Dear Dr Yeap,

# Maths or Mad? We, the educators make the difference.

## Thursday, September 30, 2010

## Tuesday, September 28, 2010

### H) Final Thoughts and Impact of this module

With a mind full of curiosity and little idea of what I can do to help children gain a better understanding of mathematics, I began this module. It is always clear to me that mathematics is important in our lives, as we are using it daily, counting money, measuring things etc. But how do we teach mathematics? How do we ‘teach’ a subject that is full of formulas? How can we make the lessons interesting and teach them in a way that children can explore mathematics by themselves? All these combined into a

**BIG**question mark to me. A lot of information and knowledge gained in this module impacted me quite a fair bit. First, I discovered that we should let children decide how they want to come out with their own methods and strategies, in order to solve a problem. (Children learn best and understand better when problems are solved using their own methods.) During our course, I noticed that Dr Yeap did not provide us with any definite answer to the various problem sums he posed. He created and allowed us a learning journey, full of trials and errors. Through this journey, we discovered our own way to computation and we were given opportunities to voice out our thinking.

Dr Yeap has indeed, demonstrated to us, how we should allow the children to explore and find out how to solve sums. This journey once again reminded me, that as an educator, we need to assume the role of a facilitator as well. This is especially so, when we have children who have difficulties in problem solving in the beginning stage. As a facilitator, we should provide them with cues or clues, engaging them through posing questions, leading them to the solution. This process is important as it helps to stir up their thinking and ultimately, they will be able to come up with their own problem solving method(s). More importantly, we need to provide children with time to discover their own learning, instead of fearing that they do not understand the concept being taught and thus, providing them with answers.

As Van De Walle mentioned in the text, “Students need a classroom environment where they can act like mathematicians and explore ideas without trepidation.” (2010, pg 218) What better ways to achieve that, other than learning through play. We played during this module and at the same time, we learnt mathematics. All the magic tricks, cookies given, outdoor experiences, quizzes were conducted in a fun and relaxing way. All those fun helped us to not only learn better but also, being able to retain what was being taught.

Having personally going through such an exciting learning experience during this module, it affirms my belief that children learns through play. As compared to a traditional classroom setting of learning Mathematics, children will definitely benefit much more when they are learning in a playful and relaxing environment.

According to Singapore Primary Mathematics Curriculum (MOE 2006), teaching mathematics should be a vehicle for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualisation, analysis and abstract thought.

As such, our job as an educator is to ensure that children learn the techniques to problem solve and not just the formulas.

Upon the completion of this fruitful module, I have gained a better understanding of what mathematics for children is. My mindset of “Mathematics, a subject with just formulas” has changed to “Mathematics, a subject that can be fun and magical.” I believe that with these valuable knowledge gained and hands- on experiences, I have benefited greatly both personally and professionally. I am definitely looking forward to sharing all that I have learnt with my children, fellow colleagues and most of all, the children’s parents.

## Saturday, September 25, 2010

### G) Geometry

It is essential for us to have good spatial sense, in order to be able to understand Geometry. Sadly, it is something that I lack in. As a result, I do not have confidence while attempting Geometry tasks.

“What is the sum of the interior angles in a pentagon?” Dr Yeap posed.

“Oh my! What is it? How am I to recall and know?” I asked myself, with tons of question marks above my head, literally.

With the drawing of the pentagon I created, I began to turn the paper around, drew different shapes within the pentagon, just to find out what could be the correct answer. After ‘killing’ lots of brain cells, I simply cannot ‘break the code’! It is definitely quite a frustrating experience.

During the discussion of finding the solution, memories of the properties of various shapes (pentagon, parallegram, rhombus, isosceles triangle, etc.) began to slowly but surely came flowing back to me. I cannot say that I remember all of them but as the discussion went on, I began to see ‘light’.

Each of us is unique and therefore, has our individual way of looking and perceiving things, analysing and solving sums. Through the exercise, this became more obvious as we shared our thoughts on getting the answer; result is that the total angle in a pentagon is 540 degrees.

As the discussion proceeds, we had the privilege to listen and understand how each of us feels towards different subject or topic. Another added advantage for me, was it provided me with a better insight of other possible ways to solve a sum, how I can help children to not only solve Mathematical sums but to apply to situations in their daily life.

Chapter 20 mentioned the content goals for geometry included shapes and properties, transformation, location as well as visualization. Understanding geometry means having a good knowledge of these aspects, being able to understand their relations to geometry.

How, then, do we provide children with these understanding?

According to Van Hiele, there are five levels of understanding spatial ideas. As an early childhood educator, it is therefore important to be able to identify which of these five levels of spatial ideas, a child is in. Only with this understanding will we be able to better plan activities according to the child’s level of understanding.

Van De Walle mentioned, “consistent introduction of experiences with shapes and spatial relationships will help children to develop spatial sense” (2010, p. 400). What better ways than to introduce and provide children with different and various kinds of shapes in their daily life, especially through play!

Below are pictures of some activities that we can provide our children with, so as to promote their spatial sense.

