Saturday, April 6, 2013

Thank You!

Thank you Dr Yeap. It's been an enriching, stimulating and wonderful experience learning from you. See you in July!

Reflection Day 6

When planning a lesson, always consider these questions:
  • What do I want the students to learn?
  • How do I know that the children undeerstand what is being taught?
  • What if they can't understand?
  • What if they already can understand?
Dr Yeap also shared that there are different stages of instructions when teaching mathematical concepts. These instructions are similar to how we apply in our daily integrated lesson plans.

The instructions are:
  • Demonstration
  • Scaffold
During scaffoling, there are also things we should consider. If the child is unable to understand, then we move back to stage one which is demonstrate. If the child is able to understand, teacher can further extend their learning by moving to enrichment.

From the video that Dr Yeap shared, some children are able to see the pattern that the combination of the last 2 digits are 9. Whereas some are not able to see it. The learning goals of the lesson itself is about subtraction within 100, and therefore, it doesn't matter if the class gets to the the pattern in the equation.

Earlier today, Dr Yeap asked "What is the value of having such slow students in the group?" ( referring to the video shown). In the group, the child is able to learn from her peers and feek encouraged to do better.

On another note, having slower students in the group, it can be challenging for the teacher. But it also helps the teacher to see in the perspective of the child and work on giving simple individualized instruction for the child itself. It also helps teacher to track the pace of learning of different group of child.  I personally feel that teaching a slower paced child could be rewarding as well, because no matter how little improvement the child made, an improvement is still an improvement and it should be something that the child should be proud of.

Reflection Day 5

Visualisation, number sense, pattern, communication and metacognition.

These are the 5 essential components that children need when doing numeracy.

In the previous reflection entry, I mentioned about how visualisation plays a role in helping students to solve mathematical problem. For younger age group, concrete objects need to be used in the teaching.

Whereas for an older age group, we can use visual representation. The reason is that visual representation are more abstract, and children of an older age group would be able to visualise something more abstract.

During the lecture, Dr Yeap mentioned that when using visuals, the items must be identical. We should also avoid interfering variables such as long and short sticks, big and small circles. Because when we mention 'big cirlce', a child may have seen a bigger circle and it can be confusing for the child.

From the video that Dr Yeap shared, it is clearly shown how he taps on children's knowledge on number sense and focuses alot on communication.  This is clearly supported by Vygotsky's sociocultural theory, where it mentioned that mental development arises as a consequence of interaction.

Reflection Day 4

The lesson today was about multiplication. When it comes to multiplication, it is important to use concrete objects for representation especially when teaching young children. As the child progresses, we can move on to visual representation by carefully removing the concrete objects.


Using concrete object of showing 2 groups of 3 by using apples in a basket.

Using visual representation.

Grouping is one form of multiplication. Multiplication is basically not about about memorising the numbers but, about understanding the concept.

Another part of the lesson was subtracting fractions. Using models, it is amazing how there are actually many different ways to get the answer. Back then when I was in primary school, the only way I subtract fractions is by changing the denominator, without understand why I have to do so.

 3 ½ - ¾ =

 I find that using models, I am able to discover different strategies on my own. I also think that its alot more faster to solve a question using models.

Reflections Day 3

So today, we talked about fractions concept.

Do you know that fractions and time are not supposed to be taught in pre-school? Yes, I wasn't actually aware of that. However, to my understanding, we are allowed to teach these 2 concepts not explicitly but as a preparation for them when these topics are introduced in primary.

For example, the concept of time can be introduced as they are able to make meaning from the concept by relating it to their daily routines in school. As for fractions,the concept itself can be introduced to children when we conduct an activity which requires them to divide something into equal  parts, such as folding a paper.

 Talking about folding a paper into 4 equal parts, that is exactly what  we did in class today!

Even though its a simple activity, but as adults, the activity keeps me engaged and it stimulates me to think of different ways how I can fold the paper into  4 equal parts. It is one way of introducing fractions to children.

Tuesday, April 2, 2013

Reflection Day 2

So... today's lesson was interesting.

We learnt about addition stories. First, Dr Yeap got showed us two numbers 8 and 6. In groups, he then asked us to come up with our own addition stories. Well, my initial though when was asked to do this was " Hey, that sounds easy. What could be so difficult in coming up addition stories using 8 and 6 right?"

