Straightening out and reaching further with friends.

Friends sit on each other.  They stretch and straighten each other up.  They cause pain to each other, then massage each other to relieve the pain.  Friends laugh and play together.  They share fun and vulnerabilities.  They can trust each other because each is trustworthy.  As a result, both emerge stronger, more flexible and with the gumption to reach further because they know that someone is watching out for them.

Your friends are a safe place for you to vent because they won’t judge you for the bad thoughts you think while doing their best to prevent you from acting them out.  They know that the horrid you is temporary and believe that the better you will overcome.  Friends civilise each other, which in turn brings about lasting marriages, strong communities, and allied nations.  In my son’s journey as a national athlete, he was constantly reminded that the purpose of international competitions is to build friendships.  After competing with each other in the arena, athletes would go for meals and game online together as friends.

I remember a chat I had with a neighbour some years ago during our daily afternoon play dates when our then little children met to play for 2 hours.  She mentioned something her mother had taught her about people: 让人吃一点不会死 , loosely translated, you won’t die if you let others win at your small expense, meaning “It’s ok to let small grievances go, there’s no need to get even.”  It was an unexpected moment of enlightenment which empowered me to view friendship from a new perspective, with the realisation that being petty wasn’t good for me.  My friend had provided me with a life-giving script to replace a destructive one that had been running inside my head and making my life miserable for forty years.

How often do you talk to your children about friendship?  Do you tell them stories about your friendships with others?  Do you ask them: what makes a friend a friend?  How can a person be a friend to another?  Who initiates a new friendship?  What’s the difference between old friends and new, and why is there a need for both?  In your conversations about friendship, you will be treading on very important concepts of collaboration, compromise and cooperation. Explain them to your child, and talk about it over and over again.  It is a conversation worth repeating because your child will see and apply the concepts differently as he matures.

The skill of building friendships requires time and practise to hone.  If it is an art that you are not good at, don’t feel embarrassed about it – it is never too late to learn.  Watch a good movie or drama, or read a book together, and have a discussion about the characters.  Talk about family issues and community news selectively with your child.  Try to be as objective as you can.  Help him see the same problem from different perspectives.

The earlier you start your child in the conversation, the more conversant he will be in the language of building friendship. In a world that is full of people to navigate around, he would be armed with  a set of skills that are far superior to having A grades in his report card.  If he is bad with numbers, it’s ok because he’ll have a friend who can help him organise his finances.  If one friend tries to cheat him of his money, he’ll have another friend to warn him.

But not everyone will respond to his efforts to make friends.  He needs to know that foes exist in this world too and it’s prudent to discuss how he should respond to them as well. 💐

Recognising Quantities

Recognising Quantities

I want five.  I wish I was five.  It is five.  It has five.  There are five.  We say these sentences so often that we overlook the fact that they are incomplete.  Are you gritting your teeth now and mumbling to yourself, “Five what, monkeys?”  Because of the missing noun, many jokes emerge from such statements.  The fact is this:  numbers are adjectives, and they describe a quantity.  When you are counting to five with your fingers, fingers is a noun that you add to the adjective five to provide context. This change of perspective can bring new life to your math discussions! 

Fingers make useful counters as they are properly organised and conveniently located on our hands.  What if we change the context to five marbles rolling in a spacious box, constantly re-organising themselves?  Most toddlers will sit and stare at such an activity because it is interesting to watch the shape of five (an idea embodied by the 5 balls) change.

Whether it is five balls, five birds, five people, five random items, we instinctively know the quantity without actually counting them because we recognise the various shapes that a quantity of 5 can take if it is visually contained within a frame of our view.  This is called subitizing, the ability to recognise the shape of small quantities without counting, and it is important to your child’s number sense.

There is a time to count, and there is a time to recognise. When you ask, “How many are there?” and your child replies, “five” correctly, do not require him to give you a reason.  Do not say, “let’s count: 1, 2, 3, 4, 5.”  If you insist on making him count, you diminish his confidence in his own ability to recognise five.  Praise him instead and move on.

Click on the links below for some 60-second videos that may give you some idea on how subitizing works.  You can show it to your toddler too.  Mute the volume and use your voice instead, if possible.

Recognising the quantity of one.
Recognising the quantity of two.
Recognising the quantity of three.
Recognising the quantity of four.
Recognising the quantity of five.
Recognising the quantity of six.
Recognising the quantity of seven.
Reconising the quantity of eight.
Recogising the quantity of nine.
Recognising the quantity of ten.
Mixed Quantities – Set 1.
Mixed Quantities – Set 2
Mixed Quantities – Set 3.

