Primary school word problems have always appeared hard for most parents. These questions are sometimes confusing and many parents find it very challenging to teach their kids.
Under the PSLE math framework, there are a total of 11 basic heuristic concepts and thinking skills to be tested.
How many out of these 11 skills does your child know?
Every P1’s student started off by learning these two skills – drawing boxes (basic model-drawing) and looking out for pattern. These are relatively simpler as their activities involve lots of drawing and coloring.
As your child enters the next level, he is required to learn more, assuming that he can catch up with his peers.
These skills include:
– making a list or tabulating,
– guessing and checking,
– working a problem backward,
– using before-after concept and
– making supposition.
Let me try to explain what these terms mean. 😉
1. Making a list – listing and writing a number of items in proper sequence and labelled with their quantities so as to arrange the data (numbers they have collected) in the right order so as to solve the question
2. Guess and check – guessing a possible scenario and working out the numbers (and hoping that you get it right the first time round). If the answer is right, Congratulations! If it’s incorrect, guess again and check and hope for the best.
3. Working backwards – you are given a scenario and a conclusion. Now, tell me the story backwards and work out the initial numbers. It’s like walking backwards in the dark. :O The good thing in math questions is that you have the numbers and keywords to guide you.
4. Making supposition – Suppose or guess the number of one of the two items are the same, how can you work out the answer. The experience? It’s like guessing what is in the bag and how many objects are there, simply based on the shape of the bag.
Of course, this is a very simple one-sentence or two-sentence explanation and there’s more to it in reality. To be able to accurately work out these math questions, your child needs basic thinking and analytical skills.
The other questions to ask ourselves are “How do we make a list correctly?”, “How do we work backwards? Where do we even start?”, “How do we check? We’re not even sure what we’re supposed to guess.” and so on.
Some of the thinking skills are:
– Analyzing parts and whole,
– Comparing them,
– Identifying their patterns and relationships and
– Working out your solutions, assuming you can see what you are solving and where you are going.
On top of that, another assumption is that your (and your child’s) math concepts are as solid as steel and you are able to apply them flawlessly.
As we know, heuristic also means learn by discovering. While the intent is good, most lessons are being taught as if they have deadlines and little time is being given to the child to learn at his own pace and to discover what it’s being taught. It’s practically like fire-fighting in school everyday! No time to loose.
I have our students sharing with us.
“My teacher gave me 2 complete sets of exam paper. Over 20 plus pages. And she said we have to hand in tomorrow.” :O
At the same time, in my opinion, there are many myths about primary school math and I hope to use this post to uncover some of them.
Having understood the math framework (hopefully a little bit better), let’s look at the common myths about primary school math problems.
1. “I must know 100% of everything”
Unless you are aiming for full marks (100 marks), why is there a need to know everything and get everything right? (Of course, almost every parent strives to get their children to score as near to 100 mark as possible.)
Let’s say, all you want is an ‘A’ and to be on the safe (“kiasu”) side, let’s aim for a high A, say 80 marks. To get 80 marks, there’s room to get 20-mark worth of answers WRONG!
Getting 80 marks may mean many different combinations of marks between paper 1 (P1) and paper 2 (P2). Is it 40-40, 30-50, 20-60 or what?
Your child can get 40 marks (full marks on P1) and 40 marks out of 60 marks from P2.
Or 30 marks from P1 and 50 marks from P2.
Or 20 marks from P1 and 60 marks from P2.
Normally, Paper 2’s word problems are considered as “traps” for anyone sitting for this paper and going through it is like walking in a maze blindfolded as they are normally more difficult and less straight forward comparing to P1 questions.
So if your child lies in this category, getting 40 marks from P1 and P2 may be a better strategy.
So what is your child’s strategy?
2. “I must always be working on new questions.”
I always have parents asking me what kind of assessment books they should get for their kids and how many should they buy.
In my opinion, I would prefer working on just one or at most two assessment books (good and comprehensive ones) and at the same time, working on school papers which are now so easily accessible. (You can even consider getting previous school papers from your child’s school or you can get them from the teachers, from their school library or even from school website.)
The better way of working on math questions is to work on a few questions, get them corrected and get you (or a tutor or a math coach like ours) to give the child’s feedback on the correct and incorrect steps. The next important step which 99% of parents fail to do, is to get their children to redo the questions some time later.
By working on the same questions, the child may learn something new.
By getting these questions right this time round, the child’s confidence will increase and this is going to help the child do better next time round.
In fact, reworking on problems can train your child in being as strong as H-U-L-K (for those who know the Marvel hero – the strong incredible HULK!):
– Harvesting data from the question
– Using them the right way
– Linking them to the right concept
– K‘etting (Getting) to the right answer
So how often is your child re-working on the old questions?
