The final chapter of AKM101

Date: 23.11.2010
Venue: Usual room
Lesson Plan:

• Lesson Study
• Professional Learning Opportunities within Lesson Study
• Concluding the Course

Dr Yeap summarised what lesson study is about and gave a simple framework on the steps to carry one out. Some of my take aways are:-
(a) to identify research theme and professional learning goal as a school
(b) to plan a lesson that is detailed but somewhat skeletal with learning goal in mind, anticipated responses and how these responses can be used to achieve the learning goal
(c) teacher to carry out the lesson should be identified close to end of the planning, not at the beginning  so that everyone in the team has greater ownership.

We discussed the benefits of a lesson study, what to observe, and to have 10 min out of an hour's lesson to interview and interact with the pupils to gain better insight into pupils' understanding of the lesson goals and the observations made.

We viewed photographs of a lesson study on circles in a primary school and discussed the learning tasks of the pupils, observations made and the measure of pupil engagement. We then looked at the 4 critical questions to ask of a PLC:
(a) What do we want students to learn?
(b) How do we know that they have learnt it?
(c) What do we do to differentiate learning instruction?
(d) What do we do if they already know it?

Dr Yeap then looked at the overview of the AKM101:- the initiatives, teaching and learning, what is math in school, assessment and professional development. We then looked at a real-life example of a newspaper article where commuters were overcharged amounts ranging from 4-20 cents and which totalled about $300 000. As usual, we were prompted and prodded and encouraged to explain what the information actually means, using the idea of average, data analysis and interpretation of analysis.

Reflections of the course
It has been a fantastic learning experience. After more than 20 years of teaching, there is still so much more to learn and re-learn and to do things better. Dr Yeap has infused in me the desire to improve both myself and my pupils. Initially, I did not enjoy Math as it is my weakest subject but I am now more positive about it and excited to do it better.
The learning environment in the class is non-threatening and conducive to ask questions, make mistakes and learn. There are no answers given for most of the learning tasks and we are encouraged to think about our thinking processes, our metacognition. The games were fun and ready to use in the classroom. I will definitely use 'Salute' and the 'magical' counting card game in class. In many of my Math classes in school, the fun element is missing and now I know some ways of infusing this.
There was a lot of collaborative learning during the group assignment and I got to know my mates better. MacDonalds in Sengkang, our venue for our assignment, has many fond memories for me.

In short, the lessons have always been informative, mentally taxing (for someone my age) but always fun and a great learning experience. Thank you Dr Yeap, Dr Ng, and my fellow course-mates.

Initiatives in Professional Development

Date: 16 Nov 2010
Venue: Usual Math Room
What's Up?

• Professional Learning Communities (PLCs)
• Lesson Study
• Polygons
• Test Date Options
• Research Lesson
• Sample Test

We started off by talking about the different learning communities in our schools, like the learning circle, lesson study and action research and some projects the teachers were involved in.
Dr Yeap then went through some of the steps of a lesson study. It was noted that a lesson study first and foremost helps the teacher to improve his craft.
The teacher would need to have a Research Theme and the learning goals, work out the learning content, and solve the problems before going to the class to engage the pupils.

Example 1: To engage the pupils in the learning of Mathematics.
Example 2: To help pupils develop reasoning and communication skills

We looked at the example of polygons and discussed how to find the sum of the interior angles of polygons of different sides. We were encouraged to work out a formula to help us find the relationship between the number of sides and the total of the interior angles. As usual, the answers were not the priority but rather the reasoning, thinking processes behind them.

Dr Yeap, as usual, pricked and prodded us with questions, making us re-look our strategies and crystallising our thoughts and reasoning. He hardly ever gives us any answers to the questions but always, always, makes us think. He then went through the PETALS framework and how a research lesson could be carried out.

The evening came to a close with a look at sample test questions from previous years and how to go about answering the questions. It was a good exercise for me.

We had a guest, Dr Peter Foley (hope I spelt it correctly) who sat in during the lesson. Dr Yeap and Dr Foley are in the midst of setting up a school in Thailand and it is initaives like these from my teachers that inspire me to want to do something for these kids in the less-developed countries too. Another such teacher who has similarly inspired me is Dr Low Guat Tin who is involved in Nepal.

