Monday, 19 August 2013

Day 6 – 17/8/2013

Ms Peggy Foo took us through the last session of this module. She introduced lesson study to us. 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 conducts the lesson would be observed by other teachers. From the observation, the teachers would examine their lessons; identify their strengths and weaknesses, so that 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.

In this lesson, I also learnt about differentiating learner types during a lesson. In a class, there are different types of learners. Some might be fast learners and others need more assistance during teaching. Planning should be based on different needs of the children.

I learnt from Ms Peggy that teachers can plan:

For the weaker learner, provide them with 10 frames and counters
                                               10 = _ +_

For the advance learner just give them countersh
                                               10 = _ +_

For the more advance learner, find different possible ways to make 10 with 3 digitser
                                               10 = _ +_ + _

I agreed that differentiation instruction would definitely benefit children with different learning abilities. However, it is not an easy task for teachers to plan and provide differentiated lessons to cater for the different needs of the children. The teacher has to be competent enough to scaffold the advance learners and at the same time, she has to assist the weaker learners. Therefore, I believe that the teacher must possess good knowledge of mathematics, perseverance, positive attitude, readiness for change and have reflective disposition.

Day 5  – 16/8/2013

What is visualization?

To get the children’s mind to see difficult things, to make them intelligent.

How do we make them good in visualization?

Visualization is the most important skill that teachers need to help children develop in their early years. Writing numerals are an abstract representation of numbers. Before children are ready to work with writing model of numbers they need to have experiences with concrete and visual models.

According to ‘Jerome Bruner's CPA Approach’, children develop concepts of the number system in three stages.

They move from working with:
  1. Concrete representations (blocks, unifix cubes, tangram)
  2. Visual representations (pictorial drawings) and
  3. Abstract representations (conventional number symbols or models)
The capable children in the class had developed in their mind, strong visual images of numbers or models. Children are engaged in the folding or cutting of paper to develop such models.
They drew shapes, different symbols, then gradually to drawing lines or circles to representing tens. These symbolic images helped children to develop mental images.with strong visual image of numbers.

Click on the link to read how to deepen Mathematics Teaching and Learning through the Concrete-Pictorial-Abstract Approach

Day 4 - 15/8/2013


 Today is the fourth lesson with Dr Yeap, we were given a geoboard to draw different polygons on it but the polygon can has only one dot inside. It’s astonishing to find some of them could even draw a large polygon with only one dot inside.  After drawing the polygon, we have to find the area. We used one square as our standard unit of measurement. Some of the polygons were easy to calculate while others are quite difficult, but we came up a formula to help us in the calculation.
The children in my centre also get to explore the geoboard, they form different shapes by attaching the rubber bands and they transfer the shapes onto geoboard dot paper.  
It is not easy to get children to measure the area of the shapes, but after this lesson I realised children can learn to measure the area of shapes using geoboard.

There are hundreds of math learning and teaching resources and games organized for you here. Enjoy the math!


Day 3 - 14/8/2013

What would you do when a child in your class cannot count? How would you inform the parents? Will they be satisfied with just answer from the teacher saying, “Your child cannot count?”
Dr Yeap got me to realise that I need to find out more about this child’s learning experience. He reminded me that a child can only count when he is able to:
  • Classify and sort
  • Do one-to-one correspondence.
  • Role count and lastly
  • Understand that the last number he uses actually represent the thing.

Dr Yeap stated that, ‘Teacher should find out the root cause of the problem and know the possible strategies to help the child.’
He showed us a dice, and asked us, “How many dots are there on the dice? Can you tell by looking? Can you tell the number of dots without counting?”  The ability to do so is one new word that I learnt from Dr Yeap, it is called subitize. It means able to tell the number without counting. Now I know the children are able to tell the numbers of objects in a group without counting them. They are subitizing.
Dr Yeap has been emphasizing on CPA Approach during the lesson. CPA Approach enables children to learn Maths in a meaningful way and translate mathematical skills from the concrete to the abstract. During the lesson, we learnt about fractions by folding paper. Each of us was given a piece of paper and to fold it into 4 equal parts (concrete representation). We checked whether they are equal parts (although they are of different shapes) by cutting, matching and overlapping them together. From there it constructs the ideas of equal parts. Thereafter, we could solve problems using pictorial form of the shapes then to abstract representative e.g. 2 1/4 – ½. This is a way of introducing fractions to children and also we must teach them to use appropriate terms, for instance, ¾ should be read as “three fourths” and not “three out of four” or “three upon four” or “three over four”.

Day 2 - 13/8/2013

Today I learnt to use numbers in different ways, and see Mathematics as a natural and part of everyday activities.