If you were math-injured as a student because you didn’t know that numbers were adjectives, and you had trouble understanding math sentences that were made up of adjectives, I hope this blogpost brings you healing and speedy recovery!  💐

Fun-filled Music Conversations: My Son’s Ukulele

The ukulele I’m playing in this video belongs to my son.  I bought it for me, but I gave it to him as a birthday gift knowing that I’ld be the one enjoying it.  What sort of a horrid mum would buy her son a present that’s meant for herself?  Me! 🤣

But seriously, what better way to give your child the gift of music than to create an environment and culture for music appreciation to take place?  Here’s the truth: your child is a sponge, the younger he is, the more absorbent.  Whatever type of music you listen to, or sing, or play, or learn, and in whatever languages, your child will be absorbing them all, whether you like it or not!

I love music and languages.  When my son came into my life, I learnt, memorised and sang songs for him in putonghua and various Chinese dialects. I figured that my imperfect accents were better than nothing.  We attended church and sang songs as a community.  In the car, we listened to different genres on different channels on the  radio.  I read up about my favourite tunes, songs and bands, and I told him about them as stories.  It was hard work but it wasn’t too painful for me because I was interested in the topics and determined to make our home as conducive as possible for my son to enjoy language and music.  My aim was to meaningfully expose him to as many sounds and words as I could, and to do so carefully without drowning him with too much at any one time.

Now, back to the ukulele and the video. If you have no prior background in music, the ukulele is an excellent first instrument to pick up for various reasons:  it is cheap, small, light and has only 4 strings, making it relatively easy to learn.  If you learn to play it, it is easy to lure your children who are 4 years and older into playing it too.  All you have to do is to leave the instrument lying on the sofa after playing it and your curious children will certainly tinkle with it. 

If you need a recommendation for a ukulele, you can find it in the description section of the video.  Let me know how your journey goes in the comments section below this blog.  I’d love to hear from you. 

In the meantime, you may like to read other related posts I wrote:  

Here’s wishing you many fun-filled hours of joy with your ukulele! 💐

School In The Bath Tub

He practically schooled himself on the topic of volume while he bathed.

I wrote about this in Fun-filled Math Conversations With Your Child .  Notice the purple 330ml Ribena carton floating in the bathtub and the white basket filled with his bath toys!

I’ve reproduced Chapter 11 Volume below for your reading pleasure.

My little son loved to play in the bathtub.  Often, he would run dripping wet into the kitchen asking for containers to play with. Eventually his bath toys included straws, syringes, plastic pumps, water bottles, milk cartons, spoons, measuring cups and more. Needless to say, he schooled himself on this topic of volume while he bathed.  

We had a name for each toy so that we knew exactly what each other was referring to when we conversed outside of bath times.

Transparent plastic measuring cups and water bottles with measurement marks made great learning tools for us.

“This is a 500m water bottle.  See this 500m marking?  If you fill this bottle beyond this mark, there would be more than 500m.

“Do you see these
markings on the side of the bottle?  If you fill the bottle to this mark, you will have 100m of water,… and 200m here,… and 300m here…and 400m here, and of course 500m here.  This space in between 2 markings is called an interval.  Get it?”  I point to the markings as I spoke.

“So, if the bottle was filled halfway, and the water level was between the 200m marking and the 300m marking, how much water would there be?” (250mℓ)

“Shall we fill this milk carton to the brim?…What happens when I squeeze the carton? …Yes, the water will overflow,… that is because the volume of the container is reduced,… but has the carton become smaller?”

Composing spontaneous questions incorporating math (and science) language is an art that required background work on my part, to familiarise myself with the subjects.

“Let’s fill the water bottle to 300m… and  let’s drop 10 marbles (or stones or toys) into the bottle.  What is the new water level? (about 350m)

The marbles displaced the water by 50m.

What do you reckon is the volume of the 10 marbles?”

As always, I doodled tables in my son’s jotter book for him to record the measurements of his bath toys.

Toys Volume
Water Bottle 500 mℓ              0 . 5 ℓ
Milk Carton 1000 mℓ              1 . 0 ℓ
10 marbles 50 mℓ              0 . 05 ℓ
Tablespoon 5 mℓ                0 . 005ℓ

When it was time to formalise his understanding at a sit-down lesson (many months later), I drew this in his jotter book : 

“Let’s recall.  These are called markings and the space in between them is called …interval.”  I gave him time to recall while I wrote it down to prompt him.

