tag:blogger.com,1999:blog-68580936896901003982024-02-07T01:54:20.156-08:00Maths MomentsAnonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6858093689690100398.post-37486978576031478552012-07-22T03:13:00.001-07:002012-07-22T03:13:48.685-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: #548dd4; font-family: "Segoe Script","sans-serif"; font-size: 16pt; line-height: 200%; mso-themecolor: text2; mso-themetint: 153;">Three things that I have
learned….<o:p></o:p></span></b></div>
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-themecolor: text1;"><span style="mso-list: Ignore;">1.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I learned
that as a teacher, I have to ask myself four critical questions before I plan
any activities that promote the learning of mathematics for the children. They
are:<o:p></o:p></span></div>
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-themecolor: text1;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><b style="mso-bidi-font-weight: normal;"><span style="color: #0070c0; font-family: Ravie; font-size: 12pt; line-height: 200%; mso-bidi-font-family: Arial;">What is it I want the child to learn?</span></b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> <o:p></o:p></span></div>
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">What is the objective behind the activity?<o:p></o:p></span></div>
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-themecolor: text1;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><b style="mso-bidi-font-weight: normal;"><span style="color: #0070c0; font-family: Ravie; font-size: 12pt; line-height: 200%; mso-bidi-font-family: Arial;">How do I know if the child has learned it?</span></b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">T</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">he teacher needs
to use multiple assessment approaches to find out what each child understands</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">, or</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;"> may
misunderstand. Child observation, documentation of children’s talk, collection
of children’s work, and open-ended questions are positive approaches to
assessing mathematical strengths and needs</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">.</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-themecolor: text1;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: #0070c0; font-family: Ravie; font-size: 12pt; line-height: 200%; mso-bidi-font-family: Arial;">What do I do if the child is struggling with the activity?
</span></b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Is there something that </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">the teacher</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> h</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">as</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> planned to ensure this child stays on the runway? Putting the child
through repeated tasks will ensure that </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">s</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">he does not veer off. That child will eventually start to take small
steps and eventually take off when the time is right. <o:p></o:p></span></div>
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-themecolor: text1;"><span style="mso-list: Ignore;">-<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><b style="mso-bidi-font-weight: normal;"><span style="color: #0070c0; font-family: Ravie; font-size: 12pt; line-height: 200%; mso-bidi-font-family: Arial;">What about the activities for an advanced child?</span></b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> <o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">A child may already know how to do the
activity. </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">The teacher</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> must remember
not to give her the same activity over and over again. Instead, </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">she</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> should plan for an activity that will
promote higher order thinking. <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><span style="mso-list: Ignore;">2.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">The use of
differentiated instructions from the concrete to pictorial to abstract (CPA)
approach is important to cater to the different learning needs of children. Concrete
materials allow beginning students to explore new concepts or extend their
level of a concept that was learned earlier. Once a </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">student </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">is able to understand a mathematical concept,
pictorial representation can take the place of concrete materials.</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;"> The abstract method
is only used after the child is familiar with the earlier two approaches. </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><span style="mso-spacerun: yes;"> </span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><span style="mso-list: Ignore;">3.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">The three big ideas in Mathematics: p</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">atterning, visualisation and number sense</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><o:p></o:p></span></div>
<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: #548dd4; font-family: "Segoe Script","sans-serif"; font-size: 16pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text2; mso-themetint: 153;">Two
questions that I have….<o:p></o:p></span></b></div>
<br />
<div align="left" class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-align: left; text-indent: -18pt;">
<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><span style="mso-list: Ignore;">1.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">How do I get parents involved in their child’s learning of mathematics?<o:p></o:p></span></div>
<br />
<div align="left" class="MsoListParagraphCxSpLast" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-align: left; text-indent: -18pt;">
<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-SG; mso-themecolor: text1;"><span style="mso-list: Ignore;">2.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">Is giving your child one-to-one tuition effective in promoting the
learning of mathematics?<o:p></o:p></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0tag:blogger.com,1999:blog-6858093689690100398.post-56664032993872273652012-07-20T15:39:00.000-07:002012-07-20T15:39:07.595-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: #e36c0a; font-family: "Kristen ITC"; font-size: 20pt; line-height: 200%; mso-bidi-font-family: Arial; mso-themecolor: accent6; mso-themeshade: 191;">Use of technology<o:p></o:p></span></b></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">These days having a
computer at home is a must. Children use it to retrieve information and play
games. Used in school, it is also an effective tool to practise mathematical
concepts and solve problems. The endless programmes and websites of games,
virtual moving pictures and sounds enhance opportunities to learn important
mathematics. Besides, it also makes learning mathematics more fun and effective
compared to just solving these problems using a pencil and paper. </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;"><o:p> </o:p></span></div>
<br />
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<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">Just like the
computer, a calculator can “promote higher-order thinking and reasoning needed
for problem solving in our information- and technology-based society” (p. 115).
