I think we all know the routine. We walk to a large classroom, we sit down for a test, we receive a large stack of questions stapled together and then we fill in tiny bubbles on a separate sheet that is automatically graded by a scanning machine. We’ve all been there. I was thinking recently about how far the humble multiple choice question has come over the last few years with the advent of systems like Maple T.A., and so I did a little research.

Multiple choice questions were first widely-distributed during World War I to test the intelligence of recruits in the United States of America. The army desired a more efficient way of testing as using written and oral evaluations was very time consuming. Dr. Robert Yerkes, the psychologist who convinced the army to try a multiple choice test, wanted to convince people that psychiatry could be a scientific study and not just philosophical. A few years later, SATs began including multiple choice questions. Since then, educational institutions have adopted multiple choice questions as a permanent tool for many different types of assessments.

One of the biggest advances in the use of multiple choice questions was the birth of automatic grading through the use of machine-readable papers. These grew in popularity during the mid-70s as teachers and instructors saved time by not having to grade answer sheets manually.

Until recently, there has not been much advancement in this area.  It’s true, Maple T.A. can do so much more than just multiple choice questions, so this style of question is less important in large-scale testing than it used to be. But multiple choice questions still have their place in an automated testing system, where uses include leveraging older content, easily detecting patterns of misunderstanding, requiring students to choose from different images, and minimizing student interaction with the system. Luckily, Maple T.A. takes even the humble multiple choice questions to the next level. Now you might be thinking, how is that even possible given the basic structure of multiple choice questions? What could possibly be done to enhance them?

Well, for starters, in Maple T.A., you can permute the answers. This means you have the option to change the order of the choices for each student. This is also possible with machine-readable papers, but this does require multiple solution sets for a teacher or instructor to keep track of. With Maple T.A., everything is done for you. For example, if you have a multiple choice question in Maple T.A. with 5 answer choices, there are 120 different possible answer orders that students can be presented with. You don’t have to keep track of extra solution sets or note which test version each student is receiving. Maple T.A. takes care of it all.

Maple T.A. allows you to create Algorithmic questions - multiple choice questions in which you can vary different values in your question. And you aren’t limited to selecting values from a specific range, either. For example, you can select a random integer from a pre-defined list, a random number that satisfies a mathematical condition, such as ‘divisible by 3’ or ‘prime’, or even a random polynomial or matrix with specific characteristics. It allows an instructor to create a single question template, but have tens, hundreds, or even thousands of possible question outcomes based on the randomly selected values for the algorithmic variables. The algorithmic variables not only apply to the question being asked by a student, but also the choices they see in a multiple choice question.

You can even create a question where every student gets the same fixed list of choices, but the question varies to ensure that the correct response changes.  That’s going to confuse some students who are doing a little more “collaboration” than is appropriate!

Some of the other advantages of using Maple T.A. for multiple choice are also common to all Maple T.A. question types. For example, you can provide instant, customized feedback to your students. If a student gets a multiple choice question correct, you can provide feedback showing the solution (who is to say the student didn’t guess and get this question correct?) If a student gets a multiple choice question incorrect, you can provide targeted feedback that depends on which response they chose. This allows you to customize exactly what a student sees in regards to feedback without having to write it out by hand each time.

And of course, like in other Maple T.A. questions, multiple choice questions can include mathematical expressions, plots, images, audio clips, videos, and more – in the questions and in the responses.      

Finally, let’s not forget, in an online testing environment, there is no panic when you realized you accidently skipped line 2 while filling out your card, no risk of paper cuts, and no worrying about what kind of pencil to use!

References:

http://www.edutopia.org/blog/dark-history-of-multiple-choice-ainissa-ramirez

http://xkcd.com/499/

http://io9.com/5908833/the-birth-of-scantrons-the-bane-of-standardized-testing

As a reminder, we regularly host live webinars on a variety of topics for our customers, and we wanted to make this information available to the MaplePrimes community as well.

This featured webinar for this month will outline the Finance Package in Maple 18 including capabilities like the mathematical, statistical, and connectivity tools required to analyse data, calculate forecasts, estimate risks, prototype and develop quantitative algorithms, and leverage parallel programming techniques.

Other topics include:

• Data feed connectivity and system integration

• Price equity and interest rate derivatives

• Populate reporting tools, deliver documents and share worksheets

• Optimize portfolios of financial instruments

• High-Performance Computing (HPC)

To join us for the live presentation, please click here to register.