Initiatives in Assessment

Date: 9 Nov 2010
Venue: NIE Mathlab
What's up today?:

• Performance Task
• Rubric
• Break
• A Look at international Assessment
• Formative Assessment

Hiya,
We had an interesting performance task today. The group had to estimate the height of a pillar that was about 2 storeys high. We were given some measuring apparatus to use as we deemed necessary. There were interesting ideas generated by this activity from the groups and individuals.
Some solutions
(a) measuring the steps leading up to the top of the pillar. (46 steps x 15cm step)
(b)taking a photograph and comparing it to the height of a known person leaning against the pillar
(c)measuring the set of 7 tiles on the wall next to the pillar and comparing it to the height of the pillar. (1 tile=30cm, approx 23 tiles needed, so 23 x 30)
(d) using a set square (isosceles triangle) and using it to align the height of the pillar and the perpendicular distance to the edge of the set square when seen from the same distance. (yeah kinda confusing when explaining in words!)
(e) connecting a couple of measuring tapes and measuring the vertical height
(f) using a set square set at eye level and then working out the height of the pillar + height of person holding the set square to get toal height of pillar (Dr Yeap's idea)

I thoroughly enjoyed the performance task as I learn best out of the classroom. The ideas generated were also somewhat novel and I learnt a lot from the task.

We then learnt about the reasons for assessment as a means of developing pupils' ability, building confidence and desire to learn, the emphasis on learning rather than grades, etc,  and the assesssment rubrics required to give both qualitative and quantitative feedback to parents.

Dr Yeap went through examples of assessment rubrics. 'Anything that is measurable is not important', 'Anything that is not measurable is important' left an impression on me. Definitely something worth pondering over.

We then saw photographs of Thai students involved in a Math lesson and the different ways they had to show their thinking processes for an addition question. Another comment about how the female students take the lead while the males were reduced to colouring, somewhat common in the Asian classroom, was also food for thought for me.

To end off the evening's class, we had an example of a test question we would have for our test. I am somewhat apprehensive about the test as are many of my coursemates and we are somewhat glad for this activity. Dr Yeap in his usual way, told us not to worry and to use the knowledge we have readily gained and shared during our classes to help us through.

Another important lesson on my learning journey. I am somewhat mentally drained after each Math lesson. There is so much to learn, think about and use in the class. Tiring but always engaging.

Thank you everyone.

Assessment 1

Date: 26 October 2010
Venue: Math  Room, usual venue
Topic: Initative-Assessment
Schedule of activities:

• Assessment-Interactive lecture
• Area is 5
• Break
• Frameworks - workbook task, word problems
• Home sweet home

Dr Yeap worked out something like a concept/mind map from the probing questions he posed to us  -the whys, the hows, the whens and the whats of assessment.
Some of the key words raised were 'reliability', 'validity', 'affective outcomes', 'cognitive outcomes', 'designing instruments', 'data collection' and ' data analysis' besides some others.
Assessment is a 2-part process, firstly collecting the data and secondly interpreting the data. From the test items, the facility and discrimination index can be worked out. Teaching leads to assessment and there must be continual assessment during the learning process and not at the end.
                                     Apply                          Develop

                                                    ASSESS


                                                   Consolidate

Dr Yeap then did the 'Area is 5' activity when geoboards and paper grids were given to the groups to come up with as many different possible areas of 5, assuming that one square grid represents one square unit. There were many interesting solutions offered and Dr Yeap himself was given a STAR(heh! heh!) for his contribution of a square(diamond) area. This was an interesting activity and one that can be easily replicated in the classroom when teaching area.
During the break, my group had a conversation with Dr Yeap on the challenges teaching pupils from Pathlight school and the role Dr Yeap has in the school.
After the break, we were shown how a simple workbook activity can be used to stretch the thinking processes of  pupils in a P2 class when doing subtraction questions, for eg, 2356 - 98, can be worked out quickly by subtracting 100 from 2356 to get 2256 and then adding 2 to the answer to get 2258. Other somewhat similar questions were also discussed and the pupils can use the space on the page to come up with their own question using the quick addition/subtraction method.
The last activity was 'Word Problems'. There was a sigh when the question was flashed as many teachers (especially those who don't teach Upper Primary MAth) are wary of how difficult the questions can be. Dr Yeap explained the Newman 6-step strategy on how/why some pupils find Word Problems challenging.
(1) reading difficulty- can't read, can't understand the question
(2) can read but cannot understand the question
(3) lack of knowledge of strategies to solve the questions
(4) cannot transform the story to the bar model
(5) cannot use the right strategies
(6) do not fit the answer/computation to the solution

Dr Yeap then proceeded to ask probing questions while at the same time breaking down the problem into simple parts with part-whole model drawing. The difficult was made simple.
Another enjoyable session. Am somewhat mentally drained after each Math lesson. But it is a good learning process to hone my skills and knowledge to become a better Math teacher.
  

