My colleagues and I took the opportunity to visit the exhibitions during lunch time today. I learnt about 3M's solar films and retroreflection material, I^2R's speech-to-text recognition app with code switching capabilities (i.e. the app is able to transcribe English-Chinese mixed sentences) and cell-based prawn meat from https://shiokmeats.com/, among other things.

There was also an informative booth on Project Wolbachia (where male aedes mosquitoes infected with Wolbachia bacteria are released into the wild to control the population). I learnt that they could separate the male from the females at the pupal stage because male pupals are larger and got to stick my hand in a box full of male Wolbachia-Aedes mosquitoes.

This is a free public lecture by Dr Nergis Mavalvala (an astrophysicist from MIT) on how her team detected gravitational waves generated from colliding black holes and neutron stars at the Laser Interferometer Gravitational-wave Observatory (LIGO). Held on this coming Friday 26 Jul 2019 from 5 to 6 pm, the venue is at the Singapore University of Technology and Design (SUTD)'s Auditorium, along 8 Somapah Road, Singapore 487372.

I have not been posting in this blog for a while as I have been rather busy in my new role at the Ministry of Education HQ. My main area of work is related to the Singapore Student Learning Space, an online portal in which curriculum-aligned resources are made available for students in Singapore to learn anytime, anywhere. It's about to be rolled out to all non-pilot schools soon, so I won't be posting here for a while longer.

Until then, please let me know if there are any simulations or resources that you would like me to work on. Any such work will have to be during my free time, somewhere between rest and family time.

My school organises a competition for upper primary pupils in Singapore annually. Called the THINK Challenge, it gets participants to engage in problem-solving with a little help from the internet, team work and experimentation. "THINK" stands for the stages of the cycle of inquiry learning: Trigger, Harness, Investigate, Network and Know.

In this year's Challenge, participants were tasked to construct a water wheel that is able to lift a 20g mass up a height of 30cm. This task is known as the "Trigger". Participants were given 30 min on the internet to gather information while also "harnessing" their prior knowledge on energy conversions, frictional force, etc.

They were then given time during the "Investigate" phase to experiment and test out their prototypes. Our student facilitators then assisted to test the efficiency of their prototypes based on the amount of water used to lift the mass over the required distance.

In the "Network" phase, participants had to make a short presentation in front of a panel of judges, explaining the scientific principles involved, design considerations, limitations and suggestions for improvement.

Finally, the competition was wrapped up with a brief summary of the learning points in the "Know" stage just before handing out the prizes.

The winning teams this year were:

1st place: Maha Bodhi Primary School Team 1
2nd place: Bedok Green Primary School Team 1
3rd place: Haig Girls' School Team 1

What Makes a Good Water Wheel?

Through this competition, we hoped that participants picked up new scientific knowledge through the inquiry-learning approach.

Some of the considerations needed when constructing and testing the water wheel include:

Ways to reduce friction. Most participants realise early on that they need to allow the axle of the water wheel to turn with minimal friction. This means that they need to insert the chopstick given to them into a straw, and affix the water wheel to the straw while clamping the chopstick to a retort stand (a requirement for the competition). They also need to ensure that the string does not end up winding around the chopstick.

Mass of water wheel. A heavy water wheel tends to be harder to turn due to a larger moment of inertia as well as greater friction at the axle.

Finding an optimal height to pour the water from. They were given a bottle to pour out the water from and were allowed to pour the water from any height. While it makes sense to pour the water high above the wheel initially to achieve maximum gravitational potential energy, it was also resulting in inaccuracy and needless splashing of water.

The type and arrangement of the water "buckets". The buckets for carrying water in order to turn the wheel can be made of disposable cups or spoons, and should be arranged in regular intervals to ensure smooth rotation of the wheel. There has to be an optimal number of such buckets because if they are spaced too far apart, the lifted mass will turn the water wheel back in the opposite direction whenever the buckets are not doing work.

The position at which to tie the string to the weight. The mass to be lifted is attached to a string and this string has to be fixed to the turning wheel. If the string is tied too close to the circumference of the wheel, there may not be sufficient torque to lift the weight. If the string is too close to the axle, it will require more turns in order to lift the weight by the requisite height. The winning team managed to create an optimal distance between the string and the axle by using ice cream sticks.

As I was teaching the use of the potential divider equation to my IP4 (Grade 10) students last week, I approached it by teaching the rules first before showing worked examples. Thereafter, as some students remained confused, I merely reverted to explaining the rules. Eventually, I resorted to simplifying the equation by substituting simple numerical values in place of the multiple symbols that we use for emf, terminal p.d., resistance (more than one of them) and current, and many students' eyes lit up. It struck me then that I should have used the Concrete-Representational-Abstract approach in the first place.

Concrete-Representational-Abstract in Singapore Maths
Potential Divider Worksheet
Incidentally, I was reminded of this approach while helping my daughter with her Primary 2 Math homework last week. Since she was absent due to a stomach flu for 3 days this week, she had to bring work home to complete. There was an exercise on subtraction of numbers by separating into hundreds and tens and the first question looked like this:

There I was stuck at a primary school problem, not because I did not know that final answer is 157 but because I was not sure what to fill in for the circles. It did not help that my daughter was not clear about what to do either.

