The traditional style of teaching math has focused on surveying an ambitious number of topics each year, rather than developing mastery. In America, our teachers have struggled through a long list of math concepts that needed to be covered in every grade level. Then, many of the same concepts had to be retaught year after year. We hadn’t established grade-level deadlines for actual mastery, and students weren’t developing a deep understanding of what they were learning.
In addition, the excessive instructional demands forced teachers to focus on lessons that were superficial, at best. Instruction focused more on imparting procedural knowledge than conceptual understanding, because it was quicker to teach. For example, students might learn the steps for division, but could not articulate the reasons for each step. If they made a mistake dividing, they did not understand what they did wrong or why.
When the Common Core State Standards came along in 2010, they changed the mathematics landscape through three major shifts: focus, coherence, and rigor.
The Common Core emphasizes fewer math topics, each grade, taught in greater depth. The standards identify and prioritize the key fluencies that students must master at each grade level. Although additional topics may be taught during a school year, there is now a deadline for mastery of certain essential concepts. For example, a key fluency for the end of third grade is for students to know how to multiply and divide within 100. This means that grade three students need to master their multiplication facts and know how to follow the procedures for multiplying, but also understand what they are actually doing when they multiply and divide. By setting a more focused goal, the new mathematics standards allow teachers and students the time to develop a deeper conceptual understanding.
The Common Core Math Standards have been written to provide coherence for instruction as students progress from grade to grade. In other words, the standards are sequential from one grade level to the next. Students’ understanding of key math concepts builds over time. This means that the same concepts will no longer be repeatedly taught grade-after-grade. For instance, a key fluency in kindergarten is for students to be able to add and subtract within 5; then, students in first grade need to be able to add and subtract within 10. One grade level’s key skills prepare a student for the next year’s expectations. This coherence under Common Core allows students to develop a solid foundation for math literacy from their first day of kindergarten, and then build upon that foundation over time.
Rigor is another important shift with the Common Core and refers to conceptual understanding, procedural skills, and fluency as well as application. Students need to learn their addition, subtraction, multiplication, and division facts, so that they will have speed and accuracy when solving computational problems. The automaticity with fact recall, however, is not the end game. That knowledge is necessary to pave the way for more complex applications of math concepts.