1) Puzzle is a good activity to kick-start children’s spatial sense. During the process, a child will have to flip, turn and rotate the puzzle. He/She will also need to identify the curves of the shapes, the sizes of the puzzle piece, in order to get the correct piece.

2) Identifying how various shapes (smaller in size) will be able to fix into a bigger shape. For example, how many triangles are needed to fill up this big square or irregular shape

## Monday, September 20, 2010

### F) Number Sense and common practises

“There were 6 sweets on the table, Tom and Jean each took a sweet. How many sweets were left?”

One child took and counted six uni-fix cubes. He then took away two uni-fix cubes and counts the remaining four.

Another child was seen using his fingers, counting out to six before bending down a finger each time the next number is said until she has four fingers showing.

According to the NCTM standard, “Number sense develops as students understand the size of numbers, develop multiple ways of thinking about and representing numbers, use numbers as referents, and develop accurate perceptions about the effects of operations on numbers” (p.80).

Personally, number sense is not a skill to be taught within a few days. Number sense is a skill that we picked up over time, determined by our individual learning process and understanding. As children’s number sense develop, they will be able to come out with more methods to problem solve. Being unique and different, children will use various strategy to problem solves and it is this learning process which makes solving mathematics exciting and meaningful.

1) Early counting

2) Relationship of more, less and same

3) Rote counting (counting forward and reverse counting)

Some not common practices include:

1) Using calculators to do doubles and near doubles.

2) Anchoring Numbers to 5 and 10

I noticed that in most preschools, mathematics appears to be a neglected subject as not enough time is given to the children to explore and learn. Teachers often find that they are lack of sufficient time for proper teaching and as such, a “touch and go” attitude develops. The group size of the class poses another problem for teachers too. Teachers might find it difficult to ensure all the children understand the topic totally.

In order to extend children’s learning and help them to develop better number sense, teachers must firstly, be able to understand each child’s current number sense. Upon the information gained, teachers then need to address their own teaching and ensure that their children understand mathematical concepts and procedures.

At the same time, it is important for teacher to recognize the various level of number sense each child has and in turn, provide him/her with new insights on problem solving. All these will be achievable, as long as teachers are able to manage their time well and access the children accordingly.

"The seeds (understanding number sense) that we sow in these children will bear fruits when the children are able to identify and problem solve by themselves. "

~Liaw Wanling

## Friday, September 17, 2010

### E) Technology! Is it a necessity or merely a trend?

All these while, I have been relying on my mental abilities to do calculation. It is deemed as the most effective, way back then, to train my mental powers. Since young, I have had a vast of real life learning experiences, use of concrete materials to do counting, using the abacus and real coins. All these were possible because my grandparents owned a stationary shop. I must say that it was a wonderful experience!

Calculator, to me, is just another tool to aid counting. They are not as interesting and enticing as other educational computer games which have detailed graphics and elaborated sound effects. Not forgetting that if an error is made, we can simply laugh at our silliness or carelessness before attempting it again! I wonder how could a calculator helped to inject “better attitudes towards Mathematics”, when there is no interesting graphics or sound effects? Don’t they (calculators) simply contribute to a laid-back personality and seen as counter-productive tool? Pressing the required buttons accordingly will instantly give anyone the answers without breaking a sweat!

It’s amazing how this research has proven me wrong! Woah! It is definitely something new and exciting for me to learn.

Although I agreed with the part from the text which said that calculators could possibly be used as another add-on tool in the process of learning mathematics, but I still have my doubts about how a calculator can bring about drastic changes in a student’s progress, especially counting. Another point which I agree with the text is that it talks about how the student should be able to know when will be the appropriate time to use the calculator. In such a situation, the student should be able to rely on his estimation ability and tackle the problem sum, using the conventional way, ‘paper and pencil’.

Although, I am for the use of Technology, being introduced to students, I think that calculators could be used effectively to suit different kinds of students. The teacher should therefore exercise her discretion when introducing the tool. Having said that, I strongly believe that students should have a firm foundation in their basic understanding of Mathematics, before they attempt to use the calculator. It is important for our students to be able to grasp the basic Mathematics concept. What better ways to grasps these besides replying on our physical method of counting with our fingers and/or concrete material.

I LOVE THEM!! Yes! This was my reaction after having laid my hands at some of the recommended Mathematics websites. This is not something that I (someone who loathe Maths, in any form) would enjoy doing but I got HOOKED on them. I personally enjoyed the website called “The Math Forum” at http://mathforum.org. The website posed as a platform for discussions on topics pertaining to Mathematics concepts and there were a variety of links to other websites, providing more choices.

Upon completion of the chapter, I do not deny the fact that using of Technology has its pro and con. However, the calculator is more of an essential tool, rather than a ‘must-have’ tool in our daily lives.

## Wednesday, September 15, 2010

### D) Place Value Sequencing

Today’s session was on Place Value. We were asked by Dr Yeap this question: “If you are asked to teach children on Place Value, how would you sequence the five learning tasks mention below? Which order would you teach first using concrete materials and why?” Well this is my take on the above question.

