H) Reflection about the course module as an early childhood educator

       Before the commencement of this module, I asked myself “Why elementary mathematics? Aren’t we in early childhood?” However, this module has brought me back to my early school years which I missed most. How a teacher assists a child in the learning is definitely an impact to a child who is struggling to learn a concept. I really learned and benefited a lot from Dr Yeap through this module. I have changed my perspectives in teaching children Mathematics and it was demonstrated in class on how can we engaged a learning child with fun activities.

         Through the whole module, I understand the importance of hands-on and concrete experiences when learning mathematics. I personally enjoyed the whole module with the all the games and activities conducted. I am so excited by the cube sudoku which I am so impressed that I could solve it within minutes! I am so thrilled and amazed to learn that all these simple activities motivated me to learn. The rewards of cookies and quizzes posted by Dr Yeap really sparked off my learning desire once more. This is something that I took home with and it definitely encourages any child to learn as well.

The completed cube sudoku activity

I have not created any blog before this module and it is not too difficult after all. With this e-learning mode, I am able to expand my understanding by reading more related write-up and push myself to find out more websites related to the topics too. After the exploration in the internet, I realized there are a lot of good activities suitable for children to use as a tool to assist their learning. I will continue to explore and work on this e-learning style and to encourage more pre-school teachers to use them too.

Some links to share:

·        Other type of 3D sudoku game

- http://www.passionforpuzzles.com/puzzles/sudoku_3d.php

·        How To Teach Kids To Solve Sudoku

- http://www.dailymotion.com/video/xcwz2n_how-to-teach-kids-to-solve-sudoku_webcam

G) Geometric thinking and reflection of pentagon angles activity

          Tangram has always been a favourite kindergarten Maths activity in the Maths learning centre. “Don’t throw the pieces everywhere!” and “Follow the picture and do it yourself.” Are those comments familiar? Yes, most of the time, teachers take for granted that children will figure out the tangram puzzle naturally and do not practice strategically with them at all. If the children are being challenged to create a square with the different pieces of shapes given such as what we had done in class, it will be fantastic!



Children playing with tangrams





         We will need to have spatial sense in order to play the next activity in class which is to find the interior angles of a pentagon. According to Van De Walle, J. (2009), spatial sense includes the ability to mentally visualize objects and spatial relationships – to turn things around in your mind.





To calculate the angles within this pentagon



         I find the above activity very challenging but fun as we need to have strong spatial sense to be able to calculate the angles of the pentagon immediately. Some will have a rectangle and two triangles to form the pentagon, where some is four triangles to form and commonly is three triangles to form the pentagon. This is a fun activity to teach or expose children to geometry, angles.

Some links to share:

·        Geometry games and videos on types of shapes

-         http://www.onlinemathlearning.com/geometry-help.html

-         http://www.youtube.com/watch?v=2439OIVBgPg (Angles)

·        Shapes games for preschoolers

-         http://pbskids.org/games/shapes.html

-         http://www.thekidzpage.com/learninggames/shapes.html

-         http://www.youtube.com/watch?v=lj-Z3f2pdCE&feature=fvw (Video)

-         http://www.youtube.com/watch?v=Jb9Zn8dzL1k&feature=related (Video)

·        Interesting Tangrams Video

-         http://www.youtube.com/watch?v=QSkLhwXpmwQ&feature=related

F) Reflect on Practice : Number Sense

        After reading the chapter and much reflection, I do agree with Van De Walle, J. (2009, p129) that he mentioned “Children continue to develop number sense as they begin to use numbers in operations, build an understanding of place value, and devise flexible methods of computing and making estimates involving large numbers, fractions, decimals, and percents.”

         However, children in preschool are taught numbers from 1 to 100 by kindergarten 2. As mentioned in the text, soon after children learned number 1 to 20, it as moved quickly to addition and subtraction instead of more exposure to other number operations such as part-part-whole relationship, counting on and back, more & less, and estimation, etc. Most of the time, mathematics is a subject with not much focus and teacher will go through concept after concept without much polishing of the skills learnt after each concept.

