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Math Forum Internet News

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Registered: 3/1/05
Newsletter: Math Forum Internet News No. 19.5 (31 Jan 14)
Posted: Jan 31, 2014 12:06 PM
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31 January, 2014 Vol. 19, No. 5

THE MATH FORUM @ DREXEL INTERNET NEWS

Solutions: 2014 Mathematics Game | Function Carnival
An Investigation of Subtraction Algorithms

SOLUTIONS: 2014 MATHEMATICS GAME

http://mathforum.org/yeargames/yeargameentrys?find=BySolutionFor&form

Tomorrow, we'll post solutions to the 2014 Mathematics Game.
Students have already sent us their arithmetic from every
region of the US, plus England, Australia, Singapore, India,
and Israel.

... but we still need answers! Sixty-seven and 87 have so far
defied expressions made from

- the digits in 2014
- standard operations
- grouping symbols

Several other odd numbers near them, in the bottom half of the
pull-down menu of solutions, have garnered only one answer
apiece. So whether you've blazed a new arithmetic path, or just
taken a commutative detour, come share your basic ops
wizardry here:

http://mathforum.org/yeargames/yeargameentrys?form

-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-

PoW taking place: math problem-solving moment of the week

"This is one of those problems where submitters used methods I
didn't think of, and almost nobody used the method that I
imagined everyone would use! Raphaella R. from Mesa Union
Junior High School mentions, in her first solution, the key to
the second method that both she and Britney used to solve
the problem."

- Annie, commenting on the Geometry PoW's Latest Solution

http://mathforum.org/pows/solution.htm?publication=4335

-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-

FUNCTION CARNIVAL

http://blog.desmos.com/post/74745817070/carnival

Step right up, step right up -- and plot some fun with Desmos'
new Function Carnival!

First, watch the animations of

- the flight of the human cannonball, dressed in green
- the route of the green bumper car
- the trajectory of the ferris wheel's green cart

Then, represent those heights or distances over time by
pointing, clicking, or dragging in the nearby graph. Press the
blue "play" button to set in motion a blue cannon man, blue
bumper car, or blue ferris wheel cart that acts out what you
sketched, all while the original light green figure re-plays in
the background for comparison.

https://class.desmos.com/carnival/teacherguide

A dashboard lets teachers track students' drawings and further
explore the meaning of holes, multiple values, discrete points,
and other features of their graphs. For an activity
guide, visit

https://class.desmos.com/carnival/about

Clarifying common misconceptions about graphs with instant
feedback, Desmos' Function Carnival came out of a collaboration
with Christopher Danielson and Dan Meyer, who blogged about the
pedagogical value of their "online math happytime" here:

http://blog.mrmeyer.com/?p=18420

-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-

Now taking place: math education conversation of the day

"If that happens in your school as well, you would have
students who never take geometry. Finally, it may be my own
personal prejudice, but the logic and proof elements of
geometry are an important part of teaching students to think,
and I believe that they are ultimately more important than the
properties of quadrilaterals when it comes to turning out
'educated' citizens."

- Evelyne, posted to the secondary (grades 9-12) discussion
group of the Association of Math Teachers of New York State

http://mathforum.org/kb/message.jspa?messageID=9375157

-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-

AN INVESTIGATION OF SUBTRACTION ALGORITHMS

http://www.maa.org/publications/periodicals/convergence/an-investigation-of-subtraction-algorithms-from-the-18th-and-19th-centuries-textbooks-and-cyphering

How do you subtract?

Does your method follow the same steps that your
ancestors took?

A PhD candidate in mathematics education has identified four
distinct subtraction algorithms from 18th and 19th century
America; and in the current issue of the Mathematical
Association of America (MAA) journal Convergence, she discusses
what this means for teachers today.

Illustrated with images from printing press textbooks and
handwritten "cyphering" books that date back to 1785, Nicole M.
Wessman-Enzinger's article also offers video demonstrations
modeling the four procedures that turned up in her research:

- equal additions
- decomposition
- complement
- Austrian

Out of hundreds of scanned source materials, Wessman-Enzinger
found scores of references to the first and third
techniques -- but none whatsoever to decomposition, which
predominates now. Observing that "decomposition was perhaps not
an implemented subtraction algorithm in North America" as
recently as the Civil War era, she then goes on to address the
questions and implications that arise from this revelation.

