Wednesday, December 1, 2010

Goodbye AKM 101

30th November 2010
Reflection 11
Just like our pupils, we were anxious about the test and were trying to cram our brains with the various initiatives. There were instant moans and sighs when we received the question paper. We had 3 questions to answer. I decided to start with question 3 ( 10 mark Q) and started penning down my answers related to PERI before I forget the initiatives. On second thoughts, not sure if that is what is required of the question.
Then I moved on the questions that required some computation.( Boy! Maths is not my cup of tea) Anyway, the test is behind us now and I believe all my classmates will share this sense of relief having completed and submitted all our assignments ( We did it people! Give yourselves a treat with the big bonuses)

I would like to take this opportunity to thank Dr Yeap for sharing the various initiatives launched by MOE in a light-hearted, engaging and illuminating perspective. I am inspired by his passion for the teaching of Math and this is translated in the way he conducts his tutorial. He is truly an exemplary to us. He always begins the tutorials by establishing our schema before proceeding further and sees to it that his lessons encapsulate the initiatives. I am amazed at the ease with which he does this. What I like most about the lessons is the tone in the classroom. It is very important to set this non-threatening climate and I must say we feel a sense of bonding during these sessions where we learn about the meta cognitive processes and not worry ourselves at providing accurate answers.

On the whole, it was a beautiful learning journey for me. On this note, I would like to wish Dr Yeap, Dr Dawn and all my classmates Merry Christmas and a Happy New Year. See you guys next year, fully revitalised and rejuvenated.

One quotation that will stay with me:

"Not everything that counts can be counted, and not everything that can be counted counts." (Sign hanging in Einstein's office at Princeton)

Professional Development 2

23rd November 2010
Reflection 10
Today’s lesson focused on the use of a facilitation tool such as Lesson Study in a Professional Learning Community. There are 5 steps in a lesson study cycle . They are :
a) Identify Research Theme—Learning Goals aligned to school Vision and Mission
b) Plan lesson ( teacher who is to conduct the research lesson is not selected yet)
c) Research Lesson
d) Post-Lesson Discussion
e) Lesson Plan Revision

Lesson Study is a platform for sharing and teachers are always involved in studying lessons. Teachers become more knowledgeable about the teaching and learning in the process and so are able to perfect their craft.

We viewed a lesson study conducted in Fuchun Primary School. Dr Yeap highlighted that a Lesson study is best observed live and teachers must be conscious of what to observe bearing in mind the lesson goals. Teachers must remain detached throughout the observation and refrain themselves from correcting mistakes observed. A good idea is to spend the last 10 minutes of a 1 hr lesson to interact with the pupils to clarify some things with the pupils. It is important to keep notes of the pupils we are observing so that they would be useful during the post-discussion stage where the 4 critical questions are examined.

Dr Yeap then introduced an article from the newspaper about SMRT overcharging its passengers and posed a question related to it. We had to estimate the average fare that passengers overpaid. It was an interesting way to teach the concept of average. Most importantly, it reflects one of the pedagogy in PERI -- Learning in the real world.

As a closure to the tutorial, Dr Yeap revisited all the initiatives implemented by MOE and its implication on the teaching of Mathematics. I must say, it is an inspiring journey to unravel the rationale behind these initiatives and take them to the next level.

Tuesday, November 30, 2010

Professional Learning Community

16th November 2010
Reflection 9

Many of us take professional development seriously as we recognise the to stay current and relevant in terms of content mastery, teaching pedagogy, and assessment. This importance is also reflected in our Work Review Document and so we find ourselves attending workshops, seminars, conferences etc. to ensure that we maximise the number of training hours. We have been moving in the right direction but it is time to add more vigour to these initiatives by moving away from teacher emphasis to one that involves the school, teachers and pupils. Hence, the origin of Professional Learning Community by Richard Dufor.

So what is a PLC? A PLC is one where teachers work collaboratively in teams to achieve high levels of student learning and positive student outcomes which are aligned to school goals. Teams meet regularly and work interdependently to bring about positive change in student learning. Teachers adopt different tools to embark on this learning journey such as Action Research, Lesson Study, Learning Circles. Teachers collaborate in areas such as refining and redesigning lesson plans and materials as well as enhance teaching strategies and assessment practices. It is an ongoing cycle of reflection that promotes deep team learning through shared experience.