For some time I have been running into the problem where uploaded worksheets that are inlined into a Mapleprimes post get gridlines shown, even when they are not specified or shown in the original worksheet. This is a problem because quite often the gridlines make an inlined plot unattractive.

I believe that Mapleprimes uses some version of MapleNet as a mechanism for inlining uploaded worksheets.

It seems that the Standard GUI and/or MapleNet have special handling for gridlines in the sense that they actually distinguish between PLOT structures generated without the `gridlines` option versus those created with `gridlines=false`.  I believe that this has something to do with the persistence of various plot qualities in an output region which (perhaps for historical reasons?)  allow re-execution of a plot input command to produce a plot output rendering that remembers whether gridlines are visible.

If the second plot below does indeed get rendered here in Primes without gridlines visible then one workaround is evident: adding `gridlines=false` instead of omitting the option.

Download test.mw

I'll submit a bug report against MapleNet.

acer

MapleSim 6.4 includes more powerful tools for creating custom components, performance enhancements, and enhancements to the model generators for Simulink® and FMI. 

We have also made important updates to the MapleSim Control Design Toolbox. This toolbox now offers a more complete set of algorithms for PID control, new commands for computing closed-loop transfer functions, and numerous improvements to existing commands. These enhancements allow engineers to design a greater variety of controllers and controller-observer systems while taking advantage of the greater flexibility and analysis options available through the use of symbolic parameters. 

See What’s New in MapleSim 6.4 and What’s New in the MapleSim Control Design Toolbox for details.

eithne

Maplesoft is holding its first ever Virtual User Summit on Feb. 27.  You’ll be able to watch presentations by both Maplesoft and Maplesoft customers, ask questions, have discussions in the lounge with other attendees, and even enter a draw, all from the comfort of your own home or office.

Here’s the agenda.  We’ll release more detailed information on speakers and session times in the next couple of weeks.

For more information and to register:  Maplesoft Virtual User Conference

We're looking forward to seeing you there. (Well, "seeing you" :-))

eithne

It is a relatively recent innovation that complex-number computations can be done in the evalhf environment. When combined with plots:-densityplot, this makes escape-time fractals in the complex domain very easy to plot. This fractal is based on the Collatz problem. This Wikipedia article has a high-resolution picture of this fractal. I've switched the real and imaginary axes and reversed the direction of the real axis purely for asthetic reasons.

Download Collatz_fractal.mw

MapleSim 6.3 includes substantial improvements to the MapleSim simulation engine, resulting in faster model pre-processing times, more flexible code generation, and expanded support for Modelica-based custom components. 

For more information, see What’s New in MapleSim.

eithne

Greetings to all.

As some of you may remember I made several personal story type posts concerning my progress in solving enumeration problems with the Polya Enumeration Theorem (PET). This theorem would seem to be among the most exciting in mathematics and it is of an amazing simplicity so that I never cease to suggest to mathematics teachers to present it to gifted students even before university. My previous efforts are documented at your site, namely at this MaplePrimes link I and this MaplePrimes link II.

I have been able to do another wonderful cycle index computation using Maple recently and I would like to share the Maple code for this problem, which is posted at Math StackExchange.com (this post includes the code) This time we are trying to compute the cycle index of the automorphism group of the 3-by-3-by-3 cube under rotations and reflections. I suggest you try this problem yourself before you look at my solution. Enjoy!

I mentioned in some of my other posts concerning PET that Maple really ought to come with a library of cycle indices and the functions to manipulate them. I hope progress has been made on this issue. I had positive feedback on this at the time here at your website. Do observe that you have an opportinuity here to do very attractive mathematics if you prepare a worksheet documenting cycle index facilities that you may eventually provide. This is good publicity owing to the fact that you can include images of the many geometric objects that appear which all look quite enticing and moreover potential readers get rewarded quickly as they discover that it takes little effort to master this theorem and proceed to work with symmetries themselves and investigate them. This sort of thing also makes nice slides.

With best wishes for happy combinatorics computing,

Marko Riedel

Just came across this

Press esc twice then enter.  Maple becomes unresponsive. 

