Why not use NEM after Singapore?

[Jen500]

It seems like quite a few families use Singapore Primary Math...I was wondering why there don't seem to be as many using NEM?

[Jenny in Atl]

We did NEM1 this year. I'm not going on to NEM2 because my math skills are just not good enough. I'm not using an easy Algebra text this fall (in siggy) but I understand what they are doing better than with NEM. If my math was stronger, I would have loved to have stuck it out and used NEM all the way through.

[Patricia in WA]

I have one child using it. He enjoys it but he is a math kid. My other child would have run away from home if I would have put her through it. She is much happier with Lial's (and so am I!!)

 

Basically, NEM is not for the faint of heart.

 

HTHs,

[Karen in CO]

:iagree:

Yep - what they said.

 

I tried it with my oldest. I could do the math, but not well enough to teach it to him. It might have been different if we had done Singapore all the way through, or if I were better at math, but the reality is that it was too hard for me.

[Miss Marple]

I used it with my oldest. But when he started high school we decided that, as a junior, he would go with a couple of concurrent classes. He wanted to do college algebra. The transition from NEM to traditional sequence math at that point was more difficult. He was doing NEM 3 in 10th so hadn't finished a full geometry program, nor completed the algebra 2 component. So...with my other guys we've decided to transition to a traditional sequence after Primary Math.

 

But I love NEM and so did my son. I would recommend it if you feel capable of teaching it. I didn't find it difficult - challenging at times, but not overwhelmingly so.

[CoffeeBean]

I have the NEM books and would have no problem teaching them but there is very little instructio in the book, more just pages of problems so there would be no self learning or self review. I love the NEM problems and kept the books to supplement with however NEM does not provide lists of theorems and postulates for algebra and do "proofs or show tha this equals this" which I think is really improtant in algebra. They also don't follow the traditional high school math sequence so you would have to watch out if public school is in your future or SAT's etc. Finally the layout of the books is absolutely unispiring - no color, no blocks, little indentation. Its hard to pick thinks out or distinguish 1 page from the next.

 

I really do like it the problems though.

 

CoffeeBean

[Testimony]

I have the NEM books and would have no problem teaching them but there is very little instructio in the book, more just pages of problems so there would be no self learning or self review. I love the NEM problems and kept the books to supplement with however NEM does not provide lists of theorems and postulates for algebra and do "proofs or show tha this equals this" which I think is really improtant in algebra. They also don't follow the traditional high school math sequence so you would have to watch out if public school is in your future or SAT's etc. Finally the layout of the books is absolutely unispiring - no color, no blocks, little indentation. Its hard to pick thinks out or distinguish 1 page from the next.

 

I really do like it the problems though.

 

CoffeeBean

 

 

That's what I heard too. I am however going to continue with it. I just plan to use it as a supplement and find another curriculum as the primary. I really like this program so, I will definitely go on with NEM after 6B. I will have to find another program too.

 

Blessings in your homeschool journey!

 

Karen

http://www.homeschoolblogger.com/testimony

[kpupg]

It seems like quite a few families use Singapore Primary Math...I was wondering why there don't seem to be as many using NEM?

 

We use it, but there are things to take into consideration.

 

It is quite advanced compared to the math expected of kids the same age in the U.S. It is "integrated" to some extent, in that algebra and geometry are presented in each year. The teacher's guides are not all that helpful for teachers who aren't all that advanced in math themselves. The geometry is taught without proofs. Well, actually, proofs are in there, but they are implicit, not the traditional 2-column proofs so well known and loved in the U.S. :)

 

So .... we do it with modification. We actually use two curriculua -- to get a different slant on the material, and to get the 2-column proofs, which I don't want the kids to miss out on. For the current child, we're using Life of Fred alongside NEM. We do math in the traditional U.S. sequence, not the NEM sequence, which means using LOF as the spine and splicing in NEM by topic/chapter. And I'm an engineer, so the content is not an issue for me as the teacher.

 

For the next child, who is good at math but doesn't particularly enjoy it, we might well have an interim year between PM 6 and NEM. I bought the Russian Math 6 and I like it a lot, so it might fill that gap. And that very delicate flower of a girl child will NOT be using LOF, so we'll have to find something else :)

 

That's a lot of modifications, which is a lot of work, and I think someone who loved Singapore less might not want to go there. And I don't blame them :)

 

Karen

[chiguirre]

Sorry for the highjack, but I've always wanted to know people's take on New Math Counts. How does it stack up to NEM. It seems easier and much more doable, but I haven't heard many (okay, any) comments about using it.

