Friday, October 22, 2010

What is that we teach less of?

Reflection 6
21st October 2010

“The mind is not a vessel to be filled but a fire to be kindled.” Plutarch

Today’s lesson clearly illustrated the above quotation. We started the lesson with a problem using tiles. We were asked to use the triangular tiles to make various shapes, some of which were parallelograms, trapeziums, rhombuses. Assuming that the length of each side was 3cm, we had to find the perimeter of the shapes formed. From here, we progressed to find the number of tiles required to form a perimeter of 93 cm. It was evident that the nature of the problem had become more challenging and we had to look for patterns, visualise the formation, and do quite a fair bit of meta-cognition.

Similarly, the next problem on Structures, illustrated how we can modify a question that looks at regular pattern formation to one that has a combination of pattern to look out for. This brings to light the emphasis on what is the little that we must teach in TLLM. We need to equip our pupils with skills such as looking for patterns as a human, form certain generalisations, logical reasoning, consider certain conditions to synthesis new learning and provide them an environment where they can consider taking risks when they are learning complex things. We should not only pay attention to the final answer, but also analyse the way in which we can sharpen the pupils’ intellectual competencies. This is the critical role we play as teachers apart from just teaching concepts which can be easily picked up from books or the internet. The scaffolding provided by the teacher is important as it covers the fundamentals of the learning theories advocated by Lev Vygotsky when the ZPD is bridged. Socratic Questioning helps in probing deeper into the problem by getting one to think through and reflect on our meta-cognitive process.

Final problem for the day: How can we find the area of a circle? Jerome Brunner’s theory of touching the materials to embody the concepts that has to be learnt shows how this can be derived. We formed shapes we can find the area of, using the circle cut out, to deduce the area of the circle. The following outcomes of PERI were skilfully crafted into the lesson: Learning by inquiry, learning by interacting, learning by doing, and learning by reflecting. This will definitely bring about more engagement in learning as the pupils will be able to relate their experiences of the learning tasks to new and novel situations. That’s what learning is all about!

Thursday, October 14, 2010

Games, Games and more Games

Reflection 5
13th October
After a four week break, it was back to class for more excitement. Dr Yeap started the day by presenting a visually- friendly outline of the activities for the day. One would not help but notice that he had listed some of the games we would be playing through the course of the day on the board. As usual, we had loads of fun playing the games. The first game was called Salute. It is actually a game to test multiplication facts. Although it was truly a drill and practice kind of activity, I believe children will have a lot of fun practising it as it does not come with the “ another worksheet again” syndrome. He then moved on to the next game: a spelling game where he would throw a card with the corresponding number after spelling out the number. That caught our attention and we were tasked to find out how to arrange the cards such that the “magic” works. Take I, Take 2 was also interesting as we had to strategise in order to win. Dr Yeap made us analyse what the winning strategy would be and we tested our conjecture. The last game was stimulating. We formed multiplication facts using the digits from 0 to 9. Some ground rules were laid, such as no digit can be utilised twice and the resultant should not be a three digit number. We then looked for patterns and came to a certain understanding to explain our conjectures. Through the activity, we were encouraged to dwell deeper into the content by re-examining the nature of the questions. Eg, What is the largest possible answer? What is the smallest possible answer? To get the largest possible answer, what digits would you use and how would you arrange it? The buzz word for all the activities was problem solving skills and along with it came the issue of managing confusion.. Interestingly enough ,Joe brought up the concept of multiplying using the Lattice Approach. That was the first time I ever saw such a method. We were truly immersed in a great deal of meta cognition which is pivotal in thinking. The key takeaway from today’s lesson would be “It is not what we teach that matters, but how we teach it” By getting the pupils to work on the games, and then leading them to investigate certain conjectures we would definitely pique their curiosity. Fun and Thinking is so closely woven into the lesson that pupils will remember this experience as a meaningful and engaging one. Phew! Too much work for my grey matter. Eventually, we re-looked at the rationale for the teaching of Mathematics and is it true that the teaching of Maths is a excellent vehicle for the development and improvement of one’s intellectual competencies. Through the experiences we provide for our pupils they will really appreciate and enjoy Maths in any situation.

Wednesday, October 13, 2010

Are We There Yet?

Reflection 4
5th October 2010

It was exciting to see magic unfold before our eyes with all of us posting all our “finds” on And it didn’t stop there. It was usually accompanied with smses and calls. We would help one another vet the power-point slides to capture only succinct and salient features of the various initiatives. And then it was back to the drawing board to see if it was all well-aligned. We met today, only this time it was over at Pizza Hut. With just two days to go, we were filled with anxiety and kept calling each other to get updates on the progress. Kong, our IT hero, synthesized all our individual projects and did a fantastic job at it. Poor guy! We must have stressed him with all our tall orders.
Looking back at this journey, I think I have come a long way. It was an enriching and fruitful learning experience. The PETALS framework has a strong underpinning in the teaching of Maths. We begin to re-examine our pedagogy, experience of learning, tone of the environment, assessment mode, learning content and student centred approach to align this to the teaching of Maths. Through this we can bring about greater joy in the learning of Maths. If only I had this experience when I was young, things would have turned out quite differently.He!He!

Friday, October 1, 2010

Reflection 3

30th September 2010

Finally, it is time for some real work. I was so excited when I posted my findings on the wiki page created by Kong. One of the good things that has come out of all this is that every day I am learning something new. Cool isn’t? We discussed what we should put together for the e-package. It was interesting to piece all the jigsaw pieces to get the big picture of all the initiatives and its impact on the teaching and learning of Maths. No matter how advanced technology is, it still feels good to meet the members face to face to hold some good heart to heart discussion and that’s what we did today. It helped to allay our fears and apprehension and it was reassuring to find strength in numbers. We sorted what the missing elements in our search were and decided to further our probe into those initiatives. Some of you may wonder what is the relevance of NE on the teaching and learning of Mathematics. To understand that, we as teachers must belief in the philosophy behind the initiative. WE ARE THE KEY TO THE SUCCESS OF THE INITIATIVE.
National Education is part of a holistic education.
“It is an exercise to develop instincts that become part of the
psyche of every child. It must engender a shared sense of
nationhood, an understanding of how our past is relevant to our
present and future. It must appeal to both heart and mind.”
Goh Chok Tong (then PM of Singapore)
Teacher's Day Rally Speech, 8 Sept 1996
So let’s get this in the right perspective.
1. NE is a requirement
2. NE should be integrated into mathematics teaching
3. Mathematics concepts/contents/topics can be introduced using Singapore
4. Provide authentic problems/real-life problems from Singapore society
5. Instill thinking & co-operative learning and self-regulated
6. Be a role model

Now, I feel passionately charged about the infusion of NE across the curriculum.