Wednesday, November 10, 2010

I shall begin this blog with a quote from Albert Einstein™ which was quoted by Dr Yeap:

"Not everything that counts can be counted, and not everything that can be counted counts." Apparently, this sign hanging in Einstein's office at Princeton.

For me, I love another quote of Einstein™: A table, a chair, a bowl of fruit and a violin; what else does a man need to be happy?"

Dr Yeap began our lesson by throwing us a challenge in the form of a performance assessment. He took us on a mini field trip and asked us to measure the height of a tall column which looked like a Doric column. It was like having an adventure in the dark as we grope and grapple to find sensible solutions.

The different ways of approaching and solving this task were discussed when back in the classroom. As usual, as Dr Yeap led in the discussion, there was never a totally 'wrong' answer. We were always encouraged to voice out our opinions, concerns and queries.

Some of the things I need to re-think:

1. The way mental sums are carried out in my school

I much prefer 'mental strategies' to 'mental sums'. Quite often, I work out sums intuitively and mentally. In so doing, I give my brain cells a form of exercise, which I believe will keep my brain from getting rusty as age catches up!

2. More holistic assessment to support learning (PERI Report, chapter 3, Pp 34-37)

Sometimes, I get the strong impression that all we teachers care about regarding an assessment, especially the SAs, is how many passes, how many failures, how many quality passes, and WHY (particularly when the number of passes is appallingly low)!

3. The frequency I give professional opinions to parents and the contents therewith

I'd like to give a report on my pupils' learning as often as a topic is covered and tested. I intend to put into practice Dr Yeap's suggestion of using a 3-column table that list the key competencies and the short phrases to be used to inform parents whether their charges are proficient in 'a limited number of tasks', 'familiar tasks', or 'a variety of tasks'.

I'd like the report to be honest, and not sugar-coated so that the pupils' and their parents' feelings are not hurt. Otherwise, it will merely be a waste of time, I figure.

If I do this next year, I wonder if I will 'spoil market' and irk parents? :)

4. The method used by pupils when doing addition

I was recently mildly irritated when I asked a 9-year-old pupil for the answer to (15+20), and she did a vertical addition to obtain the answer. Surely, she has encountered such an addition sum before, say, when she bought something for 15cents and 20cents, and she knew the total was 35cents. But she did not remember ever doing so.

I'll have to be even more vigilant in my observation of my pupils when they are doing work in the classroom. But, honestly, my pupils hardly have time to do written work in class since I use almost all the time for teaching!

Thursday, October 28, 2010

Blooming & Blossoming

It was another lesson at NIE/NTU. Due to an accident on PIE, I arrived slightly later than I'd anticipated.

We explored several engaging and enlightening purposes of 'Assessment', to which I contributed, as a purpose, 'for the child's self-awareness and self-knowledge'. This works both ways - if a child knows he has been performing well in Science (as evidenced by the various tests and scores that he has received), he, not only experiences moments of joy, but knows he has the aptitude for Science, and may, eventually, wear the hat of a Scientist.

On the other hand, if a child has been scoring only mediocre marks in Math, there are 2 options open to him: {1} buck up, pull up his sock, get his act together, and do everything within his power to improve; {2} take the view that he may not quite have what it takes to up Math to a higher level. In the latter case, he may decide to focus on building his expertise in French, and, may, end up as a teacher of French!

Bloom's Taxonomy was briefly mentioned to us as we studied on the instrument of assessment. The "interactive lecture" (as opposed to "traditional lecture") concluded with the assertation that assessment is a 2-prong process: data collection and data analysis/interpretation, for a variety of purposes. By the way, assessment is not hard science!

There are a few more examples of dichotomy that I took home that night:

1. subjective vs. objective

2. ability vs. achievement

3. validity vs. reliability

4. summative vs. formative

5. affective vs. cognitive

6. facility index vs. discrimation index

7. alternative vs. orthodox (modes of assessment)

These all need elaboration, which I will do soon!

Wednesday, October 20, 2010

Initiatives in Teaching and Learning

I had yet another enjoyable session of learning about Initiatives in Teaching and Learning in class last night. Hardly surprising!

Again, Dr Yeap gave us an outline of what we were to do that evening in class using an autism-friendly chart. It looked like this:
o Tiles Problem
o Structure Problem
o Circle Problem
o Break
o Circle Problem (2)
o Area is 5 units
o Discussion

Recently, I have begun reading "House Rules" by Jodi Pocoult in which the protagonist is a boy with Asperger's Syndrome (a boy in my last year's class has that too!). My ears are quite attuned to the word 'autism'. However, given the amount of work now piling up each day, my progress in reading is snail-paced.

We started our lesson by affirming that a triangle of length 3cm is 9cm in perimeter. When 2 such triangles are placed side by side, their perimeter is 12cm. The question is how many triangles will generate a perimeter of 93cm?