I made a small change to the Task Filtering code I uploaded a few weeks ago.  The new code has better memory performance and, most importantly has more stable memory usage which means it can actually run very large examples.  Here is the new version of the code:

FilterCombPara := module( )
    local ModuleApply,
            doSplit,
            splitCombs,
            makeNewPrefix,
            lessThanX,
            filterCombs;

    lessThanX := proc( x, i ) x<=i; end;

    doSplit := proc( i::integer, prefix::set(posint), rest::set(posint),
                                                k::posint, filter::appliable, $ )
        splitCombs( prefix union {i}, remove( lessThanX, rest, i ), k-1, filter );
    end;

    splitCombs := proc( prefix::set(posint), rest::set(posint), k::posint,
                                                                filter::appliable, $ )
        if ( numelems( rest ) < k ) then
            NULL;
        elif ( k = 1 ) then
            filterCombs( prefix, rest, filter );
        else
            op( Threads:-Map( doSplit, rest, prefix, rest, k, filter ) );
        end;
    end;

    makeNewPrefix := proc( i, prefix ) { i, op( prefix ) } end;
    filterCombs := proc( prefix::set(posint), rest::set(posint), filter::appliable, $ )
        local i, f;

        op(select( filter, map( makeNewPrefix, rest, prefix ) )):
    end;

    ModuleApply := proc( n::posint, k::posint, filter::appliable, $ )
        [ splitCombs( {}, {seq( i,i=1..n )}, k, filter ) ];
    end;

end:

This code has the small mapping functions as module members instead of declared inline.  This means that less memory is churned as this code is excuted.  For a long runs, this helps keeps the memory stable.

As an example, I ran the following example:

> CodeTools:-Usage( FilterCombPara( 113,7, x->false ) );

memory used=17.39TiB, alloc change=460.02MiB, cpu time=88.52h, real time=20.15h
                                                  []

It used 88 CPU hours to run, but only 20 hours of real time (go parallelism!)  It used 17 Terabytes of memory, but only allocated 500 M.  This example is pretty trival, as the filter returned false for all combinations, so it did not collect any matches during the run.  However as long as the number of matches is small, that shouldn't be an issue.  If the number of matches is too large to fit in memory, then this code may need to be modified to write the matches out to disk instead of trying to hold them all in memory at once.

Darin

-- Kernel Developer Maplesoft

FilterComb.mw

Two problems surfaced when I upgraded my Mac to Mavericks (OS X 10.9).

First, the old Java SE installation was removed (actually, some linkages were destroyed), so a Maple launch puts up a dialog "need to install Java." Apple hasn't yet (10/23/13) updated the software database links --- installation fails with a "can't find software" error. I reinstalled Java using the version at http://support.apple.com/downloads/DL1572/en_US/JavaForOSX2013-05.dmg. (The links can be redone, it's just easier to reinstall.)

Second, the (new?) structure for /Library/Frameworks made my Maple license invalid. I dug out the old email with my activation code, then re-activated.

And all is now copacetic.

This blog post is a response to a post on MaplePrimes.  MaplePrimes user wkehowski asked how the Task Model could be used to filter combinations.  The basic problem is formalated like this:  We want a function, I'll call it FilterComb, that accepts positive integers...

I have located a claimed webpage http://www.advanpix.com/2013/10/03/advanpix-vs-maple-sparse-solvers-comparison/ that shows Advanpix doing sparse matricies much faster than Maple.

The slowness is usually the result of poor coding or someone not well versed in Maple software. 

Anyone care to comment on the times?  I am sure the presented code there can be improved.

Greetings to all.

I have been using the numtheory package for quite some time now and it has helped me advance on a number of problems. Recently an issue came to my attention that I have known about for a long time but somehow never realized that it can be fixed. This is the fact that the numtheory package does not know about Dirichlet series, finite and infinite. Here are two links:

We’ve recently added a new set of questions to the Maple T.A. Cloud for English language proficiency tests. These questions demonstrate how Maple T.A. can be used to generate text-based questions that take advantage of the randomization feature. These questions were created by Metha Kamminga, an Independent Learning Professional in the Netherlands. Metha is a strong proponent of Maple T.A. in Europe, and transformed the testing and assessment system in Delft University before her retirement.

TU Delft University aims to transform learning through the use of technology. Its ambition is to eventually offer fully digitalized degree programs and it believes that digital testing and assessment can play an important role within this process. They are using Maplesoft’s online testing and assessment suite, Maple T.A., to move their courses to a digital assessment environment. To read the full user story, click here.

Visit the Maple T.A. Cloud to access the questions mentioned above and to browse the full collection of questions.