So what IS an appropriate sequence?

2. Expanded Notation

3. Number in Numerals

4. Number in Words

5. Tens and Ones notation

Personally, I will put the sequence as below:

**Step 1: Number in Numerals (34)**

Number in numerals can be seen everywhere and is more related to children. Children start with rote counting before they were even introduced to numbers in general. I chose this option as my priority because this method is apparently more familiar to children and therefore should be easier to introduce. As for the concrete materials and resources to aid my teaching, I would use ice-cream sticks. I would get the children to count the ice-cream sticks physically (the rote counting way) and introduce the way of writing down the particular number at the same time. This way, the children would be able to relate.

**Step 2: Tens and Ones notation**

I will next teach children the tens and ones notation using ice-cream sticks again. I will paint to represent 3 sticks in one color to indicate the value ten and 4 sticks in another color to represent the value one.

**Step 3 : Place value chart**

Next, I will introduce the place value chart to the children. I will explain to the children

why different numbers belong to different columns for eg the number ‘3’ should beplaced under the ‘tens’ column and number ‘4’ will be placed under the ‘ones’ column in the Place Value Chart, according to the value of these numbers.

**Step 4: Expanded Notation**

After knowing the place value of 34, I will go on and introduce the fourth step which is expanded notation. At this point, we could fairly explain to the children that 3 tens is actually equivalent to 30 and 4 ones is equal to the value 4. Thus when we add them

together, the new value is now 34.

**Step 5: Number in Words**

By then, the children would have familiarized themselves with place value and word numbers. The final step would be to teach them numbers in the form of words. Children would find this step a little harder to conserve as it involves spelling and learning to read these words. And even after that, the children still need to relate the number figures with the words accordingly, therefore this process might take a little longer to master.

## Wednesday, September 8, 2010

### C) Problem solving and Environment task

**PROBLEM SOLVING.**

Hmm…What goes through your mind when you hear these words?

Trying to figure how things work?

Coming out with a formula to “break the code”?

What does it mean to you?

When comes to problem-solving , I for one believe in trying and exploring different ways and means to come out with a solution for a problem. They may perhaps involve some guessing techniques, applying some trial and error concepts and of course more often than not, we need a little bit of luck too as we go along (if we are lucky enough, the problem could be solved almost immediately). I feel there isn’t one exact approach or calculated formulas to problem solving. Different people have their own personal views and opinions in tackling problems and some even embark on “tricks” or favourite techniques while trying to approach a problem. Whatever the methods may be, the objective still remains the same; they are all part of a problem-solving process.

We were given the task of developing a mathematics activity outdoor which could stir up the children’s problem solving skills. So how could we make this outdoor experience an educated and intriguing one? Our group decided to teach children the use of measurement using non-standard units. The venue for the activity:

**the Singapore Arts Museum!**Attached are some of the photographs we took as we decided on the questions we could pose for the children as well as designing some of the activities the children could do outdoor with regards to the concepts that we introduced.

Michelle and I are seen here trying to measure the length of the wall with our arms.

We had fun experimenting and predicting the reactions the children might encounter during those activities.

The 4 steps in problem solving process as described by Polya are :

**1. Understanding the problem**

**2. Devising a plan**

**3. Carrying out the plan**

**4. Looking back (or reflect)**

So in our situation children might go through this process :

**1. Understanding the problem.**

Children need to identify the given problem, for eg what can they use to measure the length of the wall?

**2. Devising a plan.**

The children have to come out with a system or plan of how to go about measuring the wall.

**3. Carrying out the plan.**

Here at this juncture, the children will have already prepared themselves to implement the plan.

**4. Looking back.**

Reflecting on their decisions and implementation of the plan is done at this point. They will have to conclude whether their plan was suitable and appropriate for the task given. Is there room for improvement or are there some loose-ends that needed to be tightened.

Below are some pictures of our centre kids tackling the measuring tasks given to them. Our centre (PCF Punggol East Blk 124A) was involved in the activities called

**‘Mathematics****Beyond the Classroom Environment’.**Child A: How many children are needed to go round this huge ring? Child B: Maybe 11? |

Child A: This bench has nice pattern Child B: And it is 9 adult hand spans long |

The children already have some prior knowledge and experiences indoor with regards to using non standard units of measurement. We extended this prior knowledge by engaging them in outdoor problem-solving tasks or activities. The entire learning process was very encouraging and we saw awesome results manifested itself in the thinking skills, teamwork and peer discussions among the children while trying to solve some of the measuring issues surrounding the tasks at hand.

We found that developing environmental awareness through numeracy activities helps the children to link information together in a natural and relevant context. The natural resources found in the outdoor space support children’s learning. It cost less or no cost at all when comes to the resources required to teach outdoor.

On a final note, I would like to close with a quote :

**“Outdoor learning sustains children’s interest through hands-on activities. The space for exploration is enticing. Children brainstorm and problem solve when facing challenges and the autonomy to decide the materials and ways to problem solve empower the children throughout the learning process”.**

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