Session 6: Teaching or Learning?

Some pointers I took note of during this session:

1. Never focus on teaching. Focus on the learning!

2. Ask yourself these questions – What do I want my children to learn? How do I know? What if they can’t? What if they already can?

When I thought back, I started to reflect and realized that I have always focused on what I want to teach to my children. But have I really bothered about those who were unable to understand my lessons? What have I done to make those children understand? How important is it for me to ensure that every single student in my class know what I am teaching? What are the changes that can be done to help my children learn better? I think I have not done enough for my children with regards to thins matter. Not too late to make this change I hope!

 

Advertisements

Session 5: More about Shapes and Numbers

photo[1]

Yet another interesting exercise that I truly enjoyed doing. Given the numbers 1, 2, 3, 4, 5, how many different ways will you be able to place these numbers in the boxes, ensuring that they add up equally for both directions? Which number would you choose to put in the middle box? Is it an odd number or an even number? Does it matter? It felt great when I was able to solve this problem. So I challenged myself and tried the numbers 51, 52, 53, 54, 55. It was such a wonderful feeling when you knew you got the hang of it! πŸ™‚

Dr Yeap also mentioned about Dienes Mathematical Variability Principle; in the sense that you have to take into consideration when you are making a choice to include variables for your children. Variables or rather materials need not be identical. When you give children identical materials, children will get the wrong idea that only identical variables can be counted, which is not true. Therefore avoid interfering variable! πŸ™‚

Can you find out which of the things in this world are bundled up in tens? If you know the answers, please let me know! πŸ™‚

Session 3: Four Equal Parts

I enjoyed today’s session so much because I love doing problems about shapes, finding the area and such. I have always loved doing Geometry since I first learnt about it. πŸ™‚

I was amazed to find out how wonderful Mathematics really is; that we are able to come up with certain formulas just by “experimenting” if this way works or that way works and finding out if we are able to solve a problem with a certain method and all. The lesson on Four Equal Parts was an interesting one, where certain irregular shapes or what we called quadrilaterals can be of the same area but different in their sizes! At the same time we were actually learning about Algebra while doing this exercise to find the area of the different quadrilateral shapes that we have created by joining four dots together. Amazing much huh? I cannot tell you much or I would end with a looooooooong post about it but trust me, it was such great fun to learn it! Now I have more ideas on what to do with my geoboards in my centre! :p

Besides Four Equal Parts, there are some important pointers that I have taken note of! (There are always interesting pointers for every session ;p)

1. In Geometry, we use the term “congruent” to describe shapes that are exactly the same and NOT identical.

2. The term “similar” in Geometry means “one enlargement of the other”. All circles and squares are similar but not the case for rectangles! Agree?

3. Squares are special rectangles.

Beg to differ? Go and find out for yourselves and you willΒ  love Mathematics! πŸ™‚

Session 2: Is That Magic?

Image

Take a second to look at the picture above. How many stars are there? Can you tell just by looking? Can you tell the number of stars without counting? The ability to do so is what you called SUBITIZE! Yes. Definitely a new word that I have learnt. Just up to how many objects are you able to subitize? Try subitizing and share this with your friends! As i thought about subitizing in class, I then recalled how my 5 year-old children were able to tell me the number of icecream sticks without counting; they simply just shouted out the answer in a second! And now I know! They were subitizing! Below is a link to a video on subitizing. It would be of some help if you were thinking of creating activities to teach children to subitize.

After today’s session, I have learnt about some great pointers that teachers SHOULD, (yes, I couldn’t emphasize more!) teachers SHOULD and MUST always remember. Here they are:

1. It is not easy to teach, even when the problem you are teaching is not difficult. So bear in mind the startegy that you use to help children understand best, and always remember to reflect on your teaching.

2. As a teacher, we must be careful with the language that we use while teaching. If the problem says, “David bought 3 cans” please do not make assumptions and tell the children, “David had …”

I think many teachers are guilty of this. Time for a change! πŸ™‚

3. Please use the word “less than” instead of “lesser than”. The former is to compare quantitative things while the latter; quality.

Hopefully I am able to remember these pointers! πŸ™‚

Session 1: Cute or Perfect?

