6th April 2013
EDU 330 Math (Day 6 )

Today was the last day of the module. We did review of previous lessons, differentiated instructions and graphic activity . Differentiated instructions is an interesting topic as we needed to look for the less probable  answer.
Creating a good lesson plan for conducting Math lesson requires the teacher to understand the What's, How  and What ifs.
Just like teaching English lesson, we introduce the KWL(Know-Want to Know- Learned) strategy in learning.
Likewise in Maths, the teachers planning an activity has to ask herself questions on what outcome she wants from the Math activity she conducts. In the lesson planning she will need to consider:
1. What I want students to learn?
    - The goal
2. How do I know?
    - They have learnt (assessment)
3. What if they can't?
    - To use concrete materials to explain
4. What if they can ?
    -  They do themselves


The most valuable lessons I am taking away from this module (apart for the maths activities practice) are the ideas of CPA approach and the 3 stages of teaching children.

The CPA (concrete-pictorial-abstract). The different stages of learning are concrete approach; through providing objects as manipulative; are necessary to help child with solving problems, items such as unifix, cubes and etc.
The next step of learning would be to use pictorial; the model method .This helps child understand word problem better and covers other types of maths learning such as ratio, average etc.
The abstract approach is applicable to primary level using symbolic representation such as  numbers, letters.

There are 3 stages of teaching children:
- Stage 1 - modelling
- Stage 2 - scaffolding-  this will be removed when the child is independent
- Stage 3 -   When they do themselves- providing enrichment if child is able to advance learning.
To achieve all this, children need to work in a stimulating environment.

We presented Mr.Yeap with a parting gift of a bottle of cookies with a problem sum, which I thought was ingenious of the planner. We ended up solving the problem together.  Finally the class ended with a Math quiz... sigh...

Today I leave the classroom enriched with new ideas of teaching young children Maths. Back then,If only my teacher was supportive when teaching Maths, I would have had a love for Maths at an early age. For sure  I will see to it that the children are not deprive of this learning experience.

THANKS MR YEAP!!

5/4/2013
EDU 330 Maths (Day 5)

Throughout all the lessons, Mr Yeap  was constantly emphasizing the importance of using the correct words or phrases when giving instructions to young children. He mentioned that the Kindergarten 2 child must be able to work with 1 noun. e.g. the child needs to understand that 10 is referred to 10 one's. That it is not the size of number but the understanding of the value. I found out today that the connecting cubes are good materials to use for young children when learning about counting in 10's.

As teachers we need to enrich the children learning instead of accelerating  their learning. These children need to improve on their social, language and psychomotor skills to help them in their Primary One learning.

Dienes theory of variability teaches us when we choose materials to teach children we have to be careful; this  refers to the numerosity or cardinality and the choice of material is important. He suggest that children should learn with different variables e.g colours, shapes.

The interesting lesson I felt was for the day was learning about area of polygon. Many of them have their idea of ways to find the area of polygon e,g, cutting it up(which was quite hard to see), cut and paste, finding half of a rectangle and subtracting way.
A good formula I have learnt is  :

A=x + y/2 - 1
A=x + 4/2 - 1
A=x + 1
y= number of dots on the sides ( when we were finding the area of polygon)

Algebra has always been my weakest topic. I  need to practice more to understand it clearer.

4th  April 2013
EDU Maths- Day 4

Today we started out our discussion with the understanding of assimilation and accommodation. Theory by Jean Piaget of about developing children's intellectual capacity.
From my understanding; through assimilation, we take in new information and incorporate them into our existing ideas, as for an example; a child sees a different type of monkey that she has never seen before and calls it a monkey. Here the child is adding information to the existing schema.
However, if that child is able to  completely change her existing beliefs, then it is called accommodation.  This learning process applies to not only children but to adults too.

