By Jessica Kelmon

Is your child’s class learning “old” math or “new” math, “Everyday math” or “drill and kill?” Does your child’s homework look like nothing you were ever asked to do? Don’t panic — though 2 times 2 is still 4, the way many schools teach math has changed since our school days. From teacher-led classes to student-centric approaches, here are some of the popular — and perhaps unfamiliar — curricula, with unique problem-solving strategies and teaching techniques, you may need to understand to help your child succeed.

This popular, effective math curriculum blends conceptual thinking, hands-on activities, and real-world problem solving with more old-school methods like lectures and “drill and kill” rote practice. Using a “spiral approach,” Saxon builds on skills gradually over time by returning to a skill repeatedly, rather than teaching discrete skill-based lessons and moving on.

**Grades covered:** K-12

**What it looks like:** In class, teachers give scripted lectures, which means two second grade teachers in different states teaching lesson three will cover pretty much the same thing. In early elementary school, for example, the class has five daily math activities sprinkled throughout the day: morning routines (typically student-led, whole-class activities focused on real-world problems.); fact practice (including practice drills, flashcards, worksheets); lecture (introducing a new concept); guided class practice (often worksheets); and homework. On every fifth day, the teacher gives the kids a quiz or an oral exam to assess what they’ve learned that week.

**Homework: **You’ll see nightly homework that ranges from rote drills to conceptual homework (say, drawing a house floor plan that requires calculations) to real-world problems tailored to your child’s age. Students are encouraged to try many different problem-solving strategies, so don’t be surprised if your child’s homework involves guess-and-check strategies, drawing, building models, working backwards, making lists, or even acting out a problem.

This inquiry-based curriculum emphasizes math thinking and reasoning over rote practice. Its aim is to teach problem solving in conjunction with discrete skills.

**Grades covered:** K-5

**What it looks like:** This “student-centered” curriculum encourages more small and large group activities and less direct instruction from teachers. Students spend time building creative representations (drawings, models, etc.) and engaging in “math talks” with other kids. Lessons are organized into themed units that last anywhere from two to eight weeks and include a series of investigations that may last anywhere from one hour to multiple days. On the first day of an investigation, the teacher introduces new concepts during a large group activity. From there, kids explore the concepts in smaller groups or pairs through a few in-depth problems or math games while the teacher floats around helping. The goal is for students to learn to reason through problems and explore different strategies. Each day, kids discuss what strategies they tried and what worked (and didn’t) to build their understanding. In addition, there are daily routines that include math writing, math skills drills, and data analysis practice.

**Homework: **Less is more when it comes to Investigations homework. You can expect to see fewer — but tougher — problems, and don’t be surprised if the “solutions” involve writing or drawing in addition to computing. Also, kids learn to use appropriate materials and tools — so when your child pulls out a calculator, that may be A-OK. The curriculum includes a “parent letter” that your child’s teacher is likely to send you at the beginning of every unit. These letters orient parents to what their children will learn in that unit, what homework problems may look like, and how best to help your kids with homework.

This effective curriculum mixes old and new math with teachers presenting new skills in a lecture format and students grappling with concepts in hands-on activities. Organized around five activities — understanding, computing, applying, reasoning, and engaging — Expressions is the opposite of a “spiral curriculum.” It goes into depth on grade-level skills to build knowledge and fluency before moving on.

**Grades covered: **K-5

**What it looks like:** Every morning, classes start with student-led math-based routines about the calendar, money, counting, time, charts, etc. Later in the day, the math lesson kicks off with a quick group activity, followed by a teacher-led lecture where kids are encouraged to participate, not just listen. While teachers introduce skills and algorithms for the kids to follow, they also foster a discussion about different ways to find answers using math language and letting kids explore creative solutions. Teachers use visual guides to help kids conceptualize what they learn and students practice new skills in pairs, small groups, or individually using worksheets.

**Homework: **Nightly homework is the norm. While homework may involve new math language and drawing, old-school math problems, drills, and worksheets are typical.

Short for Scott Foresman-Addison Wesley Mathematics (SFAW), it’s a teacher-led approach that incorporates hands-on activities, abstract models, drawing, and open-ended questions to help develop kids’ higher-level math thinking.

**Grades covered: **PreK-6

**What it looks like: **Consistency is king for SFAW math. Every day, kids get clear, teacher-led instruction about the math skills they’re learning. In first and second grade, for example, the daily routine starts with a brief review of what students have learned, a hands-on activity to intro a new concept, another short activity (could be in large or small groups or individual) to connect the new concept to prior knowledge, then a lesson by the teacher for the whole class. The lesson is followed by individual or small group practice with the new concept using models, manipulatives, or worksheets, and a closing activity with individual work to check the students’ comprehension using journal prompts, questioning, or worksheets.

**Homework:** Since teachers select the materials that are most relevant to their class, homework will vary.

One of the most widely used “reform” math curricula, it’s a blend of teacher-supported and student-centered instruction. Everyday Math focuses on building kids’ conceptual knowledge with hands-on activities, oral practice, and math games that link math to daily life while reducing emphasis on procedural knowledge and memorizing math facts. Skills are built and revisited over time, in what is known as a “spiral approach.”

