I recommend Christian Liberty K as a very good way to learn basic addition and subtraction facts within 10 but in my opinion this book didn't expose the child to any mathematical thinking. (I've used Christian Liberty K with two kids to supplement another program) You really could accomplish nearly the same thing with a set of flash cards. You may want to consider a program that teaches various ways of thinking about subtraction, such as subtraction as the inverse of addition, subtraction as a "partition", conparison of sets, and also different properties of equality, use of manipulatives (abacus, counting blocks, etc), terminology used in math, measurement, geometry. Being familiar with different views or models of addition and subtraction is what makes it easier to interpret word problems later on.

Obviously someone or a group of someones in a school district thought this sounded like a really good idea. I wonder what their thinking was? My guess is that it might have gone something like, "Math is about real life problems, not drill sheets" or "Algorithms don't teach mathematical thinking, this program does something different, therefore this program teaches mathematical thinking" or maybe they even believed that the program was teaching math "conceptually." So I guess my question is for those whose kids were in this program, what were you being told by the teachers and district?

I know that there are at least one or two people out there who are using Frank Allen's Algebra because they emal me from time to time but I never hear back from them to find out how it's going, if something was too confusing, or maybe they had some clever approach to something I had difficulty teaching, or maybe they just didn't see the point and gave it up for something entirely different. Nonetheless, in chapter 8 the switch is made from two column proofs to proofs in paragraph form and I tried to document how that that went and how I handled it along with scanned copies of my son's work that you can see the lesson at my blog In education,al rhetoric there is a lot of lip service paid to the fact that one "uses logic" in math, but the problem that my son did really illustrates this well, I think and there is also this direct connection between every day language and symbols that can be seen. And here is a good article summarizing the role of logic in teaching proofs, this might be something useful to those who are trying to teach proofs in geometry right now. More specifically, this author brings up the issue of why "bridge courses" are needed before college students take upper level math classes as well as the sorts of things that happen in math classes that promote fallacious reasoning. You may note that the author of the above article goes into the topic of quantification which is something that we haven't done yet, hence, the potential for ambiguity in the proof with the "k"...is it for some particular k or all k? That sort of thing will be straightened out by next year since we plan on doing Suppes First Course in Mathematical Logic. So I'm thinking, that when we get to Algebra II, we'll be ready to use those symbols and manipulate them even though that isn't something that is explicitly taught in Frank Allen's Algebra II. Moving closer and closer to, "for every epsilon..."

I think it has to do with how many people joined the site because they were referred to it by the original member. In other words, referral 2 might mean that two people were referred to this site and became members due to another member linking them here. I had Googled this at some point but I have no idea all that works out technically speaking. Presumibly it has to do with emails and links or websites and links.

I think there are a few ways of looking at this. 1. More and more concepts are being taught earlier and earlier, but they aren't necessarily going into depth with those concepts. It all looks impressive on paper though. 2. Standards really are being raised and "depth" is required, but the students aren't given the tools to reach the new goals. The parents have to haul the kids off to Sylvan to fill the gaps, those with advanced degrees and enough time away from work afterschool. Kids whose parents can't afford tutoring or kids whose parents don't have the educational background fall through the cracks. Kids who are on the slow end of of maturing get left behind. 3. The teaching really is getting better. I can find examples of this in math education. Some people think that it's impossible for a particular topic or skill to be taught to some kid at some particular age and then someone else comes along and figures out how to break it down in just the right way with just the right kind of practice. 4. Raising standards in one area might mean they are lowered in another. In the past there were high standards for achievement in Latin and if you look at school schedules half the day was devoted to the study of Latin and Latin literature. Now we spend that time on math and science and foreign language gets relegated to one hour per week in the lower grades and maybe one hour per day in high school. It's just not really possible to do all things in depth at once.

Propose that the tv be moved to the master bedroom and that the door be closed by the adult viewer when it's on. Before making the proposal think up something to offer in return to make it worth his while, "Let's make a deal! I'll be happy with that motorcycle parked in the living room if the tv goes in the bedroom." ;-)

Yeah, but does she remember every detail about Hannah Montana? Unless there is some learning disability, this is more than likely related to her interest in the subject matter to begin with.

I moved my older son ahead based on how well I thought he had mastered the material. However, my second son enjoys working two, three, or four days of work in one sitting. It's his idea and he can do that much work because it's easy for him so he is getting ahead without me doing anything at all.

