Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the mathematics classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.
Teachers carefully connect learning within and across grades so that, students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions such as multiplication tables so that they are more able to understand and manipulate more complex concepts.
Shift#4: Deep Understanding
Teachers teach more than "how to get the answer" and instead support students' ability to access concepts from a number of perspectives so that students are able to see mathematics as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.
Students are expected to use mathematics and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply mathematics concepts in "real world" situations. Teachers in content areas outside mathematics, particularly science, ensure that students are using mathematics - at all grade levels - to make meaning of and access content.
Shift#6: Dual Intensity
Students are practicing and understanding. There is more than a balance between these two things in the classroom-both are occuring with intensity. Teachers create opportunities for students to participate in "drills" and make use of those skills through extended application of mathematics concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.