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Numeric Response
Back - Fill in the Blank Up - Questions Next - Essay

In addition to the common question definition controls, the options to the left offer specific control over fill-in-the-blank numeric question presentation and evaluation.

You may specify the size of the box provided for the participant to enter their response. Please note that boxes that are more than one line high will not be automatically scored and considered an essay question.

For numeric responses, you may enter a single correct answer in the space provided. This answer can be a number or a formula. Formula answer specification will be discussed below.

Since answers involving irrational numbers such as pi cannot be precisely represented as decimal numbers, a precision or margin of permissible error may be specified. The error amount can be specified as an absolute quantity (e.g. + or - 0.1) or as a percentage of the correct answer (e.g. + or - 5%).

When the correct answer is reported to the participant, conversion from the internal binary format of computers to decimal numbers may result in an extremely small fractional error. Using the reporting - significant figures item, it is possible to have the result rounded.

Many mathematical problems require that units accompany the numeric results. With Test Pilot, you can specify multiple permissible unit types. Enter each on a line by itself. Comparison is case sensitive, so you may wish to specify the units in both upper and lower case. You may specify that the question be counted wrong if no units are included. You may also specify an additional point award for specifying correct units. Thus, the question's maximum point award would be the sum of the unit point award and the correct answer point award.

Expert Feature - scalable units
If you wish to permit users to use multiple units, you may specify them
along with a conversion factor. For example, if the correct answer fot the
question were calculated in meters whiule you also wanted to accept centimeters
or milimeters as valid units, you could enter:

m
cm,100
mm.,1000

in the units box and the correct answer would be scaled appropriately
according to the participant's selection of units. Thus, an answer of 1m (1 meter)
could be enter as 1m, 100cm and 1000mm and be considered correct.

Expert Feature - engineering units
If you wish to have Test Pilot determine the appropriate engineering units to
be used in a response, check the engineering units box and enter the
base unit of the correct answer. Test Pilot will consider the correct answer and
according to the table below, select the appropriate prefix to the base unit:

If 1E-12 =< # < 1E-9 then "p"
If 1E-9 =<
# < 1E-6 then "n"
If 1E-6 =<
# < 1E-3 then "u"
If 1E-3 =<
# < 1 then "m"
If 1 =<
# < 1E3 no prefix
If 1E3 =<
# < 1E6 then "k"
If 1E6 =<
# < 1E9 then "M"
If 1E9 =<
# < 1E12 then "G"
If 1E12 =<
# < 1E15 then "T"

For example, if the base unit was specified as "A" for amperes and the
correct answer was 0.0001 amperes, the the correct response would be
calculated as 100uA representing 100 microamperes.

You can enter point awards and custom feedback in the spaces provided for correct and incorrect participant responses. In order for this feedback to be shown, the appropriate options in Step#4 - Submit Actions must be set. That is, you must enable the issuing of feedback for your assessment. Point awards must be positive integer numbers.

Expert Feature - custom feedback links
If you are versed in HTML, the language of web page design, you may include links to remedial material in your custom feedback. This permits the construction of powerful tutorials using Test Pilot. For example, if a participant gets a question wrong, hyperlinks may be included in your custom feedback that, when clicked upon, will take the user to a web site where material assisting the participant in answering the question is available. A hyperlink may be entered as follows:

Click <A HREF="http://SITE/page.html">here</A> for additional help.

Substituting the appropriate URL in place of the text shown in red. If you wanted the page openned in a new window, the link could be entered as follows:

Click <A TARGET="_new" HREF="http://SITE/page.html">here</A> for additional help.

If this assessment is being offered a question-at-a-time and you have enabled branching, additional popup menus are shown to permit defining to which question to branch upon the correctness of a participant's response. Note that the branch is executed based upon the correctness of the response and not the content of the response. This behavior is unique to fill-in-the-blank questions. It is generally recommended to first define all questions before setting up branching.

