To help students grasp key concepts in Calculus and Algebra, I have been using brief writing assignments with prompts. I want students to use the formal vocabulary we have been learning, but I also want them to correctly express concepts, operations or definitions in terms that they can remember and use. There are often 3 or 4 different ways to express the same concept (in calculus such as, slope, rate of change, tangent to a curve, derivative). Linguistic understanding of the connections is essential for being able to solve a variety of problems. Vertical teaming flows naturally from this since we introduce math concepts in one way (usually "slope") in Algebra I and advance through the courses introducing additional terms. We like to say that Calculus is "Algebra on steroids"--a sweeping together and upward of lots of earlier learning--vocabulary from earlier courses takes on new meaning but never goes away!