I feel quite pleased with myself for coming out with an expression ~ 3 x (n+2), where n is the nth triangle ~ for the solution! Elegant, isn't it?

Thus, 29 triangles will give us 93cm as perimeter. {93 = 3 x (29+2)}

Things I have learnt:

1. TLLM - Teach Less, Learn More.

What is Teach Less, Learn More? How to teach less, and yet pupils learn more?

Teach Less, Learn More is about teaching better, to engage our learners and prepare them for life, rather than teaching more, for tests and examinations.
Remember why we teach
Reflect on what we teach
Reconsider how we teach

• TLLM aims to touch the hearts and engage the minds of our learners, to prepare them for life. It reaches into the core of education - why we teach, what we teach and how we teach.

• It is about shifting the focus from “quantity” to “quality” in education. “More quality” in terms of classroom interaction, opportunities for expression, the learning of life-long skills and the building of character through innovative and effective teaching approaches and strategies. “Less quantity” in terms of rote-learning, repetitive tests, and following prescribed answers and set formulae.

In other words, Dr Yeap reminded us the word 'less' must be correctly defined, and it certainly does not mean that pupils cannot do difficult stuff.

2. Metacognition

This includes ::
logical thinking
looking for patterns and generatlisation
looking for patterns that are intriguing

J. H. Flavell first used the word "metacognition". He describes it in these words:
Metacognition refers to one’s knowledge concerning one’s own cognitive processes or anything related to them, e.g., the learning-relevant properties of information or data. For example, I am engaging in metacognition if I notice that I am having more trouble learning A than B; if it strikes me that I should double check C before accepting it as fact.
—J. H. Flavell (1976, p. 232).
3. Some characteristics of weaker pupils: they will be poor in::

> looking for patterns
> generalisation and making links
> visualisation
> number sense
> communication
> metacognition (cannot think well)

4. Zone of Proximal Development

Often abbreviated as ZPD, it is the difference between what a learner can do without help and what he or she can do with help. It is a concept developed by Soviet psychologist and social constructivist Lev Vygotsky (1896 – 1934).

Vygotsky stated that a child follows an adult's example and gradually develops the ability to do certain tasks without help or assistance. Vygotsky's often-quoted definition of zone of proximal development presents it as
the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers
Vygotsky among other educational professionals believes the role of education to be to provide children with experiences which are in their ZPD, thereby encouraging and advancing their individual learning.

So, the next time I think of 'closing the gap' and/or embark on strategies to 'close the gap', I'm effectively and affectively narrowing the ZPD of my pupils!

Friday, October 15, 2010

We're Back for Business!

After 4 weeks of self-regulated e-learning, it's good to be back in the classroom face-to-face with Dr Yeap and my coursemates once again!

These days, with the acute advancement of technology, almost anything can be learnt from the internet - the amount of info is mind-boggling and staggering! Online learning is widespread and a must. However, to me, nothing can replace a teacher (thus far)! No doubt computers can be effective tools for helping our pupils learn academic subjects, yet we will always need human teachers to provide moral guidance and foster intellectual growth and social development. Computers provide pupils with information, but only we teachers can teach our children to think critically and creatively, discriminating among sources of information.

Dr Yeap mentioned the use of a calculator. It can computate huge numbers and complex equations, and generate answers in matter of seconds. But it has no brain. Can a brainless tool help a child learn? Of course not!

I'd like to draw an analogy here with the computer. Its uses are wonderful and manifold. But it has no feelings. It cannot comfort a child who is going through a rough patch in life. It cannot answer a question a pupil has in class based on what is known about this inquirer. It has no experience whatsoever to speak of, much less to share. We need empathy and sympathy. We need a human touch and understanding. No computer can to be programmed to provide these.

Moreover, whatever a computer can do, however, its ability comes from a human source. This means that the brain behind it is far more superior! Yeah!

So, it was all-so-exciting to be back together to explore and discover some initiatives in teaching and learning.

Some of the things I learnt that evening:

1. It is not what we teach, but how we teach that is the crust of our teaching.

I need to constantly reflect on my lessons to see how I can teach better so that my pupils can learn better, and have countless "moments of enlightenment and joy" ('Rationale of Mathematics Syllabus - Primary'). It's my desire that many of them will wear of the hat of a mathematician joyfully!

2. Besides being "an excellent vehicle (the word 'vehicle' suggests to me a journey, a destination) for the development and improvement of a person's intellectual competence", Mathematics is to be "a subject of enjoyment and excitement".

I figure it's my duty to infuse enjoyment and excitement into every Math lesson!

3. Jerome Bruner is the forerunner of CPA, Concrete-Pictorial-Abstract.

It is said that Bruner, in his research on the development of children (1966), proposed three modes of representation: enactive representation (action-based), iconic representation (image-based), and symbolic representation (language-based).