Before pursuing her doctorate, Wessman-Enzinger taught high
school math for five years, then -- as an assistant mathematics
professor at her college alma mater -- calculus, statistics,
and several courses for elementary teachers.

-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-

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_o \o_ __| \ / |__ o _ o/ \o/
__|- __/ \__/o \o | o/ o/__/ /\ /| |
\ \ / \ / \ /o\ / \ / \ / | / \ / \

The Math Forum @ Drexel ** 31 January 2014

An archive of all the Math Forum newsletters
and directions for subscribing can be found at
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<head>
<title>The Math Forum Internet News</title>
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<td><font color="#333333" size="1" face="Verdana, Arial, Helvetica, sans-serif"><strong>31 January, 2014</strong></font></td>
<td><div align="right"><font color="#333333" size="1" face="Verdana, Arial, Helvetica, sans-serif"><strong>Volume 19 No. 5</strong></font></div></td>
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<font color="#003399" size="2" face="Verdana, Arial, Helvetica, sans-serif">
<strong>In This Issue</strong>
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<!-- Start - Table of contents -->

<p><font size="2" face="Arial, Helvetica, sans-serif">Solutions: 2014 Mathematics Game</font></p>
<p><font size="2" face="Arial, Helvetica, sans-serif">Function Carnival</font></p>
<p><font size="2" face="Arial, Helvetica, sans-serif">An Investigation of Subtraction Algorithms</font></p>

<p>&nbsp;</p>

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If you prefer to receive a text-only version, please send a note to <a href="http://mathforum.org/electronic.newsletter/mfin.faq.html#feedback">the Math Forum Internet Newsletter editors</a> and we will subscribe you to that list.<br>
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</font>
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<font size="2" face="Arial, Helvetica, sans-serif">
<p><strong>
<font color="#003399">Solutions: 2014 Mathematics Game</font>
</strong>
</p>
<p align="center">
<a href="http://mathforum.org/yeargames/yeargameentrys?find=BySolutionFor&form">http://mathforum.org/yeargames/</a><br><a href="http://mathforum.org/yeargames/yeargameentrys?find=BySolutionFor&form">yeargameentrys?find=BySolutionFor&form</a>
</p>
<p>
Tomorrow, we'll post solutions to the 2014 Mathematics Game.
Students have already sent us their arithmetic from every
region of the US, plus England, Australia, Singapore, India,
and Israel.
</p>
<p>
... but we still need answers! Sixty-seven and 87 have so far
defied expressions made from
</p>
<ul>
<li>
the digits in 2014
</li>
<li>
standard operations
</li>
<li>
grouping symbols
</li>
</ul>
<p>
Several other odd numbers near them, in the bottom half of the
pull-down menu of solutions, have garnered only one answer
apiece. So whether you've blazed a new arithmetic path, or just
taken a commutative detour, come share your basic ops
wizardry here:
</p>
<p align="center"><a href="http://mathforum.org/yeargames/yeargameentrys?form">http://mathforum.org/yeargames/</a><br><a href="http://mathforum.org/yeargames/yeargameentrys?form">yeargameentrys?form</a></p>
</font></p>

<hr>
<p><font size="2" face="Arial, Helvetica, sans-serif">
<p align=center>
<dl>
<dt>
<i><font color="#003399">PoW taking place: math problem-solving moment of the week</font></i>
<p>
<dt>
"This is one of those problems where submitters used methods I
didn't think of, and almost nobody used the method that I
imagined everyone would use! Raphaella R. from Mesa Union
Junior High School mentions, in her first solution, the key to
the second method that both she and Britney used to solve
the problem."
<dd>
- Annie, commenting on the Geometry PoW's Latest Solution
<dd>
<a href="http://mathforum.org/pows/solution.htm?publication=4335">http://mathforum.org/pows/solution.htm?publication=4335</a>
</dl>
</p>
</font></p>
<hr>

