OnSponge Maths - Discussion

[Brenda10]

Hifive:

Brenda10:

Hi, I just go through the onSponge book 5 on topics of Fraction, ratio and percentage (all are linked) and realize there are total 175 questions for practicing.


Perhaps the drilling will make you die die remember the methods when come to Maths questions.

Hello Brenda10

For the Onsponge book, besides buying online from their website, can we buy it from other bookshops?

Hi Hifive

You have to buy through on line as I don't think so they are selling at other bookshops.

[iFruit]

NickleBee Tutors:

But its not a means to an ends. The model method has to be complemented with various other procedural skills (but not algebra, i ban algebra for all my primary school kids) together with a certain amount of reasoning ability (and some self-confidence too!).

The 'On Sponge' books which i am using for my tuition kids has several techniques that i find useful in helping the kids i teach understand the context of the question and how to solve it. I analysed the other methods from 'On Sponge' that i did not like so much and hybridized them with techniques that i had learnt in my GEP and Olympaid training to make them a little easier to visualize and understand.

Hi Nicklebee Tutors,

Please don't take offence but I am just curious...

Why ban algebra for primary kids? Is PSLE some kind of golden threshold that once kids pass through, they suddenly become eligible to understand algebra and not a moment before?

Why GEP and Olympiad training techniques are required to be fused together with MDs to teach hapless primary students who are only trying to understand how to do problems in a simple manner? Are the problems so difficult now we need a potent potion of three techniques?

It's alright to plug one's services (just to use my new vocabulary here, haha) but to unnecessarily muddle things is disservice, in my humble opinion.

Care to show us some of your new hybridized techniques which can be used to lighten the burden of primary kids ( and in turn, of the parents)?

Thank you.

[NickleBee Tutors]

iFruit:

NickleBee Tutors:

But its not a means to an ends. The model method has to be complemented with various other procedural skills (but not algebra, i ban algebra for all my primary school kids) together with a certain amount of reasoning ability (and some self-confidence too!).

The 'On Sponge' books which i am using for my tuition kids has several techniques that i find useful in helping the kids i teach understand the context of the question and how to solve it. I analysed the other methods from 'On Sponge' that i did not like so much and hybridized them with techniques that i had learnt in my GEP and Olympaid training to make them a little easier to visualize and understand.

Hi Nicklebee Tutors,

Please don't take offence but I am just curious...

Why ban algebra for primary kids? Is PSLE some kind of golden threshold that once kids pass through, they suddenly become eligible to understand algebra and not a moment before?

Why GEP and Olympiad training techniques are required to be fused together with MDs to teach hapless primary students who are only trying to understand how to do problems in a simple manner? Are the problems so difficult now we need a potent potion of three techniques?

It's alright to plug one's services (just to use my new vocabulary here, haha) but to unnecessarily muddle things is disservice, in my humble opinion.

Care to show us some of your new hybridized techniques which can be used to lighten the burden of primary kids ( and in turn, of the parents)?

Thank you.

Hi,

No offence taken : ) I welcome all forms of feedback because its the only way one can improve. Allow me to answer your questions.

Q1 : Why ban algebra for primary kids? Is PSLE some kind of golden threshold that once kids pass through, they suddenly become eligible to understand algebra and not a moment before?

I ban algebra for my tuition kids because after teaching for some years, i found that parents or tutors (who taught the kids before me) were only too eager to teach algebra to kids when they meet questions that they themselves couldn't solve using conventional means. And the algebra instructions given by the parents and ex-tutors were inconsistent to say the least! The students would be taught algebra for certain questions and for other questions, they would be taught heuristics or models. Throw in the school stuff that the teachers teach in school and the kids become hopelessly muddled as to which technique to use!

For those kids that use algebra, i sometimes challenge them to work out a couple of challenging problems sums and i give them a head start. They usually take a few mins to scribble out algebraic equations on the whole page (i guess being young and having lack of practice makes their algebra very cumbersome and much lacking in fineness) and when they finally get the answer, i just write out a few lines worth of working before getting the solution! After which i usually show them how i basically read and understand the question before settling on a method (which sometimes includes using simple tricks such as since \"80% have $24 and 20% have $12 tickets isn't it the same as 90% having $24 tickets?\") and i love seeing the look of wonder in their eyes when the finally realize that some questions are \"rigged\" in such a way that you can solve it with mental sums if you choose!