You know that 500m plus 500m equals 1000m, right?  And you know that 1000m equals 1, don’t you?”  I write in large fonts as I spoke:

I guided him through the conversion of litres to millilitres and vice versa, limiting my questions to only mulitiples of 100mℓ for the start. When I was confident that he would be able to tackle practices on his own, I gave him some.

The conversion of the more complicated volumes below 100ml (eg 25ml, 5ml) were reserved for later day.

By the way,  I read somewhere that we all experience creativity when we shower or take a bath because of the rush of alpha waves in our brains when we are in water!  Isn’t that perfect?

Try it! 💐

Our Usual Jam Session

Our Usual Jam Session

My friend Penny visited us one day and insisted on recording this part of our homeschool journey because she was amused by our routine. As it was usual for my son and me to do music together, we didn’t think it was anything special.  Anyway, little Ethan was sufficiently persuaded by Auntie Penny’s amusement to play for her camera.  I’m sharing this video with the other Auntie Pennys who might be curious about the stuff we did with so much time in our hands, and why we had so much fun.

Let’s begin with a disclaimer to provide perspective – I’m not a professional musician.  The only music certificate I have was acquired at age 5 and it wasn’t even a Grade 1.  I did, however, at age 11, enjoy 2 years of classical guitar lessons at Yamaha Music School when they first opened.

Now, back to the video and sharing two points of learning for the little Ethan:

Tempo.  An internal metronome was ticking inside his head to provide him with timing. He had to feel secure enough to pause.  Without pauses, there can be no rhythm.  Pauses are scary because the player is required to WAIT and DO NOTHING.

Tune.  At the 1:13 of the video, you will see the song sheet that he was looking at during this session.  Notice that it contained only words and chords.  The lyrics he read with his eyes had to be translated into a familiar tune inside his head in advance of the song being played.  His brains would then instruct the fingers on his right hand on the notes to hit next.  The chords provided instructions for the fingers on his left hand.  The fingers have to be strong and coordinated sufficiently to be able to carry out those instructions.  If a wrong note was hit, his ears would catch the error, and then his fingers would have to adapt until his ears were satisfied that the tune resembled the melody line that was inside his head.   This feedback will go back and forth.

Technically, it sounds pretty complex, but in practice, it was quite simple.  Dealing with the stave and semiquavers in sheet music is a lot more daunting to me, and there are many people (like me) who enjoy learning to play music by non-traditional methods.  Notice the white disc on the piano top (in the video).  That was something I created to teach him theory – major and minor scales, the chord combinations and transpositions.  I taught my son to play the piano the way I play, by ear, by numbers and by patterns.  I’m glad that the methods that worked for me, worked for him too!  In the last 10 years, thanks to technology, many other new methods of learning, consuming and producing music have evolved. Check out youtube videos, synthesia,  MIDI and other software applications (apps).

If you are planning music lessons for  your child (and yourself), you are spoilt for choice, with many of these options available at very affordable prices.  Don’t feel restricted by traditions, just go with anything that brings joy.  The best way to start music lessons is in the spirit of fun.

I remind my son always:  We are not performers. We play music because music brings people together.  That is my wish for you too. 💐

My Dancing Queen

The Dancing Queen
Mom and me

 Mom taught me to do the cha-cha when I was little.  Back then, it was socially awkward for people to dance alone, thus making me a very available and convenient dance partner for Mom because she loved to dance.  Pa had made enough money in his career to afford a turntable and several records which provided Mom and me with the privilege of having music on demand, meaning we could dance repeatedly and whenever we liked, to an instrumental stereophonic soundtrack of Cherry Pink And Apple Blossom White with the trumpet leading the way.  (Click Here to hear how it sounded like).

Right, left, right, right.  
Left, right, left, left. 
Back, two, three four. 
Front, two, three, four.

she would teach me the steps.

“Don’t start too soon.  Wait for the first beat.  Listen carefully to the music…Pay attention, it’s coming… One, two, three, go!”  She taught me to hear the music, count the beat, feel the pulse, and groove along.  She was neither a musician nor a professional dancer, so dancing was not complicated.  She was not an educator, so there was no ambition to make me cleverer.  She was mom and her purpose was simply to dance, have fun and have us entertain each other.

I used to think that everyone could feel the pulse the way I did and often got frustrated with friends who seemed clueless about what I was trying to communicate in my effort to teach them to dance.  “Listen to the song!  Start on the first beat.  Can you hear the first beat?” I would ask.