Numbers are used in four different ways
  • Ordinal numbers: 1st, 2nd, 3rd
  • Cardinal numbers: Using numbers for counting purposes Eg: 5 apples
  • Norminal numbers: Using numbers as identification Eg: Bus No. 174, our IC numbers
  • Measurement numbers:  Using numbers to measure Eg: 5 kilograms

Dr Yeap mentioned that after each number, there must be a noun for instance 1 apple, where 1 is the number and apple is the noun.This helps children when they learn addition and subtraction. Dr Yeap says “You cannot count things that have different nouns”, for example, you cannot subtract one orange from 3 apples. 2 apples and 5 oranges will never become 7 apple oranges. This can also be shown by 2x + 2y will never become 4xy.Thus we cannot give children different nouns to add and subtract.

I get to see what 10 frames is, which is a must in every preschool Maths Learning corner. This 10 frames helps children to understand e.g. 8 is less than 10 by looking at this frame.
When I asked the children how many less, the children can easily tell me the answer by looking at the blank box. Children develop number sense by using 10 frames to count. It plays an important role in the development of the children in understanding of numbers, it gives the children the visual cue to count one to one correspondence and learn number conservation. I like the 10 frames method in teaching children to learn about numbers without explicit teaching.

Day 1 - 12/8/2013

After countless of modules, I liked Dr Yeap’s style of teaching as he explains the answer clearly, especially when he got us to stop and ask questions. He also makes the lesson interesting and engaging with a lot of materials and hands-on activities.

He started off with the question ‘How do the children learn?’ and ‘How do we help children to learn?’

From today’s lesson I learnt that children learn through:
  • Exploration, scaffolding from teachers when they prompt the children by asking questions and then by teacher modelling.
  • Concrete Pictorial Abstract (CPA) approach.
The Bruner theory emphasises that in learning anything abstract, we need to do concrete learning first before going to visual and then to the abstract representation. We explored the different ways of folding the paper to get four equal parts. It was fun trying to fold it in different ways.  While doing the activity I felt as if I was a child exploring with the concrete materials. Hence, I agreed that children learn best from exploring concrete materials followed by pictorials then being exposed to abstracts representations.

Sunday, 11 August 2013

Elementary Mathematics
Note to parents,                                            

Mathematics runs many of the complicated and seemingly simplistic operations running in our lives. Thus, children are exposed to mathematics as they go about their daily lives exploring and discovering things around them. And since mathematics has become increasingly important in this technological age, it is even more important for our children to learn math in school, as well as at home. The National Council of Teachers of Mathematics (NCTM) has identified the appreciation and enjoyment of mathematics as one of the national goals for mathematics education. This goal, together with the task of nurturing children's confidence in their ability to apply their mathematical knowledge to solve real-life problems, is a challenge facing by every parent today.

There are 5 process standards set by The National Council of Teachers of Mathematics (NCTM). They refer to the mathematical processes through which children should acquire and use mathematical knowledge

The 5 process standards are:
·         Problem Solving
·         Reasoning and Proof
·         Communication
·         Connections
·         Representation

The problem solving standard - children are naturally curious learners. They question, investigate, and explore solutions to problems Children may use different ways to arrive at an answer. You can encourage your child to be a good problem solver by involving him or her in family decision making using math.

The reasoning and proof standard - able to think logically, to notice the similarities and differences about things, making connections between cause and effect and making choices based on those differences. You can encourage your child to explain his or her answers to math problems for examples like where they got the answer, how they get the answer, why do they think that their answer is correct. As you listen, you will get to your child sharing his or her reasoning.

The communication standard - use words, numbers, or mathematical symbols to explain situations. You can help your child learn to communicate mathematically by asking your child to explain a math problem or answer. Ask your child to draw a picture of how he or she arrived at an answer to a problem.

The connections standardMathematics help us to understand the workings of the world around us. Therefore, children can use mathematics to make connections in the cause and effect relationship among the processes in the world. For example, queuing up according to height or separating into groups of threes.

The representation standard – Teachers use mathematical tools like graphs, pie charts or bar charts to explain figures and their relationship with the items they represent. Manipulative is a useful visual representation, thus a concrete objects that are commonly used in teaching mathematics. They include attribute blocks, geometric shapes of different colors and sizes that may be used in classification or patterning tasks, plastic counting cubes for solving simple addition and subtraction equations. Children might use manipulative materials to mold their creativity, transform that model to a drawing on paper to express their thinking. Your may focus on representing numbers with items, pictures or even family members. For example, learning the basics of counting can use pictures of balls to help children recognize that the number represents the items depicted. Teaching through representation or pictures will allow children to make connections between the real world and the math skills that are crucial for academic success.

There are two learning theories which go with how children carry out mathematics. In the constructivism theory, Piaget emphasized self-initiated discovery. Children can construct new concept upon prior knowledge and the new information expands an existing network. Like manipulating the Lego toys where the children can add on the Lego blocks to build a fantastic model. Children can even use old concepts as basic foundations on which they can use to build their ideas and thought processes.

In the sociocultural theory, Vygotsky placed more emphasis on social contributions to the process of development; Children interact with their peers is an effective way of developing skills and strategies. Teachers use cooperative learning movements where less knowledgeable children develop with help from more competent peers - within the zone of proximal development. It demonstrates children learning from their peers, or from their seniors through coaching, asking questions and even playing.