4. There is such a method as the Lattice Method when doing a 2-digit by 2-digit multiplication.

It works this way:

Add the digits diagonally. Voila! The answer is 784.

5. A book in hand is worth two in the bookshop!

I've asked my school Math HOD if we have the book 'Teaching Primary School Mathematics' edited by Lee and Lee. We don't. Based on my recommendation, Mrs G-F immediately placed an order with the vendor and I finally laid my hands on it.

Upon reading, one particular problem in the book caught my attention. 

"Cut 7 cakes into 24 pieces and share them equally among 12 children" (Page 22, 'Teaching Primary School Mathematics' edited by Lee and Lee).

I know the quickest way of solving this! :)

Saturday, October 9, 2010

The Maiden/First AKM Project

My group - Yueh Yuan, Jingbo, Joe, Nurul and I - after grappling around and grabbing time, finally completed our Math assignment!

Here it's the fruit of our hard work and much effort!


Wednesday, September 29, 2010

Less than three...

This is a simple mathematical statement: less than three, represented by <3. When I asked my pupils to name some numbers less than 3, most of them replied '2' and '1'. However, there are no fixed number of numbers that are less than 3!

2.9876543 is less than 3.
0.123456789 is also less than 3.

To my girls, however, it means 'love'. How so? <3 is the heart-shape Y lying on its side! Can you see that?

I'm still reeling from the grief that came with my beloved dad's homegoing on 25 September. The burial took place at CCK Christian lawn on 27 September. But when I think of his love for us his children, I'm thankful for who he is. Also, I'm eternally gratefully to God for saving him. Even though he won't be able to see me when I graduate in 3.5years' time, I'll continue to put in my best efforts in all I do.

So now, it's back to work - if I want to meet the expectations of my tutors and the course, and graduate! Carpe diem!

Sunday, September 26, 2010

The Hardest Mathematical Question...

I have been asking several questions of late. Many of them have no answers, and I do not intend to get on top of them till I get to the bottom of them! Besides, I don't have the luxury of time to do so! There are so many urgent things I need to settle - and soon! This includes AKM101 group and individual work!

I remember reading the book 'The Curious Incident of the Dog in the Night-time' by Mark Haddon. In this book, the protagonist Christpher Boone asks and solves many mathematical questions. One question that was asked, if I remember correctly, was the whereabouts of the worn-off rubber tyres of our cars! It struck me as an interesting question because so many cars travel on the roads every day, everywhere, and tyres do get worn off. Now, where did the minuscule rubber bits go to? In another book I'm reading currently, "A Wrinkle in Time", the author mentioned that there is a fifth dimension called the Tesseract, and that raised several questions in my mind too.

But the question I'm now most concerned with is this: How much tears does one have? Is it an endless, infinite supply? Has anyone ever bottled tears and measure its quantity and rate of flow?

Tuesday, September 21, 2010

To be On Task at My Task

On Saturday 18 September, the 5 of us managed to get online on MSN and began a rather thrilling session of chatting with one another. At one juncture, it kind of degenerated to something akin to a marketplace as all of us seemed to be talking at the same time, and no one appeared to be 'listening' (read: reading)! I found it amusing as it reminded me of a typical classroom situation! We teachers can shout ourselves hoarse as our pupils are engaged in their own conversations.

After the initial hitches and glitches, we settled in comfortably in one another's virtual company. However, albeit reluctantly, I had some pressing matters to see to and took my leave of MSN early.

My contribution to the group synergy has to do with TSLN, I&E and NE.

After some reading and researching, these are some of the things I've learnt:

1. Towards THINKING SCHOOLS: The concept of THINKING SCHOOLS is central to this vision. Schools must develop future generations of thinking and committed citizens, capable of making good decisions to keep Singapore vibrant and successful in future.

2. Towards a LEARNING NATION: We will make Singapore a LEARNING NATION, that goes beyond schools and educational institutions.

3. People - teachers and pupils - with a strong spirit of I&E possess a mindset and outlook of creativity, initiative and self-reliance. They possess the following core attributes:
• Intellectual curiosity (eg. to question assumptions, explore and experiment) and ability to see things in new ways (eg. to recognise patterns and make connections)
• Passion, strength of character, persistence, resilience and ruggedness
• Courage to live with ambiguity (eg. to seek alternative pathways) and to take calculated risks
• Sense of teamwork and ‘giving back’ to the community
4. NE - I am still contemplating on whether this is much more than a mere infusion of NE values with Math concepts (eg. measuring the length and breadth of a standard Singapore flag and finding its area, and talking about patroticism towards our nation).

Friday, September 17, 2010

Finding My Way Around...

