Reflction

Day 6: 31/08/2011

It was the final lesson that we had for our module and Dr. Yeap got us to do something different. One of the activities was to make a trip down to the nearest MRT station (Bras Basah), to measure the height difference between level one and the basement level using a ruler.

What my team did was to use the ruler the measure the height if each step. One step was measured to be about 14cm, which was followed by counting the total number of steps between the two levels. At first, we decided to count the number of steps per flight and multiply it by the number of flights of steps. There were 14 steps per flight and there were 4 flights of steps in total. However, after checking the number of steps between the 2 levels, we decided that we cannot multiply the number of steps by the number of steps per flight because we made a double count in between the flights of stairs which was not the accurate number of steps. So, we decided to count the steps by counting it from the top to the bottom of the staircase. We got 62 steps and multiply it by 14cm to get the height of the stairs to be 868cm. It was an interesting lesson as I’d never thought about doing a lesson on measurement at the MRT station.

The other activities that we did were, making a box small enough to fit exactly 15 kidney beans, and to do a bar chart “How we come to school”. These are interesting too as what amazed me was that all we need is a tiny box to fit 15 kidney beans! The bar chart was also another practical way to teach children about handling data using bar chart.

It was another fruitful day in class as I realized that there teaching mathematics does not have to be boring and it can be done in a fun and meaningful manner as well.

Photos from Day One - Five

Here are some photos that I had taken throughout the class from 22 August - 26 August!

Day 1

Finding the letter for the 99th letter in our names!!! Interesting!

Day 2

Playing pick-up sticks in class!!

Day 3

More word problems to do!

Day 5

Creating our pegs chart!

Day 5

Pages of my notebook: Doing mathematical gynastics! Wow!

Reflection

Day 1: 22/08/2011

It was the first day of class and I went to class with much anticipation, even though I felt a little fatigued after a busy day at work.

After a few minutes when I had arrived at class, the class had started and I was greeted with my first math problem to solve:

How do we know which letter is the 99th letter in Dr. Yeap's name and in each of our name?

It was really a brain teaser for me and it has been a long time since I had to solve such a problem.

I realize that after going through much discussions with my friends and racking my brain for an answer, what Dr. Yeap had done was to get us to use our problem solving and reasoning skills to good use.

We had a fun time solving various mathematical problems in class such as we arranged the polka cards in a way that we can get the respective number card after spelling out the name of the number and putting the card back in the deck simultaneously.

I also learnt that there are different uses of numbers such as ordinal numbers, cardinal numbers and nominal numbers and we had to be aware of how we phrase our questions when ask children mathematical questions.

Day 2: 23/08/2011

On the second day of class, we begin the class by playing pick-up sticks. We had a choice to pick up either one or two sticks from the pile, and the last person to pick up the stick or sticks from the pile, is the winner. I felt that the game was really interesting as it got me thinking, what are the 'bad numbers' of sticks that we would not want to be left with, if I would to win the game.

During the lesson, what really left an impression upon me was when Dr. Yeap mentioned that we should not be confused between teaching children and teaching mathematics. It really got me to become more reflective as we teach children to not just have the conventional understanding of mathematical concepts but also the rationale and conceptual understanding of mathematical concept as well.

And, it is alright to let children make mistake and correct themselves so that they will learn to reason, think and reflect on their problem solving strategies.

The lesson was concluded with the broad goals of problem solving and thinking skills and they are:

1) Generalization

2) Communication

3) Visualization

4) Meta-cognition

5) Number sense

Day 3: 24/08/2011

During the third day of class, we examined two cases of lesson studies where we observed how teachers teach in class in the kindergarten setting.

After making my observations of teachers in the videos, I realized how important it is to always reflect and evaluate upon our teaching strategies and practices. And, we can use lesson study to do research and improve our classroom and teaching strategies.

Factors to consider for teaching and classroom strategies:

1) Sitting arrangement

2) Level of engagement/involvement

3) Use of materials/manipulative

4) Flow/Sequence if lesson

5) Classroom management

6) Communication

7) Questioning techniques

8) Attitudes/Disposition

9) Differentiation (according to ability levels)

Day 4: 25/08/2011

It was the fourth day of class and what I had learnt throughout the modules so far was that doing mathematics is about looking at patterns and how to use the patterns to help us to do problem solving.

The first activity of the day really helped me to see patterns when we are doing problem solving - we had to think of two digits, put the numbers to together  and subtract it from the addition of the two digits - the activity is an amazing example to help us to see the connections between the numbers and its pattern.

In this lesson, we also discussed about learning the algorithm of subtraction and how we represent our mathematical workings; in addition, we learnt that quantities can be continuous or discrete and the concept of part-part-whole as a fractional quantity.

I also least that we have to be aware of the language structure that we use to give instructions to children. We should say " 2 fifths" instead of "2 upon 5".

