The implementation of Singapore Math has proven a remarkable success as shown by the all round increase of our students’ abilities and mathematical knowledge. The Singapore Math curriculum meets the needs of many different types of learners by meshing the best of traditional and progressive approaches in pedagogy. Its authentic way of emphasizing a type of learning honors process, critical thinking, and meaningful understanding rather than rote learning, teaching to a test, or superficial instruction of concepts that will need to be revisited again months and years down the line. Our students have not only been performing better in math, they report to be enjoying it much more, especially our older students who have experienced other programs and can speak to the benefits of the Singapore approach. Furthermore, while the rigor, depth, and retention is far more sound in Singapore Math, students seem to be having much more fun with it, once again showing that a true love of learning is the best way to help students excel academically.
In Singapore Math, children are asked to make meaning of the math, and the focus is not simply on getting the correct answer or even just to decipher how to solve a problem, but also to delve into why various approaches work. The focus here is on mastery, and the best way to master skills is to sit with them longer and focus on fewer concepts more deeply. This slower (but deeper) pace allows our students by the upper elementary years to grasp complex concepts much more quickly, and in the long run, we end up saving valuable instruction time when concepts don’t need to be as frequently retaught. We’ve seen at Seven Arrows — and the verdict is true nationally as well — that children on the Singapore Math program can gain a year or more than children on other programs due to this deeper, learning-for-mastery approach.
Singapore Math follows the same three-step approach in virtually every lesson: it begins with the concrete, then the pictorial, and finally the abstract. The first step often includes hands-on aids like blocks, cards, chips, and other manipulatives where children physically engage with the concept. Next, students are asked to represent the concept in a picture using various drawings such as bar models. Finally, the abstract introduces children to problem solving approaches and algorithms. Traditional math instruction at its best jumps from concrete to abstract, and at its worst straight to the abstract. However, when children engage the material through multiple approaches emphasizing the tactile and visual as much as the traditional strategies, they are far better able to meaningfully master the material. Furthermore, the visualization step is truly essential not only for the purposes of reinforcement for visual learners, but also because children are asked to show what they are learning on paper rather than taking a newly learned concept straight to the abstract. This middle step helps better solidify children’s understanding when they are able to actually create and see what they’re about to do abstractly. In other words, they create concrete pictures from abstract ideas.
Not surprisingly, the biggest critique of Singapore Math instruction is its expense. Implementing the program effectively requires a great deal of resources in time and money, many hours of teacher training, and community buy-in. Singapore Math is not necessarily “intuitive” for those of us who learned math very differently, and it requires detailed and purposeful instruction by knowledgable teachers. At Seven Arrows, all homeroom teachers undergo continued instruction and support of Singapore Math from outside experts, peer collaboration among each other and our curriculum director, and class observational feedback on lessons taught. The final step is to bring in the parents to ensure we are all working toward a common goal.
In addition to the Singapore Math program, students from grades 3-6 work independently on the ALEKS (Assessment and Learning in Educational Knowledge Spaces) program, a web-based tool for assessment and fluency. ALEKS is an avenue for children to challenge themselves and further their knowledge of new concepts and skills. Grades 1-6 also use the IXL web-based program for targeting areas of mastery and specific skills. IXL motivates through interactive games and exercises while keeping teachers and parents informed and involved. The goal of IXL is to help students get in-depth understanding of concepts, thus ensuring long-term skill retention.
The graphic below provides an overview of our mathematics program structure: