Math

Our math curriculum is designed around skills that are genuinely useful in the real world.

The goal of our math curriculum is that every student deeply understands the math that they are learning, and that they can use the math throughout their lives. The skills we care about in math class are the skills that are useful in life: basic numeracy and automaticity in foundational math, concrete problem-solving strategies, and the ability to communicate logical ideas and arguments effectively. Our students learn more than just how to do typical math problems–students learn how to read, write, investigate, hypothesize, and communicate mathematics.

In 5th & 6th grade, our primary aim is to lay a strong mathematical foundation, developing numeracy and automaticity in essential, everyday math.

Our Math Foundation classes are designed to make working with numbers second-nature. We do this by utilizing cognitive science and asking non-routine problems. When students join Rock Creek, they are placed into one of two Math Foundation classes based on their skill coming into the school. (There are many paths a student can take through our math program, and we regroup students regularly, so parents can be assured that all tracks remain open to students after Math Foundations). In our Math Foundation classes, 5th graders work with concepts like decimals, fractions, percentages, and negative numbers. Students use these basic math concepts in a variety of different problem-solving contexts, so that they develop a deep and layered understanding of them. Being able to comfortably play with numbers and convert between number types in this way remains a useful skill. Most students who struggle in high school math struggle because they lack the proper math foundations. We are committed to building a strong math foundation for every student as an investment in their future math success.

Interleaving has been proven to develop strong & lasting math foundations, and yet most schools haven’t adopted the practice.

Schools around the country teach math using the method of “massed practice,” in which kids are regularly assigned a bunch of problems on the most recently taught topic. Throughout the school year, massed practice seems to be working: kids drill a skill until they’ve mastered it. But at the end of the year, kids struggle with final exams, and teachers are flummoxed. The issue with massed practice is that once students master a skill, they move on and rarely practice that skill again. They forget.

Moreover, the students’ mastery of the skill was weak in the first place, because they never used the skill in context of other math concepts and therefore never practiced identifying when each skill should be used.

The antidote to massed practice is interleaving. An interleaved problem set is mixed and asks non-routine questions on a variety of different topics. While students in an interleaved classroom may not appear to develop mastery as fast as those doing massed practice on a given day, the gains they do make are set in stone and quickly start compounding. When students work through an interleaved problem set, they must draw connections between different math skills, often using them in combination. These cross-connections build a strong, interwoven conceptual foundation, known to cognitive scientists as schemas.

Even more importantly, an interleaved problem set requires students to identify which skill applies to solve which problem. This is actually the hardest part of solving any math problem in the real world! Students often struggle on important tests because they have never practiced identifying problem types (every teacher has heard students claim: “I could’ve gotten this one right if I just knew I had to use X method!”). The best way to prepare and to build a lasting understanding of math is to assign interleaved problem sets. At Rock Creek, we interleave every math assignment.

The algebra sequence is interleaved and explicitly teaches students how to break down and solve complex problems.

Students may start the algebra sequence, which includes geometry and probability (more later), as soon as their math foundations are strong and secure. A typical student will start the algebra sequence in 7th grade and complete it in three or four years. Our algebra sequence is based on Exeter Math, which is built around interleaved problem solving. Students learn algebra skills as they become useful to problems in their problem sets, ensuring that students understand the practical purpose of new topics and when to use them.

The questions asked in Exeter Math are all one-of-a-kind; there are no “types of problems” for students to learn. Each problem in Exeter Math is a new challenge for students to solve, but we don’t leave kids to fend for themselves. We explicitly teach students concrete steps for approaching new problems. They learn first to write down everything they are given or know about a problem. Then, they write down what it is that the problem asks them to find. Most times, this is already enough for students to see the path from givens to solution, but when students are still stuck, they learn to define new variables, create new equations, and put forth conjectures to their group mates. By explicitly teaching the skills of problem solving, we go beyond algebra and teach our students a systematic and logical approach to problem-solving that will serve them throughout their lives – in academics, in work, and in general decision-making.

The algebra sequence prioritizes building mathematical communication skills.

Our interleaved and problem-based algebra sequence puts written and verbal communication center stage. Each day in class, students work through problems in groups, inviting them to explore, make conjectures, collaborate, and communicate about math. Students must be able to verbalize their hypotheses clearly and logically to their peers when working through problems with their group. They also learn to present their solutions concisely, when presenting to the rest of the class. As a part of their problem sets, students write proofs, or written, logical explanations of their solutions. In each case, we explicitly teach and practice skills for verbalizing mathematics. If students can successfully explain a complicated math topic in words, then they certainly understand the topic. Furthermore, when they write an essay in English or social science, they will find that it is much easier to write a strong logical argument, having practiced the skill every day in math class.

We teach students to leverage professional computational tools when solving algebraic problems.

There are two useful ways to approach quantitative problems in the real-world: go for a quick estimate and jot down a couple figures on paper, or use a tool and go for accurate calculation. At most schools, the bulk of time in an algebra class is spent on a third obsolete strategy: accurate calculation by hand. Students memorize and repeatedly apply rote algorithms like the quadratic formula, “slide and divide,” and synthetic division on paper. These are not skills that are used in the real world, even in STEM fields. A generation ago, many jobs required workers to do tedious computations by hand; today, all those jobs are done by computers. To be successful in quantitative fields, kids will need to be able to adapt to new problems and create their own algorithms. We are removing tedious computation from our algebra curriculum by teaching students to use computational tools like Desmos and Wolfram Alpha. Freeing up the time typically spent memorizing procedural computations allows us to spend more time on complex problem-solving and other math skills that are genuinely useful in our world today. Computational tools give us the space needed to give students a deeper understanding of math, so that the math sticks, and they are able to use it throughout their lives.

Probability and geometry are fully integrated into our algebra sequence so that students remember it long after they graduate.

Most schools gloss over probability, but we believe that probability is an essential course in mathematics. Probability is the language of decision-making. When faced with major life decisions, people are often overwhelmed by uncertainties. Probability is the study of breaking down and quantifying uncertainty. By teaching all of our students probability, we hope to give them the tools needed to make sound and informed decisions throughout their lives. Problems in probability are often solved with tools from algebra and geometry, and so it is natural for probability to be taught concurrently in our algebra sequence and not isolated as a separate class. Thinking about algebra in terms of probability and vice versa will allow students to make more connections between topics, thus building a stronger mathematical understanding.

For the same reason, we have integrated geometry into our algebra sequence. Algebra and geometry are so fundamentally connected that it does not make sense to teach them separately. In a majority of schools, the math sequence is Algebra I, then Geometry, and then Algebra II. Students pause their algebra learning to do some geometry, and then by the time they enroll in Algebra II, many students have forgotten what they learned in Algebra I. We preserve continuity in our Algebra sequence–and student learning–by integrating geometry throughout.

Once students complete the algebra sequence, they will be prepared to move on to our calculus sequence, which also integrates probability and geometry, or to explore any of our high school math electives, which you can learn more about in our curriculum guide.