My post about Singapore math has been put off for quite some time!! If you've never heard about Singapore math you should really look/read into it. There are wonderful workshops where the presenters teach you how math is taught/learned in Singapore! The students have a strong foundation of number sense, which sadly, many american children do not have. I remember being in school, learning how to add and subtract and just knowing that I had to carry over numbers without really knowing or understanding why I was doing that. In Singapore, the children are very proficient in math and are excellent mental mathletes!
At my first Singapore math workshop, I was blown away by some of the videos the presenter shared. There were double digit by double digit multiplication problems that these third graders were presented (in front of the camera) and they solved it all in their head...before I could solve it on paper!! These workshops are TIRING. The entire time you are actually solving problems and using the strategies that they teach you. Its a whole new way of thinking about your numbers and also the ways that you solve these problems. You are introduced to many different ways to do math.
The thing to always remember is CPA. Concrete, Pictorial, and Abstract.
Whenever introducing a new concept students, students need hands on experiences. They need a lot of time to manipulate the problems, solve them, and find multiple ways to represent the problems/answers.
As a teacher, we need to always accept multiple representations of the same thing and remember that we are teaching 21st century learners.We need to encourage them to think of many different ways to solve their problems, problem solve and most importantly...students need to be able to communicate their thinking. I spend a ton of time (sometimes it seems too long but it's never too long if it's meaningful) letting the kids explain how and why they know their answers is correct.
I've been working very hard on creating an environment where all children feel safe to share their thinking. What is wonderful to see is when the kids who don't understand are able to question why the answer is 28 when they think it should be 40. The students are very patient and EXPLAIN, go through steps, walk the student through the problem and answer that confused students questions. The students do not feel ashamed to ask questions or not understand. I make sure to always thank that student for giving us a great lesson. It's good for all kids because when they are able to explain..you know they truly understand!!
Once students have had enough experiences with the concrete, they move onto the pictorial approach. They need to draw representations of what they know about solving the problem. Model drawings are a big part of singapore math and are great for word problems!! Since I do all my math through word problems, my kids are pretty strong with model drawings.
Then comes abstract. Once students have been given the appropriate amount of time to familiarize themselves, they will be able to understand all of these abstract concepts that we try to teach everyday. I too often forget how difficult these concepts are for my teeny third graders and get frustrated when they don't understand my formulas (pre Singapore math training days) haha.
It's a totally new way of thinking, it's time consuming but it's amazing!! Once the students fully understand the concepts they are able to see relationships between other concepts. They are able to solve any type of problems because they truly understand the concept. BUT there are still those few students who I still hear..."I don't get this" when it's the exact same as the problem before :P
My grade level is planning on fully implementing Singapore math as our core curriculum next year. We've been getting a ton of training but I still have a lot to learn and read about over the summer! Anybody else use Singapore Math??