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A Logical Way to Learn Math

There are many schools of thought on how Mathematics should be taught (and learned). Growing up, I was taught to just memorise steps for solving questions by heart. As long as I remember which step leads to what, I did not need to wonder about the why and how of mathematics. In fact, I was discouraged to question it in class.

Back then, the focus on learning mathematics was on speed. As students, we were expected to be able to solve x number of questions in the shortest time possible, regardless of whether or not we understood what we were doing. This has been the basis of many mathematics classes around the world. Students were just supposed to remember the process of solving a problem, and then train themselves to execute it as quickly as possible. 

Common as it is, does this method really help pupils understand (or like) mathematics though? If it is effective, why do so many students get imaginary headaches the moment they look at a math problem?

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In this article, we will share another concept used in the teaching and learning of mathematics: the CPA Approach. This approach was developed by American psychologist Jerome Bruner, who proposed it as a way of scaffolding learning. He believed that learning can be difficult to children if it’s all abstract. 

For example, if you present a child with a textbook full of information and just expect them to remember everything, it will be very difficult for them to do so. It’s like giving directions to a stranger in town, who has no idea where he is or how anything looked like, and expecting him to be able to find his way around with purely verbal instructions. Instead of that, Bruner suggested that abstract concepts in learning should be accompanied by concrete and tangible aids. When students are able to visualise how mathematical concepts work in real life, their understanding of the subject will be strengthened, leading to more effective learning. 

There are three stages in the CPA Approach: concrete, pictorial, and abstract.

Concrete Stage:

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The concrete stage is also known as the “doing” stage. Students are encouraged to use real life objects to model mathematical concepts. For example, let’s say they’re learning about addition. They could be handed a set of Lego blocks, and then given the question: what is the sum of 2+1. In this case, they would be asked if they should add 1 block to 2 existing blocks, or should they remove the blocks. Since it’s addition, the correct answer would be adding a new block to the existing ones. This hands-on approach allows pupils to improve logical reasoning and thinking skills, and helps them form a connection in their brains about the application of addition in math.

The concrete stage is very important, as it helps students build their fundamental understanding on how mathematics works, before proceeding to deeper equations.

Pictorial Stage:

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The next stage is the pictorial stage, which is also called the “seeing” stage. As the name suggests, this stage involves students creating visual representations to model the problems that they’re working on. For example, if a question asks about removing 4 apples from a basket of 10, students are encouraged to draw it out to solve the problem.

One concept that can be introduced in this stage is the Bar Model, where students create visuals using bars. It is a more abstract method for representing numbers, compared to actually drawing out objects that are involved in children’s mathematical questions. This model acts as a bridge between the pictorial stage and the abstract stage, as students slowly transition from literal visuals (like fruit) to more abstract ones (like bars). Because it is very versatile, and only requires pencil and paper, it is very useful for students during classes and exams. The Bar Model can be applied to solve questions related to the four operations (addition, subtraction, multiplication, division), fractions, and algebra.

Abstract Stage:

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The final part of the CPA approach is the abstract stage. This stage can only be taught when students have demonstrated a solid understanding of the first two stages. In the abstract stage, teachers can now introduce actual mathematical symbols (e.g +, -, x, ÷, ≥, ≤ etc) and numerals in problem solving. If students have built a solid foundation from the two earlier stages, they should be able to solve mathematical questions using numbers and symbols easily.

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Tying it all up

While there are many ways that kids can learn math, the CPA approach has been shown to be extremely helpful. In fact, it is so helpful that it was designated as the mandatory teaching method for mathematics in Singapore. The CPA approach does not need to be limited to math; it can be applied to other subjects and topics as well. Since kids have a limited vocabulary and understanding of complex words, visual representations are a great way to introduce new concepts to them. The next time your child is unable to solve a question, try this approach, and see if it works. All the best!

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How to Get Parents to Pay on Time

When running a learning centre such as a tuition centre or kindergarten, the livelihood of the business depends on the number of students who signs up and stays with you. It is a no brainer that as the number of student increases, the greater the revenue / profit is. However, what comes next is a bigger challenge – getting parents to pay on time. Ultimately, this is a hurdle that most if not all education centres face. Unlike other businesses such as a gym, you probably would not deny the student entry into the class because his / her parent has not cleared their fees.

For centres who collect their lesson fee payments on a monthly basis, getting parents to pay on time is crucial as this would affect the company’s cashflow. You as the business owner have other financial responsibilities such as paying your teacher’s salary, rent, utilities etc. Hence, in this article, we will be sharing with you 3 pointers that you can apply to get parents to pay on time, every time!