<p><font size="2" face="Arial, Helvetica, sans-serif">
<p><strong><font color="#003399">Function Carnival</font></strong></p>
<p align="center">
<a href="http://blog.desmos.com/post/74745817070/carnival">http://blog.desmos.com/post/74745817070/carnival</a>
</p>
<p>
Step right up, step right up &mdash; and plot some fun with Desmos'
new Function Carnival!
</p>
<p>
First, watch the animations of
</p>
<ul>
<li>
the flight of the human cannonball, dressed in green
</li>
<li>
the route of the green bumper car
</li>
<li>
the trajectory of the ferris wheel's green cart
</li>
</ul>
<p>
Then, represent those heights or distances over time by
pointing, clicking, or dragging in the nearby graph. Press the
blue "play" button to set in motion a blue cannon man, blue
bumper car, or blue ferris wheel cart that acts out what you
sketched, all while the original light green figure re-plays in
the background for comparison.
</p>
<p align="center"><a href="https://class.desmos.com/carnival/teacherguide">https://class.desmos.com/carnival/teacherguide</a></p>
<p>
A dashboard lets teachers track students' drawings and further
explore the meaning of holes, multiple values, discrete points,
and other features of their graphs. For an activity
guide, visit
</p>
<p align="center"><a href="https://class.desmos.com/carnival/about">https://class.desmos.com/carnival/about</a>
<p>
Clarifying common misconceptions about graphs with instant
feedback, Desmos' Function Carnival came out of a collaboration
with Christopher Danielson and Dan Meyer, who blogged about the
pedagogical value of their "online math happytime" here:
</p>
<p align="center"><a href="http://blog.mrmeyer.com/?p=18420">http://blog.mrmeyer.com/?p=18420</a>
</font></p>

<hr>
<p><font size="2" face="Arial, Helvetica, sans-serif">
<p align=center>
<dl>
<dt>
<i><font color="#003399">Now taking place: math education conversation of the day</font></i>
<p>
<dt>
"If that happens in your school as well, you would have
students who never take geometry. Finally, it may be my own
personal prejudice, but the logic and proof elements of
geometry are an important part of teaching students to think,
and I believe that they are ultimately more important than the
properties of quadrilaterals when it comes to turning out
'educated' citizens."
<dd>
- Evelyne, posted to the secondary (grades 9-12) discussion
group of the Association of Math Teachers of New York State
<dd>
<a href="http://mathforum.org/kb/message.jspa?messageID=9375157">http://mathforum.org/kb/message.jspa?messageID=9375157</a>
</p>
</font></p>
</dl>
<hr>

<p><font size="2" face="Arial, Helvetica, sans-serif">
<p><strong><font color="#003399">An Investigation of Subtraction Algorithms</font></strong></p>
<p align="center">
<a href="http://www.maa.org/publications/periodicals/convergence/an-investigation-of-subtraction-algorithms-from-the-18th-and-19th-centuries-textbooks-and-cyphering">http://www.maa.org/publications/periodicals/</a><br><a href="http://www.maa.org/publications/periodicals/convergence/an-investigation-of-subtraction-algorithms-from-the-18th-and-19th-centuries-textbooks-and-cyphering">convergence/an-investigation-of-subtraction-algorithms-</a><br><a href="http://www.maa.org/publications/periodicals/convergence/an-investigation-of-subtraction-algorithms-from-the-18th-and-19th-centuries-textbooks-and-cyphering">from-the-18th-and-19th-centuries-textbooks-and-cyphering</a>
</p>
<p>
How do you subtract?
</p>
<p>
Does your method follow the same steps that your
ancestors took?
</p>
<p>
A PhD candidate in mathematics education has identified four
distinct subtraction algorithms from 18th and 19th century
America; and in the current issue of the Mathematical
Association of America (MAA) journal Convergence, she discusses
what this means for teachers today.
</p>
<p>
Illustrated with images from printing press textbooks and
handwritten "cyphering" books that date back to 1785, Nicole M.
Wessman-Enzinger's article also offers video demonstrations
modeling the four procedures that turned up in her research:
</p>
<ul>
<li>
equal additions
</li>
<li>
decomposition
</li>
<li>
complement
</li>
<li>
Austrian
</li>
</ul>
<p>
Out of hundreds of scanned source materials, Wessman-Enzinger
found scores of references to the first and third
techniques &mdash; but none whatsoever to decomposition, which
predominates now. Observing that "decomposition was perhaps not
an implemented subtraction algorithm in North America" as
recently as the Civil War era, she then goes on to address the
questions and implications that arise from this revelation.
</p>
<p>
Before pursuing her doctorate, Wessman-Enzinger taught high
school math for five years, then &mdash; as an assistant mathematics
professor at her college alma mater &mdash; calculus, statistics,
and several courses for elementary teachers.
</p>
</font></p>

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