tag:blogger.com,1999:blog-91714305257020542232024-03-22T09:22:28.094+08:00EDU330 Elementary MathTeacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-9171430525702054223.post-25702252569483190782010-10-01T02:18:00.006+08:002010-10-01T03:12:48.898+08:00Final Blog - Final Thought after 8 cookies<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCcF5c2Bwg6fV991rBubiki9esXDZ0hYQ8rdeHuq3llz7xlFjdibAteN9raZ6PxSBIasw8kSYKyGUL2t4LQSOMmWtaPRbkV20gECReDmaU2hSTWBMFJJknXKjDm5T7Dp2mVobStoPoN7cJ/s1600/3595401166_d6cd8406cf.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" px="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCcF5c2Bwg6fV991rBubiki9esXDZ0hYQ8rdeHuq3llz7xlFjdibAteN9raZ6PxSBIasw8kSYKyGUL2t4LQSOMmWtaPRbkV20gECReDmaU2hSTWBMFJJknXKjDm5T7Dp2mVobStoPoN7cJ/s200/3595401166_d6cd8406cf.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;">It has been an enjoyable 2 weeks with Dr Yeah. Not because the workload is any easier but because of the real learning that have taken place and the confident in Mathematics that I am able to build up again after so many years...</div><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">In every lesson , I felt that I was taking on the identity of both a student and a teacher. As a student, I followed closely the instructions given and allowed myself to explore and experience mathematics in a fun and brand new way. As a teacher, I am aware of the numerous modelling effort by Dr Yeah on how to conduct Math lessons to young children , the variety of the teaching materials available, the proper math language to use, the do and don't , the scaffolding technique to get the children construct their own knowledge, the various friends that I get to know - Bruner, Diene, Van Hiele, Pick, etc. Yes, I got it.</div><br />
But one very important thing that I learned from this course is that<br />
<br />
<span style="color: #073763;"> </span><span style="color: purple; font-size: large;">the reason for teaching Math is not teaching Math itself.</span><br />
<br />
And that Math is a tool for the <br />
1. development of intellectual, logical reasoning, spatial visualization , analysis & abstract thought<br />
2. development of numeracy, reasoning, thinking , and problem solving skills<br />
3. opportunities of creative work and moment of enlightenment & joy.<br />
<br />
This statement is profound! If I do not get the goal correct, the effort that I am putting in is futile. If it means that I have to rethink my teaching philosophy and unlearn everything about teaching pre-school math, i will. In this hi-tech world whereby mathematical problems and computational skill can be easily solved and accomplished by pressing a few buttons on the keyboard. What is there left for us to do?<br />
<br />
Our belief will determine our actions. So<br />
<span style="font-size: large;"> <span style="color: orange;">let's crack some heads, </span></span><br />
<span style="font-size: large;"> <span style="color: #e06666;"> let's kill some brain cells, </span></span><br />
<span style="font-size: large;"> <span style="color: blue;">let's persevere,</span> </span><br />
<span style="font-size: large;"> <span style="color: #38761d;">let's out wit each other, and </span></span><br />
<span style="font-size: large;"> <span style="color: #741b47;">let's have some fun!</span></span><br />
Cheers!<br />
From Tr AnitaTeacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-50476563951681895592010-09-29T02:08:00.125+08:002010-10-01T01:36:45.425+08:00Blog # 7 GeometryWhat is the (interior) angles of a pentagon? Easy peasy, lemon squeezey. It is <br />
<br />
<span style="font-size: xx-small;"><img alt="pentagons" border="0" height="174" src="http://www.coolmath.com/reference/images/poly-pentagon2.gif" width="210" /></span><br />
( 5-2) 180 = 540 (degree)<br />
<br />
But why is it so? Oh, that was the formula given by my Math teacher when I was in Secondary 2.<br />
But why is it so? Oh, cause the number of non-overalp triangle you can draw from the same vertex of any polygon is always 2 less than the number of its sides. and each triangle has a total angles of 180 degree. or you can put a dot in the centre of the pentagon and draw 5 lines towards the 5 angles and form 5 triangles, <br />
180 X 5 - 360 = 540 (degree)<br />
<div align="center"><img alt="pentagons" border="0" height="133" src="http://www.coolmath.com/reference/images/poly-pentagon6.gif" width="140" /></div><br />