Formula Specification

    Answers may be specified as a formula. That is, the correct answer could be the result of a calculation. Mathematical operators can be used as follows:

    • 1 + 1

    • 5 - 2

    • 5 + 9 -3

    • 2 * 3 indicates the product of 2 and 3

    • (10-3) * 5 note that an * must be inserted to indicate multiplication - implied multiplication is not allowed

    • 10 * 3 + 5 standard mathematical precedence is respected, thus the multiplication is carried out first

    • 3^2 the ^ operator is for raising a number to a power - in this case three squared or nine

    • 6 % 4 the % operator represents modulo or the remainder of a division - in this case the remainder of 6 divided by 4 or 2

    In addition, Test Pilot has a complete mathematical function library including the following constants and functions.

    • abs(..) - absolute value
    • ceil(..) - Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. Example: ceil( 3.2 ) = 4.0 , ceil( 9.9 ) = 10.0
    • exponential functions
      • euler - the constant e or exp(1)
      • exp(..) constant e raised to..
      • ln(..) the natural logaritm
      • [base]log(..) - any logaritm. Example: 10log(10) = 1.0, exp(1)log(exp(1)) = 1.0
    • fac(..) - factorial of... n*(n-1)*(n-2)*..*1
    • floor(..) - Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. Example: floor( 3.2 ) = 3.0 , floor( 9.9 ) = 9.0
    • fpart(..) - returns the decimalvalue of its argument Example: fpart(2.345) = 0.345, fpart(4) = 0.0 etc.
    • round(..) - rounds the argument to the closest mathematical integer. Example: round( 3.4 ) = 3.0, round( 4.99 ) = 5.0 etc.
    • sfac(..) - semifactorial of.. n*(n-2)*(n-4)*..*4*2 if n is even n*(n-2)*(n-4)*..*3*1 if n is not even
    • sqrt(..) - square root
    • trigonometric functions (arguments must be in radians)
      • pi - the constant pi
      • sin(..) - the sine function
      • cos(..) - the cosine function
      • tan(..) - the tangent function
      • cotan(..) - the cotangent function
      • asin(..) - the arc sine function
      • acos(..) - the arc cosine function
      • atan(..) - the arc tangent function
      • acotan(..) - the arc cotangent function
      • hyperbolic functions
        • sinh(..) - the hyperbolic sine function
        • cosh(..) - the hyperbolic cosine function
        • tanh(..) - the hyperbolic tangent function

    For example:

    • sin( pi/2 ) - the sine of pi over 2 radians or 1
    • sqrt( 2 ) - the square root of 2 or 1.414...

Random Variables

One of Test Pilot's most powerful features is its ability to generate random numbers for use in questions. This permits the generation of unique questions each time a participant requests an assessment. In a computer laboratory environment, this means that each student could get a different test. This drastically reduces the efficacy of copying your neighbor's responses. What it has meant to Purdue University's Electrical Engineering Technology department was that students stopped asking each other What did you get for #...? and now they ask How did you get your answer? - a much more productive question and one geared productively towards learning.

Test Pilot supports two categories of random variables: local and global. Global variables are shared by all questions on an assessment. That is, you may construct multiple questions referring to the same set of random data. Local variables are unique to a specific question and are not accessible for use in other questions. There is no limit on the number of global or local random variables that may be defined.

Random variables may be defined as follows:

In this sample variable definition a single variable, r, has been defined. Variable names can only consist of alphabetic letters a-z and numbers 0-9. (e.g. x, xx, var2, aVeryLongVariable ) You can use any name that is not reserved by an operator or a predefined constant, as a variable name. You should avoid beginning a variable name with a number, like 3x or 1var. Care should be taken to avoid confusion between a number in scientific notation and a variable name. (e.g. use 2.0E+5 instead of 2E5) You may specify integer or decimal real numbers as start, end and increment values. You may also use scientific notation.

Numeric variables are assigned a starting value, and ending value and an increment value. Note the sample list at the end of each row. These are example of calculated values for each of these variables and are typical of the assignments that will be made at assessment time for the participant. Please note that the assignment of these values occurs at assessment time. None of our competitors offer this powerful capability.

