Switching math curricula is difficult. When we first started homeschooling, I made a bad choice in our math. The placement test weighted non-arithmetic knowledge as heavily as the straight-up math. I would recommend anyone using the curriculum-provided tests concentrate on where the math takes you. The other stuff, can be reviewed.
I picked Saxon as our first homeschooling math program. I went to the Saxon site and had my daughter take the placement test. In her Montessori classroom, she had been doing multiplication and addition and subtraction with exchanging with four digit numbers at the end of first grade. But according to the Saxon placement test, she was placed into level 2.
The placement test included a lot of things that were not arithmetic. There was measuring, and the names of shapes, and vocabulary. So I ordered the level 2 Saxon only to find out that her arithmetic level was far beyond not just that year, but possibly the next. I stuck with Saxon hoping to rush through the boring parts. It turns out I was so bored, I didn't even do the program. I would teach her higher level arithmetic and have her do work sheets.
We switched to Singapore at the beginning of this year. I went a full grade down for both of my girls. My second grader is using 1A and 1B and my fourth grader is using 3A and 3B. I was comfortable with this primarily because Singapore advances much more quickly and with a better order of presentation. They girls are repeating things that they have done, but my eldest has actually memorized the multiplication tables (whee!) and the youngest does need review in addition and subtraction with exchanging, she will be multiplying soon, and starting on the 2A book by the end of this month. They also don't mind going through the books quickly. We skipped some things I was sure didn't need review.
Check the placement test results for any trends in the incorrect answers. If there are a lot of random errors, see if the student was careful in reading the problem. If, in an elementary example, the single and double digit addition and subtraction are correct but the three and four digit operations are wrong, the child may not understand place value correctly. Putting them in a really low math level in order to fix that one, incredibly important misunderstanding may not do them a service for the rest of the material covered. They may need intensive review or tutoring in that one subject but understand fractions just fine. I didn't even have my homeschooled student take the placement test. I knew what they had already mastered and what they were still struggling with and compared that knowledge to the material covered in the tests.
A friend of mine is ready to switch her kids from Math-U-See and I gave her the same piece of advice: pick the level based on the arithmetic questions (addition, subtraction, multiplication, division, fraction operations--but not fraction recognition, equation manipulation) in the placement tests. The time-telling, calendar, measurement, geometry, graphing, money, and vocabulary can be reviewed with independent material, or in the case of Singapore (because it's cheap) just purchasing a lower level book to use for only those topics. Having a friend who has navigated the program helps a lot. Right now, I am enjoying Singapore a lot. If I did decide to switch curriculum again, I would use these tips to help.
A note on my experiences with Singapore so far:
A friend recommended only using the textbook, which already includes problems, and supplementing with the workbook only when they needed additional work to get something. The textbook has a wonderful method of presentation and the workbook covers the same concepts in a different, complementary way. The intensive practice books cover the standard work presented in the textbook and also use more pre-algebra concepts and have some puzzle aspects that help with logical thinking. Again, that approach is different and yet complementary to the textbook and workbook. There are about 100 pages in each book with a year covering an A section and a B section. To do all of the books, adding in the challenging word problems, would require covering approximately 750 pages in one school year, more than 4 pages each of 180 school days if you try to use every book. I find it more worthwhile to limit the number of books.
I have found the teacher's manual to be completely unnecessary so far. That could be because I am very familiar with this elementary level of math (having taken many advanced math courses in engineering college), but I also think Singapore's presentation has a lot to do with it. The concepts are presented subtly. When I counted how many pages they spent in 1B showing exchanging, it was over 20! Each additional step was a very small increment so that the learning is very easy. My youngest breezed through it.
Just because she was going through it quickly and with little frustration does not mean she's not learning! She was learning more from Singapore 1A and 1B, faster, easier, more in-depth, and with more meaningful coverage than we ever got from working in Saxon 2 last year. I am fortunate to be very good at math, so I understand how each small increment advances the children toward the final concept and each one flows so naturally that the children have mastered the concept without the frustration I saw with the previous curricula.
Here and here (in the comments) are some excerpts from the New Milford school district's rejection of using the Singapore math curriculum. Unfortunately the original report has been removed from the website so these excerpts are all I have. And two more blog posts discussing the results at the time of their release.
Here's a couple of the New Milford, CT observations about Singapore Math [run as a trial to determine if it could replace the Everyday Math]:
"3. The pace of the program is quicker than anything we do and quicker even than our curriculum calls for. As a result, some special ed students actually perform AHEAD of their non-special education peers in successfully handling content almost by definition becoming non-special ed students!
5. Adoption of such a program would change the 'landscape' that we know as math programming. Students in this program K-8 would have completed Algebra I, most of Algebra II and Geometry. Currently between 20%-25% are tackling Algebra I in grade 8; under 5% in a good year are tackling Geometry by that grade level."
And one of the reasons not to adopt Singapore Math:
"4. The 'change in landscape' image sounds exciting, but presents real practical problems. Can we train 6th grade teachers to teach Algebra I well? Can we recruit grade 7 teachers who are comfortable presenting lots of Geometry and Algebra II? If not, do we have a sense we could train them and, if so, at what costs? If we went down this road, it would become necessary to redesign the scope and sequence of high school math sequences. Does the system have the funds to do that and the staff to deliver the change? We would have almost all students taking Calculus by junior year, if not before then. That means the academic levels expected of all our staff would be raised in math."
In other words, Singapore Math is too good?