All these methods suddenly came to my <span style="color: black;">mind.</span> I am trained to solve math questions through formula, traditional algoritthms. Not knowing that in order to deal with this problem, I have to reach level 2 - level 3 of Geometric thinkinf according to the van Hiele's 5 levels ( level 0- level 4) of the hierarchy model. At level 2 (informal deduction), the objects of thought are the properties of shapes and sometimes thinking about the relationship among these properties. and moving towards the beginning of level 3 ( formal deduction) which starts to look at the relationships among properties of geometric objects.<br />
<br />
Van Hiele's model provides teachers with an insight of how children develop their geometric thinking and thus be able to use different strategies to help them move from one level to another. Chapter 20 demonstrates how a teacher should nurture his/her children in geometric thinking by asking appropriate questions and using guided activities to help children construct and internalize their own learning. It is a systematic and deliberate effort, it is the finest job of a Math teacher. <strong><span style="color: red; font-size: large;">To teach by not teaching . </span></strong><br />
<br />
Interesting website on geometry to share : <strong><span style="color: red; font-family: Arial; font-size: large;"><u><span style="color: #0066cc;"><a href="http://coolmath.com/">http://coolmath.com/</a></span></u></span></strong><br />
<br />
<br />
<br />
<div align="center"><br />
</div>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-26851640797285352622010-09-29T01:01:00.000+08:002010-09-29T01:01:21.484+08:00Blog # 6 Whole NumbersChapter 10 to 12 are very useful for me as a Kindergarten teacher. We have practically two years to lay the foundation of mathematics for our young children and we should do it right. As our friend Jerome Bruner suggested, teaching should start with concrete material ( enactive represetation ), then in pictorial forms ( ikonic representation ) and finally in abstract terms ( symbolic representation ) . As I read through the chapter, I am mindful if I have been teaching numbers, tens and ones, addition and subtraction, etc., in a systematical way; and whether I have missed out any step that may be detrimental to children's understanding and learning process. I also ook out for any class activities that I can use to reinforce the concepts. It was a time for self reflection and do some serious stock taking. <br />
<br />
<br />
<span style="font-size: large;">Concepts that are in place in preschool :</span><br />
<br />
<span style="background-color: yellow; color: purple;">Ten and ones :</span><br />
Introducing the concept of 10s and 1s. First by counting in ones (unitary), then by grouping concrete materials into bundle of 10 and counting in 10s ( Base-ten). Teacher will also match grouping by numerals, placed in labeled places and eventually written in standard form.<br />
<br />
BUT we do not expose children to equivalent or nonstandard base-ten approach. such as that memtioned on p.189 ( Figure 11.1) 53 can also be represented by 3 tens and 23 ones. In fact, some teachers frown upon it when they see children represent tens and ones in this form, deeming it as unconventional , confusing, or not yet reach the undertanding of the tens and ones concept. However, we should adopt Diene's idea of allowing variety in teaching mathematics, in the use of materials and in different ways of representing a math concept. THis kind of exposure provide opportunity for children to approach the concept in different angles and will eventually increase their uderstanding and facilitate the application of the concept in the long run. <br />
<br />
<span style="background-color: yellow; color: yellow;"><span style="color: #073763;">Introduction</span> <span style="color: #4c1130;">of traditional algorithm</span></span> <br />
<br />
Teachers will definitely include addition, subtration, multiplication and division in the curriculum using the traditional algorithm. <br />
<br />
But seldom will we encourage student-invented strategies in the math calculation. By observing children's explanantion and demonstration of their invented algorithm, teachers can have a glimpse of their processing skills and understanding of concepts. In fact, experts find that children make fewer error in self invented strategies, develop better number sense, forming basic of mental computation and estimation. Moreover, they are flexible and oftern faster methods of mathematic computation. Thus, in Chapter 12 , the authors call for a delay in the introduction of traditional agorithms but put in more time to understand how chldren derive they own solutions to the problems. <br />
