To do or not to do

Primary education, a compulsory education in Singapore. Some may progress well and some may not. Math topics move on one after the other in primary education. What if some students are lacking far behind from what the school is teaching in math lesson? And clearly, they have little understanding of the math concepts taught but are forced to move on. We all know that students will still be promoted even though they do badly for exams. How should I allocate time during tuition to help strengthen the student's foundation of mathematics yet still able to keep up with the school?

Technology and Math

21st Century Education... different ways of learning.... different styles of teaching...

Technology is easily available in many schools now. Technology such as smart boards and computers could be used to teaching counting or any math concepts.
My kindergarten uses Mathematics related computer programmes that allow students to practise concepts taught during large group sessions. It acts like a following-up activity to extend learning. The math related programmes include activities such as counting, grouping numbers in tens, addition, subtraction, multiplication and many more.

Counting activity

Multiplication activity

I would say that technology is an useful tool to teach Math and an interesting tool for children to learn, however I would bear in mind the C.P.A approach of how children learn. It is important for children to go through the concrete and pictorial first before using computer programmes as the follow-up activity.

Square rectangle square rectangle???

I forgot to blog about this shocking information that I got to learn about not long ago! Read carefully.... A Square IS a rectangle! I told this to my dad and he said "60 years later then I get to know that a SQUARE IS A RECTANGLE". So for people that don't know square is a rectangle, NOW you do!ooh ya, but a rectangle is not a square. Go google and find out more. How amusing and interesting can math be! I am beginning to love you more :)

Learning Point... Big Ideas... How children learn...

C.P.A approach is being emphasised a lot in this module. C. P. A = Concrete. Pictorial. Abstract. This is how children learn and this is the way we as teachers should teach. According to Jerome Bruner, the CPA approach reaches out to a variety of learners. For students to start learning, Concrete elements such as markers, pencils, books, ten blocks etc.. that could be physically manipulated should be used. As they move on to the next level, Pictorial elements such as graphs diagrams, drawings, charts that are drawn or interpreted by students would be used. And lastly, Abstract elements refers to the use of numbers or letters as a form of representation. With this approach, students in this process of learning are taking baby-steps to the development of VISUALISATION.

NEXT...

Learning Point = 4 questions to reflect upon as a teacher
Q1. What I want the child to learn?
Q2. How do I know they learned it?
Q3. What if the child can't make it?
Q4. What if I have advance learners?
To answer Q3 & Q4, this is where differentiated learning comes in handy!

BIG IDEA...

We are not teaching content... we are teaching children to see things in multiple perspective and equip them with multiple strategies to solve problems.

So students will be able to see that one-fourth of two-thirds is...---------------------------------------->
and not purely 'cancelling'. You should know what I mean by 'cancelling'. It is not wrong to cancel when solving it, but students should be taught to do more than what a calculator can do!

BIG IDEA...
Use the correct language.
Less and Lesser, when do we use it?
Less is use when referring to countable items/quantity.
Lesser is use when referring to uncountable things/quality. Such as water.
So, like what Dr Yeap had said, the number 2 will be insulted when we say '2 is lesser than 3'.

This is how we do it

How am I to teach students to count large numbers? Instead of counting by ones, I can teach students to count large numbers by grouping.  Students should be taught different ways to count as we being 'adults' are counting in different ways too. Initial stage, students count in ones. Next, group large numbers in 5s. Then group of 10s. Most importantly is to teach grouping before we do the counting for large numbers. Learning/teaching materials such as 10 frames or egg trays would be really useful to teach counting of larger numbers.  

10 frames

In Chapter 11 under the 'role of counting' pg 194. ---> 1. Counting by ones. 2. Counting by groups and singles. 3. Counting by tens and ones. According to Thompson (1990) "Each approach helps students think about the quantities in a different way".

How did you learn to do long division? Perhaps your answer would be like mine, the procedural method where we have to multiply and subtract in order to divide. I started paying attention to long division only after Dr Yeap asked "I thought I was dividing, then why am I multiplying and subtracting?" It was then that I realised the complexity of long division. Not all students may be able to understand it. So how should I teach them? Break numbers appropriately to do long division. Long division is not a universal method. Such as 51 divided by 3= breaking the number 51 into 30 and 21 then dividing it by 3. The whole idea is to break the number 51 into manageable numbers that could be easily divided by 3.

