We set our students up for long-term math success by devoting 5th and 6th grade to building automaticity, so that working and playing with numbers and doing everyday math becomes second-nature. When students join Rock Creek, they are placed into one of two Math Foundation classes based on their skill coming into the school. Students in our Math Foundation classes work with concepts like decimals, fractions, percentages, and negative numbers in a variety of different problem-solving contexts, so that they develop a deep and layered understanding.

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

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!”). Interleaving build an understanding of math that lasts for life, and at Rock Creek, we interleave every math assignment.

Our algebra sequence is based on the math curriculum developed by Phillips Exeter Academy. Exeter Math is built around interleaved problem solving, where each problem is carefully chosen to require critical thinking. Since each problem presents a new challenge for students, we explicitly teach concrete steps for approaching new problems. Students learn to first 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. By explicitly teaching the skills of problem-solving, we go beyond algebra and teach our students a systematic and logical approach to solving problems that will serve them throughout their lives–in their academics, work, and general decision-making.

When students have figured out a solution path, we allow our students to use computational tools like Wolfram Alpha and Desmos to carry out their calculations. At most schools, the bulk of time in an algebra class is spent learning the steps of how to compute answers by hand, which is an obsolete skill. The mathematicians, scientists, and engineers of today all use computers to handle the messy parts of solving problems, so we prepare our students to do the same. Freeing up the time typically spent memorizing procedural computation allows us to spend more time on complex problem-solving 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.

We put written and verbal communication center stage in our math program. Each day in class, students work through problems in groups, exploring, making conjectures, collaborating, and communicating about math. Through this groupwork, and by regularly presenting solutions to the class, students learn to verbalize mathematics clearly and logically. If a student can successfully explain a complicated math topic in words, then we know for sure that they understand the topic. Learning how to create strong logical arguments in math class also pays off in other classes, when students write essays in English and Social Science.

Geometry is fully integrated into our algebra sequence. Algebra and geometry are so fundamentally connected that it does not make sense to teach them separately. Most schools teach Algebra I, then Geometry, and then Algebra II, pausing algebra for a year to do geometry. This doesn’t work, because by the time students enroll in Algebra II, they have forgotten much of what they learned in Algebra I. We preserve continuity in our Algebra sequence–and student learning–by integrating geometry throughout. 

We also fully integrate probability into our algebra sequence. Most schools gloss over probability, but as the language of decision-making, we believe that probability is an essential skillset. People are often overwhelmed by uncertainty when facing major life decisions, and probability breaks down and quantifies that uncertainty. Probability is closely related to algebra and geometry, so it is natural to teach them side-by-side. Thinking about algebra or geometry in terms of probability and vice versa allows students to make more connections between topics, which contributes to a stronger and more lasting understanding of mathematics.

Data Science enables our students to do real-world quantitative research. To learn more about Data Science at Rock Creek, check out our Data Science page!