I've linked to this thread from another Google group about some learning software where question generation has arisen as an idea ...
Although I don't yet understand all of the technical ideas in this thread and have yet to try SageTex, I thought I'd mention a thread I've started in the Google group for Anki (Spaced repetition software) about generation of mathematical questions within Anki. It's at http://groups.google.com/group/ankisrs/browse_thread/thread/6f8769cf557ba85f/1f6dea718c0ba08a#1f6dea718c0ba08a. Anki is designed to practice recollection of facts and thereby lodge them in long term memory. It tracks student performance statistically so it knows how frequently to ask a student to repeat their recollection of a single fact based on how hard the student found the question and whether they got it right or wrong. Although Anki is designed to help memorise facts, I've asked if the same style of intelligent repetition of posed questions and assessment of the students' experience and answers could be used to help test their learning of processes like the calculations that arise in maths. A simple example could be to solve quadratic equations. A set of quadratics could be posed (just as a text book might pose exercises) but Anki would track answers and difficulty levels and would then repeat specific questions that were posed earlier to reinforce the learning process. I don't know whether this is better than work with a text book but I suspect that, when a student gives an incorect answer through a faulty process or careless application of a good one, they may be shown what error they made, but they're not necessarily tested on the same question later to ensure the lesson has been learned. I also suspect that the repetition regime for learning of calculation processes would differ from a memorisation regime for facts. And there's a danger that too much repetition of a specific question would teach the student to rely on the specifics of that one question rather than reinforcing the calculation process of which it's an example. I mention this here though because someone's posted a comment in the Anki thread about whether maths questions could be randomly generated so I've let people know of this thread about question generation. Anki supports LaTex to some degree so I wondered if SageTex could be used. If there is any merit in repeating calculation exercises, presumably we'd want to generate a set of randomised question at first but then ensure that any repeated questions were exact copies of the originals and were not re-generated to produce a different question. Kevin On Aug 4, 10:39 pm, Rob Beezer <[email protected]> wrote: > Hi Mark, > > A couple of comments: > > 1. You can create a pille of Sage variables as illustrated. Not sure > how they will behave in SageTeX. > > sage: for i in range(6): > var('a'+str(i)) > a0 > a1 > a2 > a3 > a4 > a5 > sage: a1=6 > sage: latex(a1) > 6 > sage: a2=5 > sage: latex(a1+a2) > 11 > > 2. Harald's suggestion to set the random seed is a great idea, so > your exercise sheets are reproducible. LaTeX has an "ifthen" > package. Wrap your solutions in an \ifthenelse command so on your > first pass the solutions do not print. Then change the value of a > boolean (in LaTeX) so on the second pass the solutions to the same > "random" problems are included. I do this when I write an exam - > first pass is the questions, second pass is the questions with the > answers. But I don't use any randomness. ;-) > > Rob > > On Aug 4, 7:58 am, "M.Olson" <[email protected]> wrote: > > > > > Thanks everyone for your comments of goodness. > > > I have been using Dan Drake's SageTeX for a couple weeks now ... and > > it is nothing short of incredulous! I will be sure to share all my > > working examples once I get them going. > > > I have made some progress this weekend after playing around a bit. I > > am very confident that I can generate the randomly generated > > worksheets, but I am having a problem creating the solution sheets. I > > am sure my method of generating the sheets is not elegant nor > > optimized. > > > I have a very SIMPLE example of generating random dyadic > > operations ... let's use addition. I am using tables, so that the > > layout looks consistent. > > > %Define the greatest term, t, to be used. In this example it will be > > 44 > > > \begin{sagesilent} > > t=44 > > \end{sagesilent} > > > \begin{tabular}{|c|c|c|c|c|} > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > \hline $\sage{ZZ.random_element(t)}$ & + & $\sage{ZZ.random_element(t)} > > $ &$ =\\\hline > > . > > . > > . > > \end{tabular} > > > This works brilliantly! Awesome ... I can now create awesome sheets > > of goodness using this method. The problem is if I want to provide > > answers and in more complicated problems ... solutions. They only way > > that I have come up with is defining the operands in the sagesilent. > > The reason is that I can manipulate my defined operands, in this case > > sum them. More specifically, the problem is that I can only define > > alpha constants, which are random numbers, a-z. If I define a > > constant as "aa" or "a0", it does not compile? It would be a little > > work to assign all the constants, but I am sure it would be worth it. > > I can't figure out why this won't work. Is the following syntax > > incorrect? > > > \begin{sagesilent} > > t=43 > > a=ZZ.random_element(t) --- >this works > > a0=ZZ.random_element(t) ---> this does not work > > \end{sagesilent} > > > Any ideas on how to assign random numbers to constants? > > Any ideas on how to simplify this procedure? > > > Here is an example that I could use to generate the worksheet and the > > answer sheet by using defined constants: > > > \begin{sagesilent} > > t=44 > > a=ZZ.random_element(t) > > b=ZZ.random_element(t) > > c=ZZ.random_element(t) > > d=ZZ.random_element(t) > > . > > . > > . > > I run out of constants :( > > \end{sagesilent} > > > \begin{tabular}{|c|c|c|c|c|} > > \hline $\sage{a}$ & + & $\sage{b}$ &$ =$ & $\sage{a+b}$\\\hline > > \hline $\sage{c}$ & + & $\sage{d}$ &$ =$ & $\sage{c+d}$\\\hline > > . > > . > > . > > > \end{tabular} > > > Thank you everyone for your comments ... much appreciated :D > > > Mark > > > On Aug 1, 11:47 am, "M.Olson" <[email protected]> wrote: > > > > I am a Sage Newbie and looking to create randomly generated exercise > > > worksheets (not a sage worksheet) using both LaTeX and Sage. I create > > > random arithmetic sheets using OpenOffice Calc, but they are not very > > > aesthetic. However, with the power to be able to incorporate the power > > > of Sage into LaTeX - I was hoping to be able create random worksheets > > > for my students that look good too. > > > > Well, it is not just about looks. It would be great to generate > > > random > > > > - polynomial expressions that need to simplified OR equations that > > > need to be solved. I am sure the possibilities are endless. Of > > > course, one might also be able to use Sage to create the answer sheet > > > as well. This is most likely possible as as one can do it in > > > Mathematica ... just need a little help. Really what I am looking to > > > be able to do is something similar to > > > this:http://www.wolfram.com/broadcast/screencasts/generateexerc/ > > > > Any help to steer me in the right direction would be greatly > > > appreciated. > > > > //Mark- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en -~----------~----~----~----~------~----~------~--~---