<br />
There are many more refreshing strategies fo teachng mathematic in the text. Happy exploring.<br />
<br />
Tr Anita<br />
<br />
<br />
Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-71281619332070927872010-09-21T00:00:00.002+08:002010-09-21T00:00:48.765+08:00<table cellspacing="0" cellpadding="0" border="0" bgcolor="#ffffff"><tr><td><a href="http://smilebox.com/play/4d546b784d546b304d6a453d0d0a&blogview=true&campaign=blog_playback_link" target="_blank"><img width="386" height="303" alt="Click to play this Smilebox scrapbook" src="http://smilebox.com/snap/4d546b784d546b304d6a453d0d0a.jpg" style="border: medium none ;"/></a></td></tr><tr><td><a href="http://www.smilebox.com/?partner=smilebox&campaign=blog_snapshot" target="_blank"><img width="386" height="46" alt="Create your own scrapbook - Powered by Smilebox" src="http://www.smilebox.com/globalImages/blogInstructions/blogLogoSmileboxSmall.gif" style="border: medium none ;"/></a></td></tr><tr><td align="center"><a href="http://www.smilebox.com/scrapbooks/scrapbooking-card/" target="_blank">Free digital scrapbooking design</a> created with Smilebox</td></tr></table>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-17716484564891911002010-09-19T04:04:00.002+08:002010-09-27T21:58:12.249+08:00Blog #5 TechnologyTechnology is marching into our classroom. Like it or not, it is there. Our new generation is brought up with milk bottle in one hand and mouse in the other. Their mind is stimulated by colourful graphic and animated games even before they utter their first word.<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn_M18TElLrSWlGBm9Btp2Zlp3Ed10B9MCpkDtPYtD4i2ZJUIYbdn0cqegULF8Inig_o8mRxhNiWX_pEukww4Ysneo5EgB7GpVRqZfzQOj-FCyaTYMXC6iosTyQ3b1ZOm9c7gCajb-J-lB/s1600/27ec9cd5060622ea%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCoIBxciq0oP1LcPodLYKu2MG0G2dvIJKgOnrEtSjIfvJNh5XAgpe-Hqrb1MDXFOJp8x4bvtpCQUWBnhVfwnHhh1trkIFWXTWT5fLUzN-GW4nPhzPMaGD7SlrvZ8Nue26p-1qlrXa2z0eO/s1600/ComfyChildKeyboard%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCoIBxciq0oP1LcPodLYKu2MG0G2dvIJKgOnrEtSjIfvJNh5XAgpe-Hqrb1MDXFOJp8x4bvtpCQUWBnhVfwnHhh1trkIFWXTWT5fLUzN-GW4nPhzPMaGD7SlrvZ8Nue26p-1qlrXa2z0eO/s320/ComfyChildKeyboard%5B1%5D.jpg" width="320" /></a></div>I was amazed that there are so many softwares being developed and online site being created for developing and supporting various mathematical concepts and teaching. Tools for developing numeration? Check. Tools for developing geometry? Check. Tool for developing Probability? Check.Tool for developing algebraic thinking? Check. Concept instruction? Check! Problem Solving? Check. Drill and Reinforcement? Check, check.<br />
<br />
I suppose "resistance is futile". We as teacher should instead, embrace technology and use it as an effective tool to aid our teaching, <span style="font-family: Times, "Times New Roman", serif;">making</span> lessons more interesting and engaging. We need to be informed and be able to select suitable software that can enhance our lesson, critically review the effectiveness of each chosen program and make sure they meet the objectives we set to achieve. <br />
<br />
<span style="font-size: large;"> <span style="font-family: Arial, Helvetica, sans-serif;"> Use technology to our advantages</span></span><br />
<br />
<span style="font-family: Times, "Times New Roman", serif;">The Teacher Resource listed at the end of Chapter 7 are treasure to every Mathematic teacher. I just spent more than 2 hours surfing and getting into the different websites. Warning! It is addictive! I particularly like The Math Forum. (<a href="http://mathforum.org/">http://mathforum.org/</a> ).It provides a platform for interactions among teachers and it links to wonderful websites for different levels and different topics. As a K1 teacher, I am always looking for classroom activities to reinforce the math concept and this link that I found "Count Us In Game" has many fun games and suggested activities for younger children. I will definitely bookmark it and try out in the coming term. Cheers</span>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-87671040096925707682010-09-19T01:12:00.006+08:002010-09-19T04:10:08.030+08:00Blog #4 Which one come first?