tag:blogger.com,1999:blog-8536069763788657142024-03-13T01:40:15.491-07:00Marina HoAnonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-853606976378865714.post-18749089942981861302014-01-08T23:03:00.001-08:002014-01-08T23:03:46.153-08:007 Jan 2014: Interview with Marian Lee<iframe allowfullscreen="" frameborder="0" height="270" src="//www.youtube.com/embed/J-y7mV7eZQU" width="480"></iframe>Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-25917242475857646992013-09-14T01:59:00.001-07:002013-09-14T01:59:09.281-07:00I Teach K: EDU330 Elementary Mathematics 08/17/13 Session 6<a href="http://i-teach-k.blogspot.com/2013/08/edu330-elementary-mathematics-081713.html?spref=bl">I Teach K: EDU330 Elementary Mathematics 08/17/13 Session 6</a>: Today, you had fun with Ms Peggy Foo on lesson study and solving a bunch of enrichment lessons as well as to learn about differentiated inst...Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-88890963895147772432013-08-18T07:25:00.004-07:002013-08-18T07:25:44.160-07:00Gelman's Counting Principle
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<b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-family: "Century Gothic"; font-size: 14pt; mso-ansi-language: EN-US;">Gelman’s
Counting Principle<o:p></o:p></span></u></b></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">How do we know
whether children can count ?<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">If knowing how to
count just means reciting<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">the numbers (i.e.,
‘‘one, two, three...”) up to “five” or<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">“ten,” perhaps
pointing to one object with each numeral,<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">then many
two-year-olds count very well.<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Of course, counting
only tells you number of things if you do it correctly, </span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">following the three
‘how-to-count’ principles </span><span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">identified by </span><span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Gelman and </span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Gallistel (1978)<span style="color: black;">. These are :<o:p></o:p></span></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p> </o:p></span><span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">(1) The one-to-one
principle, which says that ‘‘in<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">enumerating a set,
one and only one [numeral] must<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">be assigned to each
item in the set.” <o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p> </o:p></span></div>
<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">(2) The stable-order
principle, which says that ‘‘[Numerals] used in </span><br />
<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span><br />
<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">counting must be used in the
same order in any one<o:p></o:p></span><br />
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">count as in any other count.” and
<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p> </o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">(3) The cardinal principle, which
says that ‘‘the [numeral] applied to the</span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">final item in the set represents the
number of items in the set.” <o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p> </o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">As Gelman and Gallistel pointed
out, so long as the<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">child’s counting obeys these
three principles, the numeral<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">list (‘‘one,” ‘‘two,”
‘‘three,”... etc.) represents the cardinalities<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt;">1, 2, 3,... etc. <o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">However, observations
have shown that three-year-old<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">children often
violate the one-to-one principle by skipping<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">or double-counting
items, or by using the same numeral<o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">twice in a count.</span><span style="color: #000066; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p></o:p></span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Children also violate
the stable-order principle, by producing different </span></div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="color: black; font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">numeral lists at different
times.<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">The cardinal principle can also be
viewed as something more profound </span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">– a principle stating that </span><span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-I; mso-fareast-font-family: AdvGulliv-I;">a numeral’s </span><span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-I; mso-fareast-font-family: AdvGulliv-I;">cardinal meaning is determined by
</span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-I; mso-fareast-font-family: AdvGulliv-I;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-I; mso-fareast-font-family: AdvGulliv-I;">its ordinal position<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-I; mso-fareast-font-family: AdvGulliv-I;">in the list. </span><span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">This means, for example, that the
fifth numeral in<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">any count list – spoken or
written, in any language – must<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">mean five. And the third numeral
must mean three..<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">If so, then knowing the cardinal
principle means having<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">some implicit knowledge of the
successor function – some<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">understanding that the
cardinality for each numeral is generated by </span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">adding one to the cardinality for
the previous numeral.<o:p></o:p></span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Thus Gelman feels that
preschoolers learn to count as a result of the </span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">perfecting of counting
procedures.<o:p></o:p></span></div>
