Door-2-Math Blog

(I’m writing a bit long article today on introducing fraction to a young child.  For best result, this should be done at home when you have more time and space.  Good luck!)

Fractions are an important building block in Algebra, introducing it properly can help your child to progress along in mathematics smoothly. One way that I’ve found works the ‘magic’ is a simple hands-on introduction. The idea is to show your child how and why fraction is used, what does the numerator (I call it the ‘number on top’) mean and how it’s different than the denominator (i.e. ‘the number on the bottom’). Before starting this exercise, it is very important that you’re not stressed with math yourself – any stress you have will transfer to your child. Our kids are remarkable in picking up stress signals (especially non-verbal ones). Be aware.

Starting with a single piece of 8×11 paper on a large, non-cluttered table. Have a pencil handy. Ask your child to tear paper into half. You can either help your child fold the paper along the short side or longer side (easier along the short side) and tear it into two halves. Hold the two halves up and ask ‘if 1 is the whole piece paper, what do you think this is?’

Most kids (3 grades or up) will answer ‘half’. Write ½ in one of the half piece you’ve just made with your child. Now, take the half that does not have any marking on it, and ask, ‘what’s a half of half?’

Depending on your child’s grasp, some will answer ‘a quarter’. If yours didn’t, do not panic. Excuse yourself from the table and get 4 quarters from your purse (or wherever your family keeps the coin draw) and calmly show your child ‘four quarters make a whole dollar – and that is why they call a quarter a quarter 1/4 of a whole dollar).

Observe your child carefully; don’t rush to the next step unless you feel your child can connect 1/4 with ‘four of these 1/4 pieces make a whole’. This is important because mathematical concepts are build on top of each other, missing one link usually leads to breaking the whole chain of reasoning. The whole point is to build bridges from ‘known’ to ‘new concepts’ and no hole on this bridge is too small! (Maybe this will help: imaging your child is crossing the math bridge you’re building with tilts – you never know how a tiny whole will get him stuck!)

If you’re convinced that the concept on 1/4 is firmly established, then write 1/4 on one of the quart piece and tear the other one into half again. Show your child that half of 1/4 is 1/8 since now it takes eight of 1/8 pieces to make the whole 8×11 paper. A good leading question here is ‘what do you think the bottom number mean?’

What you’re looking for is a connection between ‘bottom number’ determines the size of the torn paper ( 1/2 is bigger than 1/4 and 1/4 is bigger than 1/8, etc). My experience has been if they can see it in their minds eye, they can picture it when they are starting to work on fractions. Having addressed what the bottom number mean in a fraction, the next natural question a student usually ask is ‘well, what does the top number mean then?’ If your child ask you that question, congratulations! That means that he/she is actively thinking and digesting the material you’re presenting. Fear not if yours is not asking what the top number means. What you need to do is then go back, re-enforce the concept on what the bottom number means and gently guide your child to the question ‘if the bottom number means this, then what about the top number’. A fraction is made up with two numbers: one on top and one on the bottom. Sooner or later, your child is going to wonder… ‘Okay, I get one of the two numbers, what’s with the other one?’

The logic answer for what the top number mean in a fraction is ‘how many pieces of certain sized paper do I have’, where the size of the paper is determined by the bottom number. For example, 3/4; means that one has 3 pieces of paper that’s 1/4 in size. Having address your child’s questions on ‘what does a fraction mean’, now it’s a good time to show how adding fractions (which requires finding common denominators in most of cases) is really nothing but a counting game. Here is how I proceed:

Holding up a 1/4 piece, I wrote down 1/4; on it and holding another 1/2 piece with ‘ 1/2′ written on it, I ask my students, now how much paper do I have? Most students respond “oh, this is adding fractions’ and they draw a line on the 1/2 piece diving it into two 1/4 pieces. Then majority of them, at this point, tells me the answer to 1/2+ 1/4=3/4. I then show them that when they dividing the 1/2 piece into two 1/4 pieces, math follows the similar procedure, and that procedure is finding the common denominator: If this is the first time you’re explaining fractions to your child, it is probably best to leave finding least common multiple (LCM) and greatest-common-factor (CGF) to another day. Introducing new concepts to young children, it is very important to keep it bite-size, so your child will not be overwhelmed

I’m not a car person, so up keeping an old car (especially an old Ford minivan like the one we’ve got) is by no means a pleasant task. But, as it’s ingrained into any Chinese, you just simply don’t toss an old working thing in favor of a new one. Anyway, when the AC failed on of the hottest desert days, I dreaded to take my chance with a unknown mechanic with a shop that literally looked like a hole in the wall. What does this have to do with helping my child to learn math, you ask? Well, let me get to it.