<span style="color: black;">In our centre, placement value or tens and ones is introduced to children in Kindergarten 1. Although children learn rote counting and recognition of numbers at an earlier age, most do not attach any value to the numbers, to attach a value to the number, teacher need to introduce the concept step by step.</span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;">Burner recommends to teach mathematics using the CPA approach. i.e. from concrete materials, to pictorial representation to the later stage of abstract representation using symbols. Diene also advocate variability in teaching mathematics i.e. teaching the same concept from different angles and using different materials.</span><br />
<span style="color: black;">In this question, the teacher would show the children pictures of concrete object (sticks), the base ten blocks ( representation - proportionate ), and coins ( concrete representation - non-proportionate ) to help children visualize the value of 34 before moving into the more abstract notations.</span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;">In my opinion, the introduction of the 5 notations should be in the following order :</span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;"> 1) expanded notation</span><span style="color: black;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnrKXioWQ9VW6PCqKdaqj5aZkMUf-zM89ktARAmOdxuo5R2ZQ8VYJqHJ5nvGIkmDEuoAx5Js5nQ2PJcM_dKKTG3eY0rFHWrIJzl6ZiLH0lJOAYJNrAcfkmWvzS5B2ZhKxmUozssS8CHWpz/s1600/IMG_2023.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" height="150" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnrKXioWQ9VW6PCqKdaqj5aZkMUf-zM89ktARAmOdxuo5R2ZQ8VYJqHJ5nvGIkmDEuoAx5Js5nQ2PJcM_dKKTG3eY0rFHWrIJzl6ZiLH0lJOAYJNrAcfkmWvzS5B2ZhKxmUozssS8CHWpz/s200/IMG_2023.JPG" width="200" /></span></a></div><br />
<span style="color: black;"> 2) place value chart</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0Liynuu8BO6RaUSeb-Njet3iw49sD7mNhkH-NLCb-bI9oCNY9gs3Wz1YSYKGA9mp_UwSk2YJEWNP68xahIepnk3Rg6p3G4FfxriS9U0V1OUckcjiLf34G6Yq9D73BcXqmyZN80ntczBQe/s1600/IMG_2024.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" height="150" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0Liynuu8BO6RaUSeb-Njet3iw49sD7mNhkH-NLCb-bI9oCNY9gs3Wz1YSYKGA9mp_UwSk2YJEWNP68xahIepnk3Rg6p3G4FfxriS9U0V1OUckcjiLf34G6Yq9D73BcXqmyZN80ntczBQe/s200/IMG_2024.JPG" width="200" /></span></a></div><span style="color: black;"><br />
</span><br />
<span style="color: black;"> 3) tens and ones notation</span><span style="color: black;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi72fn6qbSMnuefne2fZ0PtdA3w8Lcj7QKAjOXcVurr97v0fcQV7UnVS24TW3UotFHiu6qwzt5S_KWBVUOg-5zT5B2nxpUKCQkjGt9o_uNp8FY6sJ_c11np0dgKQTpfaKMqQN7-8vdKrXEI/s1600/IMG_2027.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" height="150" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi72fn6qbSMnuefne2fZ0PtdA3w8Lcj7QKAjOXcVurr97v0fcQV7UnVS24TW3UotFHiu6qwzt5S_KWBVUOg-5zT5B2nxpUKCQkjGt9o_uNp8FY6sJ_c11np0dgKQTpfaKMqQN7-8vdKrXEI/s200/IMG_2027.JPG" width="200" /></span></a></div><span style="color: black;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><span style="color: black;"></span></div><span style="color: black;"> 4) number in numerals</span><span style="color: black;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-oK2cK1XK_xMTSYA9c7xq-dmogx5vsJ3dpJZplZ9OVfcdzAnbYeSaOpawF57UM7J7cNDWuI25QXq1nFogtP9i1Q_Ijf9yzuaWNDyALutov3NGiEb6VZkcVBxdhyphenhyphenx0FNYy_6P-VLl3lz4z/s1600/IMG_2026.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhthINdfu7EVssUOJ-zbcPgUoHozLAASskqPjfYFJMCQNl-Ih7ryXWc4OIY6jYlMZfd9kgQi6c_iSbqs65PY7utGa3ZbSecYLznV5YqGSGef2Yf3VvMoGnIaKeMIQrGTSx8ya19n5KSQQSY/s1600/IMG_2026.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" height="146" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhthINdfu7EVssUOJ-zbcPgUoHozLAASskqPjfYFJMCQNl-Ih7ryXWc4OIY6jYlMZfd9kgQi6c_iSbqs65PY7utGa3ZbSecYLznV5YqGSGef2Yf3VvMoGnIaKeMIQrGTSx8ya19n5KSQQSY/s200/IMG_2026.JPG" width="200" /></span></a></div><span style="color: black;"><br />
</span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;"> 5) number in words</span><span style="color: black;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxHUD6cJx6SW2dJHgPmFCvWaZDnwP7suDY56p4JpBfNZBeVUG2VQjyJYCRPWZUASYaBGL_l1Flkx7nAzWO5TCEHPbKhuP-nfeeNnmsO1szZI6ILKKb1oBJaqYT3K2rKT_YCO9HVK_XoIM5/s1600/IMG_2025.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" height="138" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxHUD6cJx6SW2dJHgPmFCvWaZDnwP7suDY56p4JpBfNZBeVUG2VQjyJYCRPWZUASYaBGL_l1Flkx7nAzWO5TCEHPbKhuP-nfeeNnmsO1szZI6ILKKb1oBJaqYT3K2rKT_YCO9HVK_XoIM5/s200/IMG_2025.JPG" width="200" /></span></a></div><span style="color: black;"><br />
