For some students, math is one of the more difficult subjects to master. Part of the reason is its abstract nature. Unless you can actually see what you are adding or taking away, the numbers on paper are just — numbers on paper.
Counting on fingers is helpful to some students. But there is a limit, of course. You can only count to ten. Twenty if you take off your shoes!
When JCDS adopted Singapore math in 2011, our goal was to help students get a better understanding of math by working from the concrete, pictorial, and through the abstract. It is a base-10 system which focuses on the mastery of increasingly complex skills.
"In Singapore math, students learn to think mathematically through the sequencing of concepts and how they are all related," said Director of Education Tonya Elstein. "Instead of repeating steps the teacher has demonstrated, we make sure the students have a deeper understanding of numbers — how they are built, how they can be decomposed, and how to use various strategies to get to the correct answer."
On a particular day in October, Ms. Sarah Brinson’s 1st graders are working through a series of addition problems involving 2-digit numbers. The students are working with base-10 blocks to help them solve equations. These manipulatives are a concrete way for the students to see and show what the numbers represent. The base-10 blocks are made up of single cubes, representing the 1s, and rods (referred to a "longs") that represent the 10s. These blocks are just one of the many manipulatives that students use to engage in Singapore math.
Meanwhile, Ms. Brinson is guiding the students along using the whiteboard to show how to break the problem apart. First, she separates the tens and ones, asking the students to use their knowledge of basic math facts to find the answer for the ones place. After that, the students will put the tens and ones together to get the final answer.
Easy. And easier to understand.
"Our teachers start with the concrete, move to the pictorial, and finally apply strategies in abstract equations. Some students prefer manipulatives, while others use bar models, number bonds, or mental math. We make sure students understand the connections from one concept to another, " said Ms. Elstein. "It's amazing how our students understand the foundational building blocks of numbers and over the years develop true number sense."
The goal is that, once the basic math facts and concepts are mastered, the students have the option to bypass the manipulatives and diagramming and use equations and mental math to solve the problems. Regardless of if they are working with 2 digit or 5 digit numbers, the base-10 system is always at work.
At JCDS, Singapore math is taught in kindergarten through 4th grade.
"The fifth and sixth grade curriculum, Big Ideas Math, builds upon the foundation created by Singapore math in the lower grades," said 5th and 6th grade Math Teacher Todd Link. "Topics are taught in a similar order and manner. Each lesson begins with creating connections to the student's existing knowledge and then introducing new concepts to extend their understanding. Students are challenged to think about what they are learning and how to apply new concepts."
At JCDS, we are constantly studying the latest research and seeking the best methods for instruction for our students.
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Located in Jacksonville, FL, Jacksonville Country Day School is a private school for Pre-K 3 through 6th grade. JCDS prepares students for a healthy and productive lifetime of intellectual exploration, character development, and social responsibility.