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On eIMACSby Cindy Math Monster did eIMACS (http://eimacs.com), and really liked it. He told me, "after I did the Indiana University algebra class, I was wondering if I still liked math. Now that I'm doing eImacs, it has restored me!" He now talks in logic, and talks about logic. He talks to the program as he's doing it, and sometimes talks back to it. I recommend doing it for math enrichment or an entire math program. (NOTE: He is no longer doing eIMACS because the second unit (LM2, about 5 months into the program) is not as heavily computerized as the first. Math Monster was spoiled by the very nonmanual nature of the first unit, and is annoyed by the excessive manual work in the second unit that should be computerized. I don't see this as a reason not to start, though, and for some kids it won't be a reason to quit.) eIMACS is the online iteration of what started as MEGSSS, a program for mathgifted public school students. It was designed headtotoe with highly mathy kids in mind. "Students enrolling in the EM program must have completed a standard mathematics program to at least fifth grade level." The instruction and grading are almost entirely computerized, at least at this beginning level. A teacher is available through email and phone (though difficult to catch by phone), but Math Monster has not needed much help. When he emails the teacher, he gets a response within a day almost every time. The occasional tests can be proctored by parents  they figure the parents and students are trustworthy. There are two versions  the main version (Elements of Mathematics) and a much smaller subset (Logic for Mathematics). eIMACS recommends that students do the main version as a longterm program instead of regular school math. For those who can't get out of regular school math, or who are tentative about doing it at all, eIMACS recommends doing the smaller version. They say it's easy to convert to the long version after finishing the short version. The names are confusing. "Elements of Mathematics" (EM) is the main course, and "Logic for Mathematics" (LM) is the smaller course. The first four classes of EM are LM1 through LM4.
It claims to be equivalent to college logic classes, and I think it probably is. So far he has done an intro to propositional logic, wellformed formulas (WFFs), Metawffs, propositional variables, demonstrations, and currently learning about the deduction theorem, which is part of demonstrations. A complete TOC for LM is at http://www.eimacs.com/parent_aml_overview.htm, and a very few of the topics (those with differentcolored links on the expanded TOC) are available to look at. It is not accredited in any way, but they say that the teachers will write you a detailed recommendation and progress report if you need one. I'm not sure when you would need one except to get into special programs, unless there is an AP Logic class, because this isn't like anything **I** ever saw in high school! The main unit, which he did, starts with four logic courses. After those, it gets into algebra and the normal high school math courses. The difference, presumably, is that they learn the normal high school math more deeply and profoundly. When you start, you get 20 NONgraded logic puzzles that get progressively more difficult, beginning with "You meet someone at a fork in the road on the island of Truthtellers and Liars and he tells you he is a truthteller...." (or words to that effect  that is NOT a challenge!!!. The student is asked to click a button to answer the question and then write the answer in text. After answering the question both ways, the program gives its preferred text answer, and the student is supposed to check his work against that preferred answer. After those 20 questions, you do some more GRADED logic puzzles. Then it goes into a discussion of formal logic. The formal logic is mostly formal, with some concessions to the silliness of children. Math Monster supplies additional silliness as needed. Math Monster needed help reading and understanding at first, but since then he hasn't. Maybe it's because his reading has improved or maybe it's just a matter of being hooked now and he wasn't at first. He is doing it completely independently, and I wish I had the time to do it with him! Personal comments: To me, this represents much of what is good about homeschooling. It allows learning in depth, at the child's pace, of a subject that you can't find in a normal school. I recommend using whichever version is appropriate for your child's (and wallet's) situation.  I'm surprised that it is taking so long to get through it, but maybe that's partly my son being pokey.  I'm disappointed that even this rarely challenges him  he gets a graded problem set every week or so, and only once every two problem sets do I get the complaining and stalling which signifies that he is being forced to understand or think about something difficult.  Mostly Math Monster just doesn't like the problem sets because he says they are tedious and take too long and he isn't learning NEW logic when he's doing them.  I wish the teacher were friendlier  he isn't mean  just very businesslike. He warmed up eventually when Math Monster kept sending him jokes.  I had only about two technical problems, and those were addressed very quickly. 
