 124 ANS(List($x+1,$x-1)->cmp); 125 126 See the files in webwork2/doc/parser/problems for more 127 examples of using the parser's answer checkers. 128 129 =head2 Controlling the Details of the Answer Checkers 130 131 The action of the answer checkers can be modified by passing flags to 132 the cmp() method. For example: 133 134 ANS(Real(pi)->cmp(showTypeWarnings=>0)); 135 136 will prevent the answer checker from reporting errors due to the 137 student entering in the wrong type of answer (say a vector rather than 138 a number). 139 140 =head3 Flags common to all answer checkers 141 142 There are a number of flags common to all the checkers: 143 144 =over 145 146 =item S<C<< showTypeWarnings=>1 or 0 >>> 147 148 show/don't show messages about student 149 answers not being of the right type. 150 (default: 1) 151 152 =item S<C<< showEqualErrors=>1 or 0 >>> 153 154 show/don't show messages produced by 155 trying to compare the professor and 156 student values for equality, e.g., 157 conversion errors between types. 158 (default: 1) 159 160 =item S<C<< ignoreStrings=>1 or 0 >>> 161 162 show/don't show type mismatch errors 163 produced by strings (so that 'NONE' will 164 not cause a type mismatch in a checker 165 looking for a list of numbers, for example). 166 (default: 1) 167 168 =back 169 170 In addition to these, the individual types have their own flags: 171 172 =head3 Flags for Real()->cmp 173 174 =over 175 176 =item S<C<< ignoreInfinity=>1 or 0 >>> 177 178 Don't report type mismatches if the 179 student enters an infinity. 180 (default: 1) 181 182 =back 183 184 =head3 Flags for String()->cmp 185 186 =over 187 188 =item S<C<< typeMatch=>value >>> 189 190 Specifies the type of object that 191 the student should be allowed to enter 192 (in addition the string). 193 (default: 'Value::Real') 194 195 =back 196 197 =head3 Flags for Point()->cmp 198 199 =over 200 201 =item S<C<< showDimensionHints=>1 or 0 >>> 202 203 show/don't show messages about the 204 wrong number of coordinates. 205 (default: 1) 206 207 =item S<C<< showCoordinateHints=>1 or 0 >>> 208 209 show/don't show message about 210 which coordinates are right. 211 (default: 1) 212 213 =back 214 215 =head3 Flags for Vector()->cmp 216 217 =over 218 219 =item S<C<< showDimensionHints=>1 or 0 >>> 220 221 show/don't show messages about the 222 wrong number of coordinates. 223 (default: 1) 224 225 =item S<C<< showCoordinateHints=>1 or 0 >>> 226 227 show/don't show message about 228 which coordinates are right. 229 (default: 1) 230 231 =item S<C<< promotePoints=>1 or 0 >>> 232 233 do/don't allow the student to 234 enter a point rather than a vector. 235 (default: 1) 236 237 =item S<C<< parallel=>1 or 0 >>> 238 239 Mark the answer as correct if it 240 is parallel to the professor's answer. 241 Note that a value of 1 forces 242 showCoordinateHints to be 0. 243 (default: 0) 244 245 =item S<C<< sameDirection=>1 or 0 >>> 246 247 During a parallel check, mark the 248 answer as correct only if it is in 249 the same (not the opposite) 250 direction as the professor's answer. 251 (default: 0) 252 253 =back 254 255 =head3 Flags for Matrix()->cmp 256 257 =over 258 259 =item S<C<< showDimensionHints=>1 or 0 >>> 260 261 show/don't show messages about the 262 wrong number of coordinates. 263 (default: 1) 264 265 =back 266 267 The default for showEqualErrors is set to 0 for Matrices, since 268 these errors usually are dimension errors, and that is handled 269 separately (and after the equality check). 270 271 =head3 Flags for Interval()->cmp 272 273 =over 274 275 =item S<C<< showEndpointHints=>1 or 0 >>> 276 277 do/don't show messages about which 278 endpoints are correct. 279 (default: 1) 280 281 =item S<C<< showEndTypeHints=>1 or 0 >>> 282 283 do/don't show messages about 284 whether the open/closed status of 285 the enpoints are correct (only 286 shown when the endpoints themselves 287 are correct). 288 (default: 1) 289 290 =back 291 292 =head3 Flags for Union()->cmp and List()->cmp 293 294 all the flags from the Real()->cmp, plus: 295 296 =over 297 298 =item S<C<< showHints=>1 or 0 >>> 299 300 do/don't show messages about which 301 entries are incorrect. 