About two weeks ago, a post titled “Singapore Math Is ‘Our Dirty Little Secret’” appeared on the Core Knowledge blog. It criticized the New York Times article about Singapore Math that appeared on October 1. Apparently, the author believes that the poor state of math education in the US is due to what he calls “reform math.” This ignores an entire generation of math-phobic adults who learned math through “traditional” methods, and most likely instigated the reform movement due to their dissatisfaction with those methods.
While the curricula based purely on constructivist approaches have their limitations, the idea that Singapore Math is a traditional approach is mistaken. It’s better than traditional approaches.
Below are the comments I wrote on the blog:
As a long-time Singapore Math educator and trainer, I have to disagree with a few points in this post. Overall, it seems to be advocating a “traditional” approach to math, the same approach that has led to poor US performance in math and science in the last few decades and an epidemic of math phobia among American adults. This “traditional” approach has also led to one of the main reasons elementary math education suffers these days: too many educators had poor math education and don’t understand the concepts themselves, so they have no idea how to teach it to the children. They are afraid of the subject, so how can they be successful in teaching their students? If they were taught algorithms with no idea of the workings behind them, they cannot pass an understanding of the workings on to their students.
When I teach my workshops, one of the things I see is when I demonstrate one of the basic four operations on whole numbers – addition, subtraction, multiplication and division – with number disks on a place value chart, many of the participants have an “Aha!” moment. So that’s how it works, they realize. And once they have this understanding and practice it, teaching it to the students – and being able to be flexible enough in their approaches to reach all students – becomes a reachable goal.
This use of place value disks is an example of the concrete stage of concrete > pictorial > abstract that Singapore Math is based upon. The textbooks are full of diagrams that show the place value chart being used in this way, but those diagrams are meant to illustrate what the students have already done with the place value charts and disks, which then builds into understanding of the algorithm and how it works. And yes, this is part of the process of learning from conceptual understanding to algorithm built into the curriculum. Manipulatives can be very powerful, and I find them necessary for most students. There are always the few who will understand no matter what, but those are not the students we need to help.
I had used the textbooks and workbooks for a few years, even with training, without understanding this pedagogy, and was somewhat successful – just because I understand math myself. But when I became equipped with the deeper understandings mentioned above, I became a much better math teacher, able to differentiate and address different learning needs.
Regarding the model-drawing books, the cynical comment about them in this post is misplaced. Some teachers may use the steps for model drawing as a rote formula, but that’s not how they are intended. If you have never learned how to do model drawing, you need some kind of instruction. Then after that, the steps are just there to remind you until they are internalized and personalized.
I have taught several model-drawing workshops in which participants (mostly high school teachers) have said the most valuable part of the workshop for them was the step, “Write your answer statement first.” This is a sentence with a blank for the answer, reworded from the question in the problem. It serves the purpose of refocusing the student at the end of the problem when they need to find which of the many calculations they may have worked is actually the answer to the problem. The Singapore workbook problems are set up this way, but without instruction, children may miss out on this step. I know I did!
I agree that the purely constructivist math approaches leave a lot to be desired, but the idea that Singapore Math has no constructivist elements is incorrect. I think that if it is taught well, it strikes a good balance between constructivist and elementary knowledge in such a way that children can master the math knowledge they need to succeed – and I have seen this success in my own students over the years.