Mathematics

Beginning in 2011, the Lower School developed a new mathematics curriculum centered around problem-solving. To support this effort, the Lower School faculty adopted Singapore Math, a teaching method and set of textbooks based on the highly successful national curriculum of Singapore. The innovative Singapore Math approach places a consistent, strong emphasis on problem-solving, deep understanding of essential math concepts, and mastery of age-appropriate skills at each grade level -- all accomplished through child-friendly contexts, pictures, and language.

Solving problems is at the heart of the Lower School’s mathematics curriculum, and students begin solving simple multi-step word problems in second grade, using a technique called the “bar model” method. Modeling is as old as Euclid’s Elements, written in the 4th century BC. The method consists simply in representing (mentally or graphically) arithmetical quantities by line segments. Students gain increasing proficiency in modeling and develop a wider repertoire of models to choose from as they move from second to sixth grade. By fifth grade, students are solving problems that sometimes stump adults!

The mathematics program utilizes pictorial models to bridge the gap between using objects to act out what math concepts mean and using symbols like numbers to convey mathematical ideas. These pictorial models include bar models, number bonds, ten frames, arrays and place value charts. New topics are introduced in a concrete and meaningful context at all grade levels. For example, before studying abstract decimal fractions, fourth graders learn how to measure centimeters and millimeters on a metric ruler as they draw precise geometric figures. To give a practical, real-life context, third graders use decimals to find the weight of a bag of groceries packed to donate to the local Food Bank.

Although the mathematics program feels slower paced at the earliest grades, the result is student mastery of essential math skills and an accelerated pace of learning in the older grades because of a secure conceptual foundation. By the end of fifth grade, students have mastered most operations and division of fractions, and they are comfortable doing difficult multi-step word problems. In other words, they are well prepared to complete Algebra 1 in Middle School.

Our mathematics program also minimizes repetitive drilling through intentional sequencing of apparently unrelated topics that provide significant opportunities for practice of key skills. For instance, the introduction of multiplication facts by 2, 3, 4 and 5 in the middle of second grade is followed by a unit on graphing with a non 1:1 scale. As students solve problems based on the graphs, they apply their recently acquired skill in counting by 2, 3, 4, or 5 and develop an appreciation of the usefulness of knowing multiplication facts.

Long division is introduced to third graders before they are expected to know all their multiplication facts, but they learn to solve a long division problem by applying such skills and concepts such as: estimation of large numbers, recall of easier multiplication facts, subtraction with and without regrouping, and an understanding of how 6 ÷ 3 is related to 600 ÷ 3. The satisfaction of learning such a grown-up task is far more motivating than “skill and drill” worksheets on special skills. The commitment and perseverance required to complete a long division problem builds the grit and stamina necessary for solving even harder problems in the future.

It is important to meet the needs of all of our students. Every classroom supports and challenges the many types of mathematics students the school attracts. For some students, however, we make the decision that they will be served better by providing even more challenging instruction beyond the core curriculum.

Mathematics at Dwight-Englewood is embraced by our students as they regularly realize the power and potential of problem-solving.