</span><br />
<div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">It is arranged in this way because as we go down from each level, the notation becomes further away from the concrete and thus more and more abstract to the children.</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">1) expanded notation - children can relate the counting of 30 and 4 in sticks and base ten blocks </span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">2) place value chart - children will have to recognized that a set of ten cubes is represented by 1 ten instead</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;"> of 10.</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">3) tens and one notation - children needs to convert the table format into a number words form</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">4) number in numerals - children need to internalized the concept to visualize 34 as a number with value, not</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;"> just digits 3 and 4.</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">5) number in words - children will further convert the mathematics symbols into letter symbols. </span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;"><br />
</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: black;">Some children can grab the concept ready while others may need more guidance and practices to fully understand. However, a systematic way to introduce mathematic concept will definitely help the children in their learning. </span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><br />
</div>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-41559005151642504452010-09-18T03:25:00.012+08:002010-09-18T22:04:09.974+08:00Blog # 3 Problem Solving and Environmental Learning<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br />
</div><br />
<div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0MO2QcFQP4pxj0ttFwoWIBgO-Jeyq5nFCSms4LxhyphenhyphenNN48Ukt_TBivKF4NAAyceE9VIWbe6ugEDUlqC7EWxtvFTixjHqUeDUlSfGMNoSZrcfGshUusB5dKZx6z2ZJnvOJDe9tE6x0vXav6/s1600/Picture1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0MO2QcFQP4pxj0ttFwoWIBgO-Jeyq5nFCSms4LxhyphenhyphenNN48Ukt_TBivKF4NAAyceE9VIWbe6ugEDUlqC7EWxtvFTixjHqUeDUlSfGMNoSZrcfGshUusB5dKZx6z2ZJnvOJDe9tE6x0vXav6/s320/Picture1.png" /></a></div><br />
<div class="separator" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"></div><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"> <span style="color: black;"> "How fast can you count all the light balls on the decoration posts ouside the Cathay Building?"; "Can you map out the position of the llight balls?" ; "Is there any other way to count faster?" .</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />
</div><span style="color: black;"> These were the questions we posted to the children in our environmental learning assignment. A problem based approach to teach skip counting concept. It was quite an experience for me to bring Mathematics out of the classroom, or bringing the children out in that matter. Well, I propose fieldtrips for projects, I bring children out for science explorations and I do not hesitate to bring them to the playground for outdoor play. But making a trip to learn Mathematics? I need a <span style="color: blue;">paradigm shift,</span> and a shift for my principal and co-workers too! </span><br />
<br />
<span style="color: black;"> That Monday evening, we were there, literally counting the light balls ourselves, checking out the surrounding, trying to find other ways to reinforce the skip counting concept that we want to bring across to the children; imaging our children doing the exercise and taking on the challenge, scratching their heads to find a way to beat the stopwatch. Then we found, railing in groups of 10, stairs, pebbles, fallen leaves, patterned floor slabs, feature wall... the list went on and on... Yes, Mathematics is indeed everywhere in our environment. According to <span style="color: #0b5394;">Jorome Bruner</span> , teaching should start with concrete material, to pictorial to abstract symbols (CPA Approach) As such, environment is the best place to begin our Mathematic lessons.</span><br />
