I need a new math program for my daughters who are 7 and 6. I am interested in this but where to begin? Right now they are doing typical grade 1/grade 2 math work.

I looked at the 4th book in the elementary series and the concepts are so varied, it's hard to tell where we should begin.

Thoughts and ideas appreciated!

No one can tell with certainty since nobody has used the elementary books yet, they just came out.

If money is not an issue I would start with the very first book in the series. It is supposed to be about fun anyway, not about hard work. If your DDs are confident readers they will just fly through it and be ready for the more challenging ones in no time.

My DS6 is going through Fractionsright now and it is a liitle hard for him - long hand division and such. After he finishes it I am going to let him go down a level and go through book 4 of the elementary series ([i]Dogs?)[/i. Just for fun.

By the way, in every book Stan keeps constantly going on tangents and talks about astronomy, economics, roman numerals ...you name it. So, starting with easier books still lets them learn something.

Terrilth,

LOF elementary books will not be out until end of July. In the mean time, you can give them Math for gifted kids (flashcards) from B & N. They are great and it should occupy them for the whole summer. My DD7 is doing grade 3 book. Don't let the grade number fool you. Some questions are hard enough for the average 5th grader.

Thanks Peter! I didn't know the elementary books were brand new. I really like the looks of them though and think I'll start w/the first one.

I am going to start with the first one for my 6 year old.

DS9 read LOF 3 or 4 pre-algebra books two years ago. He loved it. Once he finished the Beginning Algebra, he went on AoPS and be able to tackle some real math problems.

Here is my review of Life of Fred Fractions:

http://teachingmybabytoread.blog.com/2011/06/06/too-many-algorithims-in-life-of-fred/

I think it makes an okay supplement, but not an entire Afterschooling curriculum.

Your review says,

'I still really like the book a lot, but I�m less impressed by it as we near the end. I think the author relies too much on traditional algorithms to teacher mathematical concepts. This is completely contrary to my approach to teaching math, which is Constructivist in philosophy. (For more information on Constructivism, please see my post at: http://teachingmybabytoread.blog.com/2011/03/15/subtraction/)

Earlier in the book, it was easy to do a lot of Constructivist activities and explanations side by side with Life of Fred. To compare, order, reduce, add and subtract fractions for example, Bruce experimented with the Right Start Fraction strips in addition to working with the algorithms taught in Life of Fred. So when the book talked about 2/6 being the same as 1/3, Bruce really understood that well, because he could build those fractions himself.'

<end of excerpt>

I use EPGY with my 5.9 yo boy, who is now working on fractions among other topics. We have never used manipulatives, but he has learned a lot of math and is quite interested in it. I don't think all children need manipulatives. More broadly, I am skeptical of "constructivism" in education. Thanks for your review -- I don't mean these comments as criticism. Parents' views of curricula will be influenced by their philosophies of education.

Here is a better review of Constructivism. Maybe I can change your mind!

http://teachingmybabytoread.blog.com/math/

Like anything else, constructivism can be over-applied, though it certainly does have a lot of strengths. I read your blog post. I don't think it's accurate to make the sweeping statement, "Once a child learns an algorithm it is as if mathematical thinking stops". In addition I think the "fastest and most efficient way for [a] specific brain to work" will be more and more often a pre-defined algorithm as a child starts learning advanced math, since not all children will unerringly find the most efficient solution to a problem left to their own devices.

Good math courses will explore the development or construction of specific algorithms in depth, and give plenty of chances for development of problem-solving skills, but to reinvent the wheel by forcing a child to come up with every algorithm would be pointless, and slow down the learning process to a huge degree.

Developing one's own approach to a problem is a valuable skill that needs practice. There are plenty of other ones, including the ability to take in highly structured information and understand it quickly, then apply it.

As an example, I taught my son how to do conversions from Roman numerals to base ten, up through 100, in under a minute, after which he was flawless. This is often taught as a math skill, although one could certainly develop a wonderful math talent without ever learning about Roman numerals; it's more of an encoding/decoding and linguistic skill. But in any event, he learned it quickly, which gave him practice in learning rules and applying them quickly.

Taking the constructivist approach, I might have given him some samples of Roman numerals and base 10 numbers, then let him figure out the rules himself. That would have given him practice in problem solving, and he might have had fun, since he likes puzzles. In the end I think he gets plenty of practice in such things, though, so in a sense it would have just represented a delay of something else.