Tip 1: *Terms and Conditions Applied* The first tip is to be applied when signing up a new student. Besides a registration form, get the parents to sign off on a Terms & Conditions sheet. Highlight to them that payment for the upcoming month must be done by the end of the current month (*Depending on the rules that you have set). Here you can also consider implementing an additional charge for late payment. We know of some learning centres who uses this just as a tactic to “threaten” parents to pay on time but do not really implement this. It is up to you on how you execute this. For example, if you are aware of a certain parent who has a track record of making late payments, you can give them a gentle reminder on this T&C. This brings us to Tip #2.

Sample of a Learning Centre’s Terms & Conditions

Tip 2: Constant reminder. Part of being human is the fact that we tend to forget things. We do not do it on purpose but as we are caught up in our daily routines, rushing from one place to another, it is normal that we might have overlooked certain mundane things to do such as making fee payment. In addition, your student might be attending 4 to 5 other lessons – all of which requires the parent to make payment at the end of the month! Therefore, we need to always be reminding both the students and parents.

  • For students: When the fee payment has been due for more than a week, pass the student  a friendly reminder note and mention that the fees are not paid yet and to get his/her parents to make payment. This works best for older student as they might be ashamed when getting called out from class. For younger students such as those in pre-school, you can staple the note on the cover of their exercise book or a folder so that it is clearly visible to parents when they pick their children up from the centre.
  • For parents: Three days before the start of the new month, send them a reminder on making the fee payment. At the start of the new month, send them yet another message. By the 7th (or whenever the dateline is), give them a call and follow up with another message. This is where you can remind them of the additional charge that was set in Tip #1.
  • With AOneSchools’s announcement feature, you easily remind all parents to make fee payment with a click of a button! Click here for a free demo!

Tip 3: Reduce friction of making payment. The third and final step is an effort centres need to make in order to encourage on-time payment. One of the reasons why parents do not pay on time is because of all the hassle it involves. If the only way parents can make payment is by coming to front desk at your centre (which involves taking additional time out from their busy schedule, finding parking under the scorching heat, walking up the never-ending flight of stairs, queuing to wait for their turn – you get what I mean), you probably need to consider other payment options. Generally, learning centres accept cash, credit card (wave or pin) or online bank transfers. However, in addition to all the struggles mentioned above, it is still a back and forth process where you (or your admin staff) would receive the transfer slip from the parent, update the fee tracking sheet, issuing a receipt and then finally sending it back to the parent. Now imagine doing this for a few hundred students every month. This would take up a lot of time.

Here’s a solution: AOneSchools Parent Mobile App – it allows parents to make payment directly from the comfort of their own homes and automatically receive the receipt. It gives the option of either online banking or the usage of credit card! In addition, they no longer need to be physically present at your centre and hence, this will encourage contactless payment and reduce the risk of transmission of COVID-19.

By reducing the friction for parents to make payment, you can increase the percentage of total payment every month! So here we have three ways that you can try out! Let us know which method works best for you!

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Top 3 Strategies to Overcome Burnout

Strategies to prevent and overcome burnout
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According to the World Health Organization (W.H.O.), burnout is a syndrome conceptualised as a result of chronic workplace stress that has not been successfully managed. It is a state of emotional, physical, and mental exhaustion, caused by excessive and prolonged stress. Symptoms of burnout include experiencing overwhelm, feeling emotionally drained, and being unable to meet demands at work.

In the long run, a person who frequently experiences burnout may fall into severe depression or anxiety, and may start demonstrating an inclination towards negativism or cynicism about his/her job. If this describes you, read on to learn about the 3 strategies that you can undertake to overcome this phenomenon.

1. Improve your time management skills

A good rule of thumb that you can follow for managing your time is the Four Quadrants of Time Management, developed by the author of best-selling book The 7 Habits of Highly Effective People, Stephen Covey. He encouraged people to divide their tasks into the following 4 quadrants, based on their urgency and importance:

  • Quadrant 1: Important and Urgent 
  • Quadrant 2: Important but Not Urgent
  • Quadrant 3: Not Important but Urgent
  • Quadrant 4: Not Important and Not Urgent

You can refer to the table below for better understanding.

You may think that most of your time should be focused on the tasks in Quadrant 1, since they are both important and urgent. However, the most significant quadrant in the long run is actually number 2: important but not urgent. Why is that so?

The reason why quadrant 2 is the most crucial of all is because it contains assignments that are mostly related with planning, improvement, and prevention; which are all duties that – should they be performed well – will lead to a smaller workload in quadrant 1. While focusing on the emergencies in quadrant 1 is obviously important, more of your energy should be devoted to avoiding having to put tasks into this category to begin with. Spending a big chunk of your time putting out fires every day will put you in constant fight-or-flight mode, which is a key contributor to stress and burnout.

