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Removes multiple choice from radians_and_degrees.html exercise #11127

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4 participants

@Mathman06

This might stir up controversy, but I have added problems to these exercises that use radians in terms of tau. Personally, I find the tau conversions easier, but sadly, pi is still the established standard. For more information on tau, see: http://www.khanacademy.org/video/tau-versus-pi?playlist=New%20and%20Noteworthy

@Mathman06

Removes multiple choice from radians_and_degrees.html exercise

@Mathman06

Removes multiple choice from radians_and_degrees.html exercise

@spicyj
Owner

This is unlikely to be included but we can check with Sal and see what he thinks. (cc @mwahl)

@Christi

While this is interesting, the difference from watching the video seems relatively minor. No big difference except you divide everything by 2 to get things in tau. As Sal points out the formula for area isn't quite as nice.

But, from an educator's standpoint I can see a big problem with using this in exercises. pi has been around for over 3900 years. tau (based on the sources Sal quotes in the video) has been around just over 10 years. I know when I looked at this request, my first thought was "I've never heard of tau other than a Greek letter." And I have a Master's in math. What did I miss? Now, add into this the fact that you have teachers of math who have Elementary Education degrees... And the majority of students in my Math for Elementary Education Major's class (back when I was an Elementary Education major) said the reason they were majoring in Elementary Education because they couldn't handle the math for ...

Keep in mind that the schools piloting using Khan Academy are elementary schools and middle schools... And keep in mind that tau isn't part of standardized curriculum.

Not trying to say that we shouldn't teach it because it's new... but, if it ain't broke, don't fix it.

(Other note, one negative comment I got on my teaching was on tossing in looks at the future like ordered triplets being too complicated. And this is something students will get into when they get to 3 dimensional math.)

@Christi

Oh, and one other note: in the videos on converting between radians and degrees, Sal doesn't use tau.

@beneater
Owner

You'll probably find a number of people at KA who appreciate the elegance of tau, myself included. Sal declined to take sides in his video, but Vi Hart is certainly very vocal in her support of it.

Nevertheless, all of the other videos use pi, particularly, as @christi points out, the ones relating to this exercise.

If we want to introduce using tau to the knowledge map I think it would be preferable to have a separate set of exercises that introduce the concept and/or fully embrace it and integrate it across the exercises. In either case, I think that would need to be a decision that is coordinated to be consistent in the videos as well.

With Vi on board, I'm sure we haven't heard the last of tau, but for now I'm closing this pull request until we figure out how we want to approach it.