<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"><o:p> </o:p></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl_EtwigQPcKKUUO8hGjt1_o2Z5rRkECIX8tkaJbDmc8J7yC-UUub_Z3qrj50HMJR6D2IDk3OMk5OdTD16apA_XxtddH_5JNkLN94fcrlP19m22B6cKQ-Nsalbv9Ks9Q9zM7Oa0zze9Lpr/s1600/counting%5B1%5D.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl_EtwigQPcKKUUO8hGjt1_o2Z5rRkECIX8tkaJbDmc8J7yC-UUub_Z3qrj50HMJR6D2IDk3OMk5OdTD16apA_XxtddH_5JNkLN94fcrlP19m22B6cKQ-Nsalbv9Ks9Q9zM7Oa0zze9Lpr/s1600/counting%5B1%5D.gif" /></a></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Do you agree ?</span></div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;"></span> </div>
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<span style="font-family: "Century Gothic"; font-size: 14pt; mso-bidi-font-family: AdvGulliv-R; mso-fareast-font-family: AdvGulliv-R;">Marina Ho-BSc08<o:p></o:p></span></div>
Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-28267432807390121192013-08-17T07:16:00.000-07:002013-08-17T07:16:26.075-07:00Fast Math Tricks - How to multiply 2 digit numbers up to 100 - the fast ...<br />
<iframe allowfullscreen="" frameborder="0" height="344" src="//www.youtube.com/embed/PYrgjMubh-c" width="459"></iframe><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">The multiplication method my teachers never taught me. I wish I had learnt this way earlier. I was taught the top down method.</span>Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-89555519049745546262013-08-16T10:04:00.001-07:002013-08-16T10:04:05.235-07:00<br />
<br />
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<b style="mso-bidi-font-weight: normal;"><u><span style="color: black; font-family: Arial; font-size: 14pt;">Pick’s Theorem<o:p></o:p></span></u></b></div>
<br />
<br />
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<span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">This
formula was created by <a href="http://en.wikipedia.org/wiki/Georg_Alexander_Pick" title="Georg Alexander Pick"><span style="color: windowtext;">Georg Alexander
Pick</span></a> in 1899.<o:p></o:p></span></div>
<span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;"><o:p><span style="font-family: Times New Roman; font-size: small;"> </span></o:p></span><br />
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<span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Using
the Geoboard to Assist :<o:p></o:p></span></div>
<span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;"><o:p><span style="font-family: Times New Roman; font-size: small;"> </span></o:p></span><br />
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Draw a polygon on the Geoboard<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Determine the number of boundary points
and the number of interior points and calculate its area<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Repeat with different polygons<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Draw polygons without any interior
points and find the area<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Draw polygons with one interior point
and find the area<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span lang="EN" style="font-family: Symbol; font-size: 14pt; mso-ansi-language: EN; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Draw polygons with two interior points
and find the area<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 14pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN" style="font-family: Arial; font-size: 14pt; mso-ansi-language: EN;">Prepare a table with number of boundary
points, number of interior points, and area. Discover that the relationship
between B the number of boundary points, i the number of internal points, and
the area of the geoboard polygon is given by Pick's formula </span><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">A = I + ½ B –
1<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 18pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"><o:p><span style="font-size: small;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 18pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial; font-size: 14pt;">The diagram below explains this further.</span></b></div>
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 18pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial; font-size: 14pt;"></span></b> </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhd7mdGdu7HPvHWKlhhfGr26e9RRPmygSIUmBW1Rc8YX_GmgcXQvXhrlvk6cHuLuUWLsQEzFwKVfBGmxBpT70IBGWHe3y5dx8vOeQkDsOFasAMFOFOtZ8KcEvDRI9FUfF8J6ZbNNZHp-GuJ/s1600/picks-theorem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="317" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhd7mdGdu7HPvHWKlhhfGr26e9RRPmygSIUmBW1Rc8YX_GmgcXQvXhrlvk6cHuLuUWLsQEzFwKVfBGmxBpT70IBGWHe3y5dx8vOeQkDsOFasAMFOFOtZ8KcEvDRI9FUfF8J6ZbNNZHp-GuJ/s320/picks-theorem.jpg" width="320" /></a></div>
<br />
<span style="font-family: "Trebuchet MS", sans-serif;">I understand this better now! Wow :)</span><br />
<span style="font-family: Trebuchet MS;"></span><br />
<span style="font-family: Trebuchet MS;">Marina Ho</span><br />
<span style="font-family: Trebuchet MS;">BSc08</span><br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 18pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial; font-size: 14pt;"><o:p></o:p></span></b> </div>
<br />
<div class="MsoNormal" style="line-height: 16.8pt; margin: 0cm 0cm 0pt 18pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"><o:p><span style="font-size: small;"> </span></o:p></span></b></div>
<br />
<div style="background: white; margin-left: 18pt;">
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</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: Verdana;"><a href="http://nrich.maths.org/content/03/10/six4/picks-theorum.swf"></a><o:p></o:p></span><br /></div>
Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-80261539781609358682013-08-14T09:23:00.002-07:002013-08-14T09:23:44.033-07:00By The Numbers - Subitizing<iframe allowfullscreen="" frameborder="0" height="270" src="//www.youtube.com/embed/BMXfw_5tPkg" width="480"></iframe><br />
<br />
Watch this video on what subitizing means. Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-9143176440689824622013-08-14T09:21:00.000-07:002013-08-14T09:21:19.859-07:00Elementary Math - Day 3 Blog
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;">What is Subitizing ?<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;"><o:p> </o:p></span></b></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;">Perceptual subitizing<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">Perceptual subitizing is closest to the original
definition of subitizing: recognizing a number without counting. For example,
children might "see 3" without using any learned mathematical knowledge.