Initiatives in Teaching and Learning 2

Week 7, 19th Oct 2010, 7.00pm.
What was on for this week:

• Tiles Problem
• Structure Problem
• Circle Problem

We used green 3-cm triangular tiles for the first activity. The task was to find out the number of tiles needed to form a figure of 93cm. We not only had to solve the problem but also explain how we got it. Bee Hong, Lydia and Jeanette gave slightly different explanations. Again, Dr Yeap never gave us answers but encouraged us to delve deeper into our thought processes.
The structure problem was a bit more baffling for me. I am used to looking at 'vertical' patterns but when it involved both 'vertical' and 'horizontal' ones, it was difficult for me initially. However, after the explanations given by my peers, I am better able to bridge the gap in my learning, narrowing my zone of proximal development.
I found the Circle Problem interesting as well as it allowed us to have hands-on  to think of a simple way of working out the area of a circle, given that we know how to find the circumference of a circle.
Dr Yeap's excellent questioning technique, encouragement and non-threatening environment in the classroom enabled us to look deeper into the myriad shapes formed from a circle to a square or rectangle and finally the formula for the area of a circle which was indeed a fun learning process for me. I think he has managed to bring the 'fun' element into the learning of Mathematics for me, as like many of my pupils, I am somewhat intimidated by the seriousness of Mathematics and how I am always concentrating on the end product of a question - the answer. I am certainly learning a lot. And enjoying it!

Initiatives in Teaching and Learning

Back to NIE today, 12th October 2010, 7.00pm
On the Math Menu:

• Salute
• Card Game - 'Magic Touch'
• Take 1, Take 2
• Multiplication

Was introduced to 3 really fun activities. Firstly Salute. This involved using using gaming cards 1-10. Played in groups of 3 or 4. Each player (except one) draws a number from a deck and places it on his forehead. He does not look at the card. Player without a card then totals up the numbers on the players foreheads. The other players then have to subtract the total from the cards visible to them on the other players foreheads and work out the number on their own foreheads.
I found this activity REALLY FUN. I will definitely try this out in school.
Dr Yeap then amazed us with his 'magic' act. He placed some cards numbered 0-10 in a special order. He spelled O-N-E, moving one card for each letter at a time to the bottom of the deck and revealed the card numbered '1'. He discarded the '1' and repeated the activity until the final card '10'. In our groups, we had to arrange the cards to work out his 'magic' trick. My group managed it first and each member was tasked to share with the other groups. (4 9 10 1 3 6 8 2 5 7 is the arrangement)
Next, it was Take 1, Take 2. This involved removing one or two paper clips at a time from a pile. The last one to remove the last 1 or 2 paper clips wins. We had to find out which number of pins to leave our opponent to ensure we win. Dr Yeap allowed a lot of interaction and sharing and never revealed the answers to us. He probed and prodded us to think of possibilities and was always encouraging. He kept highlighting to us that it was never about the solution but rather the joy of learning and discovery. I appreciate this delivery method and am actually enjoying my Math classes as there is always something to look forward to.
For the activity on multiplication, we had to find out the largest 2-digit value when a 2-digit number is multiplied by a 1-digit number (given only digits 0 to 9, with no repeat numbers). We worked out different permutations that arose and how the place value of the digit affected the final answers, etc. Again, Dr Yeap NEVER told us the answers but rather led us to think through the process through interaction with our peers and shared learning as well as reflection. The Message I get from all these activities - the answer to a problem is the end, the journey of discovery and enjoyment is part of the process, which is the more important of the two. He managed to successfuly infuse some of the core essentials of PETALS in his lesson delivery. Thoroughly enjoyed my learning. Thank you, Dr Yeap.

D-Day for Group project

Thursday, 7th October 2010. 7.10pm.
Back to our usual meeting place at SengKang MacDonalds. Staff getting used to seeing us here. Same work area too. We have set ourselves a target of 8.30pm to upload our project. We worked feverishly doing our final editing and putting photographs/pictures together. We had fun looking at our individual photos depicting our 5 core initiatives.
Things were falling nicely into place. However, 8.30pm came and went. Missed our target! Then, Vincent's laptop, on which we were working, ran out of juice! Never mind, we had Jihan's to work with.
We had so much trouble trying to run the video on Jihan's laptop. Wan Lee's husband who had been waiting patiently for her in the car with their daughter who by the way, had fallen asleep (8.30pm target remember!) came to our resecue. He worked his magic and managed to run/save the video on Jihan's computer. At the same time, Jeanette managed to do the same on her laptop.Then, just as we thought the worst was over, Jihan's laptop was giving up on her. And Jihan did not have her adaptor ! It was left in school!Oh No!
Finally at 10.30pm, Jeanette uploaded the project - minus the video. Jeanette or Jihan would send it over on Friday-deadline day.
At close to 11 pm, 5 bleary-eyed and weary teachers made our way home. It was an exciting evening. (P.S. Thankfully the whole project was uploaded on Friday by Jeanette who included some music into our presentation. Thanks Jeanette!)