For more \"normal\" questions, i show them how model is a basic yet highly versatile tool that can be used to solve practically everything. After they understand the model method, i link it to the OnSponge heuristics methods and show them how the they are all basically the same on the inside though model and heuristics may look different on the outside! Its just the presentation of information that is different!

After that the kids usually wisen up to the fact that there is no such thing as \"cast in stone\" methods. There is only reading and understanding the context of the question, applying of procedural knowledge and finally solving the question as they see fit in a logical and elegant manner. I only ask that they explain the \"whys\" of their technique. Only if they can explain their thought process back to me, then i am satisfied. If they can't explain it well enough, i would go through the question again and guide their understanding and thinking of that question accordingly and i would also relate the understanding and techniques of that question to other similar questions. I am sorry to say but no kids has been able to explain to me how and why the algebra solutions that they so pain-stakingly worked out could solve the questions. And i would like to add that once they get used to my way of solving problem sums, none of them go back to using algebra again.

My stand is that Algebra from a child’s point of view is simply “magic”, for lack of a better word, because they have not yet developed the cognitive capability to understand the inner workings and nuances of the algebra required in problem solving. Even if they have been trained to use algebra for certain types of questions, they lack basic understanding of the question's concept and thus would be unable to solve the question if the fundamentals of the particular question should be change slightly.

Also, i have noticed that using algebra as a \"all-in-one-short-cut\" to primary school maths problems would result in stunted problems solving skills and mathematical cognitive ability which in my opinion would not serve them well as they progress further up the education system.

I did promise my tuition kids one thing. When they get to secondary school, i can teach them to understand and wield algebra so elegantly that it becomes an amazing tool. Until then, i counsel patience and try to get them to understand that sometimes, understanding and reasoning ability together with appropriate application of models/heuristics/other procedural knowledge in the most effective way is what they should be trying to concentrate on at this current point in time.

Q2) Why GEP and Olympiad training techniques are required to be fused together with MDs to teach hapless primary students who are only trying to understand how to do problems in a simple manner? Are the problems so difficult now we need a potent potion of three techniques?

When i was in the GEP back in the 90's, PSLE questions were pretty straightforward and its was only in the early 2000's that \"IQ\" questions such as the infamous \"1+2+3+4+...+99+100=?\" started popping up in the PSLE. Those questions were standard issue questions during my GEP primary school tests and exams so i had the luxury of being pretty well grounded in techniques of solving them. I still have my old maths Olympiad and IQ books from the early 90's and when i flip through them, i am struck by the sheer number of similar looking questions that i see in Pri 6 Prelim papers nowadays. I honestly think its an insane \"arms race\" with the \"kiasu\" parents buffing their kid's academic results to a high shine and the teachers under pressure to \"normalize\" the bell curve to prevent too many A* kids and so the teachers start setting really interesting questions and amazing problem sums. I am so glad i am not a kid taking the PSLE now!

So i am sorry to say but though most of the PSLE questions can be solved by \"simple\" methods, a growing number of questions require higher order thinking skills and of course heuristics. And i hasten to point out that at no point in time did i say that there was something called a \"GEP\" technique and \"Olympiad\" techniques. There are only the techniques that i had learnt when i was young when i was in the GEP and attended Olympaid training camps and these are the techniques (quite simple techniques i may add) which i am teaching to my young tution kids now. In fact as i mentioned in my previous post, i use those methods to make some of the OnSponge heuristics a little easier to visualize and understand.

There were quite a number of instances where my tuition kids used my problem solving techniques in their worksheets or exams and their teacher asked the kids to either explain it to them (while mentioning that they have not seen such a technique before and asking them who taught them the method) and sometimes even asking them to go to the board and explaining the method to the class. Thus i would think that my tuition kids are not \"hapless\" as you choose to put it but instead they have gained a measure of self-confidence in solving problem sums with the accumulated knowledge of what i have imparted to them.

Q3) Care to show us some of your new hybridized techniques which can be used to lighten the burden of primary kids ( and in turn, of the parents)?

