FAQ: Khan exercises

Further explanations can be found in the Vademecum and in the manual (at the moment German only).

What is a Khan exercise?

A Khan exercise makes it possible to deal with a mathematical topic interactively, individually and repeatedly. This is done numerically, graphically or semantically.

What are the characteristics of such an exercise?

Who uses Khan exercises?

Courses in German

More than 250 exercises play a central role in the learning paths of the bridge course. They are an integral part of the exercise series in Mathematics I and II and III with metaphor pages: Mathematics I/II and Mathematics III.

Courses in Englisch

There's Mathematical Tools I .

How and where do I start?

What is KaTeX?

The fastest math typesetting library for the web.

It supports a comprehensive list of functions familiar from (La)Tex.

How does Khan help me?

Personalization, transparency and control

Compared to other systems, this framework is characterized by personalization, transparency and control. Conversely, this means that I only have limited predefined functions or generators at my disposal.

It is possible to understand the mathematical operations and calculations behind the scenes, work with formulas and define your own functions and algorithms instead of relying solely on predefined functions or generators. This generates numerical values that are better suited to specific requirements or didactic concepts.

Optimizing back and forth

There is control over input and the corresponding output. Using my own formulas or algorithms, the tasks can be adapted more precisely to the learning objectives, for example in comparison to the output of a given function. This allows me to generate suitable numerical values that check the didactic concept in a targeted manner and allow the task to be tested and adapted in a comprehensible way: starting with the parameter space, through the help in the hintsto the solution values. A variation is quickly ready by copying and changing.

Creativity and efficiency

Experimenting with values or evaluating iterations allows further access or an understanding of a better procedure. If I have certain numerical values in mind as solutions (e.g. integers), I can mathematically derive the corresponding initial values in the exercise. The mathematical-didactic insight is implemented in a creative way.

How efficiently I can use the ooffer depends on my programming skills. Often, repetitive functions or algorithms can be redefined and more efficient solutions can be found. It seems to be a well-known phenomenon that this only becomes apparent later.

Which answer type should I use?

The (global) answer type atype is defined in the preamble of a Khan exercise. The most useful types are number, rational, decimal and for input in a text box text. Single-choice is possible with radio. The type multiple allows several partial answers, e.g. multiple-choice is possible with multiple and checkbox. With set, several answer entries are possible. custom promises the greatest flexibility for tailor-made exercises. See also Vademecum and manual (german).

What role do the parameters (variables) play?

For example, with 

<var id="A">10</var> 
<var id="B">A/2</var>
two variables A and B with values 10 and 5 are defined. These values can also be generated randomly, see below.

The variable values are read out later in the html: in the task, in the solution or in the hints. Their content is evaluated and output as JavaScript. For example, <var>A</var> outputs the value of variable A, and <var>A+B</var> the sum of A and B.

With <div data-if=" . . . "> . . . </div> a switch is inserted depending on the variable value.

How can I create random parameters?

Parts of Khan's manual are no longer up to date.

With <var id="A">randRangeExclude(N,M,[-1,0,1])</var>the variable A can take integer values between N and M (incl. boundaries) that are not equal to -1, 0 or 1 (for N < -1,0,1< M). Random numbers between N and M are generated with randRange(N,M). Instead of randRangeExclude(N,M,[0]) one can use randRangeNonZero(N,M).

With <var id="L">randFromArray([L1,L2,...])</var> the variable L has the value of one of the variables L1, L2, etc, which were previously determined at random.

Can I further restrict the selection of parameters?

Yes. With <div data-ensure=""> the selection is further restricted, for example: 

<div data-ensure="A > B"> 
	<var id="A">randRange(1, 10)</div> 
	<var id="B">randRange(1, 10)</div> 
</div>
Logical operations allow further filters 
<div data-ensure="condition1 && condition2 && condition3 . . ." > 
	. . . 
</div>

See also test functions on the list of Khan functions.

Are the variable values always numbers?

No, it is also possible to work with function expressions. For example, I define an array: 

<var id="functionBank">[
	"x^2", "\\sin(x)", "2x", "\\cos(x)", "x^2\\cos(x)", "2x\\sin(x)", 
	"x^2\\sin(x) + 2x\\cos(x) - 2\\sin(x)","\\frac{\\pi^2}{2}-4",
	"-\\frac{\\pi}{2}","\\frac{\\pi}{2}"
	],
	[
	"x^2", "e^x", "2x", "e^x", "x^2e^x", "2xe^x", "x^2e^x - 2xe^x + 2 e^x",
	B + "\\ln(" + B +")(\\ln(" + B +") - 2 )+" + (2*B-2) ,0,"\\ln("+ B +")"
	] 
</var>
I then select a line from this: 
<var id="fNum">randRange(0,functionBank.length-1)</var> 
<var id="f">functionBank[fNum]</var>
The value <var>f[1]</var> is \(\sin(x)\) or \(e^x\) if the variablefNum is 0 or 1.