 

This is obviously way out in the future for us, but inquiring minds want to know!

[kpupg]

Sorry for the highjack, but I've always wanted to know people's take on New Math Counts. How does it stack up to NEM. It seems easier and much more doable, but I haven't heard many (okay, any) comments about using it.

 

This is obviously way out in the future for us, but inquiring minds want to know!

 

I recommend asking at the www.singaporemath.com forum. You can find direct comparisons there, and Jenny (moderator and author of the NEM solutions manuals) is very proactive in helping/answering.

 

Karen

[Myrtle]

It seems like quite a few families use Singapore Primary Math...I was wondering why there don't seem to be as many using NEM?

 

My husband who has his MS in math wanted to use a more theoretical approach to math and so we found some obselete books which teach a lot of proofs in algebra and bring up a lot of "higher math" topics. The old 1960s Dolcianis offer a similar "theoretical" approach as well and sometimes you hear Jane in NC on the high school board talk about them.

 

Before we found out that pure math was an option over an engineering approach (officially "math methods in the physical sciences") and switched, I was well on my way teaching out of NEM 1. And in fact, this past week I've been mining the NEM series for good word problems to supplement what we are doing. You just can't beat Singapore word problems.

 

I'm also going to be ordering a Teacher's Manual for Secondary Math directly from Singapore next week and posting a review of it for those who want more support in teaching NEM.

 

Be aware that the NEM series does not cover all high school math topics. It pretty much just covers algebra I, geometry, and algebra II. It doesn't do trig in depth, it doesn't cover a lot of precalc topics such as polar coordinates and mathematical induction. However, you would be finished with the NEM series at the end of the tenth grade and would have covered a lot of trig by then as well as vectors.

[Lori D.]

We used the first half of NEM1 with older "mathy" son (who LOVED Singapore Primary, and enjoyed NEM1) to finish off 7th grade (the first part of 7th I had him do a "skim review" of Saxon Algebra 1/2), and then switched over to Jacobs Algebra (8th) and Jacobs Geometry (9th). He'll be doing Abeka's Consumer Math this year (10th), and so to keep him "on his toes" math-wise, we'll also have him do parts of NEM2 (algebraic graphing and geometry focus).

 

Similar to Jenny, Karen, and Coffeebean: NEM1 doesn't have a lot of instruction; and while I can often "figure things out", I struggled to figure out the higher math in NEM1. *Quite* often DS and I would work and rework a problem together until finally something I said or tried would make a lightbulb go on for HIM, and then he'd see how to work the problem -- and then have to explain to me! (lol)) I'm hoping that in having completed Algebra and Geometry, I'll have more of a connection again with the higher math concepts to be able to help DS tackle NEM2 as a supplement.

 

 

So, we still have and use NEM, but it has had to take a supplementary role here. However, there are several ladies on the high school board who have used NEM 1,2,3 very successfully through high school -- perhaps post there for some tips if you're interested in continuing with Singapore. BEST of luck, whatever you go with! Warmly, Lori D.

[Myrtle]

NEM does not provide lists of theorems and postulates for algebra and do "proofs or show tha this equals this"

 

CoffeeBean

 

That's why we don't like it, but the only other algebra programs that I know of that do it are Foerster's and the older Dolcianis. I've seen Saxon discuss, say the distributive law, but I haven't seen them list out the field axioms like Foester's does. Sounds like making a list of which algebra programs do this and which algebra programs don't would make an interesting project. For those of you wondering what we are talking about. This is the list of properties of numbers that everyone should know backward and forward in algebra in order to be able to do any proofs in algebra or even to be able provide justification for "why did you move x from here to there" in solving an algebra problem.

 

The argument against this is that you don't "need" proofs and formal justifications when you are doing rune manipulations and are just interested in "getting the answer."

 

To expand on an observation made by Edmund Landau, "How can you say you know math when you don't even know the mathematical reason why multiplying two negatives gives you a positive?"

[karensk]

For those of you wondering what we are talking about. This is the list of properties of numbers that everyone should know backward and forward in algebra in order to be able to do any proofs in algebra or even to be able provide justification for "why did you move x from here to there" in solving an algebra problem.

 

 

...For some reason, I can't access the link.

 

Thanks!

[karensk]

Never mind...I can see it now! Thanks for sharing this!