<br />
<span style="color: black;"> Problem based lesson needs even more planning. Teachers need to </span><br />
<span style="color: black;">1. know the children's prior knowlege, </span><br />
<span style="color: black;">2. establishe clear learning objective and decide on the environment feature that works best for the concept </span><br />
<span style="color: black;">3. design problem task and questions and extended activities</span><br />
<span style="color: black;">4. assess children's way to approach problem </span><span style="color: black;">during the exploration</span><br />
5. after the activities, discuss, justify and challenge various soluiton and summarize main idear and identify further problem.<br />
<br />
<span style="color: black;">One thing I like about problem based learning is its<span style="color: #0b5394;"> flexibility</span>. There is no one fixed solution to the problem and there is no restriction on how children should approach the problem. As such, children apply whatever resources and mathematics skills that they have internalized on the situation. It allows multiple entry points for the class regardless of their level of competency.Children who are more advanced in their mathematics ability will find it challenging as they can flex their mathematics muscles and dig deeper into the problem, trying out more advance concepts. For the weaker children, they may not be able to work out the entire solution by themselves, but by observing how others approach the problem and derive the answer, they will be benefited from the<span style="color: #0b5394;"> peer scaffolding</span> too. Through their answers and explanations, I can better assess individual's understanding how the children approach the problem, and if they are apply the concept correctly. on the particular mathematic concept and make plan for the future activities. Besides, it was more fun and hands-on to the children, arousing their interest in mathematics and making it<span style="color: #a64d79;"> alive </span>both within and without the classroom. </span><br />
<br />
<span style="color: black;">Still not convinced, , anyone feel bored in Dr Yeap's class? </span><br />
<br />
<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEwVZE0f34v7JNaIkti-qDouIovncmF5O4-JsGURcp2Mtw-Hy3utjHSAXFV74gXD9X5MBhL-b5PKWHwQUJYuTSJpuI0TpxqZZxvosqRvR29o_W7XWE4Tl7CUJNKRdnmQpNfOqAddJpLdxo/s1600/Picture2.jpg" imageanchor="1" style="clear: left; cssfloat: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="150" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEwVZE0f34v7JNaIkti-qDouIovncmF5O4-JsGURcp2Mtw-Hy3utjHSAXFV74gXD9X5MBhL-b5PKWHwQUJYuTSJpuI0TpxqZZxvosqRvR29o_W7XWE4Tl7CUJNKRdnmQpNfOqAddJpLdxo/s200/Picture2.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: black;">Rails that can be grouped in 5</span></td></tr>
</tbody></table><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHTL4dAzLWx1zpEd66bLSHNeqUGxMKCPPmZYqdhV8N4jri5EVDiDGBtmgxvlcBa2lZbUPr-pg7ZhHxdmU-GczphBw5uBvGv9yxr1u6As6hhaFx-2dXoyZN4fsa9xhGxM8vrWgyw3I1IYNg/s1600/Picture6.png" imageanchor="1" style="clear: right; cssfloat: right; height: 150px; margin-bottom: 1em; margin-left: auto; margin-right: auto; width: 196px;"><span style="color: black;"><img border="0" height="150" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHTL4dAzLWx1zpEd66bLSHNeqUGxMKCPPmZYqdhV8N4jri5EVDiDGBtmgxvlcBa2lZbUPr-pg7ZhHxdmU-GczphBw5uBvGv9yxr1u6As6hhaFx-2dXoyZN4fsa9xhGxM8vrWgyw3I1IYNg/s200/Picture6.png" width="200" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: black;">pattern that can be grouped in 5 with chalk</span></td></tr>
</tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxobV9Oxt_MEnL1S50ig-66axD_7YnqJb5CWKSbLI0Ay53-S3x3Oo2iUrxv8cYqgLCPYUZFmyzCKyUvOePZ6kExgZ_Dc6u3QFaFTmaPLSiKH7yxKVv0UKNGIDEFVjcfzJdZzHdzhXEaXHY/s1600/Picture3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="color: black;"><img border="0" height="200" qx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxobV9Oxt_MEnL1S50ig-66axD_7YnqJb5CWKSbLI0Ay53-S3x3Oo2iUrxv8cYqgLCPYUZFmyzCKyUvOePZ6kExgZ_Dc6u3QFaFTmaPLSiKH7yxKVv0UKNGIDEFVjcfzJdZzHdzhXEaXHY/s200/Picture3.png" width="150" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: black;">small stones as counters for grouping in 5</span></td></tr>
</tbody></table><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />
</div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: right; cssfloat: right; float: right; height: 140px; margin-bottom: 1em; margin-left: 1em; width: 638px;"> </div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0MO2QcFQP4pxj0ttFwoWIBgO-Jeyq5nFCSms4LxhyphenhyphenNN48Ukt_TBivKF4NAAyceE9VIWbe6ugEDUlqC7EWxtvFTixjHqUeDUlSfGMNoSZrcfGshUusB5dKZx6z2ZJnvOJDe9tE6x0vXav6/s1600/Picture1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-84806721898264475862010-09-08T00:33:00.100+08:002010-09-18T03:45:47.077+08:00Blog # 1 Reflection on Chapter 1 & 2<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilUamK1_2pQB2lOrDIi1U7Bepq9jqd3rcjYLul8QsYELRmEnCdv1ajcxKTMgxxHu9-BM4R-RON536xazk3VvXOaDy-2dl_m-CAmh-VOgaJGPvHMITOu6sWBT63FATvygglllNFE7owPjbF/s1600/bf101cae8bf879e2%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="122" ox="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilUamK1_2pQB2lOrDIi1U7Bepq9jqd3rcjYLul8QsYELRmEnCdv1ajcxKTMgxxHu9-BM4R-RON536xazk3VvXOaDy-2dl_m-CAmh-VOgaJGPvHMITOu6sWBT63FATvygglllNFE7owPjbF/s200/bf101cae8bf879e2%5B1%5D.jpg" width="200" /></a></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"> <span style="color: black;"> Preschool teachers may feel inadequate in teaching phonics or shy away from music & movement, but very rare you find teachers have problem in teaching mathematics. Afterall, how hard can it be to teach pre-school counting on and counting back, reading the clock, and forming ABAB pattern? </span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"><br />
</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"> That was the thinking before I read the text for the Elementary Mathematics module. Chapter 1 and 2 set the standard and laid down the foundation of mathematic teaching for all professional educators. To teach mathematics, we need to know the mathematic content well, demonstrate persistence in the process of investigation, develop positive attitude towards the subject, ready to unlearn and relearn mathematics concepts and be reflective in one's teaching strategies and practices. It doesn't sound easy now. </span></div></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"><br />
</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdvF4I30OqZhsVQRDuqzUGm9bn9-Giy5VLlIvUD1Ydek3iAud-lclTnysJfmbh7MMaIE3_pLoToxspyWi1E5ra-EB7Ko3toQ5MLzidBqO6vHkGrW8FFkuCLGoWlYuP5_igRsShaI_cB_jX/s1600/IMG_0518.JPG" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="color: black;"><img border="0" height="200" ox="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdvF4I30OqZhsVQRDuqzUGm9bn9-Giy5VLlIvUD1Ydek3iAud-lclTnysJfmbh7MMaIE3_pLoToxspyWi1E5ra-EB7Ko3toQ5MLzidBqO6vHkGrW8FFkuCLGoWlYuP5_igRsShaI_cB_jX/s200/IMG_0518.JPG" width="150" /></span></a><span style="color: black;"> Just as educational philosophy affects the deposition of a teacher, our believe in how mathematic is learned greatly affects the way we conduct our lessons. I personally think that both the constructive theory and the sociocultural theory explain well how children learn mathematics and the role of teacher in their learning. In the constructivist theroy, a teacher's responsibility is to provide a conducive learning environment which stimulates sensory experiences and increase exposure to physical surrounding. In the sociocultural theory, teachers need to know a child's current stage of cognitive development and scaffold him/her in the zone of proxmal develpment (ZPD). Mathematics should be introduced and taught in a systematic manner to help children build up their understanding of mathematic theories and allow self exploration of the ideas to achieve relational understanding rather than emphasizing on the procedural proficiency that only resulted in mechanical steps of getthing the answers without understanding and connection with other mathematics concepts.</span></div><span style="color: black;"><br />
</span><br />
<span style="color: black;"> As I reflected on my own teaching, I found myself</span><br />
<span style="color: black;">1. overly directive - children do not have much opportunity to exercise their thinking and problem solving skills.</span><br />
<span style="color: black;">2. lack of a systematical and well thought through teaching strategies to guide children's conceptual development</span><br />