I then looked at her textbook for examples and what I saw was pictures of blocks in groups of 100s and 10s that look like this:

These are the tools that students in her class would have played with in the concrete or representation stage of learning. They can physically manipulate the blocks in order to do subtraction, which can be fun for those who like learning with a hands-on activity.

The abstract stage required by the question is for students to

remove 100 from the first number 207, leaving 107 (so the two circles will have numbers 100 and 107 in them)

deduct the second number from 100

and add the difference back to 107.

This is a technique that allows students to make quick mental calculations when subtracting tens from numbers more than 100 but requires a fair bit of practice to get used to. My daughter eventually had no problem with the rest of her homework after we figured this out.

Being a Physics teacher, I thought about how I could transfer this method of making a complex and abstract skill easier to pick up through concrete representations.

Usual Approach: Abstract to Concrete

In my IP4 Physics classes, we are currently on the topic of DC circuits, which involves calculations involving the potential divider method.

One of the main equations is the potential divider rule, in which V_{1} (p.d. across resistor R_{1}) is given by

For two classes, I started directly with equations before introducing examples (abstract to concrete), which is what physics teachers usually do. There is nothing wrong with this approach as students still see a concrete representation eventually but I was wondering if it might be more beneficial if students could synthesize the equation on their own by generalizing from examples. By the time I taught this same concept to the second class, I realized that most students were able to understand the equation only after giving concrete examples using numerical values.

Concrete Examples before Equations

For my third class, after being inspired by my daughter's homework, instead of introducing the equations straightaway, I started by introducing the concept of dividing emf between two resistors in series according to ratio of resistance. I used simple numbers for easier reference. In this way, I felt that students could then always link the equation back to the simple concept of ratios which helps them understand the intent of the equation.

When students see after one or two examples that all we are doing is trying to distribute the emf in proportion to the resistance that each resistor has so that it follows the ratio R_{1}:R_{2 } (concrete stage), I asked them to replace the numerical values with symbols (representation stage).

or (Concrete stage)

or (Representation stage)

From the last equation, students were asked to recall that emf is equal to the sum of the p.d. in the series circuit. The equation can then be rewritten as

or (Abstract stage)

I believe that if students can arrive that the final equation from the basic principles, they will understand more deeply and will be able to apply it in slightly different contexts, such as when there are more than 2 resistors in series, or when one resistor is varying (in the case of transducers such as LDRs and thermistors) or even when considering internal resistance of the cell.

Here's a simple worksheet that students can use to work out the potential divider equation on their own.

P.S. This is not a research study that compares whether abstract to concrete is better than the other way round, but merely a way for me to record what I've tried in different classes. I welcome comments from other teachers who may have tried a similar approach and have observed positive results.

The Planning Question is the last question on Paper 2 of the 9646 H2 Physics paper in the Singapore-Cambridge GCE A-Levels. It carries 12 marks out of 72 in the paper, which lasts 1 hr 45 min. Based on the principle where ratio of marks should be roughly equal to ratio of time allocated, the question should take about 17.5 minutes to complete typically. However the reality is that students tend to spend too much time on the theory questions and more so on the data analysis question which precedes the planning question, leaving insufficient time to properly answer what is arguably the most important question in the paper.

1. Make sure that you allocate the same amount of time as you do with other H2 subjects.
This may not mean spending the same amount of time each day, but over the long term, such as the same average time over a week. An over-emphasis on subjects that are perceived as more "challenging" may cause some to neglect subjects that are supposedly "easy to score" when in reality, Physics is not as easy as it was in the O levels. It involves a lot of time spent trying to comprehend concepts (and how they are inter-connected) and practice (just like Maths).

2. Master your Maths Speaking of Maths, the solving of Physics problems employs a significant amount of Mathematical skills, ranging from basic calculus and trigonometry to vector additions and even arithmetics. You can check the list of mathematical skills needed in the syllabus details (pg 25-26). Examples include sine rule and cosine rule ().

3. Start Simple For students struggling to pass Physics, it might be better for you to start with strengthening your fundamental concepts before moving on to more challenging questions. Take half an hour to make sure you at least understand the worked examples in the lecture notes before attempting the tutorial questions because those are the simplest questions you can get. Diving into the deep end straightaway will only serve to discourage you or worse, "drown" you.

4. Read the Recommended Texts
Make a trip to the library every week to read up on the topic that is being lectured. The list of recommended books should be found in the Scheme of Work given out in the beginning of the year, or downloadable from Matrix. Some of the books recommended for supplementary reading are:

The book "College Physics" by Serway and Faughn may be found on Amazon UK, although I don't recommend that you buy the books as we have multiple copies available in our library. The books do not cover all the topics in our syllabus as well.

5. Make Your Own Notes

This helps to organise your concepts and draw connections between them. It can be in point form (e.g. list the characteristics of an ideal gas) or in a mind map form.

This video shows yet another demonstration for the effect of resonance, when the sound frequency is equal to the natural frequency of the glass. I have yet to conduct this demonstration because of the potential risks involving flying pieces of glass. A video should suffice though, especially one that is taken at slow motion.