After getting hopelessly and helplessly lost for a good 20 minutes, I finally found the 'elusive' McDonald's @ NTU, the haunt where my team mates and I were to meet for our first formal discussion of the work we were to do. Informally, we threw in our ideas about the key initiatives. Seeing how time flew by all too quickly, we decided to use MSN as a means for communication and discussion. The date for this: 18 September, Saturday, 10.30am!

For the first face-to-face meeting of erstwhile 'strangers' (except for Nurul and Jing Bo who are colleagues), I think we did pretty well!

What I'm most unclear about is pbworks. I guess I will be less hazy once I begin to explore the website thoroughly and systematically!

Some of the things I have learnt on 16 September (which happened to be the birthday of MM Lee) ~

1. Cooperative Learning -
Its benefits:
·         increase student retention
·         develop students' social skills
·         promote student self-esteem
·         promote student learning and academic achievement
·         enhance student satisfaction with their learning experience
·         help students develop skills in oral communication

I intend to make more creative and extensive use of Cooperative Learning Strategies in my classroom teaching. I think Think-Pair-Share works best for me!

2. Mathematics Initiatives -
·         some are short-fused
·         some enjoy longevity
·         some bring about notable changes
·         some are the results of another/others
·         some have influences in non-mathematical domains
·         some affect us such that our education landscape is no longer the same

Wednesday, September 15, 2010

A Little Chat Goes a Long Way...

I believe it's beneficial to speak with Mrs G-F, the Math HOD in my school, about the Math initiatives that have been put in place in our education system. Being approachable, friendly and having no airs but a wealth of experience, expertise and knowledge, Mrs G-F immediately invited me to her workstation when I waylaid and asked her if I could ask a few professional questions.

I told her I needed some info about the initiative that were implemented from 1997 to present. The year 1997 struck an immediate chord with her - TSLN! I knew I have found the right person! We chatted for about 20 minutes. After a most interesting and informative tête-à-tête and leaving the HOD Room, I quickly jotted down the things she had mentioned (before my oft-appalling memory fails me)...

Some of the things that I have learnt from Mrs G-F:

1. Although there was a content reduction in Math, it isn't significant enough. In one sense, it's simply how the teaching and learning of Math is. There is a 'ladder' of learning - many concepts are built upon what is taught earlier.

I experience this struggle almost on a daily basis: I want to teach well and I want my pupils to learn well. I want my pupils to love learning and love learning Math. However, in spite of the reduced syllabus, I still have a hard time teaching and exploring in the best possible way every single topic, especially when the exams loom near. 'Covering syllabus' - something I dislike doing - seems a norm.

There is a topic which can be done away with, in the opinion of Mrs G-F, with no real loss. Despite several appeals by teachers to get it removed, it remains. Guess which topic that is?

Speed! Zoom...!

2. There was a moving of topics to different levels. This is significant since it signals some changes in the thinking and mindset of the good people who are in charge of planning the Math curriculum.

3. Long time ago, the abacus was used in the learning of Math. This tool always brings to my mind the 'ancient' grocery shopkeeper who totalled up the prices of goods with it with ease.

4. Recently, the calculator was introduced in the learning of Math. This will enable more challenging questions to be tested as pupils are no longer hampered by the calculation parts when solving these problems.

Looking at it positively, I guess this is the right way to move ahead! It's the knowing how to solve a problem that is of a weightier matter!

At the end of our little chit-chat, Mrs G-F asked if I wanted to teach more Math next year!

Thursday, September 9, 2010

My First Taste of AKM101

AKM101 (Sep10) : Current Initiatives in the Primary Mathematics Curriculum

Some of the things I learnt and re-learnt on 7 September 2010:

1. It is possible to make a square using 1, 2, 3, 4, 5 and 7 pieces of the tangram. I found an interesting link here:

2. The scaffold we provide for our pupils, as implied by its name and by its nature, is to be removed eventually. I believe we all want our pupils to be independent learners.

3. The Mathematics Framework in Singapore is largely influenced by two documents (1980s) ~
[a] An Agenda for Action (NCTM, USA)
[b] Cockcroft Report: Mathewmatics Counts (UK)

These 2 important documents shifted the paradigm of Math teaching to problem-solving. Reading these documents reinforces the principle that our education is undergirded by our internal needs and external trends.

4. The PERI Report cited 5 examples of Pedagogies that apply across subjects ~ Learning by: [a] Inquiry [b] Interacting [c] Doing [d] In and Out of the Real World [e] Reflecting.

I spent some time browsing through the report and appreciated its relevance in our ever-changing world as well as its greater emphasis on non-academic programmes within the curriculum using the Programme for Active Learning. PAL aims to develop character and useful life-skills, something my school is actively engaging in so as to engage our pupils better!

The PERI report can be read from here:

5. TSLN & TLLM - Teaching Schools, Learning Nation & Teach Less, Learn More. Behind these acronyms lie a whole host of things for me to learn, explore and discover in this journey and adventure, and be a teacher with good practices!