Flipping through the textbook, one can find a whole chunk of online resources at the end of every chapter. I have tried some of the online resources and I found myself hooked to exploring almost every single one. If the online resources could engage an adult like me, I think they could help a lot in teaching Mathematics to the children who are used to having things digitalized and the children who are used to using the mouse and touch screens. Rather than doing meaningless worksheets, I think the children would enjoy the interactive nature of these online resources. Some of the resources also pose challenges to the children and I think that they will have a lot of fun learning Mathematics while racing against the cartoon character on their screen.

However, in my opinion, I still think nothing is better than having the concrete-pictorial-abstract approach in teaching Mathematics. Also nothing beats having a teacher who is there to guide and facilitate, who also gives high-fives and praises when the child has done something right and who gives encouragement and motivation when a child hasn't reached the objective yet. Hence, I feel that technology can be used in teaching Mathematics but only to a certain extent.

# Nurul 'Ain Kamil

## Monday, 23 July 2012

## Saturday, 21 July 2012

### 3 things I have learnt and 2 questions that I have

3 things I have learnt:

1. Use the correct language so that we will not cause misconception in the children..

2. Children must know what can be counted and what cannot be counted.

3. A square is a rectangle but a rectangle is not a square.

2 questions I have:

1. Why does MCYS use the term 'teacher:child ratio' when teachers and children are not the same?

2. I haven't thought of a question yet..

1. Use the correct language so that we will not cause misconception in the children..

2. Children must know what can be counted and what cannot be counted.

3. A square is a rectangle but a rectangle is not a square.

2 questions I have:

1. Why does MCYS use the term 'teacher:child ratio' when teachers and children are not the same?

2. I haven't thought of a question yet..

### One thing that surprised me during the lesson

One thing that surprised silly me during the lesson was that I found out that I can't really solve fractions pictorially. First, I never learned how to do Math pictorially anyway. Second, I realized that no matter how big the diagrams I drew were or how big I opened up my eyes, I still could not see the solution to the problem. Solving fractions using the methods I have learned in school did not take a lot of my time and a lot of my brain power because I could do it well and I did not have to see any reason behind it. But now, I see the importance of seeing the reason behind things and I realize that drilling methods into the children's minds would not work because they need to have the concrete and pictorial experiences first.

### Chapter 10

As I was reading through our wonderful textbook, I found something that really caught my attention and that was the whole of chapter 10. For a person who does not know most of the basic facts in Mathematics, I found the chapter most helpful not only for the children but for myself as well. Of course before this, I have never known that there were 'Big Ideas' in Mathematics or we could make 'Mathematics Content Connections'. This chapter would help me out a lot because I do not want the children to learn the same way I did when I was in school. Using the strategies in the chapter would be so much better than forcing the children to listen and just accept what I say.

### Interesting and inspirational (to me at least)

Two things that I found interesting that is related to the teaching of Mathematics to young children is that

1) The way the teacher puts the question across to the children is very important

2) Forcing things down the children's throats is not right

Let me explain...

1) The way the teacher puts the question across to the children is very important.

I've been doing a lot of reflecting lately and I have realized that sometimes, the children don't quite understand what I'm asking and I remember not understanding questions as a child. Through these past few days, I've finally made the connection between language and Math. I know now that if I do not equip the children with enough vocabulary to understand and that if I do not use proper, simpler and understandable terms to get my question across to the children, the children in my class will end up not learning anything.

2) Forcing things down the children's throats is not right

I've personally been through this and I tell you, the one who comes out as the loser is the teacher. I went to school when learning was still torturous, everything was drilled and nobody dared to ask why. I remembered closing my eyes and reciting multiplication tables and formulas at night so that I would be ready when my teacher would ask me to regurgitate them the next morning. Sadly, this went on for nearly 13 years, all the way from kindergarten right up to JC2. The only thing was as I grew older, I developed the habit of writing down all the formulas that I knew right onto my exam paper as soon as I got it. This unhealthy habit of 'unloading' onto my paper actually helped me to forget all of the formulas and other things that I have learned prior to my examinations. Also thanks to this as an adult, I have totally forgotten everything that I have learned in school. The reason why I mentioned that the one who comes out as the loser is the teacher is because I found myself cursing at all my Math teachers (except for my Sec 4 one because he was nice) throughout the whole week for making my life hell and for screwing up my Math learning. They are also the losers because in my eyes right now, they were ignorant and silly thinking we all could learn by scaring us into remembering things.

So my point is, if only I was taught to visualize and see the reason and rationale behind certain Math concepts, perhaps Math lessons in school would not have been so bad and I would probably still remember some of what has been taught to me because I would know the reason why this is this and that is that. Hence, forcing things down the children's throats is so so not right.

