Archive: November 2013

5 Tips to Avoid Careless Mistakes for Maths (Tip #5): Check Your Answers

Maths Tip - Check Your Answers

By Leon, Private Tutor, Sponge ME, Maths Tuition Singapore

As the saying goes, “Prevention is better than cure.” I cannot agree with it more. However, avoiding CSMs (Careless Stupid Mistakes) can and will never be 100% full proof – you know and accept this. That doesn’t mean you resign to it without first putting up a good fight. If Plan A fails, there is always Plan B. A backup plan will ensure you keep CSMs to a bare minimal – it’s called checking your answers!

You may be thinking that you barely have time to check your answers, let alone finish your exam papers. Yes, that may be true especially if you lack practice. However, if you make it a habit to carry out intermediate checks as you work through your maths problems, you will realise that it is a lot more time efficient compared to checking only at the end.

For instance, if you had to navigate your way across the great oceans using nothing more than a compass – would you only check your compass once at the end of the journey (provided you get there in the first place), or would you be checking your compass intermittently throughout the journey to make sure you are on track? Checking your answers is based on the same logic. By placing so-called mental check points throughout your working steps, you will be able detect an error early, rather than when it’s too late.

Of course, exactly how to check and where to check is a topic best left for another day. But in a nutshell, you should be equipped with a set of ‘check tools’, namely the Sanity Check (good for making quick sense of numerical answers), the Reverse Check (good for checking algebraic manipulative errors) and the Loop Check (good for quickly checking solutions by means of substitution) and learn how to use them effectively. There are also ways to make use of certain features available on the latest approved scientific calculators to double-check not just arithmetic, but also algebraic and statistical calculations.

Once again here are the 5 tips to avoid careless mistakes for your GCE O-Level Mathematics exams:

  1. Do NOT Skip Steps
  2. Know Your Tendencies
  3. Watch Your Units
  4. Keep It Neat
  5. Check Your Answers

I hope that you have found this series of posts educational and have realised that though CSMs can’t be entirely eliminated, they can definitely be suppressed with a high level of success and anyone can learn how to do this. All the best for your exams! 😀

5 Tips to Avoid Careless Mistakes for Maths (Tip #4): Keep It Neat

Maths Tips - Keep it Neat

By Leon, Private Tutor, Sponge ME, Maths Tuition

I know, some of you may be thinking: “This is not a tip! Everyone knows that if you are neat, it’ll help reduce careless mistakes. I just write the way I do. I know it sucks, but I can’t help it!” I hear you. Firstly, I’m not asking you to change your handwriting. That will be somewhat impractical (especially for math) and too steep a mountain to climb. What I’m suggesting is that you make a few adjustments to the way you present your mathematical solution, i.e. in a more organised and consistent manner.

So, besides making sure your ‘a’ doesn’t look like a ‘9’, or your ‘z’ like a ‘2’, the key is to find a standard format that you can easily apply over and over again for the various topics in mathematics. A standard format typically consists of the following 3 steps – (1) state your equation, (2) substitute all known values and (3) solve for the unknown.

At the end of the day, the main purpose of adopting a standard format is so that you have a familiar and reliable set up which you can consistently repeat with little effort. This will allow your mind to fully focus on solving the actual mathematical problem at hand. If done well, it will definitely improve your overall neatness and reduce the likelihood of careless mistakes.  Hooray! Yet another one bites the dust! 🙂

And last but not least, Tip #5…

Mixed-text / Descriptive / Reflective Model Essay #2

I am who I am today - Eleanor Roosevelt

Who are you? Describe the people, places and experiences that make you who you are today.

Former First Lady of the United States, Eleanor Roosevelt once said, “I am who I am today because of the choices I made yesterday.” I agree with her as the choices we make in life often define us and determine our destiny. Apart from that, there are also other important factors that make us who we are today. In my sixteen years on earth, a few people, places and experiences have made a profound impact on me and influenced my outlook on life.

A person who plays a significant role in my life is my older brother, Andrew. He is special. Born with one less chromosome, he has problems with learning and speech, which makes it difficult for him to be independent. Currently, he attends a school for the intellectually challenged, learning basic skills such as simple arithmetic. At home, he sometimes throws tantrums in an attempt to get attention, and these episodes may occasionally be violent. As his brother who has lived with him for so many years, I have grown to be more tolerant of his random outburst. I love my brother dearly and I try to spend as much time as possible with him despite my busy school schedule. Personally, I feel that I am more mature than others in my cohort as I had to step up to be the “big brother” and help to take care of Andrew from the tender age of three. I am who I am now because of Andrew and I feel very privileged to have him as my brother.

