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Maple T.A. Package

 

The new MapleTA package gives Maple users access to many of the built-in commands available for learning and assessment previously only available in Maple T.A.™, meaning that a broader range of questions can now be authored directly in Maple. Also, Maple-graded questions in Maple T.A. can now be imported into Maple, and in addition, questions authored in Maple can be exported to Maple T.A.

Builtin Commands For Question Generation and Assessment

Maple T.A.™ is an easy-to-use web-based system for creating tests and assignments, and automatically assessing student responses and performance. It supports complex, free-form entries of mathematical equations and intelligent evaluation of responses, making it ideal for science, technology, engineering, mathematics (STEM), or any other course that requires mathematics. 

 

The Maple T.A. software uses Maple's computation engine to assess student responses. Checking for equivalent results in the domain of mathematics is a hard problem that is best solved using a symbolic language like Maple. Even simple problems, such as a student answering y+x when the expected answer is x+y, can be very difficult in a system that does not understand the mathematics behind the student's answer.

 

While Maple T.A. has access to all of Maple's mathematical operations, it also has a selection of built-in commands that can be used in algorithms that do not access Maple's engine. This can be used in a broader range of questions. The functionality of these built-in commands is now reproduced in the MapleTA[Builtin] subpackage.

 

For more information about Maple T.A., see http://www.maplesoft.com/products/mapleta

Sample Question

Consider a sample question that explores the concept of binomial coefficients from Maple T.A.  The question states:

 

question  There are $A balls of different colors in a sack. How many distinct combinations of $B balls can you remove from the sack?:

 

To initialize the random variables $A and $B, you might see the code like this in Maple T.A.'s algorithm section.

$A=range(5,10);$B=range(1,4);$number=binomial($A, $B);

The range command in Maple T.A. generates a random integer in the specified range. This command is now mirrored in Maple 18 when you load the MapleTA:-Builtin package. We will do this implicitly via the uses command in the following procedure:

 

initialize  proc    uses MapleTA:-Builtin;    local a,b,n;    a  range5,10;    b range1,4;    n  binomiala,b;    Grading:-Quiz:-Set`$A`=a, `$B`=b, `$number`=n ; end:

 

The last line of the initialize procedure above makes the connections between computed variables and those used for grading or display. This is not necessary if you just want to compute with the commands in the MapleTA[Builtin] package.

 

For completeness, we will also show how this question could be created and graded using the Grading[Quiz] command:

 

grade  proc     local n, r;     n,r  Grading:-Quiz:-Get`$number`,`$RESPONSE`;     evalbr = n; end:

Now that we have the essential ingredients for the question, we can play it inside Maple as follows:

Grading:-Quiz question, grade,initialize ;

There are  balls of different colors in a sack.
How many distinct combinations of  balls can you remove from the sack?

proclocaln,r;n,r:=Grading:-Quiz:-Get$number,$RESPONSE;evalbr=nend proc

(2.1)

Click the "Try Another" button a few times to see how the variables inside the question change. Inside Maple, a student can explore calculations. One may discover the expression palette has the choose notation. For removing two balls from a bag of eight, you could compute:

 

82

28

(2.2)

Or, you might discover Maple's binomial command:

 

binomial8,2;

28

(2.3)

Or, you may derive the answer from the binomial coefficient formula:

 

8!2!82!

28

(2.4)

Letting students explore solutions within Maple creates the opportunity for discovery; that is, learning in a way that will stick with the student, rather than being forgotten as soon as the exam is submitted.  

 

Finally, this question can also be exported for use directly inside Maple T.A.

MapleTA:-Export Grading:-Quizquestion,grade,initialize,output=mapleta, coursemodule.zip ;

We re-ran the Quiz command with the option, output=mapleta to produce a form suitable for export (rather than display an interactive question).  This result is then given to MapleTA[Export] in order to generate the file named "coursemodule.zip".  This file can be imported into Maple T.A. as a course module and used in assignments.

 

Similarly, course modules exported from Maple T.A. can be loaded into Maple, and the questions they contain can be played using the Quiz command in the Grading package.

Importing and Exporting Questions From Maple T.A

The "maple-graded" style of question in Maple T.A. can be imported into Maple and run via the Quiz command.

