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Änderungen von Dokument Numerische Variablen

Zuletzt geändert von Hendrik Zschocke am 12.01.2024
Von Version 452.1
bearbeitet von Carina Enke
am 24.09.2018
Änderungskommentar: Mittels Scroll Versions veröffentlicht aus dem Bereich ONYXintern und Version 1.11.1.
Auf Version 446.1
bearbeitet von Carina Enke
am 15.10.2018
Änderungskommentar: Mittels Scroll Versions veröffentlicht aus dem Bereich ONYXintern und Version 1.12.

Zusammenfassung

Details

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Inhalt
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186 +You can generate integer or fractional variable values. For this purpose, the variable types "**Integer**" and "**Floating Point**" will be available to you.
187 +
188 +[[image:attach:image2017-3-23 8:15:49.png]]
189 +
190 +To alter the value for the numerical variable, different options are available, which will be explained in the following sections, just as the possibility to define the display accuracy of floating-point numbers. If a numerical variable is not assigned a value, the variable will be initialised with 0.
191 +
192 +[[image:attach:image2017-3-23 8:20:57.png]]
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197 +{{panel borderColor="#ddd" bgColor="#f0f0f0" borderStyle="solid" title="Content"}}
198 +
199 +
200 +{{toc/}}
201 +
202 +**Related topics**
203 +
204 +* [[Calculation task>>doc:Berechnungsaufgabe]]
205 +* [[Formula comparison>>url:https://www.bps-system.de/help/display/ONYXintern/.Formelvergleich+v1.11||shape="rect"]]
206 +
207 +**Further information**
208 +
209 +* [[MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]]
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217 +== Range ==
218 +
219 +For numerical variables, a value range can be defined. The variable value will be randomly determined within the defined value range. Please note that the specified limits are included in the selection. For variables of the type "Integer", the step size (setting steps) can be determined in addition to the limits (setting minimum and maximum).
220 +
221 +**Possible entries are for example:**
222 +
223 +* //Range: Minimum=2, maximum=11, steps=3: //The following values are possible {2, 5, 8, 11}. When the variable is used, a value will be randomly selected, for example 2.
224 +\\[[image:attach:image2017-3-22 14:9:57.png]]
225 +
226 +== Value (direct value assignment) ==
227 +
228 +You can directly assign a value to all types of variables in order to initialise them. Later on, the value can be changed depending on other variables (cf. conditions).
229 +
230 +**Possible entries are for example:**
231 +
232 +* //Value: 5: //The variable is assigned the value 5.
233 +* //Value: -2.25: //The variable is assigned the value -2.25.
234 +
235 +== Random ==
236 +
237 +Define a value list from which a value is randomly selected. The alternative values are separated by a line break or semicolon.
238 +
239 +**Possible entries are for example:**
240 +
241 +* //Random selection: -5; -3; 3; 5: //One of the specified values will be randomly selected, for example 5.
242 +* //Random selection: 0; 12.25; 13.5: //One of the specified values will be randomly selected, for example 12.25.
243 +
244 +=== **Example "probability"** ===
245 +
246 +As an example, a typical task out of probability theory and statistics will be completed. It is to calculate the probability of certain colour combinations, when different coloured spheres are randomly drawn from an urn.
247 +
248 +|(((
249 +[[image:attach:image2017-3-23 8:54:23.png]]
250 +)))|(((
251 +In the example, the numerical variables {BLUE}, {RED}, and {WHITE} are initialised with an integer value between 3 and 15, i.e. in the value range [3,15].
252 +
253 +Based on these random values, the sum of all spheres is determined ({sum}) as well as the probability of pulling a red sphere ({solution}).
254 +)))
255 +|(((
256 +[[image:attach:image2017-3-23 9:0:32.png]]
257 +)))|(((
258 +The variables are included in the task text by typing the variable names {BLUE}, {RED}, and {WHITE}. In the example, the variables are included in a task of the type [[calculation (cloze)>>url:https://www.bps-system.de/help/display/ONYXintern/.Berechnungsaufgabe+v1.11||shape="rect"]].
259 +
260 +The variables and the solutions ({RED}/{sum} and {solution}) are stored for the respective gaps.
261 +)))
262 +|(((
263 +[[image:attach:image2017-3-23 9:7:8.png]]
264 +)))|(((
265 +For the test run, values within the given value ranges are randomly selected for each participant and each test attempt. In the example, the values {BLUE} = 6, {RED} = red, and {WHITE} = 10 are randomly assigned.
266 +
267 +The solutions are automatically determined for each test run on the basis of the defined values and the calculation rule.