I am immensely sorry but my tuition kids' parents are already nervous enough that i have posted up some of my solutions online in the OnSponge forum. They have not requested that i stop doing so but since i am hired by them to teach their children, i have decided to post my solutions up only occasionally.


Dear Sir,

I have most humbly put forth the arguments for my case to you and i now respectfully request for your supporting facts and arguments for the points that you so succinctly put forth in your case to me.

I would also like to request, if you could be so kind as to enlighten me as to why you felt i was \"plugging my services\" and \"to unnecessarily muddle things\" and highlight any justifications for such an accusation, so that i may learn and not repeat it again if i feel that your accusation is justified.

I thank you for your time and kind comments and i look forward to hearing from you again.

Yours

Zhou Shicai
NickleBee Tutors

[Hifive]

Brenda10:

Hi Hifive


You have to buy through on line as I don't think so they are selling at other bookshops.

Thanks Brenda!

[iFruit]

NickleBee Tutors:

.. i look forward to hearing from you again.

Hi NickleBee Tutors,

Thanks for the reply. You write well :). Because it was a long reply I wasn't sure whether to quote the entire thing above. I will just refer to the 3 questions that you addressed in my reply.

At the outset, please allow me to set some context here so that you can understand where I'm coming from.

I'm a concerned parent of a P4 kid, incessantly worried about how to prepare her for P5 next year and for the PSLE, a year after. As a kiasu parent like most others here, I'm interested in finding out on how best to prepare her and where to get the best help from. I hope you can understand my POV.

Q1) MOE clearly states that algebra is included in primary syllabus. (http://www.moe.gov.sg/education/syllabuses/sciences/)

As per the syllabus, the following are included:[list]

[Brenda10]

Hifive:

Brenda10:

Hi Hifive


You have to buy through on line as I don't think so they are selling at other bookshops.

Thanks Brenda!

Hi Hifive

You're welcome.

You will be impressed by all those angles questions.

Wish you a nicee weekend.

[Leanne]

Hi Brenda 10,


Care to share what is the difference between A STAR series of math booklets and onsponge math?

Thank You.

Regards,
Leanne

Brenda10:

Hifive:

[quote=\"Brenda10\"]Hi Hifive

You have to buy through on line as I don't think so they are selling at other bookshops.

Thanks Brenda!

Hi Hifive

You're welcome.

You will be impressed by all those angles questions.

Wish you a nicee weekend.[/quote]

[NickleBee Tutors]

iFruit:

NickleBee Tutors:

.. i look forward to hearing from you again.

.....In summary, it is entirely your prerogative to teach your primary kids as you see fit, but I'm entitled to my opinion until I'm enlightened otherwise.

I don't particularly like to write long posts so my future posts on this topic will be short.

Thank you.

Dear Sir,

Thank you for your reply and i found it a most interesting read. I would like to give some of my remarks regarding a couple of points that you have brought up.


\"MOE clearly states that algebra is included in primary syllabus. (http://www.moe.gov.sg/education/syllabuses/sciences/)\"


Regarding the issue of algebra in primary school, you are correct in saying that algebra is included in the Pri 6 syllabus (the outline of which you have posted up in your previous post). I however, would like to point out that the algebra that is taught in Pri 6 is nothing more than an introduction to the basics (very basic i may add) of algebraic manipulations with some application of solving very simple maths problems using algebraic expressions.

As an example, i post of one of the harder pri 6 algebra questions i can find. \"Jack is now q years old. In 5 years' time, he will be 1/3 as old as his father. How old will his father be then?\" You would note that this question isn't really that hard after all. You could even draw models with 1 unit representing q if you so choose! So the algebra taught in pri 6 is woefully inadequate for solving most of the problem sums found in paper 2 of any decent P6 Prelim paper.


