Thursday, February 12, 2009

What I Learned about Switching Math Curricula

I posted this as a response to this post expressing dissatisfaction with Singapore Math. Even though my kids are in a similar situation (both are working below grade level and below their skill level), I still love Singapore math. This post touches on Singapore math specifically, but is more generally about another experience I had with switching curriculum.

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?


Amy said...

Thanks, Kim. This sounds like good advice. I'm always interested in things you've learned about homeschooling.

Veronica Boulden said...

Hi Kim,
I am wondering what you would start with if you could start from scratch... Saxon, Math U See or Singapore? We will be ready to do something for K5 in the fall of this year. I hear so many differing opinions, but nothing has been said to make me settle on any ONE curriculum for math. I'd like to hear your opinion on it. Thanks.

Kim said...

Here's one off the beaten path: I would highly recommend a Montessori math approach through multiplication and division. The strength I see in the Montessori method, which can start well before Kindergarten, is the concrete approach, the in-depth understanding of place-value, the gradual movement from concrete to abstract, the inclusion of movement with each lesson, the very sensible progression of what to learn next, and the emphasis on full understanding prior to moving on. The books Teaching Montessori in the home: The Pre-School Years and Teaching Montessori in the home: The School Years by Elizabeth Hainstock are very helpful. She explains the Montessori approach, how to make and use the materials, and how to present the materials. Here is a video of my daughter using the Montessori technique to work on a typical Montessori kindergarten/early elementary math problem (please note that my teaching technique is not necessarily to be modeled--not the least of which is that I was trying to explain for the video). It took her a few years to get to that level, but an older kid working on the things she learned in pre-school will make faster progress.

There's my blanket statement in complete support of the Montessori math program. You'll find I am just as enthusiastic about the reading and grammar approach as well. This post also includes some other pre-school/K work that is done in Montessori primary classrooms.

Where to start! There are so many math curricula, so I can only comment on the few I have experience with or have looked at from other people--which isn't many and only the elementary years. My biggest concern is full understanding. Memorization, though it is important when the kids are doing larger problems later, takes a backseat to this more fundamental concern. I abhor constructivist math programs--they do not promote real understanding.

Many people and kids like Math-U-See. I've had a chance to look at the curriculum and see the materials for the younger (gamma and under) products. I have not used it personally. It is very concrete with its approach and that is nice. One drawback would be the workbooks. Workbooks can be nice. It's great to have problems put down on paper in a progression of ideas that logically follow. A workbook, however, can lead one to think it must be fully completed even after the kids have mastered the concept, leading to boredom and a dissatisfaction with math. It can also fool a teacher or parent into thinking that the child has mastered the concept even though they might really need more work than the workbook provides. There is no substitute for vigilance! Math-U-See has teacher instruction, from what I understand, in the form of DVDs that the teacher or the student can watch. I haven't seen one, so I don't know how effective they are. From other parents who have used Math-U-See the only complaints I've heard are that some kids find the workbooks boring (perhaps because they were ready to move on?) and there was a case of a kid not getting word problems while using Math-U-See. Neither of which would preclude me from recommending it. There was a kid, however, that can find some of the lessons confusing (like area), so I think that would be a failing of the curriculum. Perhaps there wasn't enough information on teaching that concept or the materials do not lend themselves to that use. That is an isolated case, and one can supplement.

Saxon math, I used levels 2 and 3, is easy, easy, easy, easy for a parent to implement and expensive. I spent $300 to buy the manipulatives (which are good quality and thorough, with some exceptions) and the entire 2nd grade kit that included a meeting book, flash cards, homeschool teacher's guide, and two workbooks. The early grades are scripted and my kids never missed a concept when I used the Saxon script and materials to explain it.

BUT!! And this is a very serious but, I hated the repitition. I believe that everything learned is repeated something like 60 or more times. This is one case where I will say that there is a vanishly small possibility that kids will not be able to 'do' that work by the time they are done with that repetition. I disliked the reliance on flashcards. My daughter hated the timed math fact worksheets--we never did them. I hated the overly-extended review at the beginning of each year. I disliked how incredibly slowly it moved--it very much mirrors public school in that kids are not really introduced to multiplication until 3rd grade. I dislike how they teach a teeny portion of a larger subject just a little bit before introducing the next part. And example would be telling time. We did time to the hour and practiced that skill for two weeks, and then they taught numbering a clock, and reviewed that each day for two weeks, and then telling time to 1/2 an hour and practice that everyday. Measurement is treated the same way. I found that extremely annoying. The entire lesson is LONG! When we did everything they wanted in a daily lesson, it took over 40 minutes. They recommend having the kids fill out a worksheet in the morning and another in the afternoon (on top of the 40 minute lesson) and we never, ever did the second worksheet. Even on the first worksheet I had my daughter skip every-other problem. Those are problems with the implementation, not what is covered.

I do have some issues with the more fundamental aspects of the Saxon curriculum. I have a real problem with how place value is introduced. They use dimes and pennies to represent tens and ones. I find that is too far removed from the real meaning of place value. A dime does not look like ten pennies. Another issue is that the whole curriculum is adapted to homeschooling but was designed for public schools. Which means that there is a hugely long review in the front. That's great if your kids really do no math during the extended summer months, but not if you are challenging them to do calculations often or if they are just quick with math and don't need that much review. One of the biggest problems I have, though, is how entirely consistent Saxon is. Now that seems like a strange statement. Consistency is generally good. In Saxon, however, I feel that the approach to problems, the wording of problems, and even the practice problems, are all the same and that the kids may not be getting enough information on what each concept means and other ways the same concept can be used, especially with all of that repitition and practice, they may be only memorizing the mechanics of each problem instead of gaining a full understanding.

