Singapore Math and Geometry Proofs?

[amsunshine]

Hi all:

My dds are not even close to Geometry, but we are loving Singapore in elementary. I like the looks of Discovering Mathematics or NEM for the future.

I have some burning questions though, though, and maybe someone can answer them for me.

First, given that Singapore generally does very well on TIMSS and further, does not concentrate on formal geometry proofs in its upper level mathematics courses, is it truly necessary to study them in hs?

I, myself, loved geometry and proofs in hs. I understand there is a certain value in teaching/learning them. I'm just stumped as to why Singapore doesn't formally teach them...and yet, Singapore's math scores are so high in comparison to others (specifically, the U.S.) on an international scale. Perhaps this is because TIMSS doesn't focus on geometric proofs?

I've done several searches of the boards to try to see if there has been a discussion of this issue and can't find anything....so if this is an old topic, I apologize. If someone can direct me to an old thread discussing this issue, I'd be much appreciative! Or if not, if you could shed any light, I would also be appreciative.

Thanks!

[KAR120C]

However... they do emphasize all of the critical thinking skills that proofs require. So even though they never say "write the step in the first column and the justification in the second" (or anything like that), the actual process of solving the problem requires all of the same kinds of work. You could easily have your kid write proofs for any of them, but DS and I have generally done that sort of thing as discussion unless he's having trouble with a problem (in which case I have him write steps to see where it falls apart).

I like proofs, and logic in general. We're doing Mathematical Logic on the side just for extra. But I don't have any complaints about the logic required by NEM in geometry (or algebra for that matter!) -- if you don't understand the steps and the justifications you won't get to the end of the problem.

[amsunshine]

Thanks, Erica!

[mpcTutor]

Hi all:

My dds are not even close to Geometry, but we are loving Singapore in elementary. I like the looks of Discovering Mathematics or NEM for the future.

I have some burning questions though, though, and maybe someone can answer them for me.

First, given that Singapore generally does very well on TIMSS and further, does not concentrate on formal geometry proofs in its upper level mathematics courses, is it truly necessary to study them in hs?

I, myself, loved geometry and proofs in hs. I understand there is a certain value in teaching/learning them. I'm just stumped as to why Singapore doesn't formally teach them...and yet, Singapore's math scores are so high in comparison to others (specifically, the U.S.) on an international scale. Perhaps this is because TIMSS doesn't focus on geometric proofs?
New Elementary Mathematics (NEM) Volume 1 which is the first book in Singapore Math series for 7th graders has chapters 9 through 14 related exclusively to geometry. Almost 50% content in the book is geometry. So Singapore math does contain adequate geometry. A link to table of contents related to geometry in NEM is below:

http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT1&Show=TechSpecs


I've done several searches of the boards to try to see if there has been a discussion of this issue and can't find anything....so if this is an old topic, I apologize. If someone can direct me to an old thread discussing this issue, I'd be much appreciative! Or if not, if you could shed any light, I would also be appreciative.

Thanks!Now coming to the columnar proofs, the language has certainly changed, instead of asking prove angle A = Pi/3, now most books ask you to find angle A. Whether, student proves A=Pi/3 or finds A=Pi/3, the method of solution remains same in content and rigor. The solution may not be in column form but it essentially is identical to one if written in column form. I think that's what the other poster is also saying.

Best regards.

MPCTutor
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AP Calculus, AP Physics, Singapore Math Grades 7-12
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US Central Time: 10:40 AM 2/17/2010

[amsunshine]

Now coming to the columnar proofs, the language has certainly changed, instead of asking prove angle A = Pi/3, now most books ask you to find angle A. Whether, student proves A=Pi/3 or finds A=Pi/3, the method of solution remains same in content and rigor. The solution may not be in column form but it essentially is identical to one if written in column form. I think that's what the other poster is also saying.



So, given the scores of Singapore students on the TIMSS in comparison to US students, is the Singapore approach and sequence as good as or even superior to the traditional approach and sequence in the U.S.? Just thinking out loud here. I see a lot of posters who have their dc do Singapore Primary Maths through 6b and then opt for a more traditional U.S. approach. I'm not sure what I will do, but I'm leaning toward sticking with Singapore all the way through. I'm trying to wrap my mind around all the pros and cons of both options.

[mpcTutor]

So, given the scores of Singapore students on the TIMSS in comparison to US students, is the Singapore approach and sequence as good as or even superior to the traditional approach and sequence in the U.S.?

I have personally not seen TIMSS test papers and I don't know if students are allowed to use calculator or not. Whenever calculator is not allowed, kids in USA will find overseas students having certain advantage in being able to do math without calculator. This in itself is another point of debate which I don't want to start. Again, point here is not about calculator use but I am trying to make sure that we are comparing apples to apples.