Our study on Fraction and in any mathematical subject requires us to understand that our children should be taught  through the CPA approach . Only through concrete practice, pictorial experiences and later on abstract approach can children comprehend the logic thinking of any concepts.  As what we did in class , by taking a piece of paper and folding it into 8's and having to figure out how many 8's in 5/8  and how many 3/8's were there in 1/2 was challenging. 
What I learnt in school, years ago back then and now is so different.  We convert and simplify before working out the sum. 
The tips below helps not only teachers but parents as well on how to help child learn fractions the fun and concrete way.

Teaching fractions to your child

You can guide your child through the process of learning fractions. Use these tips to help answer questions they might have about fractions:

• think about sharing equally
• the numerator is the number of the top
• the denominator is the number of the bottom (memory tip: d is for denominator, d is for down – at the bottom
• Like with all math, experiencing the concept is the best for learning. Use objects and share them. Pizza is always popular.
• Discuss fractions with your child whenever you come across a “real life” example. Sporting events, newspaper articles and hardware stores are all good sources.
• Review the methods for adding, multiplying and dividing fractions yourself.

(http://www.helpingwithmath.com/by_subject/fractions/fra_teaching_fractions.htm)

EDU Maths -3/4/2013 (Day Three)

Today's first topic of discussion have me thinking about how we look at teaching  Maths  through nursery rhymes. Interesting as it may seem there are many concepts we can teach the children with  simple rhymes. Concepts such as height, measurement, classification ,counting and problem solving.

Teaching children in preschool have to be revise in order to help the children understand and learn basic concepts of Maths before they progress to  higher level thinking. It not only starts with the school curriculum and teachers, but home learning as well. We will need to provide the children a balanced learning programme so that they could progressively work on their skills in any subjects.

There are  things that children need to know before going  to primary school. They are daily language; instructional language, where children follows teachers instructions. The other is visualization. They need to have strong grounding in visual literacy, fine motor skills, physical activities or concrete thinking. All these are vital in the development of early years.  As preschool teachers we need to teach only pre numeracy skills. e.g. counting, sorting one-to-one etc.

2nd April 2013
EDU 330 (Maths)- Day Two

Today lesson covers on the use of numbers, counting and addition. Two  rather interesting activities were conducted. The first was to figure out the numbers of paper clips in 5 similar sized cans. Here the idea was for us to estimate the numbers of paper clips in each can. During break time, we had opportunity to shake the bottle to figure out how many clips there were in each bottle. An additional bottle with the number 3(benchmark) was placed together. My group members and I took turns to shake the bottles, using the labelled can 3 as a benchmark. We work out that :

Which Can?          How many clips?
      C                             Nil
      E                               1
      A                               2
benchmark                      3
      B                               4
      D                               5


I learnt that when giving children instructions in maths, we need to be careful how we  use the correct terms with them. Bruner has mentioned, children learns best when there is concrete experiences. Using real objects helps to illustrate the concept to children better.

The other activities we did was to solve a problem sum; 8 + 6. We had a card (with frame drawn) and some beans. We hade to think of many possible ways to add the two numbers. There was three ways of solving the problem. They are part/whole , word/ noun used and before/after problem.


For subtraction of numbers such as 14-9, there are several ways we can show children how to solve the problem . Firstly by doing:

-the bridging-by subtracting a small number from another number e.g. subtract to the nearest 10 and then subtract the remaining part e.g. 14-9 = 14-5-4 =10-4 = 5

-Counting back/forth- best done visually. We could use a number line to do the counting.

-Compensation effect- when the number taking away is close to the round number usually '10' e.g
   10-9  use 14-10 and then add back 1 to give  4 + 1 = 5 (the answer).

-Formal and Informal method-When we subtract by  'borrowing' from the tenths or counting with our fingers or using concrete objects. Which would be most appropriate for young children.

1st April 2013- EDU 330 Maths (Day One )


Today was the first day of our Maths class...I didn't know what to expect from our lecturer. I thought it was going to be a tough day for me ... fortunately.. it turn out well.