268 +)))
269 +
270 +== Calculation (MAXIMA) ==
271 +
272 +The ONYX Testsuite is connected with the [[computer algebra system MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]], which allows you to calculate variable values on the basis of other variables. For this purpose, you need to indicate the calculation rule in MAXIMA notation.
273 +
274 +**Possible entries are for example:**
275 +
276 +* //Calculation (MAXIMA): 5+{a}: //The sum of 5 and the variable value {a} is calculated. Please note that the variable {a} must have been previously defined.
277 +* //Calculation (MAXIMA): sqrt({a})/(5+sqrt({b})): //MAXIMA supports mathematical expressions such as sqrt() for square root.
278 +* //Calculation (MAXIMA): 2*sin({a})+log({b}): //Further, it is possible to use trigonometric functions or the logarithm function.
279 +\\[[image:attach:image2017-3-22 14:38:53.png]]
280 +
281 +=== **Example "hypotenuse"** ===
282 +
283 +As an example, a typical task out of geometry will be completed. The understanding of the hypotenuse is to be examined. The solution is supposed to be derivable from the knowledge that the hypotenuse is the longest side of a right triangle. To this end, the participant is given a variety of possible solutions, from which they need to choose the correct solution.
284 +
285 +|(((
286 +[[image:attach:image2017-3-23 15:6:59.png]]
287 +)))|(((
288 +(% class="WordSection1" %)
289 +(((
290 +The first step in the example is the random determination of the catheti ({k1}, {k2}) of the triangle for the definition of the task.
291 +)))
292 +
293 +To solve the task correctly, the value for the hypotenuse ({hyp}) needs to be calculated by means of a MAXIMA equation. In addition, further possible answer options ({a}, {b}, {c}) are computed by MAXIMA.
294 +
295 +For all variables of the type floating point, the display accuracy was set to 2 decimal places.
296 +)))
297 +|(((
298 +[[image:attach:image2017-3-23 14:39:27.png]][[image:attach:image2017-3-23 14:51:31.png]]
299 +)))|(((
300 +In the example, the variables are included in a [[selection task>>url:https://www.bps-system.de/help/display/ONYXintern/.Auswahlaufgabe+v1.11||shape="rect"]]. The variables for the task text are integrated into the task by declaring the variable names {k1} and {k2}. The correct solution ({hyp}) and the alternative answers ({a}, {b}, {c}) are additionally provided in the form of answer options.
301 +)))
302 +|(((
303 +[[image:attach:image2017-3-23 14:56:46.png]]
304 +)))|(((
305 +For the test run, the values of the catheti ({k1}, {k2}) are randomly selected for each participant and each test attempt within the given value ranges.
306 +
307 +In the example, the following random values were displayed for the variables: {k1} = 4, {k2} = 13.
308 +
309 +Based on these values and the defined calculation rules, the hypotenuse and the alternative answer options are calculated, and the following values are displayed in the example task: {a} = 17.00, {hyp} = 13.60, {b} = 8.50, and {c} = 5.39 cm.
310 +
311 +Thus, the correct rounded solution for the hypotenuse in the example is 13.60 cm. The answer options {a}, {b}, and {c} can be logically excluded due to the knowledge that the hypotenuse is larger than the respective catheti and smaller than the sum of the catheti.
312 +)))
313 +
314 +{{info}}
315 +For further information on the MAXIMA notation, please refer to the help pages of the [[computer>>url:http://maxima.sourceforge.net/||shape="rect"]] [[algebra system MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]].
316 +{{/info}}
317 +
318 +== Setting: Format display ==
319 +
320 +For variables of the type floating point, the **number of decimal places **can be configured for the display. Please note that this setting only affects the display, not the computational accuracy and the solution comparison. This means: If the variable is used for the calculation of additional variables, the complete unrounded value will be used for the calculation. If the variable is stored as a solution for a gap (calculation task), the configured number of decimal places will be used for the solution display, but not for the solution comparison.
321 +
322 +
323 +
324 +[[image:attach:onyx-variables-float.png]]
325 +
326 +
327 +
328 +
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335 +
336 +{{info}}
337 +If you want the participant to solve calculation tasks with a certain precision, use the setting for defining a [[tolerance range>>url:https://www.bps-system.de/help/display/ONYX/Berechnungsaufgabe#Berechnungsaufgabe-Schritt5(optional):DefinitioneinesToleranzbereiches||shape="rect"]] in the edit window of the gap.
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