I saw this mentioned on another thread. A gifted school I looked at uses this to enrich their regular math. I would be interested in opinions and experiences.

I have heard that Investigations is similar to Everyday Math in that it is considered "fuzzy math" in that it de emphasizes memorization of math facts and standard algorithms for problem solving.

My daughter used Everyday Math in grades 1 and 2, and it was absolutely ridiculous. It was beyond easy for her, yet the activities created by the authors were confusing and pointless.

In 3rd grade she moved to a self-contained GT program where they are using the Project M3 program and supplementing with other materials to include other units they wanted to cover.

This has been the first year she is actually learning math and problem solving at school. I have been very happy with the M3 units.

http://www.kendallhunt.com/index.cfm?TKN=7B994979-19B9-B72C-DD0EEE8F1E47D034&PID=219&PGI=246

I don't want to defend Everyday Math or Math Investigations - I don't know enough about either to do that - but I *do* want to defend "fuzzy math" defined that way, especially for bright, mathematically inclined children. Memorisation of math facts and standard algorithms are not mathematics, in the sense that mathematicians use the word, and for children who can do real mathematics they *should* be deemphasised, IMNSHO. Now, it may be (I've heard claims both ways and am not in a position to judge) that there are many children who will never be able to do real maths, by which I mean gaining such a thorough understanding of the concepts they're manipulating that they can invent their own correct algorithms, and understand why they're correct, and invent new definitions to fit new problems, etc. I doubt there are many children of parents on this board who will never be capable of that, though. To support children in learning real math is much harder than to support them in memorisation tasks, and it has to be done with the right problem material for where the child is: it wouldn't surprise me if this is being done badly by most teachers most of the time, sadly. That doesn't make it any the less important. Please let's not dismiss the effort because it's often done badly.

I would agree that an "on level" use of Investigations is going to be well below the level of most gifted students in most areas. There are some strong activities in some areas (fractions,geometry, data,probability) but I would say that if used on-level (or even just one level up)then most GT students would be able to absorb and synthesize the whole concept in one compacted Investigation (which would generally be 4-5 connected lessons in the curricular design).

I would say though that I agree with ColinsMum's comments about "fuzzy math". As an approach--especially for strong students--it allows kids to go beyond computation and actually delve into math. However, in the hands of a teacher who knows the computation routines but not the math, it definitely becomes "fuzzy" and not very effective.

Re: the school that uses Investigations: I would want to know if they just use it as a resource to draw activities from, or if they follow it lesson by lesson.

I think ColinsMum makes a valid argument for the 'fuzzy math'. Our school uses Math Investigations. What I have found is GS10 knew how to manipulate fractions & decimals a full year before MI introduced them. GS10 knew the standard way to add, subtract, multiply, divide, & convert fractions & decimals because I taught him. I taught him not only the standard algorythms, I taught him how to prove his answers and how to use manipulatives to understand what was going on with each operation.
MI uses a method of 'squares' for multiplying and really drops the ball on how that relates to multiplying using a standard algorythm. GS10 was still caught in that fuzzyness when they introduced their method of manipulating fractions & decimals.
I think GS10 finally understands MI math & how I taught him because I took the time to go through it with him. That is where I agree with ColinsMum, because GS10 can look at the numbers in more than one way and has a more thorough understanding of how they can accurately be manipulated.
GS10 appears to be typical for all the 5th graders at our school, even the gifted kids. Apparently, even most of the gifted kids didn't get it sorted out until the gifted teacher went through fractions & decimals.

MI is considered a full program, I'm not sure how effectively it can be used as a supplement. And I really feel sorry for a kid moving from another program to MI in 4th or 5th grade. I, and most of the teachers, think MI needs supplemented with drills to learn the math facts. Without the extra drills a child WILL NOT learn their math facts in MI. Give them some paper & they'll come up with the answer, but without drills they'll still be using the same paper to figure out 5+8=13 when they are 13.

