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.

## Water Wheel Challenge

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:

1. 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.
2. 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.
3. 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.
4. 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.

5. 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.

## Measuring speed of sound in air using Audacity

A physics demonstration on how to measure the speed of sound in air using Audacity, an open source audio recording software. There are Windows and Mac versions of this free software, and even a portable version that can run off a flash drive without needing to be installed on a computer (for school systems with stricter measures regarding installing of software).

The sound is reflected along a long hollow tube that somehow, existed in our school's laboratory. The two sound signals were picked up using a clip-on microphone attached to the open end of the tube and plugged into the laptop. I used my son's castanet which gives a crisp sound and hence, a simple waveform that will not have the echo overlapping with the generated sound. The timing at which the sound signals were first detected were read and subtracted to obtain the time taken for the wave to travel up and down the 237 cm tube.

The value of the speed of sound calculated is 356 m/s, which is a bit on the high side due to the temperature of 35°C and relative humidity of between 60-95% when the reading was carried out.

If you are interested, you can check out how the software can be used to determine the frequency of a tuning fork.

We are about to get students to conduct experiments to explore how tension, length and thickness of a guitar string affects its pitch (frequency). I might post some results here when there's time.

## Magnetic Force on a Current-Carrying Conductor

Using a neodymium magnet, some paper clips and a battery, you can demonstrate the magnetic force acting on a current-carrying wire while recalling Fleming's left-hand rule. Using the same frame constructed in the previous video, you just need to add a wire with a few bends in between to create a U-shape in the middle as shown in the picture below. A small piece of insulating tape (you can use any adhesive tape) is added to one end of the wire to show the original dangling position of the U-shape before current flows through it. Be sure to leave some space at the end with the insulating tape for you to switch on and off the current by pushing that end in and out.

## Building a Simple DC Motor

Using material that is easily available, you can build a simple homopolar D.C. motor (one that uses a single magnetic pole. I made the video above to help you do so.

The material used are as follows:

1. insulated copper wire
2. paper clips
3. neodymium magnet
4. 1.5V AA battery
5. plastic or wooden block (I used a 4x2 Lego block)
6. scissors
7. permanent marker

The steps involved are:

1. Attaching the magnet on the side of the battery using a long piece of adhesive tape and sticking both of them onto the Lego block. The polarity of the magnet does not matter.
2. Next, we need to shape one end of each paper clip so as to make it longer and to make a small loop at the top. The paper clips are then fixed on the ends of the battery using adhesive tape.
3. Coiling wire can be done with the help of a round cylindrical object such as a marker. Roughly 10-15 coils will do.
4. The ends of the wire can used to bundle the coils together. Make sure they are tied up tightly.
5. Since we are using an insulated wire (otherwise the current will just go straight from one paper clip to another without passing through the coils), we need to scrape of the insulation at the ends using either sandpaper or the edge of a pair of scissors.
6. Using a permanent marker, we can colour one side each end in order to insulate that side. This will prevent current from flowing through the loops for half of every cycle. It has the same effect as that of a commutator.
7. Finally, we will mount the coils onto the two paper clips and allow the motor to spin.

Do take note that the motor should not be left connected to the battery for too long as it will drain the battery very quickly and generate a lot of heat in the process.

How this can be used for the O-level/A-level syllabus

Teachers can use this as a demonstration that shows the motor effect of a current in a wire placed in a magnetic field, as well as to apply Fleming's left-hand rule.

One can also make an second coil without insulating half the surface of the points of contact with the paper clips to show the importance of the commutator in a DC motor. The coil will simply oscillate to and fro due to the change in direction of the magnetic force on the lower half of the loop every half a turn.

## Magnetic Shielding

I made this rather simple video this morning showing a physics demonstration on the effect of magnetic shielding. A paper clip is shown to be attracted to a magnet. A series of objects are placed in between, such as a plastic ruler, a steel ruler, a steel bookend, and some coins of different alloys.

It is interesting to note the types of material that provide magnetic shielding and those that do not. There is even a distinction between the types of steel, which is an alloy containing iron. Ferritic steel is magnetic while austenitic steel is not.

The theory behind magnetic shielding is that the flat magnetic material will direct the field lines of the magnet along its plane instead of allowing them to pass through, thus depriving the paper clip of a strong enough magnet field to keep it flying.

## Simulation: Faraday's Law of Induction

This simulation traces the flux linkage and corresponding emf generated by a rectangular coil rotating along an axis perpendicular to a uniform magnetic field. One is able to modify the angular frequency to see the effect on the frequency and peak emf generated.

## Simulation: How emf is generated

This simulation is really more of an animation that allows students to apply Fleming's left hand rule on a line of electrons along a conductor cutting a magnetic field in order to appreciate how emf is generated.

## DeLight Version 2

I modified "DeLight", the board game that I designed a few years back into a worksheet version (for small groups) as well as a powerpoint version (that teacher can facilitate as a class activity, pitting half the class against another).

The objectives of the game is to reinforce concepts related to D.C. Circuits such as:

1. Sum of potential difference (p.d.) across parallel branches of a circuit is the same.
$E = V_1 + V_2 + V_3 +...$
2. P.d. across a device is given by the ratio of resistance of device to total resistance multiplied by emf (potential divider rule)
$V_1 = \dfrac{R_1}{R_{total}}\times E$
3. Brightness of light bulb depends on electrical power
$P = IV = \dfrac{V^2}{R} = I^2R$
4. Current can bypass a device via a short-circuiting wire.

The worksheet and powerpoint slides contain a few examples that allow discussion on the above concepts based on some possible gameplay outcomes. For example, the following is a game where the blue team wins because the p.d. across each blue light bulb is twice that of the p.d. across each red light bulb.

In the following scenario, the game ended in a draw. Students may not be able to see it immediately, but the blue light bulb with a vertical orientation is actually short-circuited by the vertical branch on its right.

Feel free to use and/or modify the game to suit your own class needs.

## Concrete to Abstract

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

1. remove 100 from the first number 207, leaving 107 (so the two circles will have numbers 100 and 107 in them)
2. deduct the second number from 100
3. 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 V1 (p.d. across resistor R1) is given by

$V_1=\dfrac{R_1}{R_1+R_2}\times\epsilon$

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 R1:R2  (concrete stage),  I asked them to replace the numerical values with symbols (representation stage).

$\dfrac{1\Omega}{2\Omega}=\dfrac{4 V}{8V}$ or $\dfrac{1\Omega}{(1+2)\Omega}=\dfrac{4 V}{(4+8)V}$ (Concrete stage)

$\dfrac{R_1}{R_2}=\dfrac{V_1}{V_2}$ or $\dfrac{R_1}{R_1+R_2}=\dfrac{V_1}{V_1+V_2}$(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

$\dfrac{R_1}{R_{total}}=\dfrac{V_1}{\epsilon}$ or $V_1=\dfrac{R_1}{R_{total}}\times\epsilon$ (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.