“What first beat?” they would reply, then stare blankly at me in anticipation for a reply.  It finally dawned on me that they were truly clueless. 

In social dancing, people dance in pairs, and in order for 2 people to dance together, some form of synchronisation has to take place and this is governed by the tempo of the music.  If a partner can’t feel the rhythm and needs someone to count the beat throughout the tune, then dancing becomes mechanical, which is still fun, but very much less fun.

It took me a long time to realise why I could feel the pulse and how I acquired my sense of timing.  It was mom’s gift to me during my early years.  Precious, but I was slow to acknowledge it.  Thanks, Mom.

Math is about counting.  Years, days, hours, minutes, seconds, rate, speed, frequencies and etc.  These are all time-related units of measurement.  Musicians and dancers count all the time, they ought to be good in math, yet many of them struggle with the subject.  Conversely, mathematicians ought to be good musicians and dancers, but if you’ve seen them on the dance floor, uhmm… I should reserve my comments about that.

Understanding math in the form of beats or pulses, and being able to translate them into movement should be considered as legitimate as the ability to count sheep and writing the quantity as numerals on paper.  Unfortunately, civilisation hasn’t reached there yet and math exams are still conducted with ink on paper, while dance is yet to be considered a core subject.

But that said, what’s stopping you from flouting conventions and enjoying math with your child in movement rather than by sitting still?  Here’s my point, dance and consider it math lessons:

ONE, two, three, four.
TWO, two, three, four.
THREE, two, three, four.
FOUR, two three four.

4 bars of 4 beats makes 16 beats.  Write it for your child to see:

4 x 4 = 16

Let’s do math while we do the cha-cha! 

The Lunar Calendar

Counting time with 5 elements and 12 animals.

Fun facts about the lunar calendar and its naming conventions:

The Chinese built a 12-year cycle represented by twelve animals into a larger cycle of five elements:  metal, water, wood, fire, earth.  The animal changes every year, but the element changes every two years.  We are presently in the year of the Metal Rat – the first element paired with the first animal!  After this will come the year of the Metal Ox, followed by the Water Tiger, then the Water Rabbit, and so on.  The year of the Water Rat will arrive in 12 years.

12 animals x 5 elements = 60 years.

A person has to live through one complete cycle in order to acquire wisdom – the reason why the Chinese celebrate their 60th birthdays.  This means that the other surviving “metal rats” are either turning 60 or 120 years old.  Think about that! 

“Teach us to number our days that we may acquire a heart of wisdom.”
~ ancient proverb.

By the way, did you notice the use of the quinary (base 5), duodecimal (base 12) and sexagesimal (base 60) number systems here? Just because the schools teach only the decimal (base 10) system doesn’t mean that other systems don’t exist.  It’s good for your children to know that. 

Grandma taught me to recite the list of animals in Hokkien, together with its rhyme and rhythm.  If you are Chinese and know of elderly dialect speaking Chinese, get them to recite the list and record their voices.  Learn it because it’s fun, then teach it to your children and grandchildren.  That’s how we pass down the valuable tradition of counting without using numbers.

Happy Parenting!  💐

The World That Didn’t End

Wild flowers blooming. The earth is more resilient than we credit it for.

I remember March 10, 1982.  I was 14 years old, sitting in class and waiting to die.  A periodical I had read some days earlier informed me that the world was ending THAT day.  I didn’t want to go to school because facing termination with my family was much more comforting than facing termination alone, but I went to school anyway.  In class, my attention drifted between the teachers, who appeared clueless that the world was about to end, and the anticipation of a loud bang, a dimming sun or quaking floor.  No excitement happened, the end didn’t arrive.  I was a little disappointed that the day was boring as ever, but mostly relieved that every person who mattered to me was still alive!  I now know that the ending of the world on March 10, 1982 was prophecised in a book titled The Jupiter Effect.

Back then, my idea of an apocalyse was simple.  I knew exactly how The End Of The World would take place because Skeeta Davis had presented it to me in a song that had been playing in my home since my parents bought her album:  the sun would stop shining and the sea would stop rushing to shore.  Star Wars was barely in its second installment and sophisticated visual effects of movies had only begun to mess with my imagination.  Watch the original Star Wars movies before they were digitally remastered and you’ll get an idea of how far the movie industry has come.