I believe that a strength of constructivism, for early education in math as you've explained it, is simply a focus on what's going on, instead of the notation being used. For example a child certainly could learn long division by rote practice of shuffling numbers and lines around, and do little to increase their math understanding. However I also think a focus on understanding processes involved can be part of teaching; one doesn't have to depend on a student finding the understanding themselves.

Another strength of educational constructivism as you've explained it is the discouragement of passivity. I think, again, that this is helpful and necessary, but it's not true that simply explaining an algorithm will shut a child's mind off. The devil is in the details of the teaching and the balance of active thinking activities in which a child engages.

There's simply no reason that a correct understanding of a mental model can only be approached through self-led exploration. Nor can it be true that a child will always learn the best model on their own. When a child's own model is wrong, it gets replaced by the correct one that needs to be taught by the teacher anyway-- or it's not, leading to later confusion.

ETA: A few links:
http://en.wikipedia.org/wiki/Constructivism_(learning_theory)
http://en.wikipedia.org/wiki/Math_Wars
http://en.wikipedia.org/wiki/Worked-example_effect
http://en.wikipedia.org/wiki/Expertise_reversal_effect

Lucounu - Well said; your description matches our personal experience. Unfortunately, the people we've spoken to in our school district seem a bit dogmatic when it comes to constructivism and math, and don't seem to think this way...

DH would go as far as suggesting some kids might get frustrated with the expectation that they rediscover the algorithms on their own, knowing that the grown ups were holding back known, efficient ones.

Me three. The key is the false dichotomy implied by contrasting constructivist teaching, in which students discover their own algorithms, with "blindly teaching algorithms". It is possible to sightedly teach algorithms :-) As a professional mathematician I have to develop ways to solve problems nobody yet knows how to solve, but if I insisted on solving for myself problems that do have known solutions, I'd never get to the new stuff. I've banged on before about how important it is for children to wrestle with mathematical problems that are hard for them, and doubtless I will again, so I appreciate the motivation behind constructivism, but I don't like the dogma.

Good points amylou, ColinsMum. As usual I blathered on without much structure, but I think one key point is this: math students eventually have to learn how to take in prepackaged information, and do that efficiently and with as full an understanding as possible. It's like reading comprehension, but math-model comprehension. I don't think we'd get very far in any scientific field if people weren't well trained in communicating with each other.

We've also seen some posts here on how early math frustration led to an abandonment of math as an interest. But barring that, I'm guessing that one could be fairly inefficient with lots of bottom-level arithmetic concepts and procedures, or even fail to understand completely why they work as they do, and still be able to think abstractly at a high level very well.

My comment about thinking shutting down once a child had been spoon fed an algorithm comes from what I experienced teaching third and fourth grade.

I would have (average) students, who were just beginning to really develop some number sense and mathematical understanding, and then they would go home and their parents would teach them to borrow and carry. The kid would come back to school and be totally confused, grasping onto the algorithm like a life raft and unable to think any deeper.

As a teacher I found that it was often the parents with the weakest mathematical thinking themselves, that are so passionately resistant to Constructivism. In turn their children were the ones who would be still trying to cross out the one in problems like "101-99 = ?" The children of engineers, mathers or scientists usually had a leg up, because they had been talking about numbers in a global sense, since they were very little.

Regarding Roman numerals... Yes, sometimes it is easier to just teach something directly. As with any educational philosophy, you can't be too hard-core all of the time. But on the whole, I think it is best to lean into children making learning discoveries for themselves, with you as the teacher or parent providing lots of structure and guidance to make this happen.

Jen, I'm concerned that you may be feeling a bit jumped on here, which is not how any of us want new posters to feel, I'm sure, but you need to understand that many people here have experienced the frustration that results when teachers with lots of experience teaching average children think that means they know better than we do how our children's minds work. Since you have a gifted child yourself I'm sure that isn't what you mean. How about you tell us some more about your child(ren?) and about what it is you're hoping to get out of the forum? And welcome!

I want the life of Fred books, so many posts say so many kids really enjoyed reading them. Besides, it's supposedly great stories that features a precocious child doing math at a younger age than is often depicted.
OTOH, hands on equations sells a set of manipulatives http://www.borenson.com/ that's a mini balance beam designed to illustrate algebra and teach what an equal sign means, because supposedly Americans don't know:
http://kitchentablemath.blogspot.com/2011/05/equation.html?m=1
(I like the quote that says "quit trying to make it about manipulatives vs. Pencil work"), ie., use your words. Er, well I guess if you're into explaining then the visuals could just as easily be 2 or 3D. So, Jenbrdsly, how different is constructivism from unschooling? ?

