I have been thinking today about the idea that much of the confusion that parents and community members have when they cite seemingly strange examples of problems related to the Common Core State Standards in Mathematics (CCSS-M) may have to do with the difference between end goals for student learning and the instructional strategies that we may use to reach these goals.
I should add, before proceeding, that there are two types of goals for student learning in the CCCS-M. We have the Standards for Mathematical Content (the “math”, so to speak) and the Standards for Mathematical Practice (the “habits of mind” that support mathematical thinking and problem-solving throughout our lives). Often, effective instructional strategies can relate very closely to the goals in the Standards for Mathematical Practice, so we as teachers need to try to be very clear about what the goals of any given assignment are (and, perhaps, what they are not). This alone may be helpful in easing some frustration on the part of parents.
One type of example that I often see online is a problem where the student is asked to show or explain a way to get to a given answer. Parents are often frustrated when they feel that their children are required to provide long, complicated explanations or diagrams when there are “quick and easy” ways to find the answers to such problems. It is important to recognize, however, that often these explanations and diagrams do not need to be overly complicated to demonstrate a child’s understanding — precision and conciseness are still important in mathematics! Also, that explanation or diagram is often simply an extension of an instructional strategy that has been employed in class to help scaffold a child’s understanding of a concept or a child’s fluency with a skill.
Again, it is important to point out that the Standards for Mathematical Practice include goals such as representing a problem or real situation in different ways for different purposes, justifying one’s thinking, understanding another’s thinking, recognizing and using particular patterns or structures within problems, and, in general, making sense of mathematics. So, sometimes assessing students’ movement toward these goals will require teachers to assign tasks with more complex responses. Still, parents and community members need to realize that these goals also help students to move toward fluency and efficiency that are built on understanding and not just memorization — we want the general population to feel they understand, rather than shy away from, mathematics.