Calculator activities can help children become familiar with the various
symbols on the keypad so that “more complex activities are possible.” C</span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">alculators can help to offload detailed computation
hence allowing teachers to better focus on the development of flexible
strategies and make more sense of other mathematic meaning and concepts. </span></div>
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<br /></div>
<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">However, whilst the
use of technology is an integral tool in expanding student’s ability to think
about challenging mathematics, there must be some form of balance. In the end
it still comes down to the mathematical skills that the child owns. </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">It is up to the teacher to prepare the children to
learn the process and take learning to a higher level. T</span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">hat
is something technology cannot replace, well at least not completely anyway. <o:p></o:p></span><br />
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0tag:blogger.com,1999:blog-6858093689690100398.post-37854014639203383122012-07-20T00:21:00.002-07:002012-07-20T00:48:53.061-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: #00b050; font-family: "Kristen ITC"; font-size: 18pt; line-height: 200%; mso-bidi-font-family: Arial;">Lesson 4</span></b><b style="mso-bidi-font-weight: normal;"><span style="color: #00b050; font-family: "Kristen ITC"; font-size: 18pt; line-height: 200%; mso-bidi-font-family: Arial; mso-fareast-language: ZH-SG;"> - A Learning Point<o:p></o:p></span></b></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">I consider myself
someone who knows my shapes pretty well. All my life I grew up with the </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">simple </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">notion <span style="color: black; mso-themecolor: text1;">that a square is </span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">just </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">a shape with four equal sides and </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">four</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> right angles. A rectangle on the other hand,
only has two equal sides and </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">four right angles. After yesterday, </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I fel</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">t</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"> like a child with level zero visualisation. I only based </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">my knowledge </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">on the appearance of the shape – “it looks
like a square” (p. 403) so it must be a square.</span><span style="color: red; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">However,</span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;"> Thursd</span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">ay’s lesson puzzled me yet
again. <span style="color: black; mso-themecolor: text1;">Since when is a square a
rectangle? </span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">I guess a square, like a rectangle is a </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%;">quadrilatera</span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG;">l<span style="color: black; mso-themecolor: text1;"> with
four right angles. </span></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Yet a
rectangle can never be a square</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;"> because it does not have four equal sides</span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">. </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-fareast-language: ZH-SG; mso-themecolor: text1;">Why didn’t my teacher tell me all this?
Perhaps she may not have known it herself. </span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Alright, so it is not too late to find out these things. After all, I am
in this course to learn new things. <o:p></o:p></span></div>
<br />
<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><o:p></o:p></span><span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">One thing I must take note of is to never put the two
shapes together and ask children to circle or colour all the rectangles on
paper. If a child picks out a square when I ask for rectangles, it is best to
check with the child why he did that. Could it be that he picked up the square
by accident because he was not sure of the shape or perhaps he really does have
some prior knowledge about this shape from his parents or some other source. <span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-ansi-language: EN-SG; mso-bidi-language: AR-SA; mso-fareast-font-family: SimSun; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast;"></span></span><br />
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<span style="color: black; font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 200%; mso-ansi-language: EN-SG; mso-bidi-language: AR-SA; mso-fareast-font-family: SimSun; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast;">As teachers, we must prepare children to learn skills such as
patterning, visualisation and number sense. We must walk that journey with them
to the end point. It is alright for children to get lost. It is alright for them to back track a little as long as we are with them providing that continuous support. </span></span><br />
<br /></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0tag:blogger.com,1999:blog-6858093689690100398.post-28538476870000675272012-07-19T00:42:00.004-07:002012-07-19T00:42:50.216-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: #31849b; font-family: "Segoe Script","sans-serif"; font-size: 16pt; line-height: 150%; mso-themecolor: accent5; mso-themeshade: 191;">Lesson 2 and 3<o:p></o:p></span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: #31849b; font-family: "Segoe Script","sans-serif"; font-size: 15pt; line-height: 150%; mso-themecolor: accent5; mso-themeshade: 191;">Developing Early Number Concepts and Number Sense<o:p></o:p></span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Segoe Script","sans-serif"; font-size: 13pt; line-height: 150%; mso-bidi-font-family: Arial; mso-themecolor: text1;">Going back to the basics<o:p></o:p></span></b></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%;">Subitize?
I heard this word for the first time on Tuesday. What is that? I found out that
it is the ability to explore quantity before children can count. Once children
can match counting words with objects, they will begin to understand that “the
last count word indicates the amount of that set.” I never saw this as a
problem that children might have and assumed that they always had it in them
but little did I know. I mean how difficult can this be, right? It seems so simple
and natural to look at the dots on a dice and just see the number but the book
reveals otherwise. It points out that “Subitizing is a complex skill that needs
to be developed and practiced through experiences with patterned sets” (p.