18 year after my first apocalypse came Y2K, the idea that the world would be in chaos when the date changed from December 31, 1999 to January 1, 2000.  Because computer dating systems might not recognise the year rolling over from ’99 to ’00, planes might crash, bank accounts might disappear and factories might explode.  I must admit that I wasn’t completely at ease on December 31, 1999 because the cases proposed by the apocalypticists sounded legitimate.  Was I relieved when I heard the news that some nations had crossed over safely to January 1, 2000?  Yes.

Next came 2012, the doomsday that was anecdotally written about in an ancient calendar.  The prophesied event was even dramatised in a Hollywood blockbuster movie and presented as a far more frightening catastrophe than the 14-year-old me had imagined in 1982.  I didn’t have time to follow much of this story, but before I knew it, 2013 arrived.

Then came doomsday 23 September 2017, a date calculated from another ancient source.  You can guess the outcome of that prophecy too.

Which brings us to the important question:  Is the world coming to an end?  If so, when will that happen and how will we know?  Once again, somebody somewhere appears to knows exactly how and approximately when this will take place because children these days are taught that the earth is getting warmer and that its end is imminent if no action is taken to put a halt to its rising temperature!  According to them, although nothing can be done to stop the warming, many things can be done to slow it down.  The idea even has a name which isn’t worth mentioning here because the experts haven’t made up their minds about what to call it.

As a reformed doomsday junkie with the benefit of hindsight, I can identify many differences between the apocalyptic message I read about in 1982 and that which many children are taught in this generation.  Here are some:

  • The source of the message in 1982 was in the free market. I consumed the information at my free will.  It wasn’t fed to me by my school curriculum or class discussion.
  • I wasn’t made to feel guilty or bad for my view if it differed with the position held by the majority.  If I had to defend my view, I would have crumbled for the lack of maturity and the necessary vocabulary and confidence to articulate, and since my thoughts on the subject were planted in me by the media and spiced up by my teenaged hormones,  my defence would not have been worth much.
  • No prescribed response accompanied that piece of news in 1982, thus  no one was under social pressure to take, or not take, any action. In that sense, it was merely a harmless spook for most people.  However, the apocalyptic narrative that is told to the present generation of children requires nations to take real actions to mitigate an imaginary calamity made up of the collective imagination of movie producers and fiction writers.  Since it has never happened before, experts have to build mathematical models to predict the magnitude of imaginary repurcussions.  Then comes the real thing!  Other experts have to be engaged to draw up plans for real actions to prevent this imaginary problem.  Real actions cost real money.  Given that the people who believe the present apocalyptic prophecies are matured high ranking politicians (instead of a gullible 14-year-old) possessing spending power to purchase hope, hope has become a lucrative industry.  Let’s not talk about who’s money they are spending.  I invite you to read this comic piece I wrote explaining this agenda-problem-solution triad.
  • Unlike previous poorly funded apocalyptic messages that bore definite termination dates, this modern message is timeless and rich with funding.  It is timeless because the prophets haven’t made up their minds regarding when the earth would get so warm that we would all perish by roasting, either at the same time or in turns by geographic location.  There were also suggestions that some people would freeze while others roast.  Extending that logic to the tiny sea-level island of  Singapore, I suppose we would likely drown, boil or steam.  Ha!

Apocalyptic prophecies are not new.  Ancient Mayan and Jewish writings reveal that people centuries ago thought the earth would reset in their generation as well.  Many modern day Christians still believe in the impending Day when they will stand before their Judge to give an account of their lives on earth.  The Chinese, on the other hand, do not have such ideas embeded in their traditions, at least not to my knowledge.

What are your thoughts about apocalyptic prophecies?  Do you think the earth is getting warmer?  Will it come to an end?  Does your child believe that the earth will end in his lifetime?  Is he afraid or confused?  If the end was happening tomorrow, would he live wrecklessly or meaningfully today? 

Have a conversation with your child about this subject.  If your child is 5-year or older, he would have been sufficiently bombarded by commercials, school and passing conversations to have a rough idea of this topic.  Kids are clever.   Address his concerns, share your opinion and offer hope.  It’s fine to say that you don’t have an answer.  Help him see that even smart adults don’t know it all.  If you fail to engage your child in this conversation and provide necessary filters, the media is happy to educate your child with their propaganda and he will have to derive sense out of possible nonsense on his own.  A gentle nudge to you that the apocalyptic message is usually depressing and hopeless, not a healthy thought for a child to ponder over.

