tag:blogger.com,1999:blog-57342029827372056742024-02-06T22:15:05.788-08:00Maths Musings...Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-5734202982737205674.post-8588933119602196542012-07-22T02:36:00.000-07:002012-07-22T07:37:26.023-07:00Reflecting on a one-week journey that has been inspiring...<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>THREE things I have learned</b></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">1) Rebecca DuFour’s 4 Critical Questions</span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/Ds7fmtamZ5w?feature=player_embedded' frameborder='0'></iframe><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Questions
that I need to ask continuously as I focus on student learning:</span></div>
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<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>What do we want students to learn?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>How will we know when they’ve learned?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>How will we respond when they don’t learn?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>How will we respond when they’ve already
learned?</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"> A shift in thinking is required – from a focus on teaching to a focus on
learning…</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">2) I can do away with the structured lessons
on TIME</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">It’s common sense
really. Why have lessons to teach time when it should really be an everyday occurrence
as children learn to connect time to their daily lesson times, routines, etc.</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">3)<span style="font: normal normal normal 7pt/normal 'Times New Roman';">
</span>Language is important</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The
right terminology should be used to avoid confusion and mislearning. The
language that we use must help children to make connections between quantity
and number…</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Example:</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">¼
is “one fourth”, not “one out of four”</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The
questions that I ask can effectively support learning…</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Example:</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Is
there another way to make 10?</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">What
do you notice about all these shapes?</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Open
questions encourage a variety of responses and allow for differentiation.</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><br /></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;">TWO
questions that I have</b></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">1) Maths isn't about speed, it isn't about accuracy.. It's about understanding, reasoning, problem solving....... isn't it?</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">2) Who is a mathematics teacher?</span></div>
</div>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-52985469056354394612012-07-22T00:48:00.002-07:002012-07-22T01:14:34.313-07:00Technology in the classroom<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">NCTM’s position statement regards technology as
“an essential tool for both learning and teaching mathematics.”</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The kindergarten years are preparatory years for
learning and our young children should be exposed to different learning
experiences. Apart from the many hands-on opportunities we plan for children, technology
has its place in today’s classroom and it should be used to help encourage active
learning and stimulate interest.</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">There are many in-store and online programs that
can be used in the classroom as well, to support mathematics teaching. Technology can be used in a fun and educational way. As games usually appeal to children, they will be involved in learning without even noticing that they are.</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I am fortunate to have an IPad in my classroom, which I use quite often to support literacy learning. It is high time to check out the dozens of math apps available too..</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><o:p></o:p></span></div>
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</div>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-36486728316335455892012-07-19T23:41:00.003-07:002012-07-21T23:52:31.362-07:00Lesson 4<span style="font-family: Arial, Helvetica, sans-serif;">It is not new
knowledge but certainly an important point that all pre-school teachers
must adhere to –<o:p></o:p></span><span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
T</span><span style="font-family: Arial, Helvetica, sans-serif;">he early years are <strong>preparatory years for learning</strong> and we should not be overly concerned about
content and WHAT to teach. More importantly, we should be giving careful thought to HOW we teach and THE WAY we teach, as we want our children to be diverse thinkers who can
see different approaches to the same problem. We want them
to eventually be able to visualise situations from different angles.<o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><span style="font-family: Arial, sans-serif; font-weight: normal;"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span><br />
<span style="font-family: Arial, sans-serif; font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">I think that in order for teachers to effectively nurture
divergent thinking in children, we have to possess an open mind, value all
contributions, and be divergent thinkers ourselves. How else to develop strong
thinkers but to be models ourselves..<o:p></o:p></span></span><br />
<br />
<strong><span style="font-family: Arial, sans-serif; font-weight: normal;">As I watched Dr Yeap deliver his lessons in an
easy-going, candid manner, I saw how important it is to encourage discussion
and ask questions like, “Did anyone solve the problem the same way?”, “Who
found a different way to solve the problem?”…<o:p></o:p></span></strong><br />
<br />
<strong><span style="font-family: Arial, sans-serif; font-weight: normal;">Children need to feel safe in expressing their
thoughts, therefore it is important to accept all suggestions. We should learn
