Kimber Re: Singapore Math

[Myrtle]

Some time ago I was following the blog of a graduate student in math who was from Singapore. He had a post up about the deficits of Singapore math as he percieved them and here are some of the more relevant points and quotes from others who commented on his blog:

 

"I don’t think we have any idea how to create formulas in the first place."

 

"a lot of people trying out Singapore Math want to implement it wholesale for K-12. Then they get upset at how Maths Syllabus ‘D’ (E Maths) is missing all sorts of things…

 

"I don’t think the Sg math syllabus lets us understand how the principles work at all. It’s all a matter of telling us the formulas and teaching us how to use them;"

 

"I think our curriculum is awesome for the elementary school. After that it kind of loses steam as it gears up toward pre-specified ‘O’ and ‘A’ level syllabuses which may or may not reflect the skills needed in modern jobs."

 

"I also agree about the benefits of proof-based mathematics for logical reasoning. I grade the homeworks for a lower-level calculus course at my university and the number of elementary logical fallacies students commit is astounding."

 

It is very difficult finding open discussion about the flaws of Singapore math. It seems that it's illegal to speak out against the government or its programs there in any way, and in fact, this particular blogger was later sued by the Spore government for libel (but not for this particular post but of another that was critical of an entirely different topic)

 

H Wu also has publically said that there are flaws in Singapore math that deal with content but he did not elaborate on what that might be.

 

It is difficult for me to judge the merit of the above criticisms because when a mathematician or math major refers to "how the principles work" they usually mean something on an entirely different level than the rest of us do. Furthermore, I wonder if the same things can't be said about any American math program. (I've seen the same sorts of things said about Saxon, for example.) So there is what I found related to content for what it's worth.

 

While we eeventually did find an old out of print proof-based algebra curriculum the difficulty of the mechanical calculations that are in the exercises isn't anything like what NEM offers.

[Kimber]

Thanks Myrtle,

 

I'll be checking out NEM.

 

But on another note, how important is it do algebra via proofs. Other than preparing students for a math major, is there some inherent benefit as in studying Latin? This is either a really good question that takes lots to answer or a very dumb question that I should just know the answer to. I don't want to take up all of your time, so if you just have a link or a post about this on your blog somewhere, I'd love to have it.

 

I am a student of Thomas and Finney Calculus. Both my dh and I have engineering degres, but we are not mathematicians.

 

I ask because I'm so pitifully undereducated that it's frightening at times. I'm trying to do better by my kids, and I'm willing to relearn Calculus and everything up to it, if necessary. But before I dive it, is it really necessary?

 

I'm only in about 6th grade in homeschool years--that's sort of like some factor of dog years in reverse, maybe. :D

[Myrtle]

I suppose it depends on what your goals in math are.

 

This is a repost of something that I said in another thread,

 

In general, I will say that my big enlightenment was that it is one thing to train a student to use math as a tool for his future vocation and for daily use--say engineering and accounting-- but it's an entirely different thing to study math as a subject.

 

Many parents imagine the study of music, art, or literature is done simply for the sake of those fields and not for any specific vocational or utilitarian needs. For example, when a kid studies biology, while there are utilitarian needs addressed in the curriculum, the curriculum includes a sampling of the major areas of biology that a professional biologist is involved in. The same is true for psychology, your psychology 101 class gives you a sampling of all the areas of psychology. History and philosophy give you overviews of those fields but the traditional math sequence of high school does not give the student a sampling of what math is as an academic field: topology, analysis, algebra (not elementary algebra), number theory, etc. nor the methodology used in those fields.

 

The interest in such a pursuit is really subjective, no one is going to fail the SAT because they didn't prove that the multiplicative inverse is unique, or because he didn't read Ovid in Latin, for example. In the context of a classical education we are interested in proof because it is the "justification" in Plato's defintion of knowledge as being justified true belief. It is true that cross multiplication works. But believing that it works because it always has so far, or because the book says so does not constitute valid justification and therefore, philosophically speaking, according to Plato's definition, the student doesn't have knowledge of this theorem even though he can skillfully apply it.

