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!