So, do I believe that the earth is warming?  Of course not!  How can the earth be warming if hot air rises, heat gain equals heat loss, and if we lived in an enclosed dome? Yes, a closed terrarium, a geocentric earth or whatever you wish to call it!  Ha!  You’ll have to figure my logic out for yourself, and you don’t have to agree with me.  My 17-year-old son and I are still debating this after many years.  We are allowed to change our minds and positions anytime we like, no one is required to be locked into a single position.  Challenging the status quo does exercise our thinking and observation skills.  Some people call it nonsense talk,  but I prefer to call it a continuous fun-filled conversation!

Happy Parenting!  💐

Adding Colour to Math

Isn’t math so much clearer with colours? And alluring too!  You can now show your 8-year-old why the sum of odd numbers starting from one equals the square of the the number of terms.

Adding 1 Term   → 1 = 12
Adding 2 Terms → 1 + 3 = 22
Adding 3 Terms → 1 + 3 + 5 = 32
Adding 4 Terms → 1 + 3 + 5 + 7 = 42
Adding 5 Terms → 1 + 3 + 5 + 7 + 9  = 5 (See Diagram)
Adding 6 Terms → 1 + 3 + 5 + 7 + 9 + 11 = 62

and so on…..

Adding 250 terms → 1 + 3 + 5 + 7 + 9 + … + Term250 = 2502 = 62500

Here are some other ways of looking at the same sum.

You can even arrange the ascending odd numbers into a spiral mosaic!

Sometimes, math is better played than taught.  And who knows, such patterns may just show up in a PSLE exam!

By the way, I bought these colourful blocks/tiles from the toy department, not from the academic section. Fun-filled math conversations can be found everywhere!

And as we draw towards the close of the year and the beginning of a new one, here’s wishig you a Merry Christmas and a new year filled with forgiveness, love and laughter!

What Is 1 Centimetre?

Jotter Book

How do you like this page in my son’s jotter book?  It was a doodle produced during a continuous conversation about Length, a story I wrote about in Chapter 10 of Fun-filled Math Conversations With Your Child. You can see how much I enjoyed doodling and how much he disliked colouring. It was important that I taught him to translate the information floating inside his head into a readable and writable form on paper so that others can understand him.  This is called literacy.  Exams are paper-based after all.

The process went like this:

1.  He measured the objects with his personal measuring tape and read the measurements aloud. Reading aloud is important because if he couldn’t read it, then he wasn’t ready to write it. I scribbled his readings down somewhere.

2.  I turned to a blank page on his jotter book and drew some of the things he measured, after which he filled up the the blanks with his readings.  He knew perfectly well that my drawings were perfect misrepresentations of the actual objects he handled.  Despite the 17cm pencil being drawn longer than the 25cm jotter book on the page, he wasn’t bothered because he understood 17cm and 25cm in context of the actual lengths.

So here’s a teaser question for you:  What would he have learnt if I had skipped the measuring activity and given him the following worksheets instead?

Fictitious Worksheets

Now imagine yourself as a kid who is struggling to read, write and count, while figuring out how real objects are represented on paper.  How would you fill Worksheet 1?  Would the jotter book be 4cm long, pencil be 5cm, and eraser be 2cm (because you measured the picture on the book with a ruler)?  What if the ruler was drawn in for you (as in Worksheet 2)?  Would you cease knowing what 1cm actually is?  Would you be confused?  I write this post to bring humour and caution because I have found plenty of such material in the bookstores, the expensive ones are printed in full colour. 

If you are shopping for a workbook to help your children improve in math, make it your duty to check the material before buying them.  Be very protective of your children’s cognition. Handing them materials that confuse them can be disastrous. The damage will not be noticeable immediately, but its effects will show up later, making the problem hard to diagnose and expensive to undo.

Empowering your child with real life math skill should never start with worksheets.  It has to start with reading, in this case, reading a measuring tape. In a class of many students, who will your child read his measurements to?  Will guidance be available immediately if he read it wrongly?

Why don’t you provide that guidance instead? The cost to you would be $5 for a measuring tape and multiple fragments of time when both of you are in a queue together, or waiting for your bus, or just waiting.  There are so many things to measure while you are waiting – a blade of grass, a strand of hair, a $2 note,…  Convert those unproductive moments into useful fun-filled conversations.  Remember, if he can’t read it, then he’s not ready to write it.

I like to keep things simple.  Our happy moments with full freedom of expression, have been captured and collected in the blank pages of cheap jotter books that are flavoured with noodle and milo stains.  Precious.