2. Communicate, communicate, communicate

Why do people experience burnout

On top of time management, another huge reason why a person can be affected by burnout is lack of communication. Especially in a professional setting, it’s not unusual to see people bottling up their frustrations, for fear of jeopardising relationships with their colleagues. However, keeping everything in is just like creating a time bomb that’s waiting to go off. So, while we don’t suggest throwing a fit whenever you feel angsty, we do recommend facilitating honest communication at work. Now how do you do that?

First of all, forge friendly relationships in the workplace. Even if you’re a self-proclaimed loner, or just don’t feel like you fit in, it’s still beneficial to make a few friends. Scientific studies have shown that social isolation is one of the biggest risk factors for the decline of physical and mental health, so make the best of your time at work, and connect regularly with your co-workers. If you find it hard to initiate a relationship, you can always start small, maybe by giving them a friendly smile whenever they walk by, asking about their day, or discussing weekend plans with them. A little goes a long way, and while you may not realise it, these social interactions can help you ease up if you feel stressed at work.

For employees who feel overburdened by their workload, it’s time to have an open discussion with your manager. Make sure that you are able to separate work time from personal time. Work life balance is not just a catchy phrase that gets thrown around by entitled millennials; setting clear boundaries between your professional and personal schedules is actually crucial for your well-being. If you feel like the tasks delegated to you are too overwhelming, and/or the amount of effort you spent on work is not adequately reflected in your paycheck, arrange for a performance review and provide honest feedback about your thoughts. At times, your manager may not be aware of everything that is going on within the company, and it is your duty as an employee to speak up if you feel unfairly treated. Don’t be afraid to stand up for your own rights.

In addition to communicating in the workplace, open up to your personal connections as well. A part of being human is that at certain points in our lives, we will experience downfalls or get tangled up in conflict. When you feel upset, talk it over with someone that you trust. Sometimes you may feel alone in this world, especially in our social media-obsessed society where everyone is fervently showing off the highlight reel of their lives. However, please be assured that you are never totally alone. Everyone has their own inner battles that they are fighting; maybe they’re just better at hiding it. Allow yourself to open up to a confidante. For all you know, he/she has been through the same issues that you’re struggling with now, and may be able to give you sound advice to overcome your challenges. If you feel like you really don’t have anyone to talk to, consider contacting a therapist or the BeFrienders. The most important thing is to never give up.

3. Live a healthy lifestyle

Growing up, we have all heard the doctor’s recommendation of 30 minutes of exercise per day, for at least three days a week. This can include going for a jog, a session at the gym, or maybe a quick match of badminton with friends. While it’s easy to overlook this tip when work gets busy, it’s important to note that these atomic habits will ultimately lead to a healthier body, thereby elevating your mental well-being. Studies have shown that regular exercise can uplift your mood, and reduce feelings of anxiety and stress. This is because physical movement increases the brain’s sensitivity toward the hormones serotonin and norepinephrine, which relieve feelings of depression and produce higher levels of endorphins, also known as the “happy hormone.” 

A healthy lifestyle does not just consist of regular workouts; it’s also dependent on food. As the saying goes: you are what you eat. Besides exercising routinely, another part of maintaining a healthy lifestyle is to watch what you consume on a daily basis. Avoid greasy foods and sugary drinks; instead, opt for healthier alternatives like whole grains and protein-rich meals. You’ll be surprised at how much a well-balanced diet can affect your mood for the better. By having the right combination of exercise and a healthy diet, your body and your mind will thank you in the years to come.

It’s normal to feel stressed at times, and we can never be totally immune to low moods. Whenever you start experiencing anxiety and/or dread when thinking about work, try incorporating these 3 strategies – improve time management skills, communicate openly, and develop healthy lifestyle choices – in your daily life. You may be amazed at how you feel after a period of practicing these habits!

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Leaving a Legacy After School

(File pix) Based on the Philosophy of Teacher Education and Preliminary Report of Malaysia Education Blueprint (2013-2025), the Teacher Education Division  continuously boosts teachers’ abilities through its curriculum changes.  Pix by Syarafiq Abd Samad
Picture credits: Yarafiq Abd Samad

We were all students once. While many of us reminisce about our days in school every now and then, we can’t always put a name to the teachers that we’ve encountered. Who was your history teacher in Form 2? Do you remember? If so, why? 