to mediate learning. </span></strong><strong><span style="font-family: Arial, sans-serif;">Our
job is not to bring the child to the end point, but walk the path with him or
her..</span></strong><strong><span style="font-family: Arial, sans-serif; font-weight: normal;"><o:p></o:p></span></strong>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-14690690639579231902012-07-18T17:05:00.000-07:002012-07-18T23:34:07.360-07:00Making sense in their world...<strong><span style="font-family: Arial, Helvetica, sans-serif;">Lesson TWO & THREE - Making (NUMBER) sense in their world...</span></strong><br />
<br />
Number sense is an important skill to teach. Children develop this skill over time based on their experiences in school and out of school. Having number sense helps us to create strategies to problem solve. <br />
<br />
What does this imply? As a teacher, I have to provide many opportunities for children to investigate, to think about what they are investigating, gather information, organise it, use information to problem solve, explain their reasoning...<br />
<br />There are plenty of opportunities to develop number sense in the classroom. Some examples would include grouping sets into tens and ones, encouraging guessing (How many broad beans do you think are in this bottle?), playing addition and subtraction games, estimating (How many grapes do you think are in this bunch?), guessing a number (give clues, eg. It's a bigger/ smaller number, it's less than 10 but more than 5..), card games, etc.<br />
<br />
In my primary and even secondary school days, I recall that the focus in mathematics lessons was always the answer, the correct one, ideally. However, the focus today, is and should be, very different. It is important for children (and adults as well) to know WHY and not just how numbers work..<br />
<br />Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-33405842164998314662012-07-16T16:48:00.000-07:002012-07-22T01:38:12.669-07:00<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><strong>Lesson ONE <o:p></o:p></strong></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><strong>W</strong></span><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><strong>ait
till I baffle them!<o:p></o:p></strong></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">I fell asleep after midnight
with the card trick on my mind. I cannot wait to impress my children in the
morning. I know I will get a chorus of “do again, do again…” It was fun
figuring out the sequence of cards together with my table buddies. Dr Yeap
didn’t just tell us how. He urged us to find out, and we did, even though it
was after 9pm. Auto shut down had not occurred! </span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Problem
solving!<o:p></o:p></span></span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">It got me thinking about the
importance of problem solving and how I should get my children to be fearless
thinkers, do-ers, try-ers… I think that the key is to NOT hand out answers but
to encourage exploration, trial and error, and to look at situations,
activities, and problems from all sorts of angles. Perhaps, importantly, it is
how we can pose questions to the children to guide their thinking, to acknowledge
every try and accept different possibilities.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Lots
of “takeaways”:<o:p></o:p></span></span></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Numbers
are used in four different ways<o:p></o:p></span></span></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-indent: -18pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: Arial, Helvetica, sans-serif;">
</span></span></span></span><span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span lang="EN-US">cardinal
numbers</span></b><span lang="EN-US"> refer to quantities, eg. 3
cups, 4 boxes<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-indent: -18pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b style="mso-bidi-font-weight: normal;"><span lang="EN-US">ordinal
numbers</span></b><span lang="EN-US"> refer to positions in space,
positions in time –</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US"> 1<span style="font-size: small;"><sup>st</sup>, 2<sup>nd</sup>, 3<sup>rd</sup> and so on<o:p></o:p></span></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-indent: -18pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b style="mso-bidi-font-weight: normal;"><span lang="EN-US">nominal
numbers</span></b><span lang="EN-US"> are numbers as names, eg.
bus number 14<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoListParagraphCxSpLast" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-indent: -18pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b style="mso-bidi-font-weight: normal;"><span lang="EN-US">measurement
</span></b><span lang="EN-US">numbers are standard or non-standard
units, eg. </span></span></div>
<div class="MsoListParagraphCxSpLast" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo2; text-indent: -18pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US"> The box weighs as much as 3 oranges; That man weighs
62kg. <o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"></span></span></b><br />
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">How
do I get children to learn mathematics?</span></span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Pose
problems to promote thinking. Problems can be put forth in different scenarios,
in word problems, in a game (like the card trick)<o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Plan
activities to encourage children to investigate, explore, ponder over..<o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Always
remember: CPA<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Concrete
-> Pictorial -> Abstract</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Carefully
provide appropriate materials, examples (theory of variability)<o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Constantly
assess and reflect to understand how children learn so that we can provide the
appropriate level of instruction, materials, etc. <o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">It’s
often about patterns!<o:p></o:p></span></span></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The name pattern activity was
very interesting. I was very engaged in the process of pattern searching and
thought that this is something our naturally curious children are adept at.
