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The Well-Trained Mind has an excellent review of several math programs, here's a short excerpt:
Which method is better? In my opinion, the one which the student understands most clearly. In both cases, it is possible for the student to learn the mental trick without thoroughly understanding why it works, although the sheer amount of repetition in the Saxon method makes it easier for this lack of understanding to escape detection. But the strongest mathematical training of all would come from a combination of programs – in which the student is taught to do a mathematical process using several different methods and mental procedures.
Currently, Singapore and Math-U-See are “thought-oriented” math programs available to home school parents; Saxon and A Beka are “skill-oriented” programs. A combination of Saxon + Singapore, or Saxon + Math-U-See, or Singapore + A Beka, or A Beka + Math-U-See, may come closest to fulfilling the goals of classical education. Math-U-See + Singapore would also be an excellent combination, as long as you use MUS’s supplementary drill sheets. Treat one program as primary and the other as secondary; when you cover a concept in the primary program, look it up in the secondary program and see whether it is explained and illustrated differently.
I like her idea of using 2 programs. I do that all the time with phonics--I know what is best about each program and pick and choose accordingly, I have dozens of phonics programs from my tutoring. Also, if a student is struggling with a certain area, it's good to have a few books that explain it in slightly different ways. I hadn't thought to do the same with math.
There is also an interesting review at Sonlight, a basic review of their math choices from grade school through calculus, and then, they explain their choice for algebra and geometry--teaching textbooks:
- CD-ROM-based "whiteboard" lectures and step-by-step explanation of how to solve every practice problem taught by a tutor who has been teaching homeschoolers for years...since the days he tutored probability and statistics at Harvard . . . and . . .
- CD-ROM-based "whiteboard" solutions guide that works every step in every homework problem, so you see exactly how to solve each problem . . . and why you want to use the methods the instructor (or, more accurately, personal tutor) uses.
We're currently using Math-U-See with our daughter for Kindergarten math. I personally like Singapore or Saxon better, but this is what is working for her. The good thing about Math-U-See is that they have a DVD with each lesson so that if you get that "blank stare," (yes, it is even possible with kindergarten level math!), you can just plop in the DVD and have an actual math teacher explain it in field tested verbage.
Math-U-See's approach to fractions is also interesting, I'm not sure what I think about it. The rectangles do make more sense to me than the traditional circle/pie method. From their downloads page, in sample lesson pages, click on Epsilon.
For an even more interesting and thought-provoking review, read Wild About Math!'s Calculus in 4th grade? I'm really not sure what I think about that one. Luckily, we're still doing kindergarten math so I have time to figure it all out.
8 comments:
Yep. We do Singpore Math and Saxon as well. Works for us.
In the ed school class I complained about, one of the valuable pieces of information imparted (from a guest speaker) was that a good educational therapist has a number of remediation approaches at her command. For example, it isn't It isn't enough to know Wilson and/or Fundations. You need at least one more -- lots of people like Barton. So knowing and using Saxon and Singapore makes sense.
If you are using a solid combination of programs to teach (reteach) math, you might look into Making Math Real.
I use Singapore and Saxon together for my two boys, both effectively fourth graders, but we are phasing out Saxon this year and next year with be using Singapore supplemented with some geometry and a bank of word problems that I am assembling.
Saxon K-3 is a wonderful curriculum that has lots of hands-on activities plus a good amount of repetitive drill. The format changes at grade 4. Now I find it tedious. The daily "fact sheet" for mastering recall of arithmetic facts is good, but I don't like the rest of it. The increment of knowledge from lesson to lesson is tiny. This seems especially so given the way we have our Singapore overlapping Saxon. My kids learn decimals in Singapore one week, and some time later they get it in teeny increments from Saxon. Then there are a large number of "mixed practice" problems. The good new is that everything is cumulative: on lesson 68 they will have problems taken from lessons 1 - 67. But the problems are all small-scale, uninteresting. Few of them are hard, but I find that my kids make so many errors. There's just too much make work for them to care. Thus the comparison of Singapore to Saxon in grade 4 is between a smaller number of better problems or a fairly large number of tedious ones. I know, I know, you don't have to assign them all. I now assign every other problem, and my kids errors went from 5-6 per page to 0, not 2-3; very nonlinear. Still, I can't wait to jettison Saxon -- although when my 5-year old is ready for it, I will definitely start him on Saxon K. (Saxon has second graders make brownies, but Singapore does not.)