302 (default: $showPartialCorrectAnswers) 303 304 =item S<C<< showLengthHints=>1 or 0 >>> 305 306 do/don't show messages about having the 307 correct number of entries (only shown 308 when all the student answers are 309 correct but there are more needed, or 310 all the correct answsers are among the 311 ones given, but some extras were given). 312 (default: $showPartialCorrectAnswers) 313 314 =item S<C<< partialCredit=>1 or 0 >>> 315 316 do/don't give partial credit for when 317 some answers are right, but not all. 318 (default: $showPartialCorrectAnswers) 319 (currently the default is 0 since WW 320 can't handle partial credit properly). 321 322 =item S<C<< ordered=>1 or 0 >>> 323 324 give credit only if the student answers 325 are in the same order as the 326 professor's answers. 327 (default: 0) 328 329 =item S<C<< entry_type=>'a (name)' >>> 330 331 The string to use in error messages 332 about type mismatches. 333 (default: dynamically determined from list) 334 335 =item S<C<< list_type=>'a (name)' >>> 336 337 The string to use in error messages 338 about numbers of entries in the list. 339 (default: dynamically determined from list) 340 341 =item S<C<< typeMatch=>value >>> 342 343 Specifies the type of object that 344 the student should be allowed to enter 345 in the list (determines what 346 constitutes a type mismatch error). 347 (default: dynamically determined from list) 348 349 =item S<C<< requireParenMatch=>1 or 0 >>> 350 351 Do/don't require the parentheses in the 352 student's answer to match those in the 353 professor's answer exactly. 354 (default: 1) 355 356 =item S<C<< removeParens=>1 or 0 >>> 357 358 Do/don't remove the parentheses from the 359 professor's list as part of the correct 360 answer string. This is so that if you 361 use List() to create the list (which 362 doesn't allow you to control the parens 363 directly), you can still get a list 364 with no parentheses. 365 (default: 0 for List() and 1 for Formula()) 366 367 =back 368 369 =head3 Flags for Formula()->cmp 370 371 The flags for formulas are dependent on the type of the result of 372 the formula. If the result is a list or union, it gets the flags 373 for that type above, otherwise it gets that flags of the Real 374 type above. 375 376 More flags need to be added in order to allow more control over the 377 answer checkers to give the full flexibility of the traditional 378 WeBWorK answer checkers. Note that some things, like whether trig 379 functions are allowed in the answer, are controlled through the 380 Context() rather than the answer checker itself. For example, 381 382 Context()->functions->undefine('sin','cos','tan'); 383 384 would remove those three functions from use. (One would need to remove 385 cot, sec, csc, arcsin, asin, etc., to do this properly; there could be 386 a function call to do this.) 387 388 Similarly, which arithmetic operations are available is controlled 389 through Context()->operations. 390 391 The tolerances used in comparing numbers are part of the Context as 392 well. You can set these via: 393 394 Context()->flags->set( 395 tolerance => .0001, # the relative or absolute tolerance 396 tolType => 'relative', # or 'absolute' 397 zeroLevel => 1E-14, # when to use zeroLevelTol 398 zeroLevelTol => 1E-12, # smaller than this matches zero 399 # when one of the two is less 400 # than zeroLevel 401 limits => [-2,2], # limits for variables in formulas 402 num_points => 5, # the number of test points 403 ); 404 405 [These need to be handled better.] 406 407 Note that for testing formulas, you can override the limits and 408 num_points settings by setting these fields of the formula itself: 409 410 $f = Formula("sqrt(x-10)"); 411 $f->{limits} = [10,12]; 412 413 $f = Formula("log(xy)"); 414 $f->{limits} = [[.1,2],[.1,2]]; # x and y limits 415 416 You can also specify the test points explicitly: 417 418 $f = Formula("sqrt(x-10)"); 419 $f->{test_points} = [[11],[11.5],[12]]; 420 421 $f = Formula("log(xy)"); 422 $f->{test_points} = [[.1,.1],[.1,.5],[.1,.75], 423 [.5,.1],[.5,.5],[.5,.75]]; 424 425 [There still needs to be a means of handling the tolerances similarly, 426 and through the ->cmp() call itself.] 427

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