Saturday, 3 September 2011

Day 6 - 31 August 2011

Today will be the last session with Dr Yeap and his wonderful Maths activities.


I would like to share with my teachers the unorthodox way of assessing children’s Maths understanding. To bring the children outdoor as what Dr Yeap had shown at the Hort-Park.

From the Hort-Park Frame, he showed us many Maths concepts that could be applied. For instance, children can learn multiplication, division, addition and skip counting just by looking at this frame.  It would be a fun learning experience. 


This is a good example of incidental learning. We could also assess the children with questions of the Maths concepts that they have learned during the outdoor activities. He said that when assessing the children, need not be just paper and pencil. We can assess children through interviews and observations during activities in and out of the classroom.


When we were asked to calculate the height between the level one and the basement of the MRT station I thought it was madness! However, with our short ruler, we managed!
Our group found that there are 62 steps and the height of each step is 15cm.
Therefore, the height between level one and the basement is 62 X 15cm =930cm. That is 9.3 meters!


The story about ‘How big is a Foot’ to introduce standard unit in length is funny. The children would love such story. Teaching (teacher) and learning (children) Maths could be a fun experience. We can use storybooks to relate to the Maths concepts.
Dr Yeap ended the day with the story about a butterfly. It is a heart-wrenching story. As educators, we must never shortchange our children by spoon-feeding them with answers without teaching them how to get the answers. We can do a lot of damage to a child if we do not go through the proper process. Just as the saying goes, 'Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.'

Click on the  link to read the full story of the butterfly


Even though it was a 24-hour session, I have learned a lot about Maths. It is not only about numbers, it is a HOLISTIC APPROACH to develop oneself. In life, metaphorically, I do not want my children to be last in the queue. As it is, most of my children are living in a challenging situation and I hope I could help them to move up to the front of that queue. Thank you Dr Yeap for helping me to help others.

Day 5 - 26 August 2011


Another day of a 'mind boggling' session with fraction.
  1. In 1 how many ¼ are there? (1 ÷ ¼ = 4)
  2. In ¾ how many fourth are there? (¾  ÷ ¼ =3)
  3. In ¾ how many ½ are there? (¾   ÷ ½    = 1 ½)
  4. Tom has ½ liter of orange juice. He needs 5/7 litres of orange juice. How more orange juice does he need? 
I understand better when Dr. Yeap represents it with a model.


I learned about Blooms Taxonomy, a cognitive process that describes different level of learning and understanding – KCA- Knowledge, Comprehension and Application.  The teacher could assess the children’s understanding of the topic based on their knowledge, comprehension and application.


 The area of the figure is related to the dots!

To find the area of the figure was another interesting activity that Dr Yeap gave us. He introduced the Pick’s Theorem in calculating the area of simple polygons. It was amazing to see the students’ calculation of the area of different shapes. It was found that the area of the figure is related to the dots!

Click on the link to find out more!


Dr Yeap told us that Singapore’s schools adopt the Spiral Approach curriculum (made famous by Jerome Bruner) whereby the children would be given many opportunities to encounter the topic without repetition. The children will learn the topic incrementally.


We did Graphing using the clothes peg we got. Our group did a line graph that Mr Yeap said was not right, as it did not give a right representation. I learned different types of graphs; bar graph, pie graph and picture graph. Something new that I learned about graph is that when doing the bar graph the width must be equal.

Dr Yeap opened a whole new world of Maths to me. He went through a process to make us understand the word problems, slowly pulling it apart and then putting it together. He made us see the connection.

Day 4 - 25 August 2011


 Dr Yeap came back with the number tricks. It was interesting to hear different ideas of how they get the students answers.  I realized that Dr Yeap always asked, ‘what other ways, are you sure?’ He made us think discuss with our friends and find out the answers. Teachers are to allow children to experience variations of Maths problems and to explore different ways to solve it and arrive to an answer. He made me laugh when he said do not be a COMMUNIST TEACHER because I had one all my school life!


I supposed my teachers did not know about Zolten Diene the person who introduced about Maths variation, Jerome Bruner who introduced the CPA approach and Howard Gardner the multi intelligence approach.

For more information, please visit this website


I learned that it is important to use the appropriate language when giving instructions to the children as the children may have a misconception of what being instructed. For example when using ‘ illegal’ language   in fraction: one out of four instead of one fourth. No wonder my brain got messed-up when it comes in doing fraction because I got all the illegal stuff.


In the word problems I learned of 3 different situations: Part whole, change and comparisons. Examples:
  1. There are 37 students in a class. 19 students are present. How many students are absent? –Part whole
  2. Tommy had 37 marbles. He gave Peter 19 marbles. How many marbles left?-Change
  3. I have $37; I have $19 more than you. How much do you have?- Compare
Important Note:In additions and subtractions I learned that units must be the same.

Dr Yeap proved to us that equal may not be identical and doesn’t look equal doesn’t mean not equal. It was an amazing experience trying to create rectangle and   triangle of different shapes to prove the point.