Pooled random variables

In addition to calculated random variables such as shown above, Test Pilot includes the capability to define a pool of numbers or strings to be used to select from. If you enter a series of numbers, words or phrases separated by commas in the start field of a random variable definition, you create a pooled random variable.

In this example random variable definition a pooled random variable named primes is defined to be the set of the first eight non-negative prime numbers. Purdue's EET Department uses pooled random variables to define a set of resistance values common to electronic circuit construction. This lends an aura of realism for their use in Test Pilot for circuit design problems.

Pooled variables can also be strings that can be used within question text to make things interesting.

In this example there is a variable called names that can be used to randomly choose a name in a problem. For example, were the text of the question:

  • [names] has 5 dimes and 4 nickels. How much is that in decimal dollar form?

a different value for [names] would be generated by Test Pilot every time a participant entered the assessment.

Using Random Variables in Questions and Formulae

    For this example, we want to create a problem which asks the participant to calculate the circumference of a circle of a given radius. The value assigned to the radius will be a randomly generated quantity. We start the construction of the problem by creating a new fill-in-the-blank question and specifying that the response should be numeric. We then define our random variable for the radius as in the local definition above.

    Here we define a variable r which will range in value from 2 to 7 by an increment of 1. That is, it will be able to take on values from the set [2,3,4,5,6,7].

    Next, we'll define the text of the question to include the generated value for r. We do this with the special notation of including the variable's name in brackets:

The brackets tell Test Pilot to substitute the generated value for r at the appropriate location in the question's text. Thus, when the assessment is generated, participants will see, for example:

    What is the circumference of a circle of radius 7?

    or

    What is the circumference of a circle of radius 3?

Finally, we need to specify the correct answer to the question. Since we don't know what value will be assigned when Test Pilot generates the assessment, we must specify the correct answer as a function applied to the random variable. In this case, a circles circumference is determined by multiplying pi times twice the radius. In this question's formula box, the following could be entered:

Note that upon updating, a sample evaluation of the formula is shown below the formula. A quick test with a calculator indicates that the value was calculated correctly.

Question Chaining

Quite often in instruction, you want to define your problems in steps and to identify which steps are causing particular students problems. Yet, if problems occur at an early step and the results of one step is used in the next, errors compound quickly and it is very hard to determine whether succeeding steps were performed correctly. Test Pilot is unique among it competition at addressing this issue. It allows you to compose formulae using the correct answer of any problem. That is, if a student gets step #2 wrong, step #3's question is based upon a correct response to step #2. This is incredibly useful in developing powerful arithmetic, scientific and engineering tutorials. The syntax for referencing the correct answer to a problem involves enclosing it's id preceded by a Q in brackets:

[Q#101] - the correct answer to question id #101

Test Pilot's mathematical capabilities are unparalleled in the world of online assessment. For mathematical, scientific and engineering assessment online, Test Pilot is the best and only choice.


Help is Available!

    Please note that, at any time while you are editing an assessment, you can click upon the titles of the fields listed for your entries. If you do so, a pop-up window with an explanation of the items use and features will be shown.

Saving your Changes - Don't Forget to Update

    It should be noted that on the editing panels, you will see one or more Update buttons. Whenever you adjust a setting or make changes to any item, you must click an update button to record the changes. You may make multiple changes and then click Update, but if you fail to click the update button, your changes may not be recorded.

The mode popup menu allows you to adjust access to Test Pilot features and trim the detail of the automatically provided assistance for authoring.

  • for beginners - several of Test Pilot's more complicated options are hidden or preset to default values and pop-up assistance windows automatically appear to aid the user in the assessment authoring process.

  • with assistance - most of Test Pilot's features are shown as controls which may be adjusted. Pop-up help windows must be manually requested for viewing by clicking upon any feature title.

  • for experts - all of Test Pilot's features are shown as controls which may be adjusted. Help messages are minimized to maximize the number of controls that can be shown in a limited area. Pop-up help windows may still be manually requested for viewing by clicking upon any feature title.
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