\"On one hand MOE states it is included in syllabus and OTOH you are saying it stunts mathematical cognitive ability in primary but becomes amazing tool in secondary. This leaves me perplexed and confused. Who should I trust? You or MOE?\"


Regarding this statement, i would have to direct your attention to a letter that one Mr Lim Boon Tong wrote to the Straits Times back in 2007. In his letter, he wondered why children were not allowed to use algebra in the PSLE exams. The link to the PDF file of this letter is reproduced below.

http://www.moe.gov.sg/media/forum/2007/forum_letters/20070217.pdf

MOE's response quite typically trumpeted the merits of model drawing (after all they were the ones who invented it in 1980), describing it as a \"powerful approach for problem solving and learning mathematical concepts. By drawing models, pupils can represent the mathematical relationships in a problem pictorially. This helps them understand the problem and plan the steps for the solution.\" and \"The pictorial form also helps pupils visualise what could otherwise be abstract concepts. In this way, model drawing supports the learning of fractions, ratio and percentages. Pupils will find model drawing useful when they solve problems involving these concepts in Primary Five and Six.\".

MOE continued by stating that \"The model drawing method is thus a developmentally sound approach for young children. It is recognised internationally as an effective way for young children to learn problem solving and to have early exposure to algebraic concepts. At Primary Six and Secondary One, pupils can draw upon their earlier experience of using models to help them understand algebraic relationships in problems.\"

MOE also added that \"While pupils are not required to use algebra to solve word problems in the PSLE Mathematics, they are also not restricted to the use of any one particular method. In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.\"

The link to MOE reply regarding the model vs algebra debate is as follows :
http://www.moe.gov.sg/media/forum/2007/20070217.htm

Now, as you so succidently put it, \"This leaves me perplexed and confused. Who should I trust? You or MOE?\". So i put it back to you. Who should i believe? I personally think i would side with MOE here as its stand on model drawing closely mirrors my own view on problem solving skills.

To recap, as i said before, i only ask that my students master the art of reading and comprehending the context of the question, applying whatever procedural knowledge they have and finally solving the question as they see fit in a logical and elegant manner with checking to make sure they got it right.

After which i ask that they explain the \"whys\" of their technique. Only if they can explain their thought process back to me, then i am satisfied. If they can't explain it well enough, i would go through the question again and guide their understanding and thinking of that question accordingly and i would also relate the understanding and techniques of that question to other similar questions. I am sorry to say but no kids has been able to explain to me how and why the algebra solutions that they so pain-stakingly worked out could solve the questions. And i would like to add that once they get used to my way of solving problem sums, none of them go back to using algebra again.


\"I'm not very qualified to comment on education but I think mathematics at a primary level, is a simple subject just needing the right foundations. After all, how much innovation one can bring in teaching fractions/rations/percentages and other elementary stuff that's been taught for 1000s of years all over the world?\"


I would take issue with your statement of \"how much innovation one can bring in teaching fractions/rations/percentages and other elementary stuff that's been taught for 1000s of years all over the world?\"

May i bring your attention to the model method that MOE is so proud of. Back in 1980, CDIS (MOE) set new goals for mathematics education. These goals emphasized a focus on problem solving and on heuristic model drawing. This essentially became the standard for primary school maths education in Singapore and after some years, the\"Singapore Math/Model Method\" achieved international renown with educators after Singapore became the top country in the \"Trends in International Mathematics and Science Study\" in 1995.

The Singapore Model Method has been adopted by a growing number of American Elementary Schools (where it is known as the Singapore Maths method) and even up to 8% of schools in Israel since 2002.

The use of bar-models in teaching problem solving (which in my opinion is nothing more than a representation of algebra in visual forms or \"pre-algebra\" if you will) is as old as Book V of Euclid's Elements which was written in the 4th century BC. It consists simply in representing (mentally or graphically) arithmetical quantities by line segments. So what we now call the Model method is actually an improvement of what the Greek philosophers would have been quite familiar with.

Now i would perhaps call MOE's model method a revolution in maths education techniques. And since then, further tweaks and improvements of it (e.g the OnSponge techniques) have been evolutionary rather than revolutionary. Even my tweaks of the OnSponge techniques are nothing more than minor revisions of the Maths Model Method! So there you have it, all of our childeren are being taught using an innovation which was introduced less than 30 years ago and this method has been winning accolades around the world most notably in the United States!


\"So, If some one comes along and says he bans algebra and combines Model methods, On Sponge techniques, techniques he learnt in GEP and Olympiad training (okay, I hope got it right this time) to teach kids, I tend to take it (you have to pardon me here) with a large dose of salt unless I'm shown the proof of pudding.

