Concrete – Pictorial – Abstract. Sound familiar? This is the way students in Singapore learn elementary math, and since 2010, the U.S. has been trying to pattern its own math standards, known as Common Core State Standards Math (CCSS-M), after the successful Singapore Math curriculum. Unfortunately, these new guidelines have led to much confusion from parents and teachers alike. But before we blame CCSS-M, we should understand its intent and develop more effective implementations in our classrooms.
While Singapore Math and CCSS-M both focus on mastery, they differ in their approaches. For students in the island city-state off southern Malaysia, learning math starts with the concrete – blocks, cards, buttons, or some sort of solid objects. Then come abstract concepts: 15 – 9 = 6. To illustrate this, two bars are drawn, one with ten squares and a shorter one with five squares. Nine squares are then blocked out, leaving the remaining six unshaded. With this picture, children can easily bridge the concrete and the abstract while mastering the fundamental concept of subtraction with regrouping. What makes Singapore Math so effective is the consistent use of this bar modeling to solve word problems, from simple addition to complex fractions and ratios. On the other hand, CCSS-M provides teachers with no clear method of developing effective visuals to depict abstract strategies, such as decomposing a number leading to a ten (e.g. 15 – 9 = 15 – 5 – 4 = 10 – 4 = 6). Same intent, yet implementations could not be more divergent.
Even though mastery is of utmost importance, its acquisition should not take place at the expense of computational fluency. Parents often complain that, instead of the usual 40 computational homework problems, their kids “only” need to explain all the concepts behind two math problems. After much frustration, the students get some fuzzy idea about the concept and gain little exposure to practice: a double-loss! If a fourth grader is stuck explaining 15×3 as repeated addition, how will he or she handle a multiple-digit multiplication calculation such as 315×73? Memorization of basic math facts, such as the timetable should still be reinforced, as math literacy seeks to strike a balance between mastery and fluency.
At The Tutoring Center, we explain new concepts in age-appropriate ways to “make it click.” We also supplement students with timed, test-taking practice and encourage them to beat their own record in speed and accuracy. And finally, we take time to fill any “skill gaps” that students might develop over the years. With this comprehensive approach, we eliminate the bad and the ugly while achieving the good that CCSS-M meant to be.
Joseph Tran, Center Director, The Tutoring Center of Upland