A place I visited last year has also shaped me as a person. It was a small, impoverished village in Cambodia. The trip was part of my school’s community service project and I was there with two teachers and all my classmates. To be honest, I got a rude shock when I first arrived there. The place was practically made of sticks and stones. It also lacked basic facilities such as clean water pipes and sanitation. It was hard for me to get used to the living conditions there as my life back in Singapore was worlds apart compared to the shed where I stayed in for a week. Nevertheless, I took it in my stride and worked like a Trojan, repainting the only school there and even mending a leaky roof. In retrospect, my trip to Cambodia really opened my eyes to the outside world and allowed me to see how fortunate I am to be living in an urban and affluent city like Singapore. In the past, my life was rather sheltered and I was blissfully ignorant of the many hardships in this world. Now, I am an adolescent with a social conscience. I will always remember Cambodia fondly and I hope to go back for a visit in the near future.

Finally, an incident that happened nine years ago has profoundly affected me and made me who I am today. It was a typical Saturday morning and I was at a grocery shop with my mother. Back then, my parents were very strict and they forbade me from eating sweets except on special occasions. However, being a young and simple-minded seven-year-old, I furtively grabbed a handful of candies from the shelf and hid them in my pocket. When we left the shop, I felt elated that I had gotten away with the theft. Upon reaching home, I went to my room to feast on a few candies and kept the rest in my pocket, which I soon forgot. The following day when my mother was doing the laundry, she found the remaining candies and immediately questioned me. I lied that I had picked them up on the road. Needless to say, she did not believe me and demanded to know the truth. As her big eyes were boring into me, I was scared stiff and confessed my crime. She then dragged me back to the grocery shop and insisted that I apologised to the grocer. To teach me a lesson, she even suggested to the grocer to alert the police as I must pay for my mistake. Thankfully, the grocer was a magnanimous man and I was forgiven on the spot. Since that fateful day, I have learnt that stealing is wrong and that our actions must always square with our conscience.

To conclude, I am who I am today because of the above person, place and experience. I am grateful for them as they have taught me valuable life lessons and moulded me into a better person.

GCE O-Level, 2014, English Tuition

5 Tips to Avoid Careless Mistakes for Maths (Tip #3): Watch Your Units

Maths Tips - Watch Your Units

By Leon, Private Tutor, Sponge ME, Maths Tuition Singapore

Another culprit is using the wrong units, i.e. the Unit of Measurement (UOM) in calculations. This frequently occurs in questions or problems involving rates or quantities such as speed, distance, time, money, and measurements of weight, length, etc.

The likelihood of a UOM-related CSM (Careless Stupid Mistake) increases when you do not use units in your working or statements. In most cases, students trivialise the importance of UOMs and in some cases totally ignore it. Hence, it leads to mistakes. The best way to become more acquainted with UOMs is simply to use them in your calculations or mathematical statements.

In my maths tuition classes, I break down common GCE O-level maths questions into specific types or categories in order to sensitise my students to the ‘warning signs’ (among other reasons). And when they detect ‘trouble’, they immediately become prudent and convert all rates and quantities to the same units before attempting to solve the problem. Yet another CSM crushed! Woohoo! 😀

Tip #4 is on its way…

5 Tips to Avoid Careless Mistakes for Maths (Tip #2): Know Your Tendencies

Maths Algebra Pattern

By Leon, Private Tutor, Sponge ME, Maths Tuition Singapore

Having tutored many students over the years, and helping them to prepare for their GCE O-level Mathematics and Additional Mathematics exams in Singapore, I can’t help but notice certain patterns of occurrences, i.e. that everyone (myself included) has a tendency or inclination to make a specific type or types of CSMs (Careless Stupid Mistakes).

For example, some students tend to make what I call copy or transfer errors, i.e. they copy down the question wrongly, miss out a variable or index here and there, or transfer a sign wrongly from one step to the next. Others tend to make simple operational errors like adding instead of multiplying and the list goes on. The point is –  it’s likely that you will be more prone to making a specific type of CSM, and honestly sometimes all that is needed is a conscious effort and think “Aha! I’ve made a CSM doing this before, I better be more careful this time round.”

But of course, this only works if you are first aware of your own tendencies. In my maths tuition classes, I’ve developed specific exercises to help hasten this process of self-awareness. It’s not rocket science. It’s just a comprehensive collection of typical GCE O-Level maths questions intentionally littered with the most common CSMs. The goal of the exercise is to spot the CSM and make the correction. It’s a simple yet effective way to discover and weed out common CSMs in a more proactive manner.

Tip #3 coming right up…