Numerical question units and intervals

This is my proposal for how the numerical question function and interface should be improved. [_] means checkboxes that teachers could use for specifying different question behaviours.

[_]Allow evaluation of expressions

 Checking this would accept  5/2   0.5*5  5^2/2   5^(5-3)/2  25*10^-1  sqrt(25)/2

The main value of calculated or numerical question is that the student really does the calculation and gives a    
real number (which means in decimal format). 
I suggested that you use the short answer (or the multichoice) question type with the different answer forms 
that you allow. 
Pierre Pichet 04:25, 6 September 2007 (CDT)
To me the real value of the numerical question type is it's ability to really see the answers as numbers
and be able to see what things are equivalent. I have for many years used a PERL script which could treat 
3/2 and 1+1/2 and 1.5 and (1,5 for us Swedes) as the same thing, and especially to accept well defined intervals.
Often I am more interested in students knowing HOW to create the right expression moreso than doing the last step,
evaluating it. It is also interesting when looking at the statistics for a question, to see how they "thought" to
maybe add feedback for other answers.
Real numbers include rational numbers include 1/3 which cannot be correctly represented as a decimal. (Which doesn't
bother me as a physicist, but a pure matematician ought to value being able to use expressions like 1/3. 
(Even if a programmer may say it'll only work from 0.33333333333333333333333333333 to 0.333333333333333333333334 :-))
Jeff Forssell 06:21, 6 September 2007 (CDT)

[_]Allow fraction type 2 1/2 as 2.5

[_] Translate "½" as "+.5" but give warning "Avoid ½ character in numerical expressions! We have translated ½ as +.5 to evaluate your answer."

 In the student question interface the answer box should:
 1) have an easy way to access with keyboard
    a) good "tab order": when opening a quiz question page the student will usually want to 
       answer the first question as his/her first option (tab order =10) 
           Assuming there are no other taborders set this would be first.
           "BASIC" numbering allows later refinements without renumbering. 
       if available "send in question" (tab order =15)
       answer next question (tab order= 20)
       if available "send in question" (tab order =25)
        (how this looks would depend on how many question blanks are on a page
         and would end up att NEXT page link)
    b) Acesskeys (This is mined territory since there are no real standards (or
           rather several DIFFERENT standards) It would probably be best to let 
           people chose whether they want this activated and maybe which keys for which targets)
  2) Have a (?) after the answer box linked to a popup explanation, which depends
     on which options were checked by question author, saying for example:
      This is for a numerical answer. The answer can contain a unit at the right 
      end after a space. As decimal character you may use . or , . Mixed fractions
      can be written as 2 1/2  which is interpretted as 2+1/2 (2½) In this question
      you may enter an expression which is evaluated to a number before comparing to
      the correction key. [link to examples of allowable expressions]    

Answer 1:[ 2.5 ] Accepted error ± [0.5] Grade: [100%] Feedback:

Answer 2: [ 100.4..100.5) ] Accepted error ± [_empty_] Grade: [90%]

 Which would be interpreted  110.4 <= right < 100.5
  i.e. the round parentheses would mean that boundary not included in intervall
 or that one could enter evaluation strings like
 110.4<=ans<100.5||100.5<ans<=100.6
 (I know that this particular thing can be addressed by having
 100.5 +/-0  first than 100.5 +/-0.1)

Feedback:

Answer 3: ...
Feedback: (for answer 3)	

[_] Show 3 more alternative answer fields

---

Unit feedback options

[_] differentiated unit feedback, which is all of:
         [_] translate dimensionless "units": % = *0.01; ppm=*1E-6 ppb. promille   
         [_] feedback for lacking unit [_]Feedback for accepted UNIT but wrong number 
         [_] feedback for "possibly right number" if unit is adjusted
         [_] feedback for "Unit not recognized, either misspelled, wrong type,
              or just not expected"
         (o) missed unit gives standard retry reduction of points (_)no reduction 
              for missed unit (_)this reduction [___]  
 

Unit: [ ] (optional)

 Should accept arrays like kg, kilogram, kilograms , kilogramme, {"kilo gram", keelograhm} 
 where the ones enclosed in {} would be given feedback like
  We have interpretted keelograhm as a misspelling av kg Be aware that small spelling
   mistakes  like M in stead of m can lead to huge errors M=Mega=million
   m=milli= one thousandth" 

Alternative Units: Multiplier:[ ] Unit: [_______]

There should be the same possibility of unit arrays here.
The Multiplier should have an explanation (?)
  If the student answers with this unit, the student answer will be multiplied with this number 
  before being compared with the expected answer. Example:
  Answer [_10__] Unit [cm]
    alternative unit
    multiplier [_2.54_] unit [", in, in., inch] 
       (That " could be a tricky unit to handle!)

Then there are some things that I would be interested in having as options for all [maybe?] questiontypes (including numerical):

1) "Challenge" That a student is given (perhaps with a linked "!" or "Hmm..") a chance to give his/her preferred answer and his/her motivation (or why they didn't understand, like, agree with the grade or feedback they got for their answer or how the question was phrased.)

2) Hints option

3) Certainty|confidence declaration option

    [__answer___]  certainty: Hi(o)|Med( )|Low( )
    if possible with CBG grading scale including negative