[Myrtle]

...For some reason, I can't access the link.

 

Thanks!

 

I think I fixed it. LINK

 

And you also have different lists for the properties of equality (goes back to Euclid!), inequalties, and set theory, but that takes you to areas outside of algebra.

 

Here is a sample page of the old high school algebra book that we use, you can see that it's about the idea behind algebra. On this particular page they are still introducing the properties of numbers, marked with "P" and then you can see how it veers off into what amounts to a philosophical discussion. Now that we've assumed that every number has a reciprocal, how do we know that that it has only one reciprocal?

 

You just don't see that in NEM.

[Testimony]

Thank you for the link to the Algebra book and the property of numbers list.

Where did you find those old books or are they yours?

Blessings in your homeschooling journey!

 

Sincerely,

Karen

http://www.homeschoolblogger.com/testimony

[Beth in Central TX]

I did consider NEM for our high school series, but I don't like the integrated approach of Algebra I, Geometry, & Algebra II. That's one of the reasons I didn't continue with Saxon too.

[Jen500]

Thank you for the input everybody--I will have to wait until tomorrow to give out more rep.

I do like to plan ahead for math, and I love math but I don't want to be scrambling after Primary Math. I'm looking forward to your review of the teacher's manual, Myrtle!

[Myrtle]

Thank you for the link to the Algebra book and the property of numbers list.

Where did you find those old books or are they yours?

Blessings in your homeschooling journey!

 

Sincerely,

Karen

http://www.homeschoolblogger.com/testimony

 

That particular book is by an author called Frank Allen. His name came up in an online rant by a mathematician called Ralph Raimi about math education in the 1960s. Allen was described as being "too rigorous."

 

In the language of mathematicians, "rigorous" has a special meaning. It means that all assertions are proven using the axioms of that particular subject. The list of field axioms that I put up is what is used in algebra. Geometry has its set of axioms as well and axioms are used in the study of logic and set theory. At any rate, to say that a course or book is "rigorous" means that it is taught from the ground up like the way geometry used to be taught. You start with axioms and prove theorems and then those theorems are used to prove yet more theorems. Rigorous math means that every assertion that you make is backed up with this kind of formal proving business.

 

And so I laughed when I saw someone refer to something as "too rigorous"...It's a little hard to explain why this is funny, but it's like saying that someone has too much money or has memorized too many facts, or is too moral.

 

We found the book used online and we got the algebra II version as well. I did some blog entries about this a year or so ago and the remaining used copies were snapped up. Occassionally folks email me and tell me that they were able to acquire the second edition through interlibrary loan.

 

I don't usually recommend this book per se, since almost no one has a background in theorem proving and there is no answer key or teacher's guide. I can run into the other room and get help when I need it (usually getting more than I bargained for).

 

 

If you are looking for a purely philosophical approach to algebra then I highly recommend Gelfand's Algebra which can be used as a supplement to any algebra program, but he doesn't list out the axioms (Of course, you have them now!) Gelfand's approach is not as "technical" as Frank Allen's or Dolciani's though...and Gelfand does not drill. He assumes that the student is motivated and interested and willing to spend a lot of time on fun stumper problems. Allen, on the other hand, assumes he's got a reticent unmathy teen who doesn't care about math but has to learn it any way. Russian math books like Gelfand's seem very chatty and less orderly than American books, but they have amazing content for the motivated student.

 

My husband put all the solutions to Gelfand's problems online for free for anyone interested in using this program. H Wu is a Berkely mathematician involved with teacher training in California and has written a long review of Gelfand's books here. He spends the first seven pages talking about the sad state of the teachig of algebra (technique is emphasized over the intellectual aspect) and then on page 7 begins the actual review. Wu brings up the criticism that Gelfand's Algebra doesn't have every topic in it under the sun, and that is true. However, this is a small paper back book with just a few hundred problems and was designed for use in a correspondence school of gifted kids who would use it as a supplement while attending normal high school algebra classes.

 

Finally, for those with a classical education bent who don't want to redo their entire math plans , you may enjoy "Lapses in Mathematical Reasoning". It's an English translation of a Russian book from the 1950's. It is a collection of 80 false proofs that are at the high school level and you read through the solution to some problem and spot the fallacy. Some of them just reflect run of the mill mistakes and some of them lead to interesting discussions about deeper issues, long-winded answers are at the end of every chapter. As you can see by the table of contents the authors of the book chose to extend Aristotle's refutations to sophisms of a mathematical nature which gives it a very philosophical feel that I had a lot of fun with. The chapter on arithmetical errors was not as good as the others since they relied on pecularities of algorithms that we don't use any more.

