The best schools find ways to weave science together with math, reading, social studies, and even art. Children may work for long periods on units on birds, or bridges, or Central Park. Look for evidence of these explorations in the classroom. At PS 321 in Brooklyn, for example, kindergartners study trees. They post tree graphs, leaf rubbings, and diagrams based on their frequent trips to the park to observe changes over the course of the year.

Of course you want to see children’s artwork and essays on the walls, but you should see examples of math and science as well. At PS 221 in Queens, a bulletin board had fourth graders’ own questions about science: “How do snails breathe?” and “How does dust form?” and “What started the Black Death?” Science exploration that starts with children’s own questions is more likely to prompt them to ask more.

**How to spark kids' curiosity**

Most of the science experts we interviewed said it’s more important to spark children’s curiosity than to develop a particular body of knowledge in the elementary school years. Whether your child is studying the solar system or rocks and minerals, it’s important that he is excited and engaged in his work. Learning lots of facts can wait.

“Too much rote learning may well kill interest,” said Richard Seager, a climate scientist at Columbia University and parent of two children who attended PS 75 in Manhattan. “I would think that the best that can be done is to instill a sense of wonder and interest in the natural world in the kids, that they may be motivated to pursue it more in the future.”

Math is a little different. It’s important for math to be exciting and fun. But there are also specific skills children need to learn each grade in elementary school to prepare them for middle school and high school. A look around the classroom will also help you discern if these skills are being taught.

**Pre-kindergarten and kindergarten**

In pre-kindergarten and kindergarten, look for blocks and puzzles. Research shows that developing good spatial skills by learning how to put together different shapes is just as important to understanding math as learning to count. You should look for small objects (like buttons, plastic animals, or LEGOs) that children can touch, count, and sort.

Even before children learn to write numerals, they need to get a sense of what numbers are. Counting objects builds an intuitive feel for math that teachers call “number sense.” Young children with good number sense quickly figure out amounts—who has more strawberries, for instance, or which pile of M&Ms is larger. This math sense is an important foundation for developing more advanced math skills later on. In pre-kindergarten, children should learn to count to 20; identify shapes such as circles and triangles; and know relative words including “big,” “small,” “tall,” and “short.” By the end of kindergarten they should be able to count to 100; write numbers from 1-20; and know words like “above,” “below,” “flat” and “solid,” according to the Common Core standards.

**First and second grades**

In first and second grades, children should be learning to add and subtract. They need to understand the value of coins, learn how to tell time, and know how to measure distances. Look for a math area in the classroom with things like dice, play money, dominoes, and number lines. Also look for counting frames, clocks, pattern blocks, and rulers. Well-equipped classrooms have “manipulatives”—little plastic cubes kids can snap together to learn to add and subtract. Look for bundles of sticks used to represent “tens” and little cubes used to represent “ones” to help young students learn place value. Such tools help children understand the concepts underlying arithmetic, not just the rules for addition and subtraction. Classrooms often have a shelf with puzzles and games such as Sorry or Connect Four, which are fun ways for children to reinforce arithmetic skills, especially when they are indoors a lot during a long winter. Children are learning to talk about math and read word problems at this age, so look for lists of math words posted on the classroom wall to help them remember words like “sum” and “difference.” According to the Common Core standards, by the end of first grade, children should be able to add and subtract numbers up to 20; by the end of second grade, they should be able to add and subtract large numbers.

**Third grade**

In third grade, children learn multiplication and division. They need quick recall of math facts, so some drill is necessary. Look for worksheets, flashcards, and workbooks so children can practice basic math facts until they have become automatic. Children also need to understand what multiplication and division really mean. For that, teachers may ask children to color rows of squares on graph paper, or to cut strips of paper a certain width and length. Third graders learn to calculate the area and perimeter of a rectangle. Sometimes classrooms have square plastic tiles that children can assemble into rectangles so they can see concretely what area and perimeter mean. Are the desks in rows? That probably means the teacher does most of the talking. But research shows kids understand math better if they talk about it and try different ways to solve problems. If you see desks in groups, it may mean children work on problems together—and that’s a good sign. By the end of third grade, children should have memorized the times tables up to 10 x 10 as well as division facts. They should also be able to calculate the perimeter and area of a rectangle, according to the Common Core standards.

**Fourth and fifth grades**

Fourth graders need to be able to multiply and divide large numbers, and by fifth grade children should be able to multiply and divide fractions. You might see posters with drawings of problems such as: How can 8 children share 5 hero sandwiches fairly? You may see charts showing the work kids have done to solve big word problems that require them to use all their math skills—addition, subtraction, multiplication, division, and fractions. If children solve problems in different ways, that’s a good sign that they understand what they are doing and have not merely mastered a formula. Research shows children need both a deep understanding of math and the ability to solve arithmetic problems quickly, so look for evidence of both teaching approaches in the classroom. Numbers lined up in neat rows—the way most of today’s parents learned arithmetic—show a quick and efficient way to solve problems. Conversely, children’s written explanation of their work—part of most lessons today—is designed to demonstrate that they get the concepts.

Math textbooks are fine, but good teachers draw on several different math programs or resources (think instructional YouTube videos or sites such as Engageny.com, which offers an array of activities as well as games for helping students practice key skills of the Common Core Standards) because not all kids learn in the same way. Some kids look at numerals on paper and understand them right away; others need pictures and objects to make sense of arithmetic. Some prefer worksheets and workbooks. Others need to count, use number lines, or use a computer. It’s helpful if there is variety. No one set of math books works for all kids; many of the best schools use elements from a variety of math books. One of the best things we can do as parents is to be aware, interested, and open. Learning math and science is a process. Keep an eye on these classroom clues and grade-level milestones, and take note of how your child learns best.

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