Already, I see them able to grasp the common patterns (ABAB, ABCABC, etc)
easily. I really should bring them a level higher to search for patterns in the
environment, patterns in stories, perhaps even patterns in a series of numbers
like in the name pattern activity.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><strong>Excited about Lesson 2!</strong> <span class="Apple-style-span" style="font-family: 'Century Gothic', sans-serif;"><o:p></o:p></span></span></span></div>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-25476944352529212722012-07-14T02:54:00.001-07:002012-07-14T19:46:31.093-07:00<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Chapter TWO</span><br />
<br />
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Learning mathematics with understanding!</span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I recently introduced the concept of multiplication to my K2s. Apart from using the Montessori materials we have in class (golden beads, stamp game, multiplication board), I also got them to experience the whole idea of multiplication by having them make physical groups with their own bodies. They also created individual art pieces to demonstrate multiple groupings of the same number (eg. 3 vases with 2 flowers each to show 3x2). There are many ways to inject fun and creativity to a maths lesson. Maths doesn't have to be humdrum!</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Multiplication board</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAHlV1dBFkyIERAnSJOg4a2lliBzrvRsi9B9XnJfFeo8hfnErJQEWRzMGLKfrKfacVf4OWAXVEzT07RLAWjf7IOn35lsnvmj4G7POYwy_ifKhJhyhk9mE3uC4P6gZlIqzkFVyV16P-3w/s1600/Unknown" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAHlV1dBFkyIERAnSJOg4a2lliBzrvRsi9B9XnJfFeo8hfnErJQEWRzMGLKfrKfacVf4OWAXVEzT07RLAWjf7IOn35lsnvmj4G7POYwy_ifKhJhyhk9mE3uC4P6gZlIqzkFVyV16P-3w/s1600/Unknown" /></a></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Multiplication with golden beads</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbsdzDLLwx8sJ6-TR1HnOWr8baQBzJEP6L_zGHrqhhrLwq7RJS7TSoflDLKrs7WqgiOhxgPmNbVnKXInDKHIh_S5gxzERvyd_IbAI4lOK3IcNFuQgXuQA3ZRtAwt6HKZguIYXjsRzEBQ/s1600/images.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbsdzDLLwx8sJ6-TR1HnOWr8baQBzJEP6L_zGHrqhhrLwq7RJS7TSoflDLKrs7WqgiOhxgPmNbVnKXInDKHIh_S5gxzERvyd_IbAI4lOK3IcNFuQgXuQA3ZRtAwt6HKZguIYXjsRzEBQ/s1600/images.jpeg" /></a></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Multiplication with stamps (Stamp Game)</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">When I see that children are engaged in mathematical ideas all on their own, it gives me immense satisfaction that they've got it!</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">It is best that teachers consciously provide positive and meaningful experiences in mathematics in day to day activities. As they work and play together, the language that we use can help them to make connections between mathematics and its applications, for example, asking, "How many more blocks do you have compared to ....?"</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Own learning..</b></span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Recently, I introduced graphing to my K2s. We worked on many concrete activities together and I was pleasantly surprised when one of the girls in my class came up to me with a graph on "Favourite Fruits" that she had created on her own. She proceeded to write her own short story about it as well. I took this as an opportunity to invite others to try it too! It was wonderful to see them express their understanding of newly acquired knowledge.</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Scaffolding..</b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Teachers can scaffold learning in group and definitely in one-on-one situations. Learning is enriched further when classroom situations and activities are planned where children can interact, support, and learn from each other.</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Being among them.. </b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Play is an integral part of learning. I believe that it is important for teachers to mingle and be among the children when they go off to their separate areas, whether singly or in small groups. Being in their midst, we can pick up and capitalize on "maths moments" such as "I need 3 more bricks....", "I don't have enough...", "Mine is longer.." By being alert, we can help to develop thinking dispositions in children.</span></div>
</div>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0tag:blogger.com,1999:blog-5734202982737205674.post-71691983553507900782012-07-09T07:40:00.000-07:002012-07-14T20:09:15.372-07:00<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Chapter ONE</b></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span><br />
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<b><i style="mso-bidi-font-style: normal;"><span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">MOST IMPORTANT TOOLS to be an EFFECTIVE TEACHER of MATHEMATICS! </span></span></i></b></div>
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<b><i style="mso-bidi-font-style: normal;"><span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></i></b></div>
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<b><i style="mso-bidi-font-style: normal;"><span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* My knowledge of mathematics </span></span></i></b></div>
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<b><i style="mso-bidi-font-style: normal;"><span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* How children learn mathematics<o:p></o:p></span></span></i></b></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Our classrooms
are becoming increasingly diverse, with children from different ethnic and
cultural backgrounds coming together, the inclusion of children with special
learning needs, etc. In addition, children also have different learning styles.<o:p></o:p></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">A teacher’s job
is not an easy one. To be effective, we must provide an array of learning
experiences and address the diverse learning abilities and styles of the
children in class. The teaching of mathematics and any other subject for that
matter needs to be differentiated so that children can acquire mathematical
knowledge in their own unique ways.<i><o:p></o:p></i></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Personally, I feel
that it is imperative that teachers reflect a lot more on classroom practices.