<span style="color: black;">3. always hard pressed for time to scaffold individual especially those who are above class average. </span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;"> As preschool educators, we should not take teaching mathematics too lightly. Many of us are "victim" of mathematics drills in our early days of learning and thus missed out the opportunity to embrace mathematics and develop a love for the subject. We are here so we would not make the same mistake on our next generation. </span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;"> </span><br />
<div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPrjCNXtFCq3h4SczmfeRCTpVZnoKAQZhy2f-2o9B26V-RNABN8WKVtpEW-MVLPPZJD2vrm3w_y3xAn-fvwq6imx8uX6Gfl1HJSHUWwNRvXCRgYC43pCD3hflu9-ZmBXghcHZpi9Jye6AR/s1600/IMG_0199.JPG" imageanchor="1" style="height: 155px; margin-left: 1em; margin-right: 1em; width: 125px;"><img border="0" height="200" ox="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPrjCNXtFCq3h4SczmfeRCTpVZnoKAQZhy2f-2o9B26V-RNABN8WKVtpEW-MVLPPZJD2vrm3w_y3xAn-fvwq6imx8uX6Gfl1HJSHUWwNRvXCRgYC43pCD3hflu9-ZmBXghcHZpi9Jye6AR/s200/IMG_0199.JPG" width="150" /></a></div>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0tag:blogger.com,1999:blog-9171430525702054223.post-76321251432028094972010-09-02T01:23:00.002+08:002010-09-18T03:43:04.601+08:00Blog # 2 What did I learn about Mathematics? <span style="color: black;"> "The reasons of teaching Mathematics to young children is not the Mathematic itself ." and so Dr. Yeap told us during our first lecture on Elementary Mathematics today. </span><br />
<span style="color: black;"><br />
</span><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"> Indeed we had a full four hours of lecture on Math but we did not write any formula, turn on our calculator, nor try to solve an algebra equation on paper. Instead we flexed our mind to break the code of the magic poker trick, play dice together with the primary one children and try to outwit our classmate to win the paperclip game. Our concepts on Mathematics are recalled, we exercised hueristic skills, applied various thinking skills, activiated our metacognition mechanism and felt challenged and satisfied with our ability to find the solution to the problems. And all these are in fact the very essence of Mathematics.</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"><br />
</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;"> The Ministry of Education of Singapore defines the Math Framework for Primary School Curricululm as following :</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;">1. Mathematics is an excellent vehicle for the development and improvement of a person's intellectual, competence in logical reasoning, spatial visualization, analysis & abstract thought.</span></div><span style="color: black;">2. Students develop numercy, reasoning, thinking skill, and problem solving skills through the learning and application of Mathematics.</span><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: black;">3. Math is also a subject of enjoyment & excitement which offers students opportunities for creative work and moment of enlightment & joy.</span></div><span style="color: black;"><br />
</span><br />
<span style="color: black;"> Today, I am invited to look at Mathematics from a brand new angle. Mathematics is a vehicle, not the objectives of the teaching. Our goals are far beyond the conceptual and computational skills. Am I developing my children's intellectual ? Am I equipping them with problem-solve skills? Did I make them feel and look stupid by pushing Mathematics curriculum and methodology down their throats? </span><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8EGjotHh_obHJj3Dz4dq7sDjGq2cuXmZEjgdhYOifI3RMznuFIvS3apEaq_-qNmb9xrBjGYvTq5CpdsnftFooswiF4Du8FmDv6WYFPP1RBpst_4cnWueNbhADwFzMIXkKXBHzma1-HbIh/s1600/IMG_1928.JPG" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="color: black;"><img border="0" height="150" ox="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8EGjotHh_obHJj3Dz4dq7sDjGq2cuXmZEjgdhYOifI3RMznuFIvS3apEaq_-qNmb9xrBjGYvTq5CpdsnftFooswiF4Du8FmDv6WYFPP1RBpst_4cnWueNbhADwFzMIXkKXBHzma1-HbIh/s200/IMG_1928.JPG" width="200" /></span></a></div><span style="color: black;"><br />
</span><br />
<span style="color: black;"> With knowledge comes responsibility, my mathematics class will not be the same hereafter...</span><br />
<span style="color: black;"><br />
</span><br />
<span style="color: black;">Cheers,</span><br />
<span style="color: black;">Anita</span><br />
<span style="color: black;">on Teachers' Day 2010</span>Teacher Anitahttp://www.blogger.com/profile/09985833308061188460noreply@blogger.com0