Comments interspersed below... Dennis Roberts wrote:
> At 08:56 AM 11/16/01 -0700, Roy St Laurent wrote: > >It's not clear to me whether recent posters are serious about these > >examples, but > >I will reiterate my previous post: > > > >For most mathematics / statistics examinations, the "answer" to a > >question is the > >*process* by which the student obtains the incidental final number or > >result. > >The result itself is most often just not that important to evaluating > >students' > >understanding or knowledge of the subject. And therefore an unsupported > > > >or lucky answer is worth nothing. > > the problems with the above are twofold: > > 1. this assumes that correct answers are NOT important ... (which believe > me if you are getting change from a cashier, etc. etc. ... ARE ... we just > cannot say that knowing the process but not being able to come up with a > correct answer ... = good performance) Sure, I wouldn't give a student full credit if their process was correct but their final result was wrong. But an answer that shows me they know the process but have the wrong final result is worth MUCH, MUCH more than an answer that has the final result but provides me with no clue as to whether they understand how to get it. > > 2. that answers without any OTHER supplied information on the part of the > examinee can't be taken as "knowledge" when, it (sometimes) can be > > what if you asked on an exam ... the following: > > 1. what is the mean of 10, 9, 8, 8 and 7? _____ > > 2. what is the mean of 27, 23, 19, 17 and 16? ____ > > 3. what is the mean of 332, 234, 198, 239, and 200? _____ > > 4. what is the mean of 23.4, 19.8, 23.1, 19.0, and 26.4? _____ > > and, for each of 1 to 4 ... they put down in the blanks, the correct answers > > would you be willing to say that they know how to calculate the mean ... > ie, they know the process that is needed (and can implement it)? Depending upon whether they have access to a calculator and other information, I may or may not be able to conclude that they know how to calculate a mean. More importantly, the example you give is the worst possible example of how to write an examination. Why should I ask them to do four calculations when one, with properly supported work, will suffice? AND will permit me to better assess their understanding of the calculation. BTW, I would be inclined to ask questions that minimize but do not eliminate calculations in favor of questions that ask students to tell me what the quantity calculated means in the context of a data analysis (or other) problem. Though I would not eliminate evaluation of students ability to calculate, I agree with Herman that we need to focus more on students' understanding of concepts. > > i think you would EVEN though there is no other supporting process > information given by the examinee > > so, the statement that no credit should be given when there is no > supporting other evidence (ie, the process is shown) ... can't be > considered necessarily valid > > the problem here is NOT that no supporting evidence is given, the problem > is that with ONLY ONE instance of some given concept/skill that we are > attempting to assess on the part of the examinee, you are not nearly as > sure given only ONE CORRECT RESPONSE to one item ... whether it could have > been an answer because of real knowledge or, just happens to be the right > answer that was arrived at (luckily for the examinee) through some faulty > process Even several instances of correct responses of the sort you described above do not provide necessarily convincing evidence, and they require more unnecessary busy-work for the student. (I am not stricly opposed to "busy-work" in the context of student learning of a concept or calculation, but I am opposed to it in the context of evaluation of student learning.) > _______________________________________________________ > dennis roberts, educational psychology, penn state university > 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] > http://roberts.ed.psu.edu/users/droberts/drober~1.htm > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Roy St. Laurent Mathematics & Statistics Northern Arizona University http//odin.math.nau.edu/~rts ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