 

In one popular algebra text that I have sitting on my shelf the transitive property of inequalities is treated in the following manner, "...if x<y, and y<z, then it follows that x<z. It is easy to see with a number line why this is true. The inequalities x, y and y , z mean that x is to the left of y and y is to the left of z."

 

That is a lie. The graph does not show why it is true, it merely illustrates that it is true in a particular context. This can be detected by the use of circular reasoning in their graphical "proof/definition". How does the student know where to place the number on the numberline without evaluating beforehand which is greater? This perhaps doesn't seem like such a problem when working with integers, the student knows where to put five and three on a number line because he already knows which is greater, but how about determining the order of a/d and b/c if a>b and c>d?

 

Where they appear in an illustration isn't what determines their order. One counterexample for the child that thinks that greater than "means that" the number is on the right is to flip his graph with his numbers on it 180 degrees and he will see that now the greater number is on the left so that definition doesn't hold. How did we get fooled then?

 

It is true that 5 is greater than 3.

It is true that on a particular kind of number line 5 is to the right of 3.

It is not true that one of those statements follows from the other, (if p then q) yet in many textbooks the student is invited to jump to such a conclusion.

 

It's not so much that a rigorous program trains the mind, so much as that a non-rigorous program perhaps facilitates and encourages fallacious reasoning.

 

Here is a good, if not long, article written by a Princeton mathematician for a general non-specialist audience on the history of proof in math. He gets off to the typical start with the Greeks but his treatment of the 19th and 20th century is more interesting.

 

Here is a tirade by a mathematician about "proof by picture" and other picky pedantic gripes about how Calculus is taught.

[Kimber]

Thanks Myrtle,

 

My dh and I are goin' to do some investigation. We may end up trying Allen's book 1 and seeing how that goes. My main concern as the primary teacher is time and support or the lack there of from using out of print texts.

 

Thank you very much!

[Nan in Mass]

We do PM/NEM. I have had to put a significant amount of effort into getting my children to write equations for things, both in math and in physics. They can solve the problem, but are reluctant to actually show me how. I know this is often a problem, but it is even more of a problem with Singapore, I think. On the other hand, I would far rather have children who could solve the problem without an equation than ones who can only do it by the rote writing of algorithms.

[Grace is Sufficient]

When my kids were in elementary school, I used Singapore in conjunction with Miquon and/or Math-U-See, because I thought that Singapore math was strong in teaching the mechanics, but the other two were stronger in helping young children understand what was going on with the numbers.

 

FWIW

[siloam]

Some time ago I was following the blog of a graduate student in math who was from Singapore. He had a post up about the deficits of Singapore math as he percieved them and here are some of the more relevant points and quotes from others who commented on his blog:

 

 

 

It is very difficult finding open discussion about the flaws of Singapore math. It seems that it's illegal to speak out against the government or its programs there in any way, and in fact, this particular blogger was later sued by the Spore government for libel (but not for this particular post but of another that was critical of an entirely different topic)

 

H Wu also has publically said that there are flaws in Singapore math that deal with content but he did not elaborate on what that might be.

 

It is difficult for me to judge the merit of the above criticisms because when a mathematician or math major refers to "how the principles work" they usually mean something on an entirely different level than the rest of us do. Furthermore, I wonder if the same things can't be said about any American math program. (I've seen the same sorts of things said about Saxon, for example.) So there is what I found related to content for what it's worth.

 

While we eeventually did find an old out of print proof-based algebra curriculum the difficulty of the mechanical calculations that are in the exercises isn't anything like what NEM offers.

 

Here is what is funny to me. I am struggling to grasp what he is talking about exactly. Obviously I don't get some of the terminology or idea he is reaching for. This is funny to me because as a US student I got straight A's in college in Calculus because I am so good at simply taking the formula at face value and doing the math. Something was also obviously lacking in my instruction that I can do Calculus but can't grasp exactly what he is talking about.

 

All math programs have gaps, is my point.

 

My solution is to do NEM with Jacobs and Foster (Of course I keep changing my mind about what to supplement with because I haven't seen any of them :rolleyes: ) Because he hs year around we should be able to do all of NEM and skim the supplemental for different approaches and hopefully get the best of both.

 

Heather

 

p.s. And if anyone is willing to explain exactly what he is talking about I would appreciate it. :D