Taking the old grandma-car to this unknown mechanic turned out to be a blessing in disguise. As I returned for his verdict on the state of our old AC, he ingeniously read my discomfort and brilliantly used my kind of communication currency to:

1. get through to me that not only he is looking out for my best interests but
2. that he is the best one for the job and
3. managed to leave me feeling I’ve been taken care of.

Now mind you I ended up spending $300 that I was in no mood to spend. Now imagine you can get your Johnny to feel the way I felt after he spent 2 hours on the homework the he was in no mood to complete!! Talk about miracles! Reflecting back on my experience with the mechanic, here is my take on how he managed to get through to a person like myself, as non-mechanical as they come:

1. No jargon – I have no idea what a high-pressure cutout switch is nor do I care. He made sure that he had a diagram on hand and pointed to the parts that he intended to fix. That left me feeling good about not having mechanical vocabulary like he does — he was talking to me, not through me.
2. No threats – Not once did he say state the obvious that without AC, driving in a cooked minivan is uncomfortable. Maybe he was just using reverse psychology on me, but when he said that if you wait one more month, you might be able to wait till next April to fix the AC. Well, I know better. If I don’t fix it when its broken, pretty soon the whole car would be wasted away. It’s kind like saying one spoke off a wheel is no big deal, well except, with one gone, two is not far behind and pretty soon, the whole wheel collapses.
3. No denial of my discomfort – The mechanic, as unknown to me as a stranger on the road, did not try to brush away my discomfort with “it’s no a big problem. Only $300 will do”. $300 may or may not be lot, but what my discomfort of not really knowing/trusting him is. By acknowledging my discomfort with ‘I know you don’t yet know me nor my service,’ I didn’t have to keep on communicating my discomfort to him. A small passage in a Taoism text just popped in my head and it says, ” When too great forces collide, the one who knows how to yield wins”. Just like how water interacts with a stone -it is the ‘weaker’ water that shapes the stone and not the other ways around. By yielding to my discomfort and letting me be, the brilliant mechanic managed the formidable task at hand: winning my trust.
4. Reassurance – as I was signing by the X to pay for his service, he offered a 6-month insurance (or 6000 miles) for his service. What really finished me up is the following thought provoking quote he typed up on the warranty sheet:

“It’s unwise to pay too much, but it’s worse to pay too little. When you pay too much, you lose a little money…that is all. When you pay too little, you sometimes lose everything, because the thing you bought was incapable of dong the thing it was bought to do. The common law of business balance prohibits paying a little and getting a lot….it can’t be done. If you deal with the lowest bidder, it is well to add something for the risk you run, and if you do that you will have enough to pay for something better.”
- John Ruskin (1819-1900)

So what can we take away from this mechanic and apply to helping your child to do homework? We have to understand their language or their communication currency. For some, the communication currency is the language of urgency, for some is obligation, and still others is emotion. Here’s what I mean (asking a 5 year old child to put out the plates for dinner): ¨

• Urgency – Johnny, can you please put out the plates before the casserole is warmed up in the microwave ¨
• Obligation – Johnny you promised to put out the plates ¨
• Emotion – mama will be sad if I sit down at the table and there is no plates

Why does this matter? For my son Byron, it can be extremely frustrating to talk from urgency or obligation. The request has to be repeated 5 times before he does it. This can be especially frustrating for my husband. However, when you talk to him from emotion, it works every time. This is his nature. He cares about whether mama is lonely, papa is sad, or sister is angry. For my daughter Alexa, urgency does the trick. Her communication style is opposite to Byron’s. She likes direct requests but sometimes has trouble seeing other people’s emotions. It’s easier to make a request of her, but it’s harder for her to steer clear of a fight with her brother.