**Grades covered:** PreK-6

**What it looks like:** Most days, math class is split between the teacher’s lessons, when kids listen and learn together, and small group or individual activities, when kids can learn through projects, games, hands-on activities, and work on open-ended problem-solving. There are also daily drills and mental math practice, as well as a daily review called “math boxes.” Communication is key, and students are encouraged to share their thought process and explain their math thinking so they can verbalize what they’re learning and learn from one another. And math games aren’t just filler or fun – they’re threaded throughout the daily lessons and considered a big part of your child’s learning.

**Homework: **You may not recognize your child’s math homework, but this curriculum at least tries to keep parents up to speed. (Still, many a parent has expressed frustration.) At the start of every unit, there’s a parent letter to help support classroom learning. In addition to explaining what will be covered, these letters explain math games to play with your child and provide an answer key for all of the unit’s nightly homework. And, since Everyday Math embraces smart use of tools and technology, using a calculator is almost always A-OK — and if it’s not, your child’s homework will have a no-calculator icon.

Originally created in Singapore in the 1980s, this highly conceptual, visual, and sometimes physical curriculum (see a video of Singapore Math in action) was adapted for use in the U.S. after Singapore’s students skyrocketed to the top of the global list for math scores. Designed to build kids’ math thinking skills, the heart of the program is mastering a topic before moving on (so not a “spiral” method) — and friendly competition in the form of timed drills or “sprints.” Of all the curricula covered here, this is the least widely used but the only one supported with lessons on Khan Academy, which states: “We will (eventually) do all of the lectures in the Singapore Math curriculum (which we like).”

**Grades covered:** K-12

**What it looks like: **Each new unit begins with teacher-led conversations and group exercises that help students think about concepts in a flow from concrete to visual to abstract. This means your child will learn concrete, skill-building lessons through the teacher’s introduction and practice those skills with drills as well as sketching out the concept, and then move onto more abstract applications, like extrapolating that knowledge to solve related, real-world problems. Throughout each unit, there’s guided practice time, which may mean working in small groups, in pairs, or individually, and timed drills, which typically start with teacher and students chanting together: “On your mark, get set, go,” and then completing as many problems as they can in two minutes.

**Homework:** For elementary schoolers, nightly homework typically consists of a workbook practice page. Unlike old-school textbook homework where teachers may have assigned only the odd problems, the order of the problems matters: they build upon one another — and your child may discover a pattern as she works through the sequence of problems.

True, this isn’t a school-based curriculum. However, millions of kids are using this drill-and-kill, mastery-based curriculum (not a “spiral” method where skills are revisited) either because they’re homeschooled or as a supplement to what they’re learning in class.

**Grades covered:** PreK-12

**What it looks like:** Whether your child is at a learning center or at home, worksheets are the heart of this program. At Kumon learning centers, instructors are there to answer questions and help guide your child through what is essentially independent work. Kumon prides itself on teaching, reinforcing, and drilling math facts in a logical way. Kids typically start with work that’s “too easy,” which they master, then move on to more difficult skills, concepts, and problems. In Kumon’s case, “mastery” is measured by whether your child needs help, how accurate his answers are, and how quickly he can complete the work.

**Homework:** Nightly homework is assigned in the form of (surprise, surprise) more worksheets, and parents may be involved to help on concepts, to time their kids’ practice, or check their work.

Is there a "best" way to teach math? An interesting thing about math curricula is that right now, most studies about their effectiveness are conducted by the publishers that sell them. These studies are often submitted to What Works Clearinghouse (WWC), an arm of the Department of Education, which reviews studies that meet their criteria. But many studies are rejected, and the WWC reviews can be as clear as, well, mud, making the complex world of math curricula even more difficult to understand. As a result, there are very few studies that allow apples-to-apples comparisons of math curricula effectiveness.

A recent exception is a study with first and second graders with four widely used math curricula — Saxon Math; Math Expressions; Investigations in Number, Data, and Space; and Scott Foresman-Addison Wesley (SFAW) Mathematics — by the Dept. of Education published in October 2010. After the first year, the two clear winners were Saxon Math and Math Expressions. However, after the second year, when more schools and students were added to the study, the differences in effectiveness were less clear statistically; still, the study found positive effects from Math Expressions, and also implied that Saxon Math and Investigations in Number, Data, and Space were equally effective.

Many education experts believe we need a clearer understanding of which math curricula are most effective. A recent white paper by think tank Brookings argues that the government should be tracking which curricula schools use and urges philanthropic organizations interested in education reform to fund effectiveness testing for math curricula. Why? Because studies show that curricula matter — and because it’s difficult to sift through the local, minimal, and possibly slanted studies that do exist (which is why Brookings argues that one central entity should be doing it all). Also, once the expensive studies are done and effective curricula are identified, it's a relatively inexpensive solution to increase math scores in the U.S.: schools will just buy those books. In fact, an expert in the field recommends that parents lead the charge: be proactive, ask your schools and districts to pay attention to the research on effectiveness and share that information with parents and teachers.