Counting activity for the 4 years old



Activities already commonly practice in pre-school:

       



1) Early counting





2) Writing numerals and recognition





3) Less/more/same activity

Activities that are not common practice in pre-school:





           1) Doubles and near-doubles 

     2) Anchoring numbers to 5 and 10



         Though some preschool curriculum touches on 1) Counting on/back, 2) part-part-whole or 3) More than/Less than, but it is not given much practices and focus. Most of the time, it was introduced to the children on those topics and move on to another new topic. Only when children are given more hands-on activities and practices related to a new concept, they will connect with the concept and have the understanding. Having more learning centres activities may assist their own connection but teachers always lacked the time to prepare such corners.



Maths learning centre in the classroom for the 4 years old

Some links to share:

·        Number sense activities for kids  

- http://media.emgames.com/emgames/demosite/demolevel2.html    

-         More / Less / Same

- http://www.lessonsense.com/games/moreandless.html

- http://gamesvia.net/more-or-less.html

-         Counting

- http://pbskids.org/games/counting.html

-         Part-part whole / Number bond

- http://www.woodlands-junior.kent.sch.uk/maths/numberskills.html





E) Reflect on Chapter 7 & Using Technology to teach Mathematics

Reading this chapter has brought me back to my school days which I was allowed to use calculator only in secondary school. Nowadays, primary 5 students are allowed to use calculator in examination and using computer to practice Mathematics problems are so commonly observed.


Among all the others, what strikes me most was to allow the kindergarten children expose to calculator too. According to Van De Walle, J. (2009, p113), when children are learning counting on, counting by twos or threes, by using calculator can enhance their oral counting or pattern identification.

As I agreed that using calculator to teach Maths is another technology used and calculator is also a tool commonly used in our daily life which reflected on one of the rationale for teaching Mathematics in Singapore.

In one of the recommended links, I found this link which use calculator to reinforce numbers in operations for kindergarten children: http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm#applet

In this millennium, using technology to teach any subject will be a must to enhance children’s learning efficiently.

Activity / tool which I like most:

One of the activities that I like is placing the dot on the correct number line in http://nlvm.usu.edu/en/nav/grade_g_1.html  where children could clearly place the dot at the right place on the number line. After much practice, they will be familiar with the number line sequence in time to come.

As our centre is also using story-based to teach language, Maths and other subjects, I came acrossed this video which demonstrated how a pre-k teacher created the classroom learning centres using a story to extend.

    

 Story-Based Centers

      - http://www.learner.org/vod/vod_window.html?pid=908  

 
 

 

 

 

 

 

Some links to share:

 

• Maths activities for kids                 

     - http://www.coolmath4kids.com/

     - http://www.woodlands-junior.kent.sch.uk/maths/index.html     

D) What is the place value sequence and why?

I personally felt that the sequence should be as below:

1. Numbers in numeral

2. Numbers in word

3. Place value chart

4. Numbers in tens and ones

5. Expanded Notation

I felt that the sequence should be above as it has to link to our curriculum from kindergarten to primary level.

In nursery, we start exposing children to numbers in numeral and then moved on to number words. Later in primary school, children are exposed to tens and ones. After knowing what is tens and ones, then place value chart will enhance their understanding and visualizing numbers in tens and ones. Last but not least, expanded notation is introduced last as it is merely in abstract form.

According to Bruner.J, children should learn through Concrete, Pictorial and Abstract approach which I anticipated the below related to his theory:


  1) Concrete - where numbers can be counted in real objects and match numeral with concrete materials

  2) Pictorial - where place value chart and counting in tens can be visualised easily.

  3) Abstract – Expanded notation required abstract thinking and numbers replacement which is the higher level
                       learning.

Jerome Bruner

"The language of education, if it is to be an invitation to reflection and culture creating, cannot be the so-called uncontaminated language of fact and 'objectivity'. It must express stance and must invite counter-stance, and in the process leave place for reflection, for meta-cognition. It is this that permits one to reach higher ground, this process of objectifying in language or image what one has thought and then turning around and re-considering it"
 
 
 
 
Some links to share:

• Maths learning activities by levels

   - http://www.ixl.com/math/grade/first/

• Place value magic

   - http://www.onlinemathlearning.com/place-value.html 

C) Reflections on 6 Sep 2010 learnings with chapter on problem solving

As our group has decided on the maths concept of Value of Money to teach kindergarten 2 children, during the lesson, we are supposed to bring the children to the supermarket to complete the task designed for them.