The first session for this module yesterday was really an eye opener for me TOTALLY! Who would have thought that there are terms such as cute numbers and perfect numbers? I have yet to research on them though heh. There are other terms that I have learnt which I was totally awed about such as cardinal numbers, ordinal numbers and nominal numbers! Oh yes I’ve got a good grasp of what these terms really mean. πŸ™‚

I liked Dr Yeap’s styleΒ of teaching, especially when he got us to stop and ask questions and, the fact that he could answer or clarify facts so clearly just amazed me! I have got a good refreshment of the theories by Piaget, Bruner and Vygotsky just by listening to what Dr Yeap has explained. But the main idea that stricken me and got me reflecting was when he mentioned that money, yes that root of all evil money money money, is considered as an uncountable! They exist as fractional parts. You can have half a dollar, but you cannot have half a boy! So since you cannot count money like cardinal numbers, money is considered a measurement! Interesting right? Let’s see what Session Two of the module is all about! :))

Chapters 1 and 2, What’s My Take?

As seen in Chapter 1,

One’s knowledge of mathematics and one’s knowledge of how children learn mathematics are considered to be the most important tools one can acquire to be an effective teacher.Β 

I do have to agree with the abovementioned, but at the same time I asked myself these questions: “Is my knowledge of mathematics enough to impart to my children today? How do I know if it’s really enough?”

Image

Since my childhood years, as far as I can remember, I have always enjoyed learning and doing mathematics but only up to Secondary 3, when I had to take A-Maths and I was struggling to pass the subject. Elementary Maths was easy-peasy but the results of my A-Maths tests and exams have totally disappointed me. However, it was not the results alone that had dampened my heart to open up to the subject, but because of the attitude of my then Math teacher who has made me feel like I was stupid and dumb to have failed such a straightforward subject. Her comments like, “How come you don’t know?” has definitely killed my interest to continue learning mathematics as I grew older. And that is when I could relate to the abovementioned: “Does my teacher even know how students learn mathematics?”

Image

I have seen how parents teach their children mathematics and sadly, majority of them prefer to spoonfeed their children with answers when they feel their children fail to understand a particular math concept after teaching, explaining etc. I don’t blame them but what happens if a teacher does likewise?

Therefore it is of utmost importance that teachers possess the following characteristics, habits of thought, skills and dispositions to succeed as a teacher of mathematics:

1. Knowledge of mathematics

2. Persistence

3. Positive attitude

4. Readiness for change

5. Reflective disposition

In my experience as an early childhood professional up till today, I still do expose my children in mathematics as a daily process. I would train the children to line up according to their numbers that they were assigned to, ask them to count the total number of children present on that particular day, got them to always follow the 8 steps of handwashing while washing their hands and rote count to a 100 everyday. I would also measure their height and weight every beginning and middle of the year, expose them to number operations like addition and subtraction, teach them sorting, patterning and geometry (shapes). I feel children could have lots of opportunity to learn mathematics and I would have to say, that mathematics is an essential part of life.

Chapter 2 is an interesting and interactive read. It got me thinking deeper on many issues and one of it is to find out what it means to “do mathematics”.

Image

Before I read this chapter, I have always thought that to do mathematics, one just had to find the correct answers either through memorizing, or knowing the formula to solve a certain problem. Now I have learnt that doing mathematics involve generating strategies to solve problems and also checking to see if our answers make sense. Like for one of the exercises in the textbook, Start and Jump Numbers: Searching for Patterns, before I read about it, I was just focusing on what number comes next and yes, there is a pattern to it, by adding the jump number. But after reading further into this chapter, I realized that hell yeah we have to think about the “pattern length” too?

What does it mean to learn mathematics? I do agree with Jean Piaget that learners are not merely blank slates but creators who are able to give meaning to things that they perceive or think about. Indeed, mathematics is all about having the common sense to construct ideas to help us understand about the things we see, hear or touch.

And I hope that after having gone through this module, it would help me to become a better mathematics teacher before I slowly climb my way up to become an effective mathematics teacher in the near future. (it is hard, but I will try my best!)

Getting Started

hi.

after much thinking, ive opted for a change so instead of my usual blog using blogger, ive created a new blog (tadah!) using wordpress. this blog as you can see from the title, will be all about numbers, specially created for my new course module which requires me to blog as a preassignment. a new personal blog will be created using wordpress too. (a more refreshing and positive blog i suppose! ;p ) alright left my textbook at work so gotta wait till tmr before i get the chance to read it and blog about it yaw!

meanwhile, lemme share a quote with you, by Albert Einstein, which goes:

Small is the number of people who see with their eyes and think with their minds.

AGREE?