Day 3 – 24 August 2011

 Today session we had a guest lecturer – Ms Peggy Foo. She showed us a video of a teacher conducting a Maths lesson and we are to observe and make comments on these areas:
-          sitting position
-          level of engagement/involvement
-          use of materials/manipulative
-          flow/sequence of lesson
-          communication(teacher-pupil, pupil)
-          classroom management
-          questioning techniques
-          attitudes/disposition of teacher
-          differentiation

After the feedbacks from the students of what went right and what went wrong and the areas that can be improved, she showed us a video of the same teacher conducting a revised Maths lesson after the feedbacks from the observers. We saw a mark improvement in the teacher’s lesson. The video made me to be more observant when I am observing my teacher teaching. I gives me the skills on areas to look for and be more analytical.

This lesson study provided the teacher with constructive feedback for her professional development and growth. I think lesson study is great for teachers to exchange ideas and introduce strategies that can improve ones teaching. The teachers and children would benefit from this professional community collaboration.

In the third case study, Ms Peggy showed a video of herself teaching number conservation to K1 children. The children were given 5 unifix to construct different structures. No matter what structure they made, the number will be the same.
That's me exploring unifix!


Ms Peggy communicated and engaged the children with questions. The children’s thinking was stretched when she asked them how many ways can be done to make different structure. They were also asked how the structures are the same and how are they different. I thought these questions were difficult for the K1 to understand. Nonetheless, I learned that the teacher plays a very important part in developing children’s learning. To facilitate, to scaffold, to challenge and design task for differentiation of capabilities would give all children the opportunity to learn and progress.

I took a longer time to complete the tangram activity than I thought. I supposed my visualization skill is not that sharp. Some of my friends said that it was easier to form a triangular shape with the tangram than a square which I found otherwise. Nevertheless, I enjoyed the exercise very much!

Day 2 – 23 August 2011

Another thought provoking day. The game of Spinning wheel- Making the largest even number, taught us to look at the probability. Probability - a branch of Maths that gives a numerical value the chance of event happening. This game made us think the probability of the numbers that would result to the answers. Dr Yeap challenged us further with questions, “are you sure? Do you think so? 
When we played the pick up sticks’ game, we were taught to use our observation skills. We are to observe the number patterns. What would be a good number or a bad number? We tried different ways to see the results.  After three games with my friends and prompting by Dr Yeap we then realize the patterns.
He said children should be given the opportunities to try different ways and to explore to find the answer. We are to look at the skills that the children could acquire when playing this game.

Maths after all is about problem solving and we should use Maths as a tool. We so often give the children the questions and correct for them. We should give the children enough time to correct themselves, make connection and figure out what and how to do!

Children have different level of intellectual and capabilities. Teachers should give differentiated instructions for children’s learning.
Dr Yeap showed us the ‘traditional’ way of doing the long division and using the language that my teacher used, I could help but laugh out loud. That was why I could not understand Maths. I just listen and did as instructed without understanding – my teacher must be a COMMUNIST with illegal license to teacher!

Dr. Yeap modeled of how Maths should be taught.
He gave steps by steps instructions, using concrete materials or cutting papers, he would then make a representation by drawing on the board and finally in numbers. He said that what he showed us is the Jerome Bruner CPA Approach. It is a learning process from concrete, pictorial and then abstract. It is important that at the kindergarten level, when teaching Maths to begin with real objects (concrete) and then pictorial. At this level children learn Maths through representation.
I will always bear in mind that the ability to memorize is not a human strength. Maths is not about memorizing, it is about developing the children’s number sense (which my son said that I am lacking) L metacognition, visualization and generalization (patterns, relationship and connection).

Wednesday, 24 August 2011

Reflection on first day of class -22 August 2011

My fear of Maths and Maths teachers stayed with me even untill today at the age of 59. Whenever I see numbers I just have mental block! I do not want the children under my care to feel the same way as I am. I want them not to be fearful but to have fun when learning maths.
The Maths teachers that I have experienced with when I was young was a nightmare. I was hoping to see a friendly teacher who would accept someone who is slow in Maths who would give opportunities. The day made a difference in my 'Maths  life'. The first lesson was such a  wonderful experience. The numbers come alive with the name game. We were made to look at patterns. I did not know that there are rules to it. I learned that every pattern has a rule. A pattern cannot be answered unless there is a term and rules being stated. I am also more aware of the different uses of numbers.
We were given challenging problems to solve. We were encouraged to solve the problems in different ways and prompt with questions to look at the problems at different angles. The class shared their thoughts and ways of solving their problems. Every students that gave the answer would give their own method of solving the problem. I also learned from  with the others around me to solve the challenging problems. I felt enlightened when I was able to solve the problems.What a learning experience!
I felt guilty when I thought of how I taught Maths to the preschool  children. Teaching Maths is not only teaching the children to count and recognising the numbers but a lot of consideration have to be put into it. When using concrete materials we have to ensure to use the same unit and that we can count the things that belong to the same set.
The most important thing that I have learned from the first day session was about the prerequisite to meaningful counting. First, the children should be able to classify, second rote counting, third the appreciation of the last number they utter is the number represent the things in the group and lastly one to one coresspondence. If the children are not able to do Maths I have to find out why and to see whether the children have the prerequisite or prior knowledge to begin new concepts.
It was  a great learning experience . I hope to gain more knowledge for the benefit of the children.