We need to constantly ask ourselves if we are providing enough, teaching
appropriately, catering to the different developmental levels and learning
styles, etc.</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span style="font-family: 'Century Gothic';"><span class="Apple-style-span" style="color: blue;"><br /></span></span></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Knowledge gained from research</span></b></span></div>
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<b><span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;">+<o:p></o:p></span></b></div>
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<b><span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;">Leadership of the NCTM<o:p></o:p></span></b></div>
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<b><span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;">Public and political pressure<o:p></o:p></span></b></div>
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<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">has led to </span></b></div>
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<b><span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;">STEADY CHANGES </span></b></div>
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<b><span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;">in the way mathematics is being taught in the US<o:p></o:p></span></b></div>
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<span style="color: #262626; font-family: Arial, Helvetica, sans-serif;">These changes were initiated because US students had been underperforming in national and international studies as compared to students from Asia, notably.</span><br />
<span class="Apple-style-span" style="color: blue;"><b><u><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span></u></b></span><br />
<span class="Apple-style-span" style="color: blue;"><b><u><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The revised NCTM principles and standards</span></u></b></span></div>
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<span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">These principles and
standards act as a guide and were developed to improve mathematics education in
the US. They provide educators with learning goals for students from pre-K
through grade 12, serve as a resource for teachers to improve instruction, and
help guide the curriculum. <i style="mso-bidi-font-style: normal;"><o:p></o:p></i></span></span></div>
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<b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="color: blue;"><u>NCTM Principles </u></span></span><span class="Apple-style-span" style="background-color: yellow;"><o:p></o:p></span></span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="color: blue;"><br /></span></span></span></b></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Equity</span></span></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Curriculum</span></span></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Teaching</span></span></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Learning</span></span></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Assessment</span></span></div>
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<span class="Apple-style-span" style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-weight: 800;">* Technology</span></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">These principles reflect basic perspectives on which mathematics educators should base their decisions. They underline the foundation for mathematics programs by considering the broad issues of equity, curriculum, teaching, learning, assessment and technology.</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-family: Times;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>What struck me most - The Teaching Principle</b></span></span></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-family: Times; font-weight: bold;"><b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></span></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Effective mathematics teaching requires
understanding what students know and need to learn and then challenging and
supporting them to learn it well. (NCTM, 2000, p.16)<o:p></o:p></span></div>
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<span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I believe that as an
educator, I need to plan developmentally appropriate lessons and constantly
assess progress and identify areas for improvement. Learning should be
maximized for each child within his or her own ‘zone of proximal development’
(Vygotsky, 1978).<o:p></o:p></span></span></div>
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<span style="color: #262626;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I also feel that It
is important to keep abreast of current knowledge, constantly learn, practise
and reflect i<a href="http://www.blogger.com/blogger.g?blogID=5734202982737205674" name="_GoBack"></a>n order to teach more effectively.<b><o:p></o:p></b></span></span></div>
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</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;"><u>NCTM Content Standards</u></span><o:p></o:p></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;">* Number and operations</span></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;">* Algebra</span></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;">* Geometry</span></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;">* Measurement</span></b></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="color: blue;">* Data analysis and probability</span></b></span></div>
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</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">These outline the specific mathematics
concepts for each grade level.<b><o:p></o:p></b></span></div>
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</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">An outline is an important guide to rely on however a teacher's responsibility especially in the kindergarten classroom, is to capitalize on play and everyday activities to promote learning. </span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Concepts should be taught in an experiential way. Children should be allowed many opportunities to explore and build their knowledge through concrete manipulations. This brings me back to the basic principles of HOW we teach. The teacher's mindset and attitude makes a world of difference to how much and how well a child learns.</span><br />
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<span class="Apple-style-span"><b style="mso-bidi-font-weight: normal;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><u>NCTM Process Standards</u></span></b></span><br />
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<b style="mso-bidi-font-weight: normal;"><o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* Problem solving</span></o:p></b><br />
<b style="mso-bidi-font-weight: normal;"><o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* Reasoning and proof</span></o:p></b><br />
<b style="mso-bidi-font-weight: normal;"><o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* Communication</span></o:p></b><br />
<b style="mso-bidi-font-weight: normal;"><o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* Connections</span></o:p></b><br />
<b style="mso-bidi-font-weight: normal;"><o:p><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">* Representation</span></o:p></b></div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">These process standards help teachers to make
informed instructional and curricular decisions when teaching mathematics. </span></span><br />
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<span class="Apple-style-span"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Apart from planning appropriate lessons and creating a supportive environment with meaningful interactive mathematical activities, teachers can help to build process skills by asking questions that would help children to make sense of what they are doing.</span></span></div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">We can ask questions like..</span></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Why did you do that?</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">What would you do if....?</span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">How could you show....?</span></div>
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</span></div>Anonymoushttp://www.blogger.com/profile/00301932578550989302noreply@blogger.com0