SARAH.. Which letter is counted 99th?

Haha.. Who would actually take the time to find out which letter of our name is counted as 99th. Yes! We all did. This activity was kinda interesting. I mean like who in the world would have so much free time to come out with such an activity. Haaha! Ooh yes peeps, after monday's session, please don't ask for my weight! Instead,ask "how much do I weigh?" or even better ask for my mass!

Exploring what it means to know and do Mathematics

Chapter 2

What does it mean to learn mathematics? The answer lies in learning theory and research on how people learn. The two most commonly used theories by researchers in mathematics education are:

• Constructivism theory - rooted in Jean Piaget's work, which was developed in the 1930s.
• Sociocultural theory - the work of Lev Vygotsky, emerged in the 1920s and 1930s.

It is explained that making connections between mathematics concepts are connecting blue dots (ideas we already have) to red dot (emerging idea). Whatever existing ideas (blue dots) are used in the construction will be connected to the new idea (red dot) because those were the ideas that gave meaning to it.

Multiplying, dividing, adding, subtracting, fractions, decimals, ratio, algebra are some troublesome equations to solve without calculator. To solve those equations, I was taught to use either workings or diagrams/models. To solve multiplication and division, I had to memorise the times-table. To solve algebra equations, I was taught to memorise formula. I was taught specifically on how to solve problems; neither promoting thinking nor engaging in productive struggle. Strangely, I understood those concepts, and surprisingly, I did rather well. Its just that exploring problems and understanding mathematical ideas wasn't the way I was taught to do mathematics.

Reading this chapter was interesting as it was a total contrast of how mathematics was taught to me. It mentioned about providing opportunities to talk about Mathematics, providing opportunities for reflective thought, encourage multiple approaches, consider solutions of others, scaffolding new content, engaging students in productive struggle and treat errors as opportunities for learning. This chapter is a whole new learning point of teaching and understanding mathematics concepts. "This shift in practice, away from the teacher telling one way to do the problem, establishes a classroom culture where ideas are valued. This approach values the uniqueness of each individual." (Van de Walle, J.)

Van de Walle, J. Elementary and middle school mathematics: Teaching developmentally (8th Edition). New York: Longman. ISBN: 9780132879040

Teaching Mathematics in the 21st Century

Chapter 1 

"What a heading!" I thought to myself as I read the title of chapter 1. Reading through the five content standards brought back memories of my years in school. From what I have remembered, my Math Teacher with a textbook on his hand, would always be standing in front of the white board explaining concepts and showing plenty of examples of how questions are being solved, then similar questions would be distributed to be completed. Clearly, the method that my teacher had adopted was very different from what NCTM had discussed in this chapter; where students should acquire and use mathematical knowledge through problem solving, reasoning and proof, communication, connections and representation.

"High-quality mathematics education" is being emphasised in this chapter. This is a goal that all educators in Singapore, which includes me, should work towards to. It is easier said than done, however with determination, I believe it is achievable. To achieve the goal of implementing high-quality math education as a successful Teacher of Mathematics, one should have the characteristics, habits of thought, skills, and dispositions that the author has described in this chapter.

If you were to ask me how different is Pre-school's mathematics teaching now as compared to how I was taught in my years of study, my answer would be 'not much difference, but trying to improve'. From what I have observed, some curriculum are still planned in a way that pre-schoolers learned numbers through rote counting and memorising of number names/words, concepts are taught by 'saying', worksheets that does not encourage thinking, problem solving, reasoning and questioning are frequently used. In short, there are little opportunities for pre-schoolers to be active learners to achieve in-depth learning.

Lastly, here's a quote from the author "it is you, the teacher, who will shape mathematics for the students you teach. Your belief about what it means to know and do mathematics and about how student make sense of mathematics will affect how you approach instruction." We are in control!...to a certain extent...


Can you guess what is this?



Can you guess this too?