Comparing US and Singapore curricula, I would say Singapore is more traditional than US. We are always experimenting. In US, the goal for all round development of child results in sacrifice in other areas such as math. In Singapore and in most Asian countries academic competition is so intense that kids cannot afford time for other activities during 10th, 11th and 12th grade years. These are the kids who have competed in TIMSS. So one can attribute their success in TIMSS to curriculum sequence or to their effort or to both. I think it is largely the effort put in by students that makes the difference.

Just thinking out loud here. I see a lot of posters who have their dc do Singapore Primary Maths through 6b and then opt for a more traditional U.S. approach. I'm not sure what I will do, but I'm leaning toward sticking with Singapore all the way through. I'm trying to wrap my mind around all the pros and cons of both options.Singapore curriculum was introduced only recently in US schools with history of less than 12-13 years. If you are leaning towards Singapore math, my suggestion is to aim for finishing "New additional syllabus math" by end of summer after which your child enters 11th grade. One could accelerate and go faster but I have yet not seen any real benefit in acceleration. Again, success or benefit in any curriculum must be measured only by a national level standardized test such as AP/SAT/ACT/CLEP.

Best regards.

MPCTutor
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AP Calculus, AP Physics, Singapore Math Grades 7-12
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US Central Time: 2:26 PM 2/17/2010

[amsunshine]

Thanks so much for your detailed response! Much to think about....

[Nan in Mass]

The sequence is NEM1, NEM2, NEM3+NAM, NEM4+NAM. NAM is meant to be done by the college prep math classes concurrently with NEM3 and NEM4. NAM contains many of the things missing in NEM, like more slope-intercept form equations, matrices, more exponant manipulation, and logs. There are informal proofs in NEM. Occasionally one of them says something like this challenger problem from NEM3:
The diameter AB of a circle, centre O is produced to T so that OB=BT. Frm T a tangent is drawn to touch the circle at N. Prove that AN=NT.

Most of them are more like this example problem from NEM3:

Worked Example 6
TA and TB are tangents to the circle with centre O. Find the value of x and of y. (diagram shows AT=12, OA=5, BT labeled x, OT labeled y)

Solution:
BT=AT (equal tangents from ext. pt.)
Therefore x=12
In triangle AOT,
y^2=5^2+12^2 (Pythagoras' Theorem)
=169
Therefore y=square root of 169
=13 (y>0)

What isn't included is the sort of proof-oriented geometry class that I had in high school, where we began by showing that 1+1=2 and worked everything up from a set of whatchamacallums, the things you don't have to prove. Grrr. The word escapes me at the moment.

I think it might be a bad idea to choose NEM just because of its country of origin scores high on TIMSS. To ensure that your student do that, you would need to know how it is taught, teach it the same way, and provide the same cultural background and suppliments. The culture matters, I think, because expectations differ. Even something like the grading scale is different, with "average" a much lower number than in the US. I suspect that students are expected to spend longer trying to work out how to solve a problem, and to spend longer on their math in general. NEM takes a lion's share of our school time. The calculations are long and tedious. I let my sons use a calculator more than the book expects (again changing the TIMSS equation). We've stuck with it because it explains math in a way that matches how *I* think about math, so it is easy for me to teach, but I have often wondered if my younger son wouldn't be better off with the Dolciani that I had when I was growing up and which gave me such a good understanding of the basics. I was more sure that I was doing the right thing with my older son, who needed a very applied math program. NEM teaches all the new algebra crammed into the first few month of the year, and then spends the rest of the year on geometry and other applications, practising it. It is about as opposite from Saxon's gradual steps as you can get, and he needed that. He was unable to put together all the tiny steps in Saxon into a coherent picture. It wasn't ideal, but at least it worked. He went from NEM3 to pre-calc at the CC. (He placed into pre-calc less than halfway into NEM2 but there was no way he would have survived the class, so we waited another year.
HTH
-Nan

[amsunshine]

The sequence is NEM1, NEM2, NEM3+NAM, NEM4+NAM. NAM is meant to be done by the college prep math classes concurrently with NEM3 and NEM4. NAM contains many of the things missing in NEM, like more slope-intercept form equations, matrices, more exponant manipulation, and logs.


This is helpful to see, thanks!


What isn't included is the sort of proof-oriented geometry class that I had in high school, where we began by showing that 1+1=2 and worked everything up from a set of whatchamacallums, the things you don't have to prove. Grrr. The word escapes me at the moment.



Hmm....postulates? :-)

I think it might be a bad idea to choose NEM just because of its country of origin scores high on TIMSS. To ensure that your student do that, you would need to know how it is taught, teach it the same way, and provide the same cultural background and suppliments. The culture matters, I think, because expectations differ. Even something like the grading scale is different, with "average" a much lower number than in the US. I suspect that students are expected to spend longer trying to work out how to solve a problem, and to spend longer on their math in general.

I agree with what you are saying here. I think one can't really ignore the cultural part of the equation.