But surprise surprise. There's more to it than just using the two number to come up with additions stories. So today, I learnt that there are actually different types of addition stories. I meant, I have never really thought of it. Back then in primary school, I thought that it must have been a breeze for my teachers to come up with additions stories for us to do during exams. Hehe.

So back to the actual topic, there are 3 types of addition stories and they are:
  • Part whole problem
eg: Jolene has 8 sweets. Trace has 6 sweets. How many sweets do they have altogether.
  • Classic before after 
eg: Lila has 8 pencils. Shanti gives her 6 more pencils. How many pencils does Lila have now?
  • Comparison
eg: I have $8. You have $6 more than me.

Another takeaway that I learnt from today's lecture is the importance of the sentence structure when we construct and write our addition stories. From the group work, unintentially, some of us arrange our sentence in a way that can be questionable. It won't be a good question then, because the children will then have to work and answer the questions based on assumptions.

With that, I end this blog entry with a quote by Meister Eckhart.

 "Be willing to be a beginner every single morning."

Reflection Day 1

From today’s lecture, I learnt that there is no definite way to solve a mathematics question.

I enjoy solving  different types of mathematics problem that was asked during the lecture. My favourite question has got to be using the number cards, spell out the number words as we flipped the cards. Me and my partner was so engaged and excited throughout the process we were solving the problem. I would definitely like to try the activity my children and I am sure it will keep them engaged too. 

In some mathematics problem, I realised that there are times where you can do trial and error method. But in this problem, it wasn't easy to do the trial and method. Therefore, me and my partner discussed some strategies and we applied them to solve

What are the strategies we used to solve the problem?

  • figure out the spelling of each number words. ( if we're using 8 cards, hence we need to know the spelling of the number words from one to eight.)
  • count from the left, in cardinal order

Ordinal, cardinal, rational and nominal numbers. Understanding the meaning of these numbers can be quite confusing. I shall go and read up the textbook and my notes to have a better understanding of these numbers.

Sunday, March 31, 2013

Chapter 2

Mathematics requires effort. One need to generate strategies, apply the approaches, see if it leads to solutions and check it the answers make sense. Somehow, I feel that trial and error method can be applicable too in mathematics.

Jean Piaget believed that learners construct their own learning. And to construct or build something, one requires tools, materials and effort. Here are some concrete mateirals that children can work with when exploring mathematical concepts. Alternatively, teacher can also come up with tteir own teacher made materials.

Listening, copying, memorizing, drilling and compute are lower thinking activities that do not adequately prepare students for real act of doing mathematics. The environment setup plays a very important role. It should be inviting and ample opportunities are provided which allows children to be actively engaged and explore with materials. Teachers also play a role as facilitator to scaffold children’s learning.

Above all, there are benefits of developing mathematical proficiency in children. Some benefits to mathematical proficiency are enhancing problem solving abilities, improved attitudes and beliefs, increased in memory to retrieve information and connect concept to entire web of ideas.

Saturday, March 30, 2013

Chapter 1

As educators, we play a very important role in educating young children. Mathematics, is also considered is as important as any other subjects. Because mathematics education has been undergoing a steady change over the years, our knowledge of mathematics and how students learn mathematics are the most important tools we could acquire to be an effective teacher of mathematics. 

Personally, I wasn’t very good in mathematics. And because of this weakness, I learn to hate the subject. But lucky for me, becoming a teacher, I can’t seem to hate that subject for long. I feel that if I  want the children under my care to love mathematics, I as a teacher should love the subject itself first. Only then I will be able to make the lesson interesting so they can understand and grasp the concepts taught.

Out of the Five Content Standards, number and operations is the most heavily emphasized strand from pre-K through grade 5. Only in grade 9-12 then it will be given a lesser emphasis on the content. Therefore, I personally feel that it is important that children have strong foundation knowledge in number and operations.

This is the reason why having a strong foundation knowledge in number and operations is important.

Following that, this chapter also mentions the Five Process Standards, which are:

·         Problem Solving

·         Reasoning and Proof

·         Communication

·         Connections

·         Representation

The standards direct the methods of doing all mathematics. Personally, I feel that problem solving is achievable to adults as well as children. On the other hand, reasoning and proof may be more challenging to acquire. It not only requires one to recognize reasoning but also to develop and evaluate mathematical arguments and proof and investigate mathematical conjectures.

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.

 -John Kemeny