3. “I must know all the thinking skills before I can work on any problem sum”
There is NO way to grasp all the thinking skills before working on any problem sum. In fact, such skills are cultivated while working on problems, getting them wrong, struggling through them till these children get them right – eventually. Period. There is no short cut to this.
Remember the word “heuristic”? It’s about discovery – your child’s discovery.
So my Number One advice to parents (I know all parents are busy, including myself) is to stop giving the solutions to the child or marking for them.
Let the child struggle and learn how to solve them by themselves. Yes, they may not get them right the 2nd time or the 3rd or 4th. It’s more time consuming but it’s goes a long way once they discover the right answer.
So how often do you allow your child to discover and teach himself these skills?
4. “I can buy as many assessment books as I want because by working on more books, my child will definitely do well”
Assessment books are quite useless unless there are used in the right manner. Just like a sushi knife, unless the chef can make good sushi, having a good sushi knife is pointless.
My preferred way of buying assessment books while helping you to save money is to get one or two books (at most). I prefer those that have their pages arranged according to topics so you can refer to them easily. School teachers teach by topics anyway.
Use red pen to mark and green pen for correction.
Those questions mark with green ink will be your indicators. Use these questions for future revision. So one book is always used twice, at least. 🙂 “It’s like double your investment!
So how many assessment books do you plan to get for your child?
5. “The longer the math tuition is, the more my child learns (and the higher the chance he can do well.)”
In general, a child’s attention span is about 15 to 30 minutes at most. (Actually, adults too, only if you realise that. We get restless really fast if the lesson is boring.)
Our mind is always thinking of something else though it seemed to us that we are “listening”. Hehe.
Some parents told me their tutors are asking for 3 hours or even 4 hours tuition based on the fact that their exams are coming. Yes, SO??
Unless your tutor is really creative, he understands how your child learn (is it visual, auditory or kinesthetic?), sitting through for a lesson for more than 2 hours is really a torture for most children and a poor investment of your money.
What you should do to help your child learn most effectively is to first be aware of how your child learn. If your child prefers to use her hands and work on problems, having a tutor who talks non-stop (assuming your child is listening) doesn’t serve your child well.
If your child is visual, your tutor should be drawing diagrams, pictures and explaining with hand movements and get your child amused. I used YouTube videos to get my students to be more interested in their studies and you can try out this method too. Occasional look into the child’s eyes (and smiling) also mean respect for the child and acknowledging he is there.
If your child is auditory, your teaching tactic should be using of voice and varying of tone and cracking relevant jokes to get your point across. Consistent praising, encouraging and reassuring will also come in handy to get your child to feel motivated and to really want to do well.
If your child is kinesthetic, your child learns the best by doing, writing, touching and feeling teaching tools (like blocks, plasticine, sticks). I remembered I emptied a student’s pencils and pens from his pencil case (of course with his permission) to explain ratio method. As we were using something he was familiar with, he immediately grasps the concept. Now, whenever he saw his pens and pencils, he can recall how to calculate ratio.
So which group does your child fall in?
6. “As long as my child doesn’t give me any feedback, it means he is ok.”
Really? I’m not sure about you but my experience tells me that whenever a child choose to remain quiet, it also means he has things to say and he is waiting to be asked – in the right way.
For all my students, the first lesson will always be getting to know the child first. Normally, I will ask “How he feels about math?” The common response will be “Ok lor.”
However, this simply reply has many meanings. Always, after rapport is built, most will talk more and share more. So, as caring adults, we have to learn to probe further – patiently. =)
So how often do you ask your kid?
7. “I always check if he does his work and this is good enough”
The secret to scoring well for primary school math is the same, still the same and will always remain the same.
Learn -> Apply -> Feedback -> (back to) Learn
and the cycle repeats.
Learning covers two aspects – academic and the child’s learning process (which again explains why is called heuristic which also mean discovery)
While grades from school exam and test papers will always be giving the child feedback on how much he knows, little feedback is given on how well the child’s learn.
Remember the visual, auditory and kinesthetic? Every child learns differently. Checking a child’s work can only show you so much about how well your child had answered the questions.
However, how much do we know about our children’s preferred learning style? How much do we know about their favorite topics and topics which they really hate or dislike? How much do we know about their struggles and how much they want their inner voices to be heard or how much they want a caring adult to ask how they are coping?
I was helping a child who once hated math because his previous math tutor believed in hard love and were scolding him all the time and were tearing his worksheets whenever this child did wrongly. He hated math SO MUCH!
When I started to coach him, I just wanted to find out and listen to him, without judging him, how much he really hated math and I wanted to hear the reasons. After some prompting, he shared and just like unchoking a pipe, he became much happier and as I gave him more assurance and affirmation, his grades soared.
So isn’t it good to help our children to “unchoke” their pipes once in a while? =)