 

The MapleTA:-Import command will read a course module zip file and import all of its questions into a Record-based data structure that closely mirrors the XML in the course-module manifest. A sample structure might look like the following (omitting optional fields):

 

TAQuestion := Record("name" = "  Quadratic Factor Question  ", "mode" = "Maple", "text" = "    Factor the following algebraic expression x<sup>2</sup> + ${A}x + ${B}. Your answer should be in the form (x+a)(x+b).  ", "algorithm" = "  $a=rint(1,10);$b=rint(2,10);$A=int($a+$b);$B=int($a*$b);$factor=maple(\"factor(x^2+${A}*x+${B})\"); ", "mapleAnswer" = "    $factor;  ",         "maple" =  "    evalb(($ANSWER)-($RESPONSE)=0);  "  ):

 

This imported structure is recognized by the Quiz command and it builds the appropriate question in Maple.

 

Grading:-Quiz TAQuestion &semi;

    Factor the following algebraic expression x2 + x + . Your answer should be in the form (x+a)(x+b).  

A course module usually contains multiple questions.

 

cmfile  catkerneloptsmapledir&comma;/data/help/MapleTA/coursemodule.zip&colon;

cmquestions   MapleTA:-Import cmfile  &colon;

numelemscmquestions&semi;

18

(3.1)

Grading:-Quiz cmquestions1 &semi;

  Convert  feet to meters. Answers require 4 significant digits.Do not include units in your response.  

 Grading:-Quizcmquestions3 &semi;

  Solve the expression x3 - x = 0.


Enter only the expression for x, omitting "x =".  

Similarly, all Quiz-based questions can be exported back to Maple T.A. The Quiz command takes an 'output' = 'mapleta' option that will generate a Record structure as described above. This Record can then be passed to the MapleTA:-Export command to generate a course module suitable for importing into Maple T.A.

As an example, let's define a question and see how it looks.  

qinit  proc       local p  nextprime rand2..7 &semi;       Grading:-Quiz:-Set`$P` &equals; p &semi;        p&ast;rand1..2 &plus; 1&comma;         p&ast;rand3..4 &plus; 1&comma;         p&ast;rand1..2 &plus; 0&comma;         p&ast;rand1..2 &plus; 2&comma;         p&ast;rand1..2  1 &semi;    end&colon;

Grading:-QuizFor which values of X does ( X mod $P) = 1&comma;1&comma;2&comma;qinit&comma;style&equals;multipleselect &semi;

For which values of X does ( X mod ) = 1

 

Now, let's use the same question parameters, but specify the 'output' option. We'll also give the question a name so it can be easily identified inside Maple T.A.

Q  Grading:-QuizFor which values of X does ( X mod $P) = 1&comma;1&comma;2&comma;qinit&comma;   style&equals;multipleselect&comma;output&equals;mapleta&comma;name&equals; Imported MS 15 (mod)

Recordmode&equals;Multiple Selection&comma;name&equals; Imported MS 15 (mod) &comma;algorithm&equals; $MAPLE_INIT = maple("randomize(): proc() local r := (proc () local p: p := nextprime(rand(2 .. 7)()): Grading:-Quiz:-Set(`\x24P` = p): [p*rand(1 .. 2)()+1, p*rand(3 .. 4)()+1, p*rand(1 .. 2)(), p*rand(1 .. 2)()+2, p*rand(1 .. 2)()-1] end proc)(): MapleTA:-ToString(op(r), Grading:-Quiz:-Get(`\x24P`),'print','sequence'): end(): "); $MCCHOICE1 = switch(0,$MAPLE_INIT); $MCCHOICE2 = switch(1,$MAPLE_INIT); $MCCHOICE3 = switch(2,$MAPLE_INIT); $MCCHOICE4 = switch(3,$MAPLE_INIT); $MCCHOICE5 = switch(4,$MAPLE_INIT); $P = switch(5,$MAPLE_INIT); &comma;text&equals; For which values of X does ( X mod $P) = 1 &comma;type&equals;formula&comma;answer&equals; 1, 2 &comma;_attributes&equals;Record...&comma;choices&equals;Record...

(3.2)

 

This can be exported as a course module:

 

if FileTools:-Existssample.zip then    FileTools:-Removesample.zip&semi; end if&semi;

MapleTA:-Export Q&comma; sample.zip &semi;

See Also

What's New in Maple 18, Overview of the MapleTA Package, Maple T.A. Integration, New Features for Education, Grading


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