Day 5: 26/08/2011

On the fifth day of class, we learnt how to do division of fractions and using models to represent that concept. I thought that it was really a meaningful way to start the class by thinking about how we are going to use models to explain division of fraction to children.

The question "3/4 ÷ 1/2 = ____" triggered me to think of how to represent it in model form. At first, I misunderstood it and I got 6/8 as my answer. However, after much discussion in class, I had got the correct answer which is 1 & 1/2!!

I also learnt that in division/grouping, the units are the SAME; while in sharing, the units are NOT the same.

Another math concept that I had learnt was shapes and the different transformation: rotation, translation, shear, and reflection.

We also learnt about area and the correct way of saying units², is "square units".

Tessellation was also a fun activity where we had to find out the areas of the different shapes we had created using the tessellation sheet without using actual measurement.

I felt that it was short but fruitful week of learning mathematics in this module. And, I am looking forward to final class for the module on Wednesday!

Self Introduction

Hello! I'm Joyce Lim, teaching English and Mathematics, in Mee Toh School (Primary). At the same time, I'm also doing my Bachelor of Science in Early Childhood Education (Cohort: Bsc 05). I graduated from Ngee Ann Polytechnic in 2010 and have been working in the childcare sector  for one and a half years before I started to work in my current job as a primary school teacher.

"What sculpture is to a block of marble, education is to the soul." -Joesph Addison

Chapter 2: Exploring what it means to know and do Mathematics

Chapter Review Two

The educational theories mentioned in this chapter are constructivist theory and sociocultural theory.
Jean Piaget's constructivist theory suggested that children or learners "are not blank slated but rather creators of their own learning". Piaget mentioned that when we learn and construct ideas, we are actually creating schema; and such schema can be changed through assimilation and accommodation. Assimilation is the acquiring of new ideas or concepts while accommodation is 'fitting' new ideas to prior ideas to replace existing schema. And, when reflect, we look for ideas that are newly acquired which can be connected to the existing ones.
The other theory that is stated in the chapter is the sociocultural theory, which is the work of Lev Vygotsky. Vygotsky's believe that when learners interact with the people in his environment, especially those who are more knowledgeable; can help the learner to reach his full potential  learning capacity, which is his Zone of Proximal Development (ZPD).
This two theories implies that I, as  an educator, have to help children to build on their prior mathematical concepts by first getting to know what they have already know; and build on their knowledge by introducing new ideas that build on their existing concepts. Using real life mathematical questions, giving children a chance to express their mathematical views and allowing the multiple approaches to solving mathematical problems can help children to build on their concepts and introduce new ideas. It is about helping children to find the connection and relationship between their old and new ideas, thereby creating new concepts to replace existing ones. Furthermore, I am working within the range of their ZPD when I scaffold them through teaching strategies such as questioning, reasoning, explanation; by using manipulative and models to aid them in understanding mathematical concepts.
When I help children to see the connections between the mathematical ideas and concepts, I can help them to understand mathematics relationally. It is an effective way to help children to learn new concepts and procedures as compared to getting children to learn mathematical concepts by rote counting, which is not effective for the long term. Relational understanding also help children to remember less, increased in retention and recall concepts as they see the relationship between such ideas. It also enhanced children in their problem-solving skills as they transfer ideas they had use in one concept and apply it in another. I also strongly believe that when children or learners managed to solve a mathematical problem, they would feel confident and have an improved attitude towards learning of mathematical concepts and a sense of belief and faith in themselves.

Chapter 1: Teaching Mathematics in the era of the NCTM standards

Chapter Review One

After reading the chapter on principles, standards and curriculum for teaching  elementary and middle mathematics.
I agree that all students should have the opportunity to learn mathematics and we can set high expectations for children to achieve (Equity principle).
As teachers, we have to plan coherent classroom strategies that can help children to understand the various concepts on the elementary and middle mathematics (Curriculum Principle).
Being teachers, we have to understand the subject areas that we are teaching well; understand how children's mathematical  development and how they learn mathematics concepts, and choose instructional task and strategies to improve children's learning. (Teaching Principles).
Learning mathematics with understanding is essential, and teachers need to encourage the children to think, reason and solve problems (Learning Principle).
Assessment is also critical in understanding children's learning growth and development. It provides teachers with information on children's mathematical understanding and also to develop lesson and activities to enhance their learning (Assessment Principle).
Living in this age of technology, it is essential to use technology to teach and enrich children's learning.
Teaching mathematics require educator to know the five process standards: problem solving, reasoning and proof, communication, connections, and representation; and have a deep understanding of the curriculum.
Besides knowing the principles, standards and curriculum; teachers also need other characteristics such as perseverance and persistent in not giving up on teaching children. Believing in children and having a positive attitude, adapting to changes are also attributes that an effective teacher should possess.