Honestly, I wasn't referring to your primary kids when I said \"hapless\". I was just talking about kids like my child and I was just questioning the need for teaching maths to them in such a purportedly complicated (in my view) manner \"



As you so rightly put it, we have the right to our opinions. But in this case, i would like to point out that its not very nice claim that my methods are \"purportedly complicated\" without having seen them at all. That would have your arguments based on unsupported suppositions which does not make very rigorous debate. I hope you would take some time to peruse the couple dozen methods i have posted up in the OnSponge maths forum over the last couple of months. Please let me know your opinions and any insights you have after looking through some of my methods.


\"I am a newbie at KSP and based on my limited experience here, I believe there are two types of vendors here. Some actively participate and help here and some just plug their services and their miraculous cures and disappear. So my comment about plugging services was my opinion on the second type. If you say it was not your intention to plug your services, I'll totally accept it. \"


I would definitely not like to be lumped into the 2nd group which just plugs their services and miraculous cures. If i were a parent i would be wary of \"snake oil\" claims! In fact i would only want the best for my child next time too!

I personally am here to learn from the parents who frequent this forum and i hope to gain insights and lessons from the many challenges parents face when guiding their kids through the Singapore education system and how they solve them. My aim is to learn from all the parents here so that i may become a better tutor and am able to improve my teaching techniques so as to better prepare my tuition kids for the exams and schooling life. I would also love to participate in some of the debates and answer some of the questions regarding primary school academic affairs so that all of us can benefit from each other. So i hope i will be a \"active participating\" vendor!

Thank you for your time and effort in replying to my post and i look forward to hearing from you again.

Yours

Zhou Shicai
NickleBee Tutors

[atutor2001]

Hi iFruit

iFruit:

Why ban algebra for primary kids? Is PSLE some kind of golden threshold that once kids pass through, they suddenly become eligible to understand algebra and not a moment before?

Above is most aptly coined phrase regarding use of algebra for primary students. It hits my raw nerve whenever someone says algebra is not for Pr school.

I am just a kiasu parent not an expert in education. However, when I find that what is being preached by these \"experts\" does not match the outcomes, I am old and wise enough to see the \"CRABs\". This personal incident which I encountered 3 years ago still make me feel very sore.

A niece in P5 then was weak in math approach me for help. She had no clue at all on how to compare model so we taught her units, ALGEBRA and simultaneous equation. She took it like fish to water though she may not fully understand all the concepts behind. Her marks soared from 60 to 90 plus. Everybody was elated. Greatest credit goes to her math teacher, a young gentleman who not only did not discourage her, actually explained her work solution and method to the class. This help build her confidence and love for math.

Then disaster struck. In P6, since it is a crucial year, her school assigned the most \"competent\" teachers to the P6 classes. The specialists for math was someone as intelligent, if not better than the one that crawled through the ventilation hole recently. She scolded her for using algebra and BANNED the class from using such method. Immediately her grades dropped to 70s. The upset mum went to bang table and like all specialists in the field of math, the explanation was \"primary students do not understand what they are doing when they use algebra and is bad for her development\". (how I wished she also got locked up on a Saturday and crawled through a ventilation hole) She relented and let the poor girl continue using algebra. (I notice she didn't mark her works in algebra which I suspect is because she herself did not know how to solve using such method - relying only on answer keys provided to the teachers which are using model method) Unfortunately, damaged is already done and the poor girl, out of fear, tried to use models first and her grades never improve. Why do we have so many such specialists in our education system and worse even in the private tuition world.

There is no fixed way to learn. No 2 child are identical except maybe twins - not completely same though. As an educator, one should never limit the working method. We must be open-minded and assess individual trait - just like most kids like meat but there will be some who like vegetable. So we do not conclude that all kids like meat and force everyone to eat meat - especially when meat is not as healthy as vegetable.

Lets wake up and stop stereotype our kids. If you give me a GEPer that solve all questions using model then I really question the GEP selection process.

[Brenda10]

Leanne:

Hi Brenda 10,


Care to share what is the difference between A STAR series of math booklets and onsponge math?

Thank You.

Regards,
Leanne

Hi Leanne

I think is hard to compare since both are highly recommended.

As such, I think if time allows will be best to practice on both.

Just my 2 cents thought