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Using Concrete, Pictorial, and Abstract Math Progressions

saint_theresa_catholic_school_-_sugar_landSaint Theresa Catholic School, (Sugar Land, Texas). Using the Singapore math method, Saint Teresa Catholic School employs a Concrete, Pictorial, and Abstract (CPA) progression in mathematics instruction emphasizing number bonds, bar modeling, and mental math. This progression enables students to master concepts by stages. Beginning in PreK through grade three, the school teaches mathematics in two-block periods each day. Teachers introduce students to new concepts during the first period, while the second period is devoted to practice. Each day the school identifies struggling students through formative assessments in Math 1. The struggling students then receive daily remediation through direct instruction in Math 2.

Problem-based learning is foundational to this approach. In kindergarten through grade two, number bonds help children decide which operation is needed for solving specific types of word problems. Students, from kindergarten through eighth grade, practice a variety of mental math strategies to solve computational problems before learning to solve them using an algorithm. Students learn to solve two- and three-digit addition and subtraction problems using the “Make 10” strategy. Students in grades one and two solve math word problems using number bonds. Knowledge of whole and part relationships helps students analyze and decide how to approach word problems. These children count money, read analogue clocks, and begin to study geometry. By the end of first grade, students can count money in both coins and bills, and readily recognize geometrical shapes, both plane and solid figures. Students also analyze geometry using symmetry, congruency, and patterning. Students are introduced to bar modeling at the end of second grade. The use of bar models is a versatile and transferable skill that students use to visualize a range of math concepts, including, fractions, ratios, and percentages. Drawing bar models for word problems allows students to determine the knowns and unknowns in real-world scenarios. In grades four through eight, students learn specific applications of math concepts for the fields of engineering, art, and chemistry. The school’s goal is for students to demonstrate their understanding of quantity and the meaning of numbers, rather than to simply apply algorithms.