## Saturday, 14 July 2012

### Reflection on chapter 2

'Doing mathematics means generating strategies for solving problem, applying those approaches, seeing if they lead to solutions, and checking to see whether your answers make sense (Van de Walle)' was the quote from the textbook that struck out to me while I was reading the second chapter. This is because I feel that as a student, I did mathematics only to get the right answers and get good grades. This led to me turning into a teacher who taught children to do mathematics to get the right answers and to get good grades. I know now that this should not be the case and I should change my perspective and my objectives when teaching math in my classroom. The quote made me see that doing math and doing a literacy-based lesson is similar because both lead to solutions and the person who solves the problem has to check whether the answer makes sense.

I do agree that an appropriate classroom environment is essential when teaching math. I believe that no learning will happen in a classroom where the teacher makes math a chore and where hands-on learning and investigation are not encouraged. The list given on page 14 of the text will help me in ensuring that my classroom is always ready for learning and is always ready for mathematics. I also agree with the part where it said that students should be engaged in a little productive struggle. This is because the children in my class love investigating to find out about things and they always like to do things on their own. A large majority of them will encounter setbacks but they are able to pick themselves up and try to find the answers on their own again. The reactions that they give when they solve a problem on their own or when they find out something new by themselves is priceless and they tend to remember their experience compared to when I teach them something in a lesson where they just have to look and listen to me. I feel that being in a productive struggle somehow makes the lesson more meaningful and the concept that is being taught really stays with the individual.

As a teacher, I am still trying to break out of the habit of asking the children to 'do it as I do'. I hate having to succumb to that feeling whereby I feel like I have no choice but teach in a certain way and it's faster and less of a hassle if the children just follow me. I want to learn how I can make mathematics fun for both the children in my class and for myself. I guess a big mindset change would do me a lot of good.

I do agree that an appropriate classroom environment is essential when teaching math. I believe that no learning will happen in a classroom where the teacher makes math a chore and where hands-on learning and investigation are not encouraged. The list given on page 14 of the text will help me in ensuring that my classroom is always ready for learning and is always ready for mathematics. I also agree with the part where it said that students should be engaged in a little productive struggle. This is because the children in my class love investigating to find out about things and they always like to do things on their own. A large majority of them will encounter setbacks but they are able to pick themselves up and try to find the answers on their own again. The reactions that they give when they solve a problem on their own or when they find out something new by themselves is priceless and they tend to remember their experience compared to when I teach them something in a lesson where they just have to look and listen to me. I feel that being in a productive struggle somehow makes the lesson more meaningful and the concept that is being taught really stays with the individual.

As a teacher, I am still trying to break out of the habit of asking the children to 'do it as I do'. I hate having to succumb to that feeling whereby I feel like I have no choice but teach in a certain way and it's faster and less of a hassle if the children just follow me. I want to learn how I can make mathematics fun for both the children in my class and for myself. I guess a big mindset change would do me a lot of good.

### Reflection of Chapter 1

As a person who struggled with Math my whole life, I found it a chore to even start doing this assignment. However, I saw this sentence in the textbook and it made me realise a few things. The sentence was, 'Those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures' (NCTM, 2000). The first thing I realised was that even though I struggled with Math, I never did badly during my examinations or during daily assignments because I found that once I saw the rationale behind a concept, I could start to do things on my own. The second thing I realised was that since I am in the field of giving opportunities and preparing children to face the world, I would really want them to have, like what the sentence says, enhanced opportunities and options for shaping their futures.

The text states that teacher's knowledge of Mathematics and how students learn Mathematics are important tools that can be acquired to be an effective teacher of Mathematics. I strongly agree with this because if the teacher had a shallow knowledge of Mathematics and when the teacher is not aware on how the children in the classroom learn, then no learning will be done. Wrong information will be taught and there would be a high chance that the children will be disengaged from the lesson within minutes. I feel that presently, given the national standards and curriculum guides that us teachers have to follow, we cannot afford to have the children not being engaged during Math lessons. Hence, I hope to learn to be a better Math teacher during the course.

From this chapter, I feel that I appreciated the 'Principle and Standards for School Mathematics' part in the textbook the most. This is because I could use it as a reminder for myself on how I should be as a teacher. My centre practices a Science-based curriculum and the curriculum is also very much inclined towards literacy. Hence, I would like to know how I could tune these principles and standards to fit the Math aspect of my teaching. Honestly, I follow whatever that is given to me by the curriculum department very strictly and I realise that the Math curriculum that the children are going through now is very different from the Math curriculum that I went through in Kindergarten. The biggest challenge for me now, I feel, is that I have to overcome what I previously know about teaching Math and to make myself focus on 'mathematical thinking and reasoning (NCTM, 2009)' rather than just spoon feeding answers.

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