I also like this lady on YouTube. She teaches structured drill. It's free. Use a whiteboard. Check out this video on YouTube:

Ditto, no jumping intended.

Jen, I think we're actually closer than I thought to being on the same page, although obviously there's no need for us to be. I would call the steps of writing lines here and there, the mechanics of carrying, a "procedure" or something similar, but didn't think you were referring to that specifically by using the word "algorithm" (ex-computer science guy here). But I totally get what you mean and agree. Focusing on writing and rewriting symbols in particular ways could obscure understanding, especially if a kid's not taught the proper concepts in the first place.

Sorry to get in the middle here...but I saw somewhere online a parent had taken exception to some of the material that is in the Fred books. Any one know what that might be about? I got the feeling it was about exposing kids to questionable material...

Fred, a 5yo, lives in his office at the university, where he's lived since he was 6 months old, carted around by various undergraduates when he was too young to walk. His parents are nowhere to be found, and he lives off of vending machine food, which is why he's so short. He also tries to open a box with a very sharp, very heavy knife, and nearly bleeds to death before Roman numerals save him.

If you have a working-on-5th-or-6th--grade-math child who might conclude from that that living like Fred is desirable, Life of Fred might not be for you.

I found this:
http://maureenwittmann.blogspot.com/2008/02/life-of-fred-comes-clean.html

It looks like the author responded to comments from concerned parents.

I don't feel jumped on! Gifted people like to argue, as I'm sure we are all aware. Here's a bit about me:

http://teachingmybabytoread.blog.com/about/

I grew up in the Seminar program in San Diego CA, for hg/eg/pg kids, and my six year old is about to start 1st grade in our district's GATE program. I don't think it will be as good as the Seminar program, but I'm just thankful our district has anything for gifted children at all.

My concern with Life of Fred Fractions is that while it is fun and entertaining, it mainly teaches with algorithms. I would not just hand the book over to a child like the author intends, UNLESS that child had already learned about fractions in a meaningful, conceptual way.

Here are a couple of examples about how I taught my son fractions in a meaningful and real way, while we were concurrently reading Life of Fred Fractions:

http://teachingmybabytoread.blog.com/2011/06/07/outside-fraction-lesson/

http://teachingmybabytoread.blog.com/2011/06/10/peanut-buttering-reducing-fractions/

As for what I want to get out of this board? I really like hearing from and sharing ideas with other parents on the Well Trained Mind message board, but it is nice to find a forum that specifically deals with gifted issues.

This is the kind of discussion I'd love to have irl with a cup of coffee or a glass of wine.

I like the ideas of constructivism, but I also agree that sometimes children can feel like we are holding all these answers and we just won't give those answers to them. I also remember too many teacher trainings where we had to do an exercise as if we were students when I could already 'see' how it worked in my head, and I imagine children could easily feel the same way.

In my home education program, I try to introduce new concepts concretely, but try to be willing to let go of the concrete pretty quickly if it becomes necessary. I sometimes think my oldest DS was just sent to 'break me' so I wouldn't cling to any particular method too tightly. Sometimes it would be lovely to have that certainty back.

Lol, now if I argue with that sweeping generalisation I get into logical trouble, don't I? Actually I only like to argue about some things, in some ways, with some people, sometimes. But yes, as generalisations go...

Yes, I browsed your blog. Can I ask why you decided to teach your children so systematically from so young? [Maybe you've written about it, I didn't read every entry.] I thought and read about such decisions a lot, and came to the opposite conclusion to you: I decided not to teach my baby to read, for example, and did no more than answer his questions in maths before he started school. Yet as we were recently discussing, he was starting to read before he could talk and was spelling-obsessed by 2.5: I know exactly what GeoMamma means:

Similarly, I'm a bit bemused by the idea of teaching an understanding of fractions (though I'm sure teachers have to be able to do it!) I don't remember teaching DS, but he learned anyway. The one thing I do remember was that as he was interested in fractions we gave him a set of magnetic fraction tiles in his Christmas stocking just after he turned 5. I have a piece of his writing that he did in school shortly afterwards. It says
I treasure that

I fully agree with jenbrdsly about Life of Fred being algorithm driven. I have used the Fractions, Decimals, and the first Prealgebra book with my son as a supplement and I was horrified to see that the author very rarely develops concepts. For example, when teaching fraction multiplication, the *only* instruction in the entire book was simply to multiply the numerators and denominators. That's it. No discussion of why one might want to multiply fractions. No discussion of why you can multiply denominators together but you can't add them together. Nothing. I would never use Fred for primary instruction.