Now what about doing homework? Both the parent and the child hate nagging that typically happens with the homework. But this is a familiar pattern that us parents typically get into when it comes to homework. Figuring out your child’s communication style is a shortcut. If you are not sure which one it is, first mimic his/her method of communications, and if this doesn’t help try several styles until you find something that works. Children inherently want to please their parents, and talking to them a certain way is not “manipulating” them but finding a language that they can understand.

Did he get my car fixed, you ask. You bet! Was I happy about his service? Absolutely!  Am I stubbornly hanging on to my old minivan? You bet, but I’m also looking for a Toyota just in case!

(C) Feenix Pan, 2007. All Rights Reserved.

 When I was young, math was a scary thing. It was scary for two reasons: one, I simply didn’t get it and two, the scary of the scary, was that Mom and Dad didn’t get that I didn’t get it. I remember dreading the pending ‘homework’ help after dinner when the last rice dropped on our small dinner table was picked off and someone, somewhere says ‘now let’s take a look at your math homework’. I could still feel the stomach get tighter; ready to throw out the food I just ate! Being a child who did not understand math and trying to complete math homework was like being dropped off into a different world where everyone speaks a different language and you had no clue what’s been said. The feeling was always that the joke is on you.

Now that I’m on the other side of the ‘fence’ and started a business to teach math to others, I look back and understand what it was that I wish I could’ve verbalized to my parents back then when they tried to help me. And that is: Please don’t grab my pencil.

Grab pencil? You might be wondering what on earth am I talking about. You’re not alone. In the past few years, while working with parents who wish to help their children on the math, I noticed that sooner or later, the child’s pencil ends up in the parents’ hands and low behold, that’s when the tension goes way up and a fight is imminent – tears start to flow, voices are raised, papers are pushed around and within minutes, either the child or the parent, sometimes both, give up, look at me and say ‘you see, I can’t work with him/her on math!’ Working with your child on his/her math homework does not have to end with a ‘volcano eruption’.

One of the most useful and productive thing I ask parents to do is refrain from grabbing their pencils. Sounds almost to trivial to do, yet over the years, the results are unbelievable. I had one client whose mother had several advanced degrees and happened to be very passionate about mathematics – she didn’t know that she was grabbing her son’s pencil and solving his math problems all along. When I first pointed out to her, she said, ‘oh, no, but he is solving the problem himself – I just help out.’ Determined to help this family, I asked ‘Would you like to sit across the table from him and try the next problem?’. She took up the challenge and within minutes, her son’s pencil was in mom’s hand again – she had grabbed it across the table without realizing it!! What the mom shared with me later on is that being a typical type A personality, watching her son struggling in each and every one of the steps was too much to take – it was much easier and quicker to just show him how to do it. Except that ‘showing’ had, over the years, became ‘doing’ without her noticing it.

We tried several things for this Mom to temporarily occupy herself when she sits down help her son with his math homework and in the end, reading a trade magazine was what worked for her. When he asked a question, she’d listen and then, without using his pencil but her own, she’d answer his question and go back to reading her magazine. Over the course of few months, the quality of his questions improved from a generalized ‘how do you do this problem’ to very specific ‘I don’t see why you’d have to find common denominator first’.

Mother-and-son relationship improved and so did his math performance. Upon completion of my program, the mother jokingly said, ‘only if I knew it was the darn pencil!’ Pencil or not, the key to successfully transferring your math knowledge is to give your child the space to be. Seriously, can you imagine when your car broke down and you went to a mechanic – only to have him grab the car key from your hands and show you how you should’ve been driving? Would you ever go back to him again? See, you and I have choices when it comes to our mechanics, but our children do not have a choice when it come to parents. We are stuck with them and they are stuck with us – or like we say it in Chinese, ‘we are stuck together like cooked rice.’ Suddenly, ‘be and let be’ takes on a new meaning and letting go of that pencil may just be the key to unlock the door to math for your child!

Happy Zen Math!!

(c) 2006 Feenix Pan. All Rights Reserved.