129). Why didn’t anybody tell me about this before? Well now I know better. I also
found the idea of using dot plates interesting and easy to make. I intend to
try this out with my class next week. <o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%;">I
just wanted to say that I am learning something new in class every day. Wednesday’s
lesson was no different. I found out that equal parts of a fraction can be both
the same shapes, or different ones and that it is wrong to say “three over
four”, “three upon four” or “three out of four”. Instead, we should use three
fourths or two fifths. All these little bits of information are a revelation to
me! I am really glad this degree includes mathematics modules. Indeed, these
past few days have been a learning journey for me. <o:p></o:p></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0tag:blogger.com,1999:blog-6858093689690100398.post-71677119048072660022012-07-18T00:29:00.002-07:002012-07-18T00:29:33.701-07:00<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Chapter 1<o:p></o:p></span></b></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">As mathematics education around the world undergo changes,
it becomes inevitable that teachers have to be on top of things, mainly in the
methods used to teach the subject as well as the content that is being taught. With
the </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%;">National
Council of Teachers of Mathematics (<span style="color: black; mso-themecolor: text1;">NCTM) emphasising that </span>“mathematics taught at each grade level
needs to focus, go into more depth, and explicitly show connections” (p. 2), <span style="color: black; mso-themecolor: text1;">more changes can be expected over the
next few years. Going “back to basics - reading, writing and arithmetic” (p. 1)
and the work of theorist, Jean Piaget also helped to focus research on how
students can best learn mathematics. <o:p></o:p></span></span></div>
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I have also observed significant adjustments in the way
mathematics is taught in the schools in Singapore based on the curriculum of my
two older children. <span style="mso-spacerun: yes;"> </span>In fact, it has
recently been reported that p</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%;">upils entering primary
school next year will be given more breathing room to grasp basic numeracy skills
as the Ministry of Education (MOE) plans to drop part of the Primary 1
mathematics syllabus as part of its regular curriculum review.<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">It is important for schools to enforce and intertwine the
six principles and standards for school mathematics in their programme. These
principles which include <o:p></o:p></span></div>
<br />
<div align="left" class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; text-align: left; text-indent: -18pt;">
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">1.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Equity</span></div>
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<br /></div>
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">2.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Teaching<o:p></o:p></span><br />
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">3.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Learning<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">4.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Curriculum<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">5.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Assessment
<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-fareast-font-family: "Times New Roman"; mso-themecolor: text1;"><span style="mso-list: Ignore;">6.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Technology<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">will act as a guide and provide some form of direction
for teachers of mathematics. <span style="mso-spacerun: yes;"> </span>Of all the
six principles, I feel that the teaching aspect is the most important. As more
children of diverse learning abilities are integrated in schools, it is
necessary for a teacher to firstly, find out what her student’s needs and
understanding are before proceeding with ways to help them. I had a very poor
understanding of mathematical concepts even in primary school. I do not ever
recall my teacher having a keen interest and awareness in my individual
development, and selecting “meaningful strategies” to support my learning. Math
was taught one way - my teacher talked and I listened. There was not much
hands-on or interaction amongst the students, let alone the teacher. She left
me very much on my own to fend for myself. So yes, you can see why mathematics
has never been my first love. However, I must admit the teachers of today are more
proactive and responsive to the different challenges and uncertainties. Added emphasis
is also now placed on teacher’s education, teaching approach, and curriculum
content. <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">A teacher of mathematics has to be flexible, and vary her
knowledge of any mathematics content to fit the different learning styles of
her children in the class. She must be equipped with the necessary strategies to
counter any hindrance that might slow her down. She has to be diligent and persistent
when faced with any challenging cases. Having a positive attitude and being
ready for changes are also crucial skills for today’s teachers of
mathematics.<span style="mso-spacerun: yes;"> </span>More important, making time
to be reflective and being self-conscious allows such teachers to relook at
which areas need improvement or reflect on accomplishments and plan their own
growth. I aspire to be that teacher and not let what happened to me in school years
ago rub off on the children I am teaching now. <o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I must admit I was very sceptical when I saw teachings of
fractions (decimal, percents, ratio), and algebraic thinking included in some
of the sessions of the course outline. I asked myself why we needed to learn
all this when I was only teaching in a pre-school. As I read on, I realised
that these topics were parts of the five content standards. Each standard had a
set of goals that was relevant to all grade bands but with different emphasis,
and exclusive to only what students of that level needed to know. This provided
me with a better picture about why my daughter could not initially do well in
even very simple mathematical topics in primary school. Her lack of
understanding of a concept, and the ability to connect new ideas to existing
conceptual webs were the main reasons. These days she is much better, thanks to