As for constructivism--I agree that math instruction should be grounded in developing conceptual understanding (this is why I love the Singapore series). However, I don't think it is necessary for a child to "discover" every last concept and algorithm for himself. One can "construct" knowledge without "discovering" it.

ok, so that's the difference between unschooling and constructivism; a constructivist CAN choose to teach a child something, you just don't spoon feed them you put it on their plate and give them the tools. An unschooler would wait for them to ask for it before you offered it to them.

Sure! My husband and I both went to Stanford University, where we both felt just average. What we noticed, were that the kids there from academically advantaged homes (children of alumni, children of alumni from ivy league schools, children of Phds, kids who had gone to prep school etc) found Stanford much easier than we did. It wasn't necessarily that they were so much smarter (although a lot of them were), but many of them were just better prepared.

My own parents who had gone to state college, did everything they knew how to do to prepare me for college. But what they knew, and the parents of some of these other kids knew, was really different.

I believe in making learning fun. I believe in spending a lot of one-on-one time with my kids, and yes, I believe in helping them accomplish as much as they can from an early age. Here is how I start teaching reading at 18 months: http://teachingmybabytoread.blog.com/where-to-start/

Yes! Constructivism is very different than unschooling. A Constructivist teacher provides lots and lots of facilitated activities for a child to conceptually understand concepts.

First, I need to admit that I haven't read the entire thread.

Yes, constructivism is very different from unschooling. Once a child demonstrates interest in a topic, an unschooler may or may not choose a constructivist approach to helping that child learn. An unschooler may choose a very traditional approach and still be unschooling.

As for the facilitated activities that help a child understand concepts, those activities do not need to be hands on. In fact, I would argue that as you move away from lower level math, it is preferable that they *not* be hands on, as you are trying to develop a more abstract approach to math.

On the general topic of LoF, I think the interview of the author at

http://www.homeschoolchristian.com/allabout/interviews/interviewschmidt.php
Life of Fred - A Living Approach to Math
An Interview with Stanley F. Schmidt, Ph.D.
by Martha Robinson

is interesting.

That's curious; some of my core decisions about educating my son are driven from my own experience of feeling I wasn't as well prepared for university as I could have been, but my decisions have gone a completely different way. In my case, the problem, as I see it, was that I hadn't been challenged enough at school - instead of giving me harder tasks (especially in maths), those around me had encouraged my perfectionism. So I went to university with an absolutely rock solid basis of school-level material, but when I finally got to a level where some of the work wasn't easy for me, I had no idea how to deal with that situation and felt the universe was broken! Took me years to get back on an even keel. It would have been far better for me if I'd gone to university with some gaps in the prerequisite knowledge but with experience of getting through somehow when I didn't understand something. I determined that my DS should always have problems that were hard for him, including things he couldn't do, no matter how good he was at something, and not too much direction; I want him to struggle a bit and to know that that's OK. Before he started school I was very happy he should work at whatever he was interested in in the way that preschoolers do; I stepped in to influence his maths when he started to complain that what they did at school was boring. In fact this was part of why I positively decided not to teach him to read (even though I knew my mother had taught me) - when he was a baby, I had a vision of this being his first experience of struggling with something and getting there with effort, and that seemed good. Of course in the event, he doesn't remember not being able to read, but I tried!

The bottom line is surely that we do what feels right in our families, influenced by our experiences and whatever else we find to assimilate. One of the things I find interesting about this place is the different decisions people make.

It is interesting that parents (including my wife and me) are trying to prepare their children to thrive at elite colleges when their children are so young. I think a great book for parents trying to ensure their children are competitive with children from "academically advantaged homes" is "What High Schools Don't Tell You" by Wissner-Gross.

I would agree with this. There are many aspects of constructivist approaches that I have come to appreciate relative to the traditional, algorithim/property memorization style of instruction I recieved, but there are some significant weaknesses as well. One of the greatest weaknesses I see is that students don't learn the same appreciation for precision and efficiency. It's interesting to me that constructivist approaches in all areas emphasize focusing on process vs. content without recognizing that learning and applying rules is itself a process that needs to be developed. I definitely favor a combined approach to instruction in all areas. As it relates to math specifically, I think that constructivism--at least as it is applied--overlooks the fact that while some students/adults work best by gathering parts and constructing a whole understanding, other students and adults work best by deconstructing the whole,examining the parts, and then imagining or exploring different ways to work those parts to get the same, or a similar, result.

