Mathematics -- Singapore Approach using Modeling Method

"Mary has one pen. Her mother gives her two more. How many pens does Mary have?"

When I looked at the question above, I always wondered why the teacher never asked like this? 1 + 2 = ? Now... consider these primary one questions.

1) There are 10 chickens and cows in a farm. John counted 32 legs in total. How many chicken are there in the farm?

2) Mary gives 120 apples to Tom and Tim such that Tom has 10 apples more than Tim. How many apples does Tom get?

3) Complete the number sequence : 1, 1, 3,4,5,7,?,?,9,13. What are the two missing numbers?

These questions were our secondary school questions (during our time 20-30yrs ago), weren't they? I was taught to use algebra, to form mathematical equations to solve these problems. At that time, it did not matter to me whether I understood or not, as long as I got the equation right, I could produce an answer to score marks.

Mathematics in Singapore today is very different. The question is no longer routine and needs a lot of analysis. I think you will agree by looking at those questions I posted above. More importantly, I like the modeling approach adopted in Singapore Mathematics teaching. The purpose of this posting is to introduce the modeling approach. If you want to know more about Singapore's method using modeling approach, the following book is relevant. The price is SGD28.80. This is a little bit expensive to me as I am interested in only a few portions of the book. I found this book from a nearby library.



The modeling method starts with simple questions, however, pictures are drawn to model the question so that children can visualize the problem. Look at my note below...

You can see that the pictures are later replaced with the two "bars" to represent the numbers. Please do not under estimate the effect of drawing those "bars"... Please take a look at the following question that I selected and observe how those bars are used to visualize the problem.... (oh)... as well as the answers.

Can you see that the bars are drawn to deduce that 3 units equal to 24? If you are not convinced? Ok, how about this question (a lower secondary school question). The book has shown how the modeling method can be applied to solve this question.

My son is interested in Mathematics. He tried to read the book and persuaded me to teach him. After learning the tricks, he even brought the questions to discuss with one of his good friends in school. Why? I think he loves "seeing" the answer.

This is the type of mathematic education I want for my kids. The contents is interesting and useful. Most importantly, it is none routine and focus on understanding. This is a piece of good work by Singapore's educator. Wonderful work, isn't it? I really salute them and thank them for the efforts to improve teaching of mathematics.

Mathematic --- Maths Olympiad

I had shared this Maths Olympiad book by Terry Chew to many friends. Most of them like this. Almost all of them bought the book after checking the book out. The author has a facebook page on the new book that I am going to get soon. For complete list of the Math book by the author, please refer to the publisher's link here.

I had bought the following 2 books from the author.


I am sure later I will buy more for the upper primary levels when my son reaches that stage. There are samples in the publisher's link . However, let me share 3 pages from the Junior 1 book (Primary 1-2) for reporting purpose to illustrate better about the quality of those questions provided in the book.

Sample 1:

Most children at age 7-8 can tell the time, but they need to think to calculate hours and minutes. Yes, they can do it!

Sample 2 :

Another problem question.. I was surprised that my son can do this.. without using algebra or the "standard" method that I learned in secondary school. He "drew" 110 circles and divide them to get the answer!


Sample 3 :

A systematic approach for 7-8 years old to count..the kids need to "visualize" those hidden cube!

I believe the above questions shows the "true color" of the book. Those questions may be more challenging questions, I admit, but manageable.

My intention is not to prepare my son for any competition. Rather, I use this book to encourage him to think, to analyze and to solve the questions. During my school time, I practiced mathematics like robot.. My teachers always said, "practice makes perfect".. yeah, I practiced up to hundred over equations per day (many students at that time did that). But I would say, I memorized the trick, rather than to think and understand the skill. I suffered in university. Well, some people still feel proud of those "traditional Chinese school" method. For me, I prefer something different. I don't want my son to lose interest solving hundreds of questions per day. This book is the solution to my problem!

In fact, my son loves solving those questions. Some times he may get frustrated when he does not know the answer. But with a little bit of coaching and encouragement, he is on his way... If you think that you are not good in math, don't worry, answer is given at the back of the book!

Pentago - Mind Twisting Game

I came across this game Pentago at Narita airport. Seeing the content and the fact that it won so many awards, I was attracted. Here are the awards that this game has won.



I appreciate intelligent games like this. Therefore, I decided to add this to my collection partially because I was afraid that I might not find it elsewhere as I thought this is a Japanese game that might not be available elsewhere.

The game is pretty simple, it's just like a usual "5 in a row" game. Each player takes turn to put a black or white marble on a 6 x 6 board. The first player having 5 balls in a row either horizontal, vertical or diagonal wins the game. But the trick is that the 6 x 6 board is divided into 4 sub 3 x 3 boards, which can be rotated. This feature definitely adds a new dimension and difficulty to the game. I am impressed by the mechanical design of the board, simple and elegant!



I like this game because it's simple. There's no need to learn many rules and I can enjoy the game together with my son almost immediately. In fact, after the first game, my 6 year old son can beat me.

I think this game is really a mind twisting game. The possibility that the board can rotate 90 degree clockwise or anti-clockwise actually twisted my brain. No wonder this game won the Mensa Select Award.

Recently, I saw a version of this game being sold at SGD14.90 in some toy shops in Singapore, almost half the price I paid. The packaging is very similar to what I have but I can tell that it is of lower quality. Since in Singapore, pirated products are dealt with strictly, I am not sure whether those are legitimate products. Perhaps it's local low cost legitimate version? I am not sure.

For those of you staying in Singapore, you may be able to find this in any toys shops at your local shopping mall. Alternatively, let me put down some links below in case you want to shop online.