Task at Supermarket

 After reading chapter 3 from Van De Walle, J. (2009), I would like to relate the three phrases – before, during and after phrase of a lesson. The trip to the supermarket seems to be during phrase and getting them to do the drawing of the coins on paper can be the after phrase of the lesson. What we did not plan was the before phrase of the lesson and we can actually set up a supermarket setting in class to allow children to practice counting money. Money chart can be introduced for children to be familiarized.

Coin chart can be downloaded at link below

With the supermarket trip being the during phrase, we can extend lesson by providing more money counting exposure using technology from link below.
 
Some links to share:


• Learning Mathematics activities at Home

   - http://www.earlylearningathome.com/math-for-preschoolers

• Money matching game

   - http://www.dr-mikes-math-games-for-kids.com/money-memory-game.html?cur=sgd

• Counting money game

   - http://www.mathsisfun.com/money/money-master.html

• Counting money chart

   - http://iantan.org/archives/1512

B) Reflections on 1 Sep 2010 BSC 04, EDU 330 lesson

It was indeed a mind blowing lesson that I had today especially with all the new mathematics games that I have learnt. I agreed that teaching mathematics today is not just teaching methods alone but to help children with the learning process in experiencing their true understanding.


The few mathematics games really refreshed my personal understanding of multiplication of 3s and addition. They were like simple tricks for children to practice repeatedly and to sharpen their understanding through those experiences.

I have also learnt that the rationale for mathematics is a vehicle to higher thinking skills, matches the needs in our daily life and for enjoyment. Having all the skills to process our thoughts are important, and that is mathematics! One thing that I gathered was the importance of mathematics in our life, and I could not imagine what world it will be if there is no mathematics.


Some links to share:

• History of Mathemtics

   http://www.youtube.com/watch?v=wo-6xLUVLTQ

• Why mathematics is important? (Experimental-Slide)

   http://www.youtube.com/watch?v=gDkd0Vaxf-c&feature=related
     (Can you imagine if there is no mathematics in the above situation?)

• Mathematical magic trick to share:

   - “I can read your mind!”
      http://www.youtube.com/watch?v=Hc1WXBtum2o&feature=related

   - “How do you do the trick?”
      http://www.youtube.com/watch?v=AIjoEPVERRc&feature=related

A) My personal thoughts on chapter 1 & 2

During a mathematics lesson in the past, we were always being told by the teacher what we can do using certain strategies and protocol to solve the problem without understanding how and why. Today, mathematics should be fun and interactive, and at the same time, focusing on the process will allow children to enhance their thinking skills and understanding of the concept.


According to Van De Walle, J. (2009), a mathematics classroom in today’s context is so different from the past with the six major shifts in the environment.

• Communities that offer an equal opportunity to learn
• A balanced focus on conceptual understanding and procedural fluency
• Active student engagement
• Well-equipped learning centres in which technology is used to enhance understanding
• Incorporation of multiple assessments that are aligned with instructional goals and practices
• Mathematics authority that lies within power of sound reasoning and mathematical integrity (NCTM, 2007, p7)

Teaching children how to fish is relatively more important than fishing for them. Just like mathematics is a subject that we no longer teach or explain how to do the sums but to assist their learning process with logical thinking involved. Only through their personal experiences, they will grasp the skill with impression. In this era, technology is widely used as a media to assist children to process their thinking such as:

• online maths games or video
http://www.primarygames.com/math.htm
http://www.youtube.com/watch?v=ARptMWpgLbE&feature=related

The physical mathematics lesson needs to be fun, interactive and hands-on such as the brainetics way of deliverance.
• (parents/educator’s views) http://www.youtube.com/watch?v=qpFOfHZPKDk
• (kids’ view) http://www.youtube.com/watch?v=bAYg2OkRBlk&feature=related

Getting the children to be involved in the process of solving the problem will then equipped them with the skill.

To become a mathematics teacher is no longer an easy task now. Not only that it takes having great mathematical knowledges to become one but most importantly is your passion for children. A successful mathematics teacher should not kill a learner's interest in logical thinking processes but to have the passion and enthusiasm to facilitate their understanding in mathematics. I agree with Van De Walle, J. (2009) that becoming a mathematics teacher, you need to have the 1) knowledge of Mathematics, 2) persistence, 3) a positive attitude, 4) readiness for change and lastly 5) reflective disposition, especially being the mathematics teacher of the millennium.