<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;"><o:p> </o:p></span></b></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;">Conceptual subitizing<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">But how is it that people see an eight-dot domino
and 'just know" the total number? This is Conceptual subitizing. They are
able to see the relationship between numbers when dealing with different
quantities. These people are capable of viewing number and number patterns as
units of units (Steffe and Cobb 1988).<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">Spatial patterns, such as those on dominoes, are one
kind. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<b><span style="font-family: Calibri;">Subitizing and counting<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">Young children may use perceptual subitizing to
make units for counting and to build their initial ideas of cardinality.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"></span> </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGiJzwKDdOjA_u0nq5BHlWlPNFERlavDvm4VMvRno9mP34Tx64ie8hUUu_pmzDX7OjqeoQkGkx2aChJ-p6CV-QjmVcy9xFCVJP-rZ3uS6osj2mg7VevgqNEQMOaZvkY6UeOEtTnzIxLgKa/s1600/Subtizing.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGiJzwKDdOjA_u0nq5BHlWlPNFERlavDvm4VMvRno9mP34Tx64ie8hUUu_pmzDX7OjqeoQkGkx2aChJ-p6CV-QjmVcy9xFCVJP-rZ3uS6osj2mg7VevgqNEQMOaZvkY6UeOEtTnzIxLgKa/s1600/Subtizing.jpg" /></a></div>
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<span style="font-family: Calibri;"></span> </div>
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<span style="font-family: Calibri;"></span> </div>
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<span style="font-family: Calibri;"></span> </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKAogV7-qMY2pASc_oTa_jVdM9ZOd6VjJ4qeegbfRIUH52vapj_deW0ERPxttACdw70KdlP0Hu5w5VoGT2ZpDU7GHQaBu5PMT_zSEQSfAVlC7Hb-MqH1XirzmMvNUG1gJ2R6tDIo5mPIlA/s1600/1-dice.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKAogV7-qMY2pASc_oTa_jVdM9ZOd6VjJ4qeegbfRIUH52vapj_deW0ERPxttACdw70KdlP0Hu5w5VoGT2ZpDU7GHQaBu5PMT_zSEQSfAVlC7Hb-MqH1XirzmMvNUG1gJ2R6tDIo5mPIlA/s320/1-dice.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">By : Marina Ho - BSc08</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;">Seed Institute</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;">
<span style="font-family: Calibri;"><span style="color: black; font-family: Helvetica; font-size: 10pt; mso-ansi-language: EN-SG; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体; mso-fareast-language: ZH-CN;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
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<span style="font-family: Calibri;"><o:p></o:p></span> </div>
Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-26096329296419737042013-08-13T09:42:00.003-07:002013-08-13T09:42:46.427-07:00<h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Elementary Math - BSc08</span></h2>
<strong><span style="background-color: cyan;">What are Nominal Numbers ?</span></strong><br />
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<strong>Numbers used to name something eg. Blk 543, a bus number 963 or your IC No. 7612345B.</strong><br />
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<strong>How we have often mistaken the bus numbers to be nine hundred and sixty three, instead of "9" "6" "3". </strong><br />
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<strong><img alt="" aria-label="First Group has introduced additional late night bus journeys on the number 73 Bristol City Centre to" height="311" id="yui_3_5_1_5_1376411581651_437" src="http://www.bradleystokejournal.co.uk/wp-content/uploads/2010/01/number-73-bus-in-bradley-stoke.jpg" style="height: 311px; width: 450px;" width="450" /></strong><br />
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<strong><span style="background-color: yellow;">What are Ordinal Numbers ?</span></strong><br />
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<strong>Ordinal numbers are used very often to label the position of children lined up in a row, eg. 1st, 2nd, 3rd, 4th, 5th etc. </strong><br />
<strong></strong><br />
<strong>In the picture below children can also learn to count from the 2nd person (Sam) and also backwards in position, to determine how many children are before Sam. Thus ordinal numbers can be used children a different way of understanding number counting. </strong><br />
<img alt="" aria-label="<b>Ordinal </b>Numbers - EDpaX International Ltd" height="600" id="yui_3_5_1_5_1376411814498_590" src="http://shop.edpax.com/168-124-thickbox/ordinal-numbers.jpg" style="height: 576px; width: 576px;" width="600" /><br />
Marina Ho - BSc08<br />
Seed InstituteAnonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-90668677815568937102013-08-13T09:13:00.000-07:002013-08-13T09:13:48.728-07:00Elementary Math - Daily Blogs<h2>
Learning About Numbers for Children</h2>
Children have to learn about counting in 2 different ways; Rote counting and Rational Counting.<br />
When children learn rote counting they are counting in sequence without knowledge of quantity. However, when children learn rational counting, they learn how to count wth knowledge and understanding. They count with cardinality in mind.<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/jsKpazuC0RY?feature=player_embedded' frameborder='0'></iframe></div>