Friday, 19 August 2011

EDU 330 Elementary Mathematics-Blog Entries

How Maths was to me...
My poorest subject in school was mathematics. I was repeatedly asked to do correction of the maths problems that I had done wrong. I was asked to stand by my maths teacher's side and to recite the time-table. If I got it wrong, I would be caned on my palm. I hated maths and I hated my maths teacher. Their concern was to get the right answers from the students. The problem sum was a real problem to me! Therefore, I would like to make sure that the children enjoy and understand what they are learning when they are mathematics.

Elementary and middle school mathematics - Teaching developmentally

Chapter one

As the supervisor of the childcare centre, I have to ensure the teachers have the knowlege of how children learn mathematics and the right approach of instruction. I believe the children must be able to make sense  of mathematics and to know that mathematics is a way of life. The teachers on the otherhand have to challenge and support  the children in their thinking and reasoning  when they are doing mathematics. Learning mathematics are not only from text books in the classroom but it can also be learnt outside of the classroom and intergrated with other subjects such as science, cookery and art.

As stated in chapter one in the principles and standards for school mathematics that all children to be given the opportunities to learn mathematics, it is important that I ensure that all the children in my childcare centre have the opportunities to learn mathematics.

My childcare centre being a voluntary welfare organisation having children of diverse bacground; children from dysfunctional families, low and average income and of different races, the school is the place where the children would be able to  focus on learning mathematics. It is more so for these children to learn to  think and reason to solve problems. They have to understand that they have to communicate, make connections and that there are many different  approaches to solve problems. These are important life skills.

To give these oppportunities to the children, the teachers have to look into the features of the six principles especially the teaching principle that requires them to know what how and what the children need to learn and what the teachers need to know to enable them to find different strategies to enhance the children learning. It is also important for teachers to assess and evaluate the children's understandings so that the children could be given the needed support and challenge to enhance their learning. Though I feel that very young children learn best  through concrete materials, using technology such as calculator and computer with their great animation would increase exploration and enhance representation of ideas (pg. 3). Technology could extend the range of problems that can be accessed (pg 3) and enhance children's learning where traditional methods cannot. As I had very bad experience in learning mathematics, it is important that the children understand the concepts what they are learning and find different ways to understand. In my childcare centre, the children are given the opportunities to learn mathematics in different ways and settings. At the block and manipulative centre, children learn geometry , number and operations and measurements through play. The teachers would engage the children in learning the concepts with problems solving so that the children are able to make sense of what they are learning and  thinking logically the answers that they provide.

I believe in striking a balance of the traditional circular of repetitive conditioning and conceptual understanding.

                                         Children learn through exploration at the block centre

Logical assumption - Problem Solving

Investigating shapes

Matching - Exploring Maths Concept

Sorting according to colours

Chapter Two
I was afraid to make mistakes when doing mathematics problems. The teachers would focus on getting the right answers with the right procedures. I have to make correction of my wrong answers by copying from my friends who had the right answers. I did not understand why I did wrong and I did not understand either why my friends did right! Doing mathematics was so fearful and agonising.

I would like to create a culture whereby children would explore, investigate, share ideas and take risk in solving the problems. The teachers should see that the children should not be afraid to make mistakes and that the children should learn to figure out different ways of solving the problems.
The atmosphere of the class should be that of children be allowed to give ideas in solving problems in whatever methods they contributed. Their contribution should be appreciated and that mistakes made should be corrected and learned. The correction of the mistakes from the children‘s contribution give everyone the opportunities to learn in many ways to solve problems. I also increase the children’s level in analytical thinking and reasoning.  As such some children would have the opportunities to build on (scaffolding) the prior knowledge that they had and some children would be a new knowledge that they acquire. This is the

Constructivist theory of Piaget’s who suggested that the children’s schemas could be changed through assimilation and accommodation. Therefore is important to give opportunities for children to construct their own knowledge based on their prior knowledge and build understanding of current ideas and knowledge. On the other hand the Sociocultural theory involves children’s learning not only learning through having communication and interaction with each other but also with diagrams and pictures. Through their engagement in discussion and reflection to find solutions to solve problems, a foundation of children’s learning has been built.

In teaching mathematics, the teachers should look into the five strands of mathematical proficiency to guide them. It involves in strategic competence, adaptive reasoning, conceptual understanding, procedural fluency and productive disposition. The children should be able to solve problems based on logical assumption, making sense of solving the problems and justifying the correct answers.  In doing mathematics the children should understand the connections of different concepts and their relationship. They should also be able to see the connection in everyday lives- real world situations.

When doing mathematics, the children develop their thinking skills (reasoning and analytical skills), social skills and emotional skills.The process of solving problems would built a resilient child who would look at problems with different perspective. I wished I would have this opportunity to make maths an easy process to learn - so that all children would not fear Maths like I did.