 

So, just because NEM or Saxon is not perfect, there are things you can do to supplement whatever you have without throwing the baby out with the bathwater.

[abbeyej]

That's why we don't like it, but the only other algebra programs that I know of that do it are Foerster's and the older Dolcianis. I've seen Saxon discuss, say the distributive law, but I haven't seen them list out the field axioms like Foester's does. Sounds like making a list of which algebra programs do this and which algebra programs don't would make an interesting project. For those of you wondering what we are talking about. This is the list of properties of numbers that everyone should know backward and forward in algebra in order to be able to do any proofs in algebra or even to be able provide justification for "why did you move x from here to there" in solving an algebra problem.

 

The argument against this is that you don't "need" proofs and formal justifications when you are doing rune manipulations and are just interested in "getting the answer."

 

To expand on an observation made by Edmund Landau, "How can you say you know math when you don't even know the mathematical reason why multiplying two negatives gives you a positive?"

 

But aren't those properties all taught it most elementary mathematics programs? Or am I being naive? Certainly they've been featured and reviewed constantly in the program we've used. ... I'm not saying they're immaterial -- just that they're basic enough principles that I would expect students to know them well before they reach algebra (if not expressed in exactly the way that they are in your link). Am I wrong?

[Myrtle]

But aren't those properties all taught it most elementary mathematics programs? Or am I being naive? Certainly they've been featured and reviewed constantly in the program we've used. ... I'm not saying they're immaterial -- just that they're basic enough principles that I would expect students to know them well before they reach algebra (if not expressed in exactly the way that they are in your link). Am I wrong?

 

They aren't "basic" in the sense of being simple. They are more like foundational. Mathematicians have made careers talking about the differences between things (groups) that follow some of these rules and things that follow all of the rules. Essentially all of these various properties and what happens when they are or aren't true is the sum total of what one learns in Abstract Algebra so this isn't something that can be covered in its entirety in a K-8 arithmetic program. Usually what you might see in arithmetic is the appearance of the distributive, commutive, and associative properties and the book states it and then has the kid apply it in the simplest way possible or identify the use of it in a very simple way.

 

However, what you don't see (but if your arithmetic book does this I'd be interested) is go in depth into distinguishing between properties of numbers, axioms, definitions, theorems, and notation. It's all thrown in there and all mixed up. It's all ad hoc. And the students aren't required to use them as axioms, but instead they are taught "facts."

 

That 2 X 3 = 3 X 2 is true is not "learning the commutative law". In fact, even learning that such a property is called "the commutative law" is not "learning the commutative law."

 

"Learning the field axioms" entails being able to write down the general statement of the principle involved, not merely as a fact about the integers, but as a property that any set of elements together with any kind of operater on that set may or may not satisfy. "Learning the field axioms" also entails being able to use the list of axioms/properties that some given set and its operators might satisfy and actually derive significant mathematical results from that list through an unbroken chain of completely valid logical deductions. :tongue_smilie:

 

What seems to happen in most algebra books is that the student never is expected to make a distinction that multiplication distibutes over addition is axiomatic, but that it distributes over subtraction is not. Or, that the natural numbers are closed under addition is axiomatic but that they are closed under subtraction must be proved. And, they would "know" and use the rules of order of operations but they wouldn't know how those fit in with the other rules they've memorized. The rules about order of operations are not on "the list" of field axioms, for example. So, unless there is a master list ,the student is likely to go through his algebra book lumping it all together because he's never been given an indication that there is some sort of structure or hierarchy to all these facts that he's memorizing.

 

Once this list is memorized then there can follow discussion about what happens if one of the properties is missing, so beginning in ninth grade algebra, with a text like Allen or Dolciani the student is getting an introductory taste of groups, rings, and field theory along with the skills it takes to prove theorems. This maturity of proving theorems, to gauge the appropriate amount of rigor for a given problem, constitute "true" math skills that cannot be acquired over night, skills that are absolutely necessary in doing in higher math (not to be understood as engineering calculus), For instance, after a diet of Allen, Gelfand, Oakley and Allendoerfer even an average student has acquired the skills needed for a Calculus text such as Spivak. Even a really good program like Singapore would leave a student unprepared for Spivak.