a teacher who helped her “think and reason mathematically” and “connect within
and among mathematical ideas” (pp. 3-4). <o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><o:p> </o:p></span></b><b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Chapter 2<o:p></o:p></span></b></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">Children’s interest in maths begins with me. I create a
classroom environment that is conducive for children can take risks and share
their mathematical ideas. I am aware that some children in my class take a
longer time than others to grasp concepts. I use various tools and
manipulatives as aides to represent the concept in the math corner for children
to explore and enhance their learning. <span style="mso-spacerun: yes;"> </span>I
feel children pick up concepts faster when I use more concrete tools. Children
are also encouraged to learn to evaluate their own ideas and those of others, scaffold
each other’s learning, make decisions, test them, and develop reasoning and
sense-making skills. I must admit I am still working on how to balance
“productive struggle.” I often step in to show or explain to the children how
to solve a problem too quickly. <o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><span style="mso-tab-count: 2;"> </span></span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;"><span style="mso-spacerun: yes;"> </span><o:p></o:p></span><br />
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">The attached pictures show how using different tools and
manipulatives can give children a clearer picture of various math concepts and help
them understand patterning and matching numeracy to number words.<o:p></o:p></span><br />
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I seem to be able to relate to what Lesh and his
colleagues said, “that children who have difficulty translating a concept from
one representation to another also have difficulty solving problems and
understanding computations” (p. 24). I had a very weak understanding of concepts
e.g. I may be tested on the same concept but once the equation changed
slightly, I could not solve it. My reaction was exactly what was stated on page
27 – “I can’t remember the way to do this type of problem.” Very seldom did I
have a “can do” attitude (p. 28). I lack that perseverance and confidence. I did
not understand the ideas and they did not make any sense to me. Hence, I feared
the subject and tried to avoid doing my math homework or copied where possible.
<o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">I learn mathematics the instrumental manner – “endless
list of isolated skills, concepts, rules, and symbols that must be refreshed
regularly and often seem overwhelming to keep straight” (p. 29). As I look back
now, I wonder if this inability to do mathematics came about because of my lack
of interest or perhaps practice or could it have been a shortage of
opportunities and adequate support from the teachers to learn mathematics. <o:p></o:p></span></div>
<br />
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 200%; mso-themecolor: text1;">The book talks about employing “invented strategies” (p.
27) and the use of flexibility to compute an answer which I totally agree.
However, in the case of my daughter when she employed a different method to get
her answer, her math teacher insisted that she use the way she taught her to
get the answer. My daughter became confused and found it difficult to
understand the method her teacher was using. She did not like the topic after
that because of the “lack of retention and increased errors” (p. 27) when she
used her teacher’s method. Overall, developing mathematical proficiency has
more useful and worthwhile benefits for both the teacher and the student. It
plays a significant role in art, science, language arts, and social studies. Indeed,
knowing how to do mathematics indisputably connects one to the real world. <o:p></o:p></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0tag:blogger.com,1999:blog-6858093689690100398.post-82054079021195655192012-07-17T00:57:00.001-07:002012-07-17T00:57:38.719-07:00<br />
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<span lang="EN-US" style="color: #548dd4; font-family: Ravie; font-size: 16pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-themecolor: text2; mso-themetint: 153;">Lesson
1 Interesting and Inspirational<o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US;">I have never enjoyed Mathematics as I did yesterday. Numbers always
scare and confuse me. Yesterday’s lesson got me all excited! For once I saw
numbers as something I could understand and relate to. <o:p></o:p></span></div>
<br />
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<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US;">I was indeed intrigued by the first problem – which letter is the number
99? What was more interesting was the various methods that were used solve this
problem. I saw patterns everywhere in this name game. Children are naturally
drawn to patterns. I thought to myself, hey this is not so bad! I can do this!<o:p></o:p></span></div>
<br />
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<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US;">I was inspired by the use of cards to teach children number words. Wait
till I show this trick in class! I bet you they are going to be all in awe.
They must be sure to think what an awesome teacher they have! Huh, little do they
know that there is a trick to all this. <o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US;">A few things struck me. One was to always use a noun behind every
cardinal number. I never really gave it much thought until yesterday when I saw
the reason behind it and why children so often misinterpret these concepts.
Something else that struck me was the Concrete to Pictorial to Abstract (CPA)
approach. I now have a clearer understanding of why the use of concrete
materials is necessary when introducing various mathematics concepts to younger
children. Yet another thing was the use of the word ‘mass’ more than ‘weight.’
It never donned on me that I had been using the wrong word all this while. I must
remember to ask children questions such as ‘How much does this weight?’ or “How
heavy is this bottle?’ when I teach the children the topic on measurement. <o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US;">I must keep in mind to choose activities that promote the thinking and
learning of mathematics in my classroom. I must develop an environment where
children can ask questions, explore and investigate. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/02042612248167430754noreply@blogger.com0