p.s. I left a comment earlier on Wild About Math about the 4th grade calculus. I am very skeptical about that. The notion that multiplying length x width is the same as computing integrals is hooey. Calculus is sophisticated math, and eliminating the essence so that you can pretend to teach it to fourth graders seems to be a waste of time, given that fourth graders still need to learn arithmetic, geometry, and can begin algebra. (I have not seen the curriculum, only the description on the other blog and the publisher's site.)
I'm not impressed by the credentials of a "Harvard Tutor" and these people have yet to say what they actually do have their degrees in. They don't claim to have a math degree, they don't claim to have classroom experience nor do they even claim to be certified math teachers. I've read positive reviews of Teaching Textbooks none of which were done by anyone who has an actual degree in math or is familiar with state standards. The only parents I've seen who use TT are those that don't know enough math to teach it to their kid from a standard textbook and someone who "doesn't know math" or thinks that placing into college algebra is some kind of gold standard of a good high school math program is going to be the last person I trust to tell me how good a program is.
The main defense I see of those who use TT with their kids is the vague, "they finally like math." Well, once they get into college their exam is going to be one in a stack of 500 being graded by teaching assistants who would rather be off playing bridge and don't care how much a student "liked math" in high school. They will only be checking for correct answers.
A parent doesn't need a "curriculum specialist" like Cathy Duffy to tell them about this program or a distributer to tell them what its merits may be. What any parent ought to do before buying Teaching Textbooks is print out the placement exams of TT and Saxon or Singapore and simply place them side by side to see what's going to be learned and what isn't and the level of difficulty of the problems.
For a program which is both 'thought' and 'skill' oriented I second Making Math Real. I just got back from their Overview class and highly recommend it.
I have also heard that Singapore and Saxon are a good combination together.
Calculus is sophisticated math, and eliminating the essence so that you can pretend to teach it to fourth graders seems to be a waste of time...
Why that's just exactly what we do with college freshman.
When my son started at a charter school in seventh grade, having skipped sixth, he was in pre-algebra. When I brought my son home to homeschool three years later he placed into pre-algebra using the Singapore and Saxon placements tests that are available. Thank you progressive math programs.
My son wants to be an engineer and it really steamed me, still does, that he lost three years of math advancement. Anyway, we used Teaching Textbooks Algebra, which started at a pre-algebra level and worked from there. It was good in that my son was able to regain one of the lost years, but I wasn't that impressed with the program. The sample problems and the practice problems were almost identical. I kept thinking that if a problem were presented in a slightly different way, my son would have no idea how to do it. We used Math-U-See for Geometry, including the supplementary Honors book, and I gave him a choice of which program he wanted for Algebra 2. He chose Math-U-See.
For the most part he is able to teach himself from
the teacher's manual, with only occasionally having to ask me for help because he doesn't understand something. What I really like about the program is that it's totally mastery based. He stays on a lesson until he understands it. He keeps doing worksheet pages until he gets 100% right. As soon as he does, even if it's the first worksheet page for the lesson, he takes the test. Our requirement is that he earn at least 90% on the test before he can do the Honor's page for the lesson and move on to the next lesson. As I keep telling him, it doesn't matter how far in math he's gotten if he doesn't understand any of it. It's far better to not get as far (he's not going to get to Calculus in high school thanks to the lost years) and have a really strong foundation for the advanced math he'll need as an engineer.
Heather in OR
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