For a PLC to take off, we should start by considering what The 3 Big Ideas are:

a. Ensuring Students Learn
b. Building a Culture of Collaboration
c. Focusing on Student Outcomes
And we should ask ourselves the 4 Critical Questions, namely:
a) What is it we expect our pupils to learn?
b) How will we know that the pupils have learnt?
c) How will we respond if the pupils have not learnt?
d) How will we respond if the pupils already know what is to be learn?
Dr Yeap then discussed the use of Lesson study as a tool. He highlighted the need to formulate Research Themes so that we can bridge the gap between the ideal situation and the current reality.
An example of a research theme in a Lesson Study is: To engage pupils in the learning of Mathematics; To help pupils develop reasoning and communication skills.
After a rich discussion about PLC, we moved on to the hands-on session, where we were required to find the sum of the interior angles of a polygon giving the cut-outs of some polygons. Some of us remember learning this in schools many years ago and were trying to recall the formulae.
Other used the knowledge of the sum of the interior angles of a triangle to arrive at the answer which was 720 degrees (6 sided polygon) We then explored the ways to get this answer and incidentally came to this: ( n-2) x 180 Through effective questioning, we made us conscious of our meta cognitive processes.
Dr Yeap used this lesson to demonstrate how it encapsulated the principles of PETALS. The important factor to bear in mind is the crafting of the anchor problem. The nature of the problem should be open-ended and we could see the interplay of all the principles. I always enjoy the way Dr Yeap concludes the lesson by tying up all the fragments of the lesson neatly into a package. It is a simply a delight.

Friday, November 19, 2010

Authentic Performance Task

9th November 2010
Reflection 8

Initiatives in Assessment

In view of the changes recommended in the PERI Report, it is important to provide a foundation upon which pupils can build future knowledge and skills. For this to materialise, we have to consider the holistic assessment of the child and provide support in keys areas of his learning. Unlike formal assessments which can be intimidating to our young learners, performance assessments could be introduced to our pupils to build their confidence and shape their attitude towards learning.
So WHAT IS Performance assessment? Performance assessment or authentic assessment, is a form of testing that requires students to perform a task rather than select an answer from a ready-made list. Through the task, we can systematically document what the children know and can do based on the activities they engage in. through the use of rubrics. This is very useful as it provides feedback for the teacher in terms of improving instruction, and allows the teacher to plan a comprehensive, and developmentally oriented curriculum based on their knowledge of each child.
Performance assessment can take the form of developmental checklists, portfolios, and summary reports. Ongoing checklists allow the teachers to keep track of children's progress towards widely accepted curriculum goals. The use of portfolios enable us to see the differences in the quality of one child's work over time which might be hidden, and children's ability to take an active role in evaluating their own work ignored. And a summary report is a comprehensive report that provides a holistic report of the child’s capability. With this teachers would be in a better position to provide valuable, and in-depth information to parents, both in terms of quantitative and qualitative feedback.
Having established the context for the tutorial, we were given an authentic task. We were provided with some resources and asked to measure the height of a column on level 1. ( a very tall column! )
Some of the methods employed were:
1) Using direct measurement
2) Multiplying the height of I step by the number of steps
3) Estimating the height using one tile as a base
4) Using the trundle scale to measure the length of the shadow
5) Using the concept of ratio

We discussed the various strategies taken and examined the reliability and accuracy of the data collected. Throughout the session, we were constantly reflecting on our metacognitive process.

This is a good example to show how a teacher can assess the pupils’ understanding of concepts through observation, and allowing the pupils to articulate their strategies and documenting it in the form of rubrics or checklists. We watched a video of a Maths lesson conducted in Thailand. The pupils were asked to show the concept of addition ( 5 + 6 ) provided in a story context. The pupils showed various ways as to how it can be done. The teacher can then assess the pupils level of understanding based on the presentation of their answers.

Where international assessment such as TIMMS and PISA are concerned, the emphasis of assessment is on mathematical literacy. Questions are modelled after real authentic situations and pupils are tested on the reasoning ability. Hence it is pertinent to provide our pupils with various opportunities to experience Maths in the real world.

Monday, November 1, 2010

Can We Run Away From Assessment?