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The above video show rational counting, where children have to learn 1 to 1 correspondence in counting different objects.<br />
This shows how children need to be shown concrete objects or have a pictorial representation to have a realtionship about what a number quantity means.<br />
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Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-74605087203529296032013-08-04T01:40:00.005-07:002013-08-07T00:36:14.708-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Understanding Mathematics</span></u></b></div>
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<b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span></u></b><b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span></u></b><b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span></u></b> </div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"><o:p> </o:p></span><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Parents who endeavour to know if a school math
program is</span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span> </div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">well planned should examine whether 6 areas are present.</span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span> </div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">These
are;<span style="mso-spacerun: yes;"> </span>high standards and strong support
for students, </span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span> </div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">curriculum that is focused and coherent, teaching that </span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">challenge
and support students. Next would be learning with </span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;"></span> </div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">understanding from prior
knowledge, assessment for </span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">students to find new information, and lastly
technology like calculators and computers are </span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">used to enhance learning.<o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">The Math classroom should also have 6 components
:<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">an environment that gives students an equal
opportunity to learn<o:p></o:p></span></div>
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<!--[if !supportLists]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">teaching that has a balance of both conceptual
understanding and procedural fluency<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">ensures active student participation in problem
solving, reasoning, communications, connections and representation<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">use of technology to improve understanding<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">emphasis on reasoning of math <o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Parents also need to know what it means to
understand math in today’s classroom. Relational understanding means knowing
what to do and why, while the opposite is instrumental understanding (just
doing without understanding). Thus students who have proficiency in math would
have mastery in 5 areas :<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">conceptual understanding : knowledge about the
relationship between ideas in a topic.<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Procedural fluency : able to use rules and procedures
in carrying out math processes.<o:p></o:p></span></div>
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<!--[if !supportLists]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Strategic competence : able to use different methods
to eventually solve a problem.<o:p></o:p></span></div>
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<!--[if !supportLists]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Adaptive reasoning : able to reflect, evaluate and
adapt or use different methods.<o:p></o:p></span></div>
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</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">Productive disposition : when solving a problem you
should rely on a how to and applying your knowledge rather than a recall method
of how you can solve it. <o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: Arial; mso-ansi-language: EN-US;">I trust these
points in mind would make parents see Math in a different light.. Math is not
to be approached through rote drilling and countless worksheets but with
crystal clear thought and understanding.</span><br />
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By : Marina Ho Mee Lin<br />
SEED - BSC08</div>
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Anonymoushttp://www.blogger.com/profile/11055422096507235899noreply@blogger.com0tag:blogger.com,1999:blog-853606976378865714.post-90162569335043201002013-07-31T06:24:00.000-07:002013-07-31T06:24:02.066-07:00Elementary MathHi Seed Babes<br />
<br />
Here is my new Blog ! See you soon.<br />
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