In my college biology classes in the 80s evolution was discussed the first day of class and after that I don't ever remember it being discussed or taught. We were too busy figuring out the chemistry we needed to know to understand cell biology and how one species of fungus reproduced vs the reproductive method of another. I imagine that if biology and astrophysics works the way any other field does, the research topics are dictated by what the "open questions" in biology are and if everything has been figured except a whole bunch of issues in evolution or cosmology then there's going to be more emphasis on these kinds of topics than there were in the past. (Maybe someone can confirm this?) Being a lowly liberal arts major I have no idea what's going on in those fields so I'm going to avoid the whole the thing by sticking to something everyone will hopefully happily agree is useful: Cell biology, chemistry, physics. I don't feel like I have any business promoting or attacking a particular origin of the universe or any other high level theory that relies on knowing lots of facts about energy, radiation, gravity, and nuclear physics, string theory, rope theory, yarn theory whatever, when we/I don't have even the basic facts nor the math down that it would take to really understand the arguments. Sometimes it really does take a rocket scientist.

I have rarely used my Extra Practice books. They only offer a single exercise on a topic and if real remediation is needed this simply isn't enough. All topics are given the same emphasis and this doesn't reflect the fact that some things, such as long division, simply require more practice sheets than others. Intensive Practice offers more practice problems for those that need remediation, more word problems, as well as more challenging problems and stumpers for kids who need more of a challenge. When my youngest needed "extra practice" on basic facts, say in the form of drill, I went outside Singapore (Saxon, Rod n Staff, Christian Liberty Press, Flashmaster) for it. The handful of extra sheets in the Extra Practice book were not even close to the kind of work she needed to do to catch on. The most common thing that my kids needed extra practice on were two step word problems and for that I rely on the challenging word problem books more so than the Extra Practice or even the Intensive Practice.

I had my dyslexic son read that and he did it perfectly with the exception of, ", but the word as a wlohe" which he read as "but the world as a whole"

I should have been more careful in my original response to promote a distinction between "Eurocentric" and "Western Civ" or Western Canon. It is not clear that the teacher has made such a distinction or that such a distinction is being made by the students. The phrasing by the teacher is very clever, "IF you are embedded in a non-European social group..." (And so now we must disambiguate non-European from Eurocentric!) It seems almost certain that this was not said to a group of Quiche women in the tropical forest of Guatemala by a Peace Corps volunteer, but rather to Westerners in a Western institution. Perhaps the best response would be, "The conclusion is true but irrelevant since we are Westerners of various colors in a Western institution in a Western culture." I did not discover until I was an adult that Western Civ has so much more to offer than what the multiculturalists claimed it did. It reflects the voices of both strict Puritans and Greek pagans, monks and libertines, luddites and inventors. Without a Celsus using Western rhetoric and philosophy to argue his case, Origen's "Contra Celsum" would have never existed. Medieval theologians and American Puritans did not have a monopoly on the definition and scope of Western Civ or Western literature, but neither do the more modern polemicists whose world view is very narrowly limited to identity politics and personal therapy.

This seems a typical modern defense of multiculturalism. They use literature as the instrument by which they will attempt social engineering of their students, much like a pastor delivers a sermon to a congregation. The author of the passage speaks as though there is no selection bias on their part made in what constitutes the "canon" and yet alludes to the bias of this unnamed other. There is nothing but vague refences to "otherness" in this passage. Any specifics would probably meet with criticism. My guess is that their idea of multiculture tolerance doesn't include FLDS literature, for example. I'd be hard pressed to come up with a "value" that hasn't been expressed by some "Eurocentric" author. From communism to anarcho-capitalism, utilitarianism, deontolgy, misogyny, misandry, equality, involuntary servitude, death penalty, religous extremism of every variety, atheism of every variety, arguments for every imaginable form of government, you name it, there is a western author that has written about it either in a fictional novel or directly via political philosophy, moral philosophy, or theology. I am weary of being "exposed to other people's values" in the guise of literature to ease someone else's anxiety that I might not vote the way they want me to. I'm all up for good discussions about politics and religion as part of an education, but I want to call that for what it is.

Here is the thread at singmath in response to this same question, in case any lurker is interested. It looks like they are pushing some algebra topics into arithmetic (graphs and negative numbers) and whether that is something you need to do would depend on what program you plan on using after sixth grade, I suppose. If you stay with NEM it will teach these topics. Many American algebra programs do not assume that the student has an understanding of this as well and teaches it from scratch (Jacob's Algebra, Dolciani come to mind) In the past whenever I've had to make a decision that seems like it's based on six of one/half dozen of another I just went with the cheapest $ option.:D

You may find that someone has already addressed one of your questions in the thread about who is or isn't switching to the New Standards edition and why.