We when through:

     4 stages of carrying out instructions in Maths, as teachers we are to:
     * Teach children by modelling
     * Scaffold child's learning ( we prompt them by asking questions)
     *Provide children opportunity to solve the problems (if they cant, we can ask questions to prompt
       thinking and / or by modelling
     * Explaining (last stage of teaching)
       

Children learn by the CPA Approach. Which is through concrete, pictorial and abstract. Bruner theory emphasis that in learning anything abstract we need to do concrete learning first before going to visual(visual become important for understanding) and to learn the abstract ideas.

We had two interesting activities:
- Finding out which letters is our name is at number 99. This activity teaches us about various patterns we can use in counting and coming up with an answer. Almost everyone had the same answer.

- The other activity was a card 'trick'. This activity requires the use of mathematical language, spelling ,positioning of cards so that the stack of cards forms into a correct order of 1-10. It was interesting however a little challenging

I must confess that I will need to read more on terms such as cardinal, ordinal , rational, nominal to understand it better.

Chapter 1

Mathematics is one of the core subject taught in schools. The emphasis and pressure in teaching and

learning Maths falls on both teacher and student alike.

 

The Principles and Standard for School Maths  (NCTM) created six principles to guide teachers as they work towards continual improvement of educating Maths in class and to improve the educational system. The NCTM recognises the importance of including Pre K into the framework. This confirm the importance and value of Maths instructions for young children.

 

Out of the five content standard stated in Chapter 1, numbers and operations, Geometry and Measurement are said to be the most important for creating a strong foundation in Maths for the Pre K. It helps nurture Mathematical thinking skills.

 

We as teachers have to upgrade our knowledge of Mathematics content to better help the children. As far as I know understanding or 'learning' Maths is all about practice ,practice and more practice! To become a efficient teacher in this subject requires one to be persistent in way we demonstrate to student, have positive attitude, a readiness to change and reflect on our teaching and learning as an on going process.

 

To help students achieve their learning goals in Maths we need to consider two important factors that are necessary, that would be to provide an environment that is inviting, create challenges, attract children interest, provide opportunity to them to question their thinking and knowledge of the subject matter. To further enhance learning, integrating technology (IT) plays a vital role in this modern age of learning.

 

My experience in learning Maths in school was unpleasant. My Maths teacher was not supportive. She always chided me for not getting my answers right. She would 'drill me to the ground' with Maths homework, because I was poor in this subject. It was a frustrating experience. I have missed out so much. I believe the teacher and the learning environment play a crucial role in cultivating the interest in  learning Maths. And the love for learning Maths should start from young. I was not that fortunate, however I will like to ensure that the children under my charge will learn to love Maths before entering Primary school.

This video shows exactly how confused I was when learning Maths in school!.. Its so funny that I needed to share with you.

 

 

 

Chapter 2

 

Doing Mathematics takes time and effort. Basic facts such as computation of whole number, fraction, decimals are necessary for children to understand in able to do Maths. The fact remains that children should not be taught to memorize the facts and procedures of Maths. Children should be given opportunity to explore and learn before practicing. Teachers need to allow children to learn by doing, interacting and explaining. Children need to be taught to make decision of their own and that the teacher should scaffold to help children develop higher thinking.

 

Using terms such as compare, explain, develop etc.in the classroom  helps them to become active thinkers about the mathematical ideas that are involved.

 

Providing an appropriate  environment to learn Maths is necessary to help children concentrate, listen, share ideas and connect to Maths concepts and to the real world.

 

Children learning Maths helps them to fit new concepts to their prior knowledge and the teachers role is to ask probing questions that will keep children engaged until they derive with an answer.

Generally, children will definitely benefit from learning Maths as it develops their knowledge on various concept. With regular practice their ability to recall ways of solving problems or finding solution is not overwhelming for them. They are able to 'workout' the problem to find solution.

Thus with constant practice , children will eventually develop a positive attitude and confidence in understanding and learning Maths.