For sure we don't want students to look at problems like 101-99 and set it up with a standard algorithm (something I too have seen students do on multiple occasions), but I think we do want students to have efficient tools for the computations that aren't easily done without pencil and paper. I like to work on having students identifying for themselves problems that they need algorithms for and problems they don't need algorithms for so that they are in the practice of considering the tools they have and choosing the best tool for the job.

Re: fractions. Fractional understanding is probably the area in which I most support an almost universal constructivist approach, at least with initial concepts. If a student can't grasp the relative size/meaning of a fraction, I question the wisdom of teaching them to solve equations which include fractions.

I so want to read this now!

ABSOLUTELY. I think that principle goes for pretty much every subject, too.

I am not a teacher and for all of my DDs various issues it would never occur to her to do any sort of long process with 101-99. Surely the failure to see the simplicity of this question is far bigger than what method of math curriculum is in use? Is that something that is taught or needs to be taught? Surely anyone that can could knows when two numbers are two digits apart and so knows that 10-8 is 2, 9-7 is 2 and 101-99 is 2? I am genuinely curious here. Is it common to not just see how this works? I would honestly never have imagined this as a problem. Though I guess it is similar to my never having realised that children could "read" without comprehension, which I now know is a real problem but it would never have occurred to me and I still can't understand how it works.

Yes, it can

Yes and no. It is bigger than just curriculum, because it represents and fundamental lack of understanding in the number system. BUT some curriculum do emphasise that kind of rote behaviour without understanding more than others do.

Jenbrdsly, is constructivism a philosophy that has been mangled in Everyday Math?

I have not seen Everyday Math, but I can tell you that the Dale Seymour Investigations series which many schools in CA use to use, is a Constructivist program.

I think Dale Seymour Investigations was formerly known as TERC Investigations , and lots of parents and math professors dislike it:

http://www.nychold.com/terc.html

...

Mathematically Correct Second Grade Review of TERC [then Dale Seymour] Investigations in Number, Data, and Space. Some observations and conclusions: "Poor focus, lots of child centered discovery activities and no meaningful mathematical content. [...] [T]he authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a `100 chart.' [...] With the exception of some discussion of counting by 2's, 5's and 10's, multiplication is not obviously introduced. [...] This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding... There is nothing to recommend about this program."

Mathematically Correct Fifth Grade) Review of TERC Investigations. Excerpts: "This program received the lowest rating of Mathematical Depth of the fifth-grade programs in this review. [...] The quality of presentation for this program also received the lowest rating among the fifth-grade programs reviewed. The lack of a student text by the fifth grade contributes to this as it leaves students without such resources as a glossary or the opportunity to review prior instruction independently. [...] Although there is a fairly reasonable number of student worksheets, the actual work expected is severely limited in depth and scope and is unlikely to support mastery of content."

Mathematics Program Reviews Comparative Summary for Second Grade and likewise Comparative Summary for Fifth Grade, by Mathematically Correct. The previously cited MC program reviews of TERC Investigations are part of a comparative review of eight mathematics programs for both 2nd and 5th grade. For both grades two of the eight programs (Everyday Mathematics and TERC Investigations) are deemed to fall far short of the Mathematically Correct review criteria, and in both cases the Investigations in Number, Data, and Space curriculum is rated unambiguously the worst of all that were reviewed.

TERC Hands-On Math: The Truth is in the Details. An Analysis of Investigations in Number, Data, and Space by Bill Quirk. This is a detailed analysis of the mathematics in TERC's Fifth Grade teaching materials. Bill Quirk writes: "But math is a vertically-structured knowledge domain. Learning more advanced math isn't possible without first mastering traditional pencil-and-paper arithmetic. This truth is clearly demonstrated by the shallow details of the TERC fifth grade program. Their most advanced `Investigations' offer probability without multiplying fractions, statistics without the arithmetic mean, 3-D geometry without formulas for volume, and number theory without prime numbers."

This is why people have a negative knee jerk response to the notion of "constructivist math". Investigations is one of the reasons my children are homeschooled. I have compared the output expectations of Investigations and Singapore math very carefully and there is *no* comparison. Investigations is beyond a joke. And I'm not just talking about the number of problems or that Singapore actually teaches the standard algorithms. The depth and complexity of the problems is markedly different.

My personal understanding of "constructivism" is that it refers to what goes on in the learner's head and does not refer to the mechanism for getting there. I think the whole discovery learning thing is a misinterpretation of constructivist theory.