Amazon Website : The most trusted online store in my opinion; shipping rate is reasonable if the seller is Amazon.

Official Website : I believe this is the official website, some of the links do not work on my browser.

Wikipedia : provides some background information on the game.

Well, I think this is a good game for adults too. For kids, definitely the game will help to sharpen the young mind, as we all know, the more we use our brain, the better the brain will develop. And more importantly, there's a lot of fun!
 

MiniLuk and BambinoLuk

I came across this wonderful children game in a booth selling IQ games at Tesco 3 years ago. I was impressed because of the innovative contents. Besides, children can play on their own and checking their own answers. I still remember one of the puzzles showing the top view of a swimmer wearing a cap, and the children are asked to identify the respective side view of the swimmer. That requires quite some imagination from the children. However, the price scared me off. It's at least RM600+. The sales lady told me that this game had more than 30 years history in Germany.

Okay, you may not know what is this Luk and Bambino Luk, I have found a website that demonstrates this. Check out the demonstration and you will understand what I mean

Links to Amazon for MiniLuk (I hope this give you the latest price)


Links to Amazon for BambinoLuk (I hope this give you the latest price)



BambinoLuk (2-4 years old) : Introduction, Demonstration , Samples

MiniLuk (4-8 years old): Introduction, Demonstration , Samples
(note: I tried to purchase from them in mid 2009 but looks like they did not sell outside US)

I think you will be impressed too looking at the Samples and demonstration . I strongly believe that by exposing the children to these games, we are developing their intelligence, in terms of sequencing, imagination and association. You can tell that I am convinced and I would buy, but forking out RM600++ is very painful, especially at a stage that I am not sure my children would like it.

By the way, I am a big fan of Dr Glenn Doman(proposed use of flash cards) and Dr Howard Gardner(proposed Multiple Intelligence concept), I believe that parents should stimulate children to think and to sharpen their brain because brain development happen at early childhood. I had finish reading their books years ago. That's the reason I was convinced quite easily.

It so happened that I had a short trip to Germany in the following month. Although lack of time, within the available 2 hours, I managed to visit a bookstore to find out about this Luk system. Yes, the sales girl was right that it had been popular in German for more than 30 years. I had a hard time to decide what to purchase. Unlike other parts of the world, in Germany, the Luk system has a very wide varieties, and I was selecting from a range of 50-100 books. Each of them is about 5-7Euro. I bought several books and a controller, amounting to RM200 with the kind help from the Germany salesman translating for me. That's 1/3 of the price compared to what I saw.

My son had completed all the exercises of this miniLuk set. I wanted to get more, but I did not have any chance to visit Germany and I could not afford a trip like that. I came across a toy shop in United Square Singapore located at the basement. The official website could be found here. My son had a chance to look at it and tried out before I paid SGD100 for a set of 5 books. I knew in Germany and US, this would be cheaper but considering that we had a chance to try it out, I decided to pay. May be partly because the owner was very friendly and kind. As expected, I found out later that it was sold cheaper, about half price in US. My friend tried to purchase from Amazon, but again, since not offered directly by Amazon, they did not sell outside of US.
( Update 2015 : All the local selling this are out of business)

I also came across a "cheap version", sold in "pasar malam"(night market). The controller looked very similar to the miniLuk system. It was sold at cheaper price, but still at RM160! But the quality had no match to the miniLuk system. Besides, I also suspected that it might be pirated copy. Checking the contents, I found that the "Germany Intelligence" in the game was missing. It looked like a compilation which consists of many different subjects, without a key learning theme. Will be a waste of money if you buy those.

I always admire German engineers for their innovation and good engineering. I believe IQ games like this have a role in this. I value innovation products like this. But please do not get me wrong, I do not believe that IQ games will make a child more "clever" and definitely you cannot create a genius out of these. But the IQ games will make a child more "intelligent" in a way defined by Dr Howard Gardner. But unfortunately, it's not commonly available to us....

Update 2015 :
Some broken links removed.  Also, I counted 7-8 websites copied this post. Well, you can tell that mine is the original as my writing style (with grammatical error) etc. 

IQ Games -- River Crossing

I saw this game, "River Crossing" selling at less than 50% of the original price in Barn and Nobles during my business trip to US. I was very sure that if I were to buy this in Malaysia or Singapore, the price would be higher.




Now, itturned out to be one of my son's favorite games. My wife loves puzzle games too. So, the mother and son would sometimes spend some wonderful time together solving the puzzles. This game is about how to cross the river by moving around wood pieces that serve as the bridge, one at a time.



My son also has some other puzzle games like "Hide and Seek" and "IQ Logic". Frankly speaking, these two are quite difficult even for me. The level of difficulty for "River Crossing" is just nice.







I enjoy playing "River Crossing" together with my son too. Sometimes he would get very frustrated because he could not figure out the answer. I guess this is also part and parcel of life that he has to go through. I would just ask him to try again, or some times, I would sit down and think together with him.



I really feel thankful to the creators of these games. Not only does the game sharpen the mind, but more importantly, it also trains children to concentrate, to analyze and to solve a problem. Isn't this what is needed?

If you are getting one of these, let me warn you first that the games are not easy. Go to a shop that has a display set and let the child try the game first. Sometimes I really need to think out of the box in order to get the answer. Oh... you may want to ask me where in Singapore or Malaysia you can get these? Check out my favorite toy shop in Penang Elly and Friends, Queensbay Mall 3rd floor. In Singapore or Kuala Lumpur, I think you can find these games in many of the toys shop which sell children games and puzzle. If you know where to find them, add your comments to this blog...

Enjoy!

P/S: FYI