Reflection 7
26th October 2010

We started the lesson by brainstorming on ideas related to assessment and Dr Yeap skilfully mapped them out into a concept map to represent the big picture. This led to framing the definition of assessment as an on-going process of gathering, analysing and reflecting on data collected to make informed and consistent judgement to improve student learning. To put this in perspective, we need to understand the rationale for assessment. Is it for formative evaluation, authentic evaluation or summative evaluation. And based on these purposes, different testing instruments are used to validate the data so that a certain degree of reliability is achieved. Hence, assessment is a critical stage in the continuum of teaching and learning as we have to analyse the performance of the students, the validity of the test questions, identify the misconceptions
students surfaced in the test, see if it is aligned to learning outcomes and reflect on our teaching practice.

Assessment itself can be categorised as assessment for learning, assessment of learning and assessment as learning. Asessment as learning is very important as we want to encourage our pupils to become self-directed learners. Students are required to reflect on and monitor their own progress to develop and sharpen their intellectual competencies.

To give us a better understanding of how assessment can be crafted into an activity, Dr Yeap made us form quadrilaterals of 5 sq units on the geoboard. From this activity, we discovered certain things about the way we processed information. Certain strategies came naturally like combining triangles to form squares and decomposition while other strategies surfaced with a bit of scaffolding. Effective questioning techniques can also be used as a tool to assess students’ learning. This is an effective way to gauge what kind of direct teaching is required to bring the students to a higher level of learning. Creativity is also encouraged and a culture of success should be promoted so that all pupils can achieve based by building on their previous learning. To reiterate his points, Dr Yeap highlighted an exercise on subtraction from My Pals Are Here Workbook. I shared this with my colleague who is teaching a high ability class and she was amazed. It is important that as teachers we recognise the need to help children see beyond the obvious.

The most essential take away of the lesson is providing feedback to pupils and parents with regards to problem-solving. Newman’s six step strategy is very helpful in error analysis.
1. Pupils cannot read
2. Pupils cannot comprehend
3. Pupils lack knowledge of heuristics
4. Pupils unable to transform the story into a mathematical strategy
5. Pupils encounter error in computation
6. Pupils do not fit the computation into the solution

Wow! Truly another power-packed tutorial. This is only part 1 of Assessment. We’ll unravel more theories and concepts in a fortnight’s time.

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.

Tuesday, September 21, 2010

Reflection 2

Prior to our meeting, I was reading the PERI report. It was conceptualized to meet the changing trends in the education landscape. And it got me thinking about the need to stay relevant in today’s ever changing world. And I’m so glad that I have decided to pursue this course of study or else by 2015, I would be obsolete. ( Walking Dinosaur). Finally we had our first meeting on the 16th of Sept to discuss the issues related to the current initiatives. We listed the various initiatives starting from 1997 to date and each of us decided to read up more about the assigned initiative. Using the “jigsaw” method of as part of CL strategies would definitely enhance our learning. Having done that, we would post our learning on a common platform which Kong ( our IT hero) had so graciously agreed to set up. I had to source out information pertaining to NE. Thanks to technology, I came across this website which seemed to have everything I was searching for. Here’s the tricky part; how does this impact the learning of Maths? Will need to see how NE can be infused in the teaching of Maths since NE is not a subject per se.

Friday, September 10, 2010

Reflection 1

Back to school after a very long while Actually, I was quite tensed about attending the first lesson on Current Initiatives in Maths because I haven’t been teaching Maths for a long while. But the approach that Dr Yeap adopted very quickly settled my nerves. Bravo to you, Dr.Yeap.
I found the lecture very engaging and insightful. The lesson started with a hands-on approach and through the use of effective questioning, many underlying concepts were surfaced. It is amazing how a relatively simple activity such as forming squares can lead one to discover other aspects of concepts such as area etc. I believe this approach of self-discovery will have a greater impact on the pupils’ learning as they have ownership of their learning.
This inductive approach to portray the overview of the initiatives and the framework of the Maths Curriculum was indeed an eye opener for me. I was introduced to the framework before but the manner in which it was presented was very didactic. But today’s lecture, tied in very neatly some of the learning theories, principles behind the initiatives based on national needs and international trends. This comprehensive package had got thinking about how Maths is taught in schools where the pre-occupation is just the completion of the syllabus. If we are to equip our pupils to become “intellectually competent” we must firstly reflect on our beliefs. Sorry, I meant to capture a short entry, but when I started I just could not stop. Ha!Ha! Am looking forward to the group presentation.