Today was my first mathematics lesson with Dr Yeap. He had made the learning of the mathematics fun, interesting and even magical. Dr Yeap had created the environment where I was able to experience the 5 Process Standards from the class activities. I learnt that there are many different ways to solve a problem and that more than one answer is possible. I was encouraged to communicate with my course mates when trying to think through the questions and come up with possible answers. I understand now that mathematics is not an isolated skills and procedures. It is a combination of different concepts. When Dr Yeap used poker cards, buttons and the ‘ten-frame’ chart; I was able to visualize and understand the mathematics ideas better.

In lesson 1 and lesson 5, I was asked to look for pattern when trying to solve the questions. I learnt that pattern is a sequence; it has a rule and a term.

I learnt that number sense is more than just counting; it involves the ability to think and work with number easily and to understand their uses and relationship.

Another important fact that I learnt was about the prerequisite to meaningful counting. Firstly, children must be able to sort thing or classify before counting. Secondly, they have to know rote counting. Thirdly, they need to know how to do one to one correspondence. Lastly, they must be able to understand that the last number counted in a group is the final answer.



In today lesson, Dr Yeap emphasized that mathematics is a vehicle for children to develop their logical thinking, to be a more independent learner and to acquire the abilities to correct own mistakes and make appropriate decisions. To allow us to understand what he meant; he introduced us to Jerome Bruner’s CPA approach. This approach provides the opportunity for children to learn mathematics or even other subjects by allowing them to experience and learn from using concrete before pictorial. And when children have acquired the skills or understanding, they would then proceed to do abstract.  

In the mathematics process, there are 3 types of understandings we could introduce to children.

  1. Procedural / Instrumental Understanding – children learn “how” to do the questions
  2. Conceptual Understanding – children learn “why” something works for the questions; they learn the meaning behind procedure
  3. Convention Understanding – children learn that mathematics has certain “rules” or “laws” to observe

 There are 5 elements that would promote thinking and problem solving skills in children.

  1. Generalisation
  2. Visualisation
  3. Meta-cognition
  4. Communication
  5. Number sense

New word I learnt today is “Subitize” – the ability to look at the items without counting and tell how many are there. It is easier to subitize on small number of items.



Ms Peggy started the class by showing us 2 videos in relation to professional development using “Lesson Study”. Lesson Study is founded in Japan and it is a teaching improvement process where a group of teachers plan, discuss learning objectives and design lesson plans based on their discussions. After which, a teacher conducting the lesson would be observed by other teachers or mentors. From the observation, the teachers would examine their lessons, identify their strengths and weaknesses. As such they would be able to make changes to their teaching strategies or lesson plans.

I felt that Lesson Study is a good practice as it allows collaboration and peer learning among teachers. It is less stressful; as teacher is observed by peers or mentors and not by some strangers from other organisation.

I had learnt 5 important facts from the videos on 2 case studies using “Lesson Study” approach.

  1. Design of task (mathematical  investigation)
  2. Clear instruction and demonstration
  3. Effective questioning
  4. Effective use of materials/manipulative
  5. Differentiation for different ability learners

I totally agreed that differentiation instruction would definitely benefit children with different learning abilities. However, it is not an easy task for teacher to plan and provide differentiated lessons to address the various needs of the children. The teacher has to be skilful enough to scaffold the higher level learners and at the same time; she has to be sensitive enough to assist the struggling learners. Therefore, I believe that the teacher plays an important role as an instructional leader armed with good knowledge of mathematics, persistence, positive attitude, readiness for change and reflective disposition.



Today, Dr Yeap again demonstrated that mathematics is a science of concepts and processes that have a pattern of regularity and logical order (Walle et al., 2010, p.13) when he introduced lesson 13 to us. At first, I was so fascinated with his ability to know the 2nd digit number and worked out the difference of the 2 digits. Wow…., the magic is the “pattern of regularity” where any 1st digit we thought of multiplies by 9; we would be able to get the answer for the difference of the 2 digits.

 In lesson 14 and lesson 15, Dr Yeap reminded us that there is on one way to do mathematics. Teachers need to be flexible and to close the loop that will anchor the lesson. According to Zoltan Dieness we have to provide variation and not repetition for any mathematics activities. I learnt that to make story problem interesting; I could consider using the 4 problem structures.

  1. Join problems – result unknown/change unknown/initial unknown
  2. Separate problems – result unknown/change unknown/initial unknown
  3.  Part-Part-Whole problems – whole unknown/part unknown
  4. Compare problems – difference unknown/larger unknown/smaller unknown

Fraction made easy when we use the CPA approach. Dr Yeap gave us coloured paper to do fraction. We found out that even when the part does not look obviously equal, but the parts are equal. I believe that children would not be able to understand this concept unless they have personally folded the paper equally and cut out the parts to compare. Another thing I learnt was that the condition for naming fraction is when all parts are equal.