We all know a few educators that stand out vividly in our memories, some of whom we may even still keep in touch with years after graduation. Have you ever wondered why that is so? What is so special about them, that we can’t seem to forget how they looked or spoke or walked, while the recollection of other instructors fade into a foggy echo? According to Coach Mohd Noor from CMN Academy, it’s because the memorable teachers don’t only teach, they focus on leaving a legacy.

Coach Mohd Noor Mohd Tahir is a coach for Malaysian educators, and owns numerous successful tuition centres spread across the country. He is the creator of the “Tutor Beyond Expectation” and “Success Tutorpreneur Mentorship (STM)” programs, which help tutors and entrepreneurs in the education industry operate their businesses in a systematic and professional way. Together with CMN Education Group, Coach Mohd Noor has mentored more than 2000 “edupreneurs” throughout Malaysia to achieve business success. During a Facebook live session in August with him and Coach Baahir from AMPAC Penang, the topic of memorable instructors came up. According to Coach Mohd Noor, there are 3 reasons why certain educators leave a deeper impression in their students’ minds. These are: content, context, and character. He calls them the 3Cs that define an educator’s legacy.

The First C: Content

We attend classes to learn. As a student, do you like having an idea of what you’ll be learning throughout a course term; or would you rather attend lessons without knowing what will happen? Most students we know prefer having the outline of their syllabus, and also a preview of what they can expect throughout their learning period. With this in mind, teachers can provide students with a lesson framework for the semester or year during the first lesson. This allows students (and perhaps their parents as well) to know what to expect for upcoming lessons. On top of that, they will also know what they will miss out on if they do not attend classes, which allows them to plan vacations and important events more strategically. 

In addition to sharing a lesson framework, teachers can also think outside the box, and furbish students with trial papers from other schools, or even other countries. A quick Google search will reveal analytics of public examinations in the past, as well as topics that should be emphasised in school and extra-curricular lessons. Teachers can use this information to add value to their lessons, by giving students tips and tricks to answer questions effectively and do well in exams. Always think about how you can give more to your students, instead of just sticking to content from textbooks. You may not realize this, but students do know when their teachers are going the extra mile. When your students feel like they’ve gained a lot from your lessons, they will remember you more fondly.

The Second C: Context

Context is where educators apply their creativity in delivering teaching material to their students. Whether it’s a funny way to memorise a certain formula, or a reenactment of historical events during a history class; there are countless ways to leave an impression in your students’ minds. How about conducting friendly competitions and interactive quizzes every now and then? Activities that can pump up students’ excitement and challenge them in a healthy way will help them learn more effectively, and help them think back on your classes with a smile as well. As quoted by John Holt, “Learning is not the product of teaching. Learning is the product of the activity of learners.”

Another aspect of context is the “why.” As a teacher, I’m sure you have heard this more than once: “Teacher, why do I need to learn this? It is not like I will use this at all.” I still remember all the times I was slumped across my desk, almost in tears over my Biology textbook, trying to memorise the 10 steps of glycolysis and the byproducts of the Krebs cycle. “Why do I even need to know this?” I used to think, “Who cares about ATP?” (Note: Almost everybody in science cares about ATP. Yes, I realise that now). But back then, nobody told me how important energy generation is for the human body. I was only told to commit all of these information into memory. It wasn’t until years later, when I came across these dreaded processes again in my nutritional studies, did I realise how essential they are for our bodies to function properly. That made me look at these cycles in a different way, and I found it much easier to absorb the learning material then. 

The Third C: Character

How do you want to be known as? Are you the loving type of teacher, or are you the formidable instructor who always carries a cane in your hand? Will you reward your class if they do well in a test?

I still remember one of my teachers in high school who bought Vitamin C tablets out of her own pocket for the whole class during exam periods. Together with this, she would also advise us to always prioritise our health. Back then, 16 year-old me had never experienced such warmth and care from an educator before, and this left a lasting impression in my mind. I will never forget this teacher.

As an educator, sometimes you might forget that all eyes are on you when you are standing at the front of a classroom. What this means is that your character, as well as how you act, will be an example to all the future leaders of the world. Take this once-in-a-lifetime opportunity to be a role model for all your “children.”

“Education is what remains after one has forgotten everything he learned in school.” ~ Albert Einstein

No student is going to remember everything that is taught by their teachers. What will continue to remain a legacy is the teacher him/herself. I am fortunate enough to have been taught by a group of passionate teachers throughout my schooling era, and I’m proud to say that I have become a better person because of them.

So, teachers, if you’re reading this, the question you need to ask yourself is: How do you want to be remembered by your students? Or do you not want to be remembered at all?