In past years, it was common for teachers to cover topics in a week, knowing it was not possible for every student to absorb the information. The new Common Core “narrow and deepen the scope of how time and energy is spent,” prioritizing specific topics and ensuring that sufficient time is given to major concepts. A 7th grade math curriculum will now have four major focal points -- proportions, linear equations, geometric constructions and population samples -- with underlying math concepts taught when necessary, not as a separate lesson.
One important aspect of the updated Common Core is sequential learning. As previously stated, all mathematical concepts are interwoven and may be used in various appropriate circumstances, rather than in isolation for a unit exam. A coherent and comprehensive math curriculum spans all grade levels, leading to deeper and more mature understanding of familiar areas as students' background knowledge grows. In other words, algebra will no longer be taught during the first marking period, only to disappear until the final exam in June. Everything learned will be important to know throughout the academic year and beyond.
These two shifts are fundamentally intertwined, as fluency relies on students’ ability to readily apply mathematical thought. Students will be expected to become masters of grade level standards, easily recalling and utilizing formulas and mathematical concepts to solve comprehensive problems. Although repetition and memorization is part of fluency, true fluency requires students, not only to recall necessary formulas, but to understand why a specific formula is necessary for a given problem. For example, knowing a²+b²=c² may be enough to pass a test, but understanding the underlying concepts behind the formula leads to true mathematical knowledge.
Along with fluency, students now need to have a deep understanding of what they are learning. A common mnemonic device to remember order of operations is "Please Excuse My Dear Aunt Sally" (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). However, this “trick” may confuse students who rely on it to remember the order of operations without in-depth understanding of the concept. A seventh grade student who is able to verbalize this notion clearly understands much more than one who relies on a silly sentence to answer a couple test questions. "Dual intensity" means that students are constantly practicing and understanding in a simultaneous continuum. Rather than learning concepts during school and practicing “drill and kill” homework problems, assignments and projects will encourage students to find new ways to solve problems, always considering real-world application of abstract ideas.