I found DS Investigations very troublesome to use as a teacher, because there didn't seem to be enough opportunity for pencil and paper practice. I don't really like "drill and kill", but there should be at least a little bit of it. There were pages like this with Investigations that you could use, but it was really left up to the teacher to decide whether or not to print them out.

A teacher who really knew what she was doing could make Investigations works in a fabulous way. A teacher who didn't know what she was doing, could really bomb with it.

Singapore would be a really good choice to help augment a program like Investigations at home.

From the posted references it appears that the Investigations material is seriously defective as a math course. Perhaps it could be used to supplement Singapore Math or something else, but not the other way around.

Having bought Singapore Math, in my opinion it's not perfect but it doesn't have any big weaknesses either. It does plenty to strengthen conceptual understanding, with lots of different types of illustrations to make sure that students have a strong conceptual framework before getting into any pencil-and-paper drill. One can add extra reinforcing practice with the workbook, which has problem solving interspersed with more traditional drill on what's been called "algorithms" in this thread.

I think Singapore Math is a good example of how a good basis for understanding can be taught without necessarily needing to be discovered by a student first, and the emphasis on problem solving would tend to keep most students from being too passive or bored. The Singapore Math approach in third and fourth grade seems to be to illustrate a concept graphically; when appropriate to have a student do some discovery (e.g. in the 3B materials introducing fluid volume, students are given small explorations with real-world / household materials to get a feel for combining volumes, etc.); and when a conceptual basis has been established, get into working problems. Regarding problems, it starts with simple non-word problems first, then gets into simple word problems, then multi-step word problems. In addition Singapore Math seems to intentionally remove explicit instruction on how to do the problems as the student progresses, so that by the end of a section the student is (hopefully) fully self-sufficient.

I would definitely agree with this statement. There are certain investigations in the geometry and fractions units that I absolutely love, and I use some of the conceptual number activities as warm up or for independent activities, but after trying to implement it as core curriculum for a couple of years, and watching my children bring home work from the curriculum in the earlier grades, I consider it to be dangerously incomplete.

The more time I spend with the Singapore Primary Math curriculum, the more impressed I am with it. I will use it as a core curriculum for the first time this year and use Investigations and other sources to supplement and in some cases pre-assess conceptual understandings. That said, I will still post-pone teaching the standard algorithms until I can verify a certain level of mental math ability with groups of students. I will definitely postpone fraction work until I am confident that students actually grasp relative size and meaning of fractions. Those particular area have been critiques of the Primary Math curriculum that I have found valid for students who don't have good number sense. However, those critiques have led to a throwing-the-baby-out-with-the-bathwater response to Primary Math which I find to be both illogical and foolish.

I agree about the fractions in Singapore Math, Taminy. My son already had a solid grasp of what they are before we started with Singapore Math, and I could see value in different types of clear models and hands-on exploration to make sure that students got the concept before really digging into the work. In fact that goes for a lot of early topics, including multiplication, division, etc. I really think that good-quality "Investigations"-type modeling and discovery might make a good addition to just about any curriculum, actually. It could always be slotted in during the introductory period on that topic. I just don't think sole reliance on that approach would be good.

In my local school district here in New Hampshire, they seem to take that approach to some extent, and it's one thing I like here. They begin with multiplication, division, and fractions all at the same time in first grade, long before any emphasis on learning times tables, doing pencil work with long division and the like, etc.

Oh arrgh. This talk about a sub par "investigations" program is really making me more anxious about our schools new junior school curriculum - which I was already worried about. It's NOT the curriculum you are talking about it, it's been developed here in Australia. But "investigations" are at the core of the program and it's all about "authentic" learning experiences. My husband and I are already very dubious but trying to reserve judgement...

What are they using in Australia? I'm curious.

I read as far as the part about constructivism and then I jumped to the end. Sorry if I'm just repeating what others said, but I wanted to say that I ordered all the new elementary Life of Fred books for DS5 and he absolutely loves them. However, I don't know whether I'd use them as a curriculum, but they're a great supplement, and DS loves the quirky stories and humor. Truth be told, some of the subject matter is far below his ability, but because of some of the math concepts and vocabulary to which he's not otherwise exposed and even non-mathy concepts covered in each book I decided to get all of them. The stories make the stuff that is review for him interesting enough that he doesn't seem to mind. I think depending how much work you wanted to do you could create lessons that expand on the material covered in the books, or you could use them as a way to figure out which things your child needs to work on more and skip the things that they don't.