@beneater beneater closed this
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36 exercises/degrees_to_radians.html
@@ -13,29 +13,40 @@
<var id="NUM_RADIANS">roundTo( 2, toRadians(NUM_DEGREES) )</var>
<!-- Common degree and radian values -->
- <!-- (index rather than member-based selection is for wrong answer generation) -->
+ <!-- (reformatted to include tau) -->
<var id="COMMON_INDEX">rand( commonAngles.length )</var>
<var id="COMMON_DEGREES">commonAngles[COMMON_INDEX].deg</var>
<var id="COMMON_RADIANS">commonAngles[COMMON_INDEX].rad</var>
+ <var id="COMMON_TAURADIANS">commonAngles[COMMON_INDEX].trad</var>
+ <var id="PIRADIANS">COMMON_DEGREES/ 180</var>
+ <var id="TAURADIANS">COMMON_DEGREES/ 360</var>
</div>
<div class="problems">
<div id="degrees-to-radians">
- <p class="question">Convert the angle <var>COMMON_DEGREES</var>&deg; into radians.</p>
- <p class="solution"><code><var>COMMON_RADIANS</var></code></p>
+ <p class="question">Convert the angle <var>COMMON_DEGREES</var>&deg; into radians. (Note that answer is in terms of <code>\pi</code>)</p>
+ <div class="solution" data-type="multiple">
+ <span class="sol"> <var>PIRADIANS</var></span><code>\pi</code>
+ </div>
<div class="hints">
<p>To convert from degrees to radians, you multiply by <code>\pi</code> and then divide by <code>180^{\circ}</code>.</p>
- <p><code><var>COMMON_DEGREES</var>^{\circ} \times \frac{\pi}{(180^{\circ})} = <var>COMMON_RADIANS</var></code></p>
+ <p><code><var>COMMON_DEGREES</var>^{\circ} \times \frac{\pi}{(180^{\circ})} = <var>COMMON_RADIANS</var>= <var>PIRADIANS</var> \pi</code></p>
</div>
-
- <ul class="choices" data-show="4" data-none="true">
- <li><code><var>wrongCommonAngle( COMMON_INDEX, 1 ).rad</var></code></li>
- <li><code><var>wrongCommonAngle( COMMON_INDEX, 2 ).rad</var></code></li>
- <li><code><var>wrongCommonAngle( COMMON_INDEX, 3 ).rad</var></code></li>
- </ul>
+
</div>
+ <div id="degrees-to-tau-radians">
+ <p class="question">Convert the angle <var>COMMON_DEGREES</var>&deg; into radians. (Note that answer is in terms of <code>\tau</code>, which equals <code>2\pi</code>)</p>
+ <div class="solution" data-type="multiple">
+ <span class="sol"> <var>TAURADIANS</var></span><code>\tau</code>
+ </div>
+ <div class="hints">
+ <p>To convert from degrees to radians, you multiply by <code>\tau</code> and then divide by <code>360^{\circ}</code>.</p>
+ <p><code><var>COMMON_DEGREES</var>^{\circ} \times \frac{\tau}{(360^{\circ})} = <var>COMMON_TAURADIANS</var> = <var>TAURADIANS</var> \tau</code></p>
+ </div>
+
+ </div>
<div data-type="degrees-to-radians">
<p class="question">Convert the angle <var>NUM_DEGREES</var>&deg; into radians. (Round to the nearest hundredth of a radian.)</p>
<p class="solution"><var>NUM_RADIANS.toFixed( 2 )</var></p>
@@ -45,11 +56,6 @@
<p><code><var>NUM_DEGREES</var>^{\circ} \times \frac{\pi}{180^{\circ}} = <var>NUM_RADIANS</var></code></p>
</div>
- <ul class="choices" data-show="4" data-none="true">
- <li><var>wrongRadians( NUM_RADIANS ).toFixed( 2 )</var></li>
- <li><var>wrongRadians( NUM_RADIANS ).toFixed( 2 )</var></li>
- <li><var>wrongRadians( NUM_RADIANS ).toFixed( 2 )</var></li>
- </ul>
</div>
</div>
</div>
View
32 exercises/radians_to_degrees.html
@@ -13,27 +13,39 @@
<var id="NUM_RADIANS">roundTo( 2, toRadians(NUM_DEGREES) )</var>
<!-- Common degree and radian values -->
- <!-- (index rather than member-based selection is for wrong answer generation) -->
+ <!-- (reformatted to include tau) -->
<var id="COMMON_INDEX">rand( commonAngles.length )</var>
<var id="COMMON_DEGREES">commonAngles[COMMON_INDEX].deg</var>
<var id="COMMON_RADIANS">commonAngles[COMMON_INDEX].rad</var>
+ <var id="COMMON_TAURADIANS">commonAngles[COMMON_INDEX].trad</var>
</div>
<div class="problems">
<div id="radians-to-degrees">