Another thing about MI, it's a circular curriculum, and it's a real bore for gifted kids up until about 5th grade when it seems to become confusing.
Something else that seems to support my view of MI. Our school performs well on the state achievement tests at every grade level, on every subject, EXCEPT 5th grade math!

I guess my bottom line is, no matter what program our school uses for math, we'll supplement at home.

It's become popular to excoriate "fuzzy math" programs, but here's my view: they help the student to "think mathematically" instead of just "doing math." Ideally, a math program would combine EM principles with some drills/memorization. I have seen my kids make a very easy transition to higher math concepts - much easier than I remember in my school days of drill, drill, drill. I think there is an important role for concept-based math programs. They may need to be supplemented with math facts, however, to have the best results.

Thank you so much for that essay!! I have been worrying a lot about math around here lately--and it helps a great deal to have one's eyes refocussed on the prize.

mm

"Lockhart's Lament" changed the way I thought about math last year. It's a really smart argument.

"Lockhart's Lament" is great! Thanks for sharing.

As a non-mathy person, I need to ask the advice of you math folks. DS6's school just switched to Math Expressions this year. I'm curious if anyone has heard anything of it. It seems OK, based on the worksheets that DS6 brings home. He gets math compacted for him, and he's at 2nd or 3rd grade level, but he also does the kindergarten stuff too, since the math teacher comes at a different time. He doesn't mind the kindergarten stuff, and he likes his daily math class (although I think he could handle more). Not knowing much about math, it seems to include a little bit of both the EM-type world plus the standard stuff I remember from school.

The only comparison we have is EPGY math, which DS found quite dull (and I agree with him). I think we made the mistake of not wanted to have gaps, so we started him too low. But his school math does seem more fun for a 6yo.

I'm not saying these programs are ideal - far from it. I'm just comparing concept-based approaches to traditional approaches. My kids have had the same level of success in their above grade-level achievement tests (>99.9%), so I know it works for some kids.

Many of us have no choice of how our schools approach math education. AoPS would be great, but that's not an option at any school in my area.

This crossed my path and I thought it was interesting and relevant:

http://www.psychologytoday.com/blog...e-the-case-teaching-less-math-in-schools

I have two kids who are "quantitatively gifted." They both do MI one year above grade level in a gifted program. Our school is using the second version of MI and also drills for memorizing basic math facts. For DD10, MI is boring and repetitive. For DD8 who is dyslexic, MI is very word intensive. She has had issues with "explaining or showing her work." She can look at a problem and know the answer. Then we have to go back and do excruciating busy work to draw number lines or sticks and dots that don't honestly reflect how she got the answer. Even worse she has to write sentences like, I know that 49 is near 50 and I know 22 is near 20, so 49-22 is about 30. She hates this since she can look at it and know that the answer is 27. Also, MI won't let them use column addition in the early grades so, my DD is not allowed to use a method that makes sense to her. For gifted dyslexics, MI is a nightmare.

Wow! The part about teachers figuring the area of a rectangle floored me. I'll continue my "supplementary informal �home schooling' of children."

It does reinforce the notion that problem-solving and thinking skills may be getting short shrift in some places, if not generally speaking.

And Inky, the teachers not knowing how to figure area was pretty horrifying to me, too! I'd really hope for better everywhere, no exceptions.

I looked up the original note (in Notices of the AMS 2005 Feb) that had this, because I found it so horrifying. Turns out that she was asking for the area of an x by y rectangle. Kids are supposed to have a "not ready for algebra" stage in which they find things harder when put in those terms than when given actual numbers, aren't they (though I can't say I ever observed such a stage with DS!)? So maybe that was really the issue for these teachers. But even so...

Kids, not adults. I'd like to hope that all college-educated teachers know how to find area, even with variables instead of numbers.

It's very disappointing.

You got me interested in reading it too and I was glad I did. Here's the link if anyone else is interested and I pulled out some other interesting parts:
http://www.ams.org/notices/200502/fea-kenschaft.pdf