We revisited the lesson on fraction again today. Dr Yeap used model to solve the problems. I felt that I could make sense of the question when I used model to find the answer. It was effective when I used it to solve the quiz on how many monsters would have 19 eyes all together when some monsters have 3 eyes and some monsters have 2 eyes?

I learnt about Spiral Curriculum Approach by Jerome Burner. In this approach, children are encouraged to encounter the core idea again and again at a higher level. I was told that in Singapore, we are using this approach in our school system.

According to Bloom’s Taxonomy (KCA), there are 3 levels of learning in mathematics:

Level 1 – K (Knowledge) Level 2 – C (Comprehension) Level 3 – A (Application)

I learnt that “artificial stimulus” is giving signal whether right or wrong answer to children. Dr Yeap informed us that we should not use any external artificial signal to show approval or disapproval to children’s responses; as it would cause children to rely on teacher’s signal and they would feel lost if their teacher is not with them. As teacher, we should encourage children to develop their ability to explore, think through an issue, and reason logically to solve problems. Moreover, children need to know that it is alright to make mistake and to learn from mistake.



Dr Yeap highlighted what we should assess in children’s mathematics learning.

  1. Assessing the procedural knowledge – children would be tested on their knowledge of the rules and procedures used in carrying out mathematics processes and also the symbolism used to represent mathematics (Walle et al., 2010, p.24)
  2. Assessing the conceptual knowledge – children would be tested on their knowledge about the relationships or foundational ideas of a topic (Walle et al., 2010, p.24)

There are 2 types of assessments commonly used:

  1. Paper and pencil test
  2. Oral / interview test

I concluded that assessment in the classroom should be designed to help children learn and to help teachers teach. We should not focused on assessing what children do not know but what children do know – what ideas they bring to a task, how they reason and what processes they use (Walle et al., 2010, p.76-77).

Dr Yeap ended the last session with a passage “How to make sure the butterfly cannot fly” by Lim Siong Guan, Head Civil Service. This passage reminded me that children are not passive learners. Instead, they are encouraged to be active participants, to create their own problems and work towards solving them. They are asked to work in groups, communicate their ideas, apply reasoning, and making conclusions. All these would help children developed confidence and positive attitudes towards learning mathematics.

The answer for the MRT activity is :

16 (stairs) X 4 (flight of stairs) = 64 stairs

64 (stairs) X 15cm (height of each stair) = 960cm




Mathematics has never been a favourable subject to me during my school days. I learnt maths by rote memorization and had never understood the principles that form the foundation of mathematics. As such, maths was something abstract and to make the matter worse; I did not have the privilege to learn from teachers who “encourage students to think, question, solve problems, and discuss their ideas, strategies, and solutions” (NCTM, 2000, p.18). Needless to say, I was unable to do well for maths and would shun away from this subject and would try to avoid doing any maths problem whenever possible.

However from the reading, I was convinced that “teachers’ attitudes toward mathematics may enhance or detract from children’s ability to do math.” (p.9). I learnt that to be an effective teacher; I have to increase my knowledge of mathematics and to have a better understanding on how children learn maths. I agreed that teaching mathematics now is very different from the past. Mathematics has a much wider score and it is more than just learning how to count, read and write numerals. In the preschool mathematics curriculum, topics like matching, classification, comparison, ordering, patterns, learning about space and shapes not only build a foundation for later number concepts but also help to expand and deepen children’s conceptual knowledge which will prepare them for later study and work.

I liked the Five Process Standards (problem solving, reasoning and proof, communication, connections and representation) mentioned in the book. This process standards will allow teachers to plan and implement maths activities that encourage children to acquire and use mathematical knowledge.  Children being active learners have a natural desire to learn. They learn better by doing, exploring and experimenting manipulative materials in the classroom through fun filled play. Learning mathematics must be relevant for children. They learn best when maths has real meaning for them. In mathematics this means doing a lot of practical activities, where they learn skills “on the job”. For example, it is more meaningful when children are allowed to eat the cookies that they have counted rather than counting things in a book. Therefore children should not just learn mathematics concepts by rote learning and rules but be actively involved in the learning process. Ultimately, they may realised that the problems they have solved come from an interrelated set of mathematics concepts previously learnt.

When I read the section about “Where Are the Answers? I realised that I am guilty of sending the wrong message to my students, as I am always trying to provide the answer, solution or verifying their answers during mathematics lessons. I learnt that I should be a resource to be used rather than the source of all information; the facilitator of learning rather than instigator. I should asked questions that encourage the children to think about mathematics as they are actively doing mathematics.

Last but not least, I agreed that the mathematics curriculum should enrich children’s aesthetic and linguistic experience, provide them with the means of exploring their environment and develop their skills in logical thinking. When children have built a strong foundation on mathematical understanding, they will develop confidence and have positive attitudes towards the learning of mathematics.