<p class="question">Convert the angle <code><var>COMMON_RADIANS</var></code> radians into degrees.</p>
- <p class="solution"><var>COMMON_DEGREES</var>&deg;</p>
+ <div class="solution" data-type="multiple">
+ <span class="sol"> <var>COMMON_DEGREES</var></span><code>^{\circ}</code>
+ </div>
<div class="hints">
<p>To convert from radians to degrees, you multiply by <code>180^{\circ}</code> and then divide by <code>\pi</code>.</p>
<p><code><var>COMMON_RADIANS</var> \times \frac{180^{\circ}}{\pi} = <var>COMMON_DEGREES</var>^{\circ}</code></p>
</div>
- <ul class="choices" data-show="4" data-none="true">
- <li><var>wrongCommonAngle( COMMON_INDEX, 1 ).deg</var>&deg;</li>
- <li><var>wrongCommonAngle( COMMON_INDEX, 2 ).deg</var>&deg;</li>
- <li><var>wrongCommonAngle( COMMON_INDEX, 3 ).deg</var>&deg;</li>
- </ul>
+
+ </div>
+
+ <div id="tau-radians-to-degrees">
+ <p class="question">Convert the angle <code><var>COMMON_TAURADIANS</var></code> radians into degrees. (Note: this angle is given in terms of <code>\tau</code>, which equals <code>2\pi</code>)</p>
+ <div class="solution" data-type="multiple">
+ <span class="sol"> <var>COMMON_DEGREES</var></span><code>^{\circ}</code>
+ </div>
+ <div class="hints">
+ <p>To convert from radians to degrees, you multiply by <code>360^{\circ}</code> and then divide by <code>\tau</code>.</p>
+ <p><code><var>COMMON_TAURADIANS</var> \times \frac{360^{\circ}}{\tau} = <var>COMMON_DEGREES</var>^{\circ}</code></p>
+ </div>
+
+
</div>
<div data-type="radians-to-degrees">
@@ -45,11 +57,7 @@
<p><code><var>NUM_RADIANS</var> \times \frac{180^{\circ}}{\pi} = <var>NUM_DEGREES</var>^{\circ}</code></p>
</div>
- <ul class="choices" data-show="4" data-none="true">
- <li><var>wrongDegrees( NUM_DEGREES )</var>&deg;</li>
- <li><var>wrongDegrees( NUM_DEGREES )</var>&deg;</li>
- <li><var>wrongDegrees( NUM_DEGREES )</var>&deg;</li>
- </ul>
+
</div>
</div>
</div>
View
34 utils/angles.js
@@ -1,22 +1,22 @@
jQuery.extend( KhanUtil, {
commonAngles: [
- {deg: 15, rad: "\\frac{\\pi}{12}"},
- {deg: 30, rad: "\\frac{\\pi}{6}"},
- {deg: 45, rad: "\\frac{\\pi}{4}"},
- {deg: 60, rad: "\\frac{\\pi}{3}"},
- {deg: 90, rad: "\\frac{\\pi}{2}"},
- {deg: 120, rad: "\\frac{2\\pi}{3}"},
- {deg: 135, rad: "\\frac{3\\pi}{4}"},
- {deg: 150, rad: "\\frac{5\\pi}{6}"},
- {deg: 180, rad: "\\pi"},
- {deg: 210, rad: "\\frac{7\\pi}{6}"},
- {deg: 225, rad: "\\frac{5\\pi}{4}"},
- {deg: 240, rad: "\\frac{4\\pi}{3}"},
- {deg: 270, rad: "\\frac{3\\pi}{2}"},
- {deg: 300, rad: "\\frac{5\\pi}{3}"},
- {deg: 315, rad: "\\frac{7\\pi}{4}"},
- {deg: 330, rad: "\\frac{11\\pi}{6}"},
- {deg: 360, rad: "2\\pi"}
+ {deg: 15, rad: "\\frac{\\pi}{12}",trad: "\\frac{\\tau}{24}"},
+ {deg: 30, rad: "\\frac{\\pi}{6}",trad: "\\frac{\\tau}{12}"},
+ {deg: 45, rad: "\\frac{\\pi}{4}",trad: "\\frac{\\tau}{8}"},
+ {deg: 60, rad: "\\frac{\\pi}{3}",trad: "\\frac{\\tau}{6}"},
+ {deg: 90, rad: "\\frac{\\pi}{2}",trad: "\\frac{\\tau}{4}"},
+ {deg: 120, rad: "\\frac{2\\pi}{3}",trad: "\\frac{\\tau}{3}"},
+ {deg: 135, rad: "\\frac{3\\pi}{4}",trad: "\\frac{3\\tau}{8}"},
+ {deg: 150, rad: "\\frac{5\\pi}{6}",trad: "\\frac{5\\tau}{12}"},
+ {deg: 180, rad: "\\pi",trad: "\\frac{\\tau}{2}"},
+ {deg: 210, rad: "\\frac{7\\pi}{6}",trad: "\\frac{7\\tau}{8}"},
+ {deg: 225, rad: "\\frac{5\\pi}{4}",trad: "\\frac{5\\tau}{8}"},
+ {deg: 240, rad: "\\frac{4\\pi}{3}",trad: "\\frac{2\\tau}{3}"},
+ {deg: 270, rad: "\\frac{3\\pi}{2}",trad: "\\frac{3\\tau}{4}"},
+ {deg: 300, rad: "\\frac{5\\pi}{3}",trad: "\\frac{5\\tau}{6}"},
+ {deg: 315, rad: "\\frac{7\\pi}{4}",trad: "\\frac{7\\tau}{8}"},
+ {deg: 330, rad: "\\frac{11\\pi}{6}",trad: "\\frac{11\\tau}{12}"},
+ {deg: 360, rad: "2\\pi",trad: "\\tau"}
],
// Convert a degree value to a radian value
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