The expression B + "\\ln(" + B +")(\\ln(" + B +") - 2 )+" + (2*B-2) links the value of the variableB with the formal LaTeX expressions. Assuming the values <var>B</var> = 3 and<var>fNum</var> = 1 then<var>f[7]</var> has the value \(3 \ln(3)(\ln(3)-2) + 4)\). The value of Bis inserted and calculated with it, and any result is then linked to the LaTeX code.

Which functions/commands should I have in mind?

A Khan exercise (with hints) is an amalgam of html, Khan functions and KaTeX. See below for details.

Can I use LaTeX as usual?

Yes, see the list of (La)Tex's usual KaTeX functions.

How do I combine variables and KaTeX?

The value of a variable is inserted into KaTeX with <var>...</var>, e.g.:

<code>f(x) = \cos(x) \cdot <var>negParens(A)</var> \cdot x</code>

Which part of the code is KaTeX, which is JS, html, etc?

As an html file, a Khan exercise is primarily interpreted by the browser as html. Only when the exercise concludes with kekse, our version of Khan, is the html of the exercise specifically interpreted and the ready-to-use Khan exercise built from it.Therefore, a Khan exercise may look "broken" if kekse is not loaded properly (slowly).

In contrast to normal html, the contents of certain html elements of the exercise have special meanings. For example, there are elements that can/should contain JavaScript code or LaTeX code, even if this is not usually possible in html.

html escape

Conversely, if the special html characters <, >, & are required in such content, they must be written with html escape sequences &lt;, &gt;, & amp;. For example, if there is a size comparison in a JavaScript sectionif (x > y), then there must be if (x &gt; y).

Direct html

There are sections in which the html of the exercise is interpreted directly as html:

Wherever html is interpreted directly as such, LaTeX code can be inserted using<code>...</code>, which is then displayed accordingly as a formula. This is done with KaTeX, so the command set of KaTeX is decisive, see examples in the Vademecum.

JavaScript

JavaScript is expected in the following places:

It is possible to use <var> within <code>, see examples in the Vademecum.

How can I include loops in html?

How can I evaluate numbers in an interval as correct?

This is possible with the custom response type. The validator function must then implement size comparisons:

<div class="solution">
    <div class="instruction">
        <form class="needs-validation" autocomplete="off" novalidate="">
            <label for="custom_input" class="control-label visually-hidden">B=</label>
            <div class="input-group">
                <span class="input-group-text bk-input-group-addon">
                    <code>{\color{red}X=}</code>
                </span>
                <input id="custom_input" type="text" class="form-control" autocapitalize="off" />
            </div>
        </form>
    </div>
    <div class="guess">[document.getElementById("custom_input").value]</div>
    <div class="validator-function">
        return (X &gt; a) && (X &lt; b);
    </div>
</div>

Here, X is evaluated as correct if X > a and X < b, where a and b are variables. With &gt;= and &lt;= numbers can be queried in closed intervals. The html in <div class="instruction"> determines the appearance of the input field. This is used here, for example:

What else?

How do I give step-by-step instructions?

The hints are (hidden) in the <div class="hints"> ...</With a series of <div>, step-by-step hints are displayed, each time by pressing the Hint button. KaTeX and variables can also be used here. The example uses <data-if> for a switch depending on the random parameters: 

<div data-if="V == W"> <p>Here, the orientation of <code>\gamma</code> is <b>positive</b>. </p> 
</div> 
<div data-if="V !== W"> <p>Here, the orientation of <code>\gamma</code> is  <b>negative</b>. </p> 
</div>

Which graphical elements can I use?

Depending on your own programming affinity, the graphic elements are not very limited.

How do I prevent radio to be identical by mistake?

If single-choice answers are assembled from several random variables, it can happen that two answers are the same even though the original variables were not equal. For example if two answers are fractions X1/Y1 and X2/Y2.

Although X1 != X2 and Y1 != X2, it might happen that X1/Y1 == X2/Y2, e.g. \(\frac12 = \frac 24\): 

<div class="vars"> 
	<var id="X1">randRange(-10,10)</var> 
	<var id="X2">randRangeExclude(-10,10,X1)</var> 
	<var id="Y1">randRange(-10,10)</var> 
	<var id="Y2">randRangeExclude(-10,10,Y1)</var> 
</div>
One possible solution is more careful programming with data-ensure, e.g. 
<div class="vars" data-ensure="X1/Y1!=X2/Y2"> 
	<var id="X1">randRange(-10,10)</var> 
	<var id="X2">randRange(-10,10)</var> 
	<var id="Y1">randRange(-10,10)</var>
  	<var id="Y2">randRange(-10,10)</var> 
</div>
or we can generate more than enough answers and then clean up this selection, as in the following example

Can I evaluate a Khan task?

Yes, all interactions with an exercise are recorded (anonymously) and can be evaluated.

Pending tasks

How can I combine several tasks in one task?

How can I give feedback depending on the entries?