There were things I though Saxon did quite well. I like how they introduced skip counting and pattern recognition and that they introduced it early. I loved how Saxon taught about word problems. They would have the kids act-out the problem with stuffed animals or other toys. That is very engaging for the kids and really helps them visualize what the word problem is saying and what it is asking for. They also make a big deal out of making sure the children know if 'more came' or if 'some went away' to help realize whether to use addition or subtraction. Again, though, they never varied from that wording in the two years I used it.

Now for Singapore. I like Singapore a lot. I like how each new concept is introduced and then incrementally built upon without being slow. It is easy to switch from the textbooks (which have a lot of practice problems in them, in case, like me, you thought the textbook was only explanations and entirely different from a workbook) to the additional workbooks in case extra experience or a different approach is needed. I like the progression of topics. The curriculum is incredibly cheap. It uses pictures to represent concretes and then eventually that tapers away to working completely abstractly. They are short lessons and we only spend about 20 minutes on math each day (or could if there was less daydreaming and less of the occasional dramatic meltdowns when the number of problems reaches 27). I also like that the review is much less so it's easy to continue doing math over the summer (mwah-ha-ha).

Singapore also has a good approach to word problems. While the Saxon program (the levels 2 and 3) that I dealt with had a great, concrete, hands-on approach to problems, Singapore found a great way to move from that level to a more, though not entirely, abstract representation.

A huge drawback used to be that the parent/teacher was entirely on their own. Now Sonlight has written homeschool guides and Singapore has published answer keys so that their is guidance. The homeschool guids include a suggested schedule and ideas for teaching the new concepts. They also have some nice books for parents and teachers discussing math outside of the specific curriculum guides. Since both of my kids are working below their actual level, the topics progress in such a logical fashion, and because my arithmetic is really strong, I have not had any use for the guides at all. While Singapore uses concrete pictoral representations, it's up to the parent to bring in the real manipulatives. They sell some really nice manipulatives on their site. I really like the Comp-U-Mat, and the Base 10 interlocking blocks.

Another thing that may turn parents off is the number of versions that currently exist. When I was shopping for this year they had the Singapore program translated to English, but all of the measurements were metric and the money was yuan (?). They have the US version, which I have, which uses some Imperial measurements, but also includes metric (Yay) and uses dollars and cents. They also had another version aligned to the California curriculum standard. The CA standards are good (now) from what I've gathered, so that could be a fine option.

In summary, I feel concrete manipulatives are extremely important in the early years. Every concept should be introduced concretely and then removed the concrete representation as the children do not need them any more (in Montessori, this is when you notice that the kid is writing down numbers before even counting the beads). I feel it is more important to make sure the kids understand what they are doing than to finish or start any workbook. When it comes to selecting a program for homeschool, it is important to take the child and the parent into account. If your child 'gets' math quickly, then Saxon will be a bore. If the parent has never been a math kind-of person, then go with a curriculum that offers more guidance like Saxon or Math-U-See.

I do enjoy Singapore a lot. It is less expensive (in that Montessori materials are expensive to buy) and involves less preparation from the parent than Montessori (in that unless you buy all of your Montessori materials you need to spend a lot of time making them). It is also fairly well aligned with Montessori. I feel that, depending on your homeschooling goal (mine is academics and a strong math and science background as opposed to religion, family dynamics, attachment parentingetc), it could really move the kids along quickly--much faster than public school.

Amy said...

I've spent most of the morning poking around your links and transcribing notes into my Future Homeschooling files. Thanks!

Kim said...

I try to present some practical advice, like I got from LB when I first started. I hope you do find some things useful. I'd love to know what type of approached you are looking at and whether you'll be starting for pre-school, etc. With my little one a bit more than a year behind yours, I'd love to find out what you decide for that!

Always happy to entice another innocent to the dark side!

Amy said...

Kim - I'm planning to send my little one to Montessori for preschool and then homeschool after that. I'm a big fan of Lisa VanDamme's school. I want her to sell her curriculum, but I know people who have tried to get her to do so and she's just not ready yet. Hierarchy is probably going to be my number one principle. It takes care of so much when you get things in the right order: motivation, method, enjoyment, etc.

I think Montessori can do a much better job than I can at home for the early years. We've done as much M in the home as we can up until now, but I can already see that my daughter learns a lot more from watching her peers than I can figure out how to show her. I think when they are that young, we adults are just so far removed from their context that it's hard to break things down to the level they need.

Anyway, that is the tentative plan, so it's too early for me to have much more than a vague idea of what I want to do. Have you listened to Leonard Peikoff's lecture on the Philosophy of Education?

Kim said...

Peers are so important. I miss that regulating factor in homeschool.

I loved Peikoff's lecture. I also very strongly recommend "Why Johnny Can't Think." Very worthwhile if you haven't listened to it yet.

kat said...

We switched to Singapore with my 2nd child after she was floundering in MCP. I bought Math-U-See manipulatives and have found the program a great fit for her. Using the textbook and the workbook we have almost finished up 2A and 2B this school year (we have 7 days of work left). I do like the teacher workbook, not for the lessons, but for the scheldule and the mental math exercises in the back.

Right now we have 1 child in Saxon (4/5), one in Singapore, and one using Seton's Math for Young Catholics, but since they are all doing well I can't complain!

Kim said...


Good for you for not being afraid to switch up! I felt locked into Saxon because I had invested so much time and money into it and was worried I was going to make the same mistake with whatever I picked next. You know, if it works, it works! You will certainly have a broad base from which to pick as you go along.

No complaints!