We are sticking with Singapore 3rd edition because back in 2001 I was so thrilled to have found this series that I bought the entire series for all three kids in advance fearing that one day this might go out of print. The third edition does not include problems with our system of measurement but once the kid knows how to do multi-step word problems and has their basic facts down cold that it doesn't require much explaning at all for them to measure items in feet and inches and convert units between ounces and pounds. My sixth grader is about 2/3rds of the way through ninth grade algebra right now after finishing the primary series and if there is a "gap" in the third edition I certainly haven't seen it slow him down in algebra one bit. My second son doesn't need extra review of basic number facts or algorithms, but he needs more help with two step word problems. For that I am keeping a separate notebook and I write out each of the word problems that he misses. After some time has elapsed I go back and have him solve these problems again. It may very well be the case that an American version of Singapore must include extra practice because, unlike Singaporean culture, the teachers can't count on their students' parents reviewing with extra workbooks at home. About those California standards. For a long time California did have notoriously rotten standards but it seems that they have recently reformed them and they are now considered some of the best in the nation. (So, I do know where the lady is coming from when she says she's going to stay away from them! They weren't always good and for that matter I still would use them only as a starting point rather than as commandments) Fordham has a "grade card" of math standards from around the nation and I recognize the names of three research mathematicians that contributed to that: David Klein (from mathematiciallycorrect.com) Ralph Raimi (New Math guy from the 1960's, (he's got a fabulous website about math education) and William Quirk (with whom I corresponded about math programs before I found Well Trained Mind) As a homeschooler it was useful for me to look through the standards at Fordham as well as mathematicallycorrect.com and Ralph Raimi's articles to get some idea of how to judge a good math book for myself.

Sailing and homeschooling in the same thread! So, where have you guys been?

You won't run out of math to teach. While we think of the normal sequence as leading to Calculus, but there are books written for high school students (self teaching) that are on other areas of math as well. Each one of these is a mini-course, for example. And there is Art of Problem Solving online classes once he can do K6 arithmetic. My second grader magically teaches himself many things that my older son needed a teacher for.

#1 Not enough practice provided for the child to master the topic being taught. #2 Not enough review.

I did a blog entry on why invert and multiply works some time ago. It's sort of an interesting philosophical question. So we have these three ideas. We have the idea of division as in 1 ÷ 3, we have the idea of multiplicative inverse, "There is some number such that if you multiply 3 by this number you will get one" and then you have the idea of a fraction as in 1/3. And why exactly 1/3 is the multiplicative inverse is a whole nother ball of wax so we'll just assume it for now and worry about the relationship betewen the ÷ and the fraction 1/3. So how exactly do we know with metaphysical certainty ;-) that each of these three all lead to the exact same point on the number line? That is the underlying issue of why invert and multiply works. Here is an example using numbers instead of letters: I want to figure out why it is that 2 ÷ 3 = 2 x 1/3. So here is our fact family: a. 2 ÷ 3 = 2/3 b. 2 ÷ 2/3 = 3 c. 3 x 2/3 = 2 d. 2/3 x 3 = 2 So let's start with, 3 x 2/3 = 2. But if you look at the equation in "a" you can see that 2 ÷ 3 = 2/3 so I am going to replace the 2/3 in expression c with 2 ÷ 3 using substitution so I end up with this. 3 x (2 ÷ 3) = 2 And now I'm going to multiply both sides by 1/3: 1/3 x 3 x (2 ÷ 3)= 2 x 1/3 and I can use the associative law to move the parentheses (1/3 x 3) x 2 ÷ 3 = 2 x 1/3 But we already know that 1/3 is the multiplicative inverse of three since 1/3 x 3 = 1 So, I can then substitute the expression 1/3 x 3 with 1 like this, 1 x 2 ÷ 3 = 2 x 1/3 and since anything multiplied by 1 is itself (another one of those field axioms) I'm left with tah dum 2 ÷ 3 = 2 x 1/3 I don't know that a child in arithemetic would be able to follow such an argument. Because algebraic principles are needed to explain why, it's probably better left for algebra.

Reminds me of a post I recently read.... "You can measure the amount of mathematics in any number of ways. I use pounds and ounces. When asked why my son is so much farther ahead than his peers, I explain that if you take out all the pages of problems and exercises that students have done, and weigh them, my son will have done many more pounds of mathematics than his peers."

How many word problems would you do in a set?

A very good way of becoming familiar with what is currently being sold on the market is to make a short wish list of the traits that the ideal textbook should have and then to email the major publishers and get a sales rep to contact you. Depending on the size of her classes she may very well qualify for free desk copies which she will be able to take her time in personally evaluating. She may have in mind that the ideal textbook should emphasize literature rather than pop culture or take a grammatical approach rather than pure immersion, for example. But also as a teacher you need to have an idea of what sorts of supplements you are interested in. Test bank? DVDs? Etc. Once she has this in mind publishers will be better able to help her. I would start with Prentice Hall. If there is a university near her with an education department they will very likely have a resource room in the library with a lot of Spanish textbooks in it.

Replacing content with entertainment is rewarding the non-thinkers and punishing those willing and able to think. It doesn't surprise me that it's been heading in this direction. You get a bigger market catering to the nonthinkers since there are more of them. And it sounds like from the structure of his own lecture he's made the presumption that his audience falls into the former category.