The Standards for Mathematical Practice, which are part of the Common Core State Standards, must be the clear foundation for everything that we do in mathematics classes, from kindergarten through high school and beyond. In essence, they are the mathematical “habits of mind” that we want students to retain and be able to apply when they have forgotten specific mathematical content.
Educators have, for all practical purposes, been able to “ignore” previous sets of practice standards because they were never made explicit as part of standardized testing. However, this is no longer the case, as the PARCC assessments will include a significant number of tasks that are specifically designed to assess students’ application of the Standards for Mathematical Practice. If students are not used to applying these standards on their own while working through problems, they will not be prepared to do so on these high-stakes assessments. Visit this link and this link (both in the PARCC website) to learn more about how these standards will be assessed; for more specific information, see the PDF files that apply to given grade levels and courses.
Two years ago, I created what I call “student-friendly” titles for each of the eight Standards for Mathematical Practice. Many of the teachers with whom I have worked have these sentences hanging on signs in their classrooms, and when teachers refer to them frequently, students begin to do so as well. This is one indication that these standards are truly becoming part of students’ mathematical “habits of mind”. These “student-friendly” titles are:
1. Make sense of problems, and keep working to solve them.
2. Reason about numbers in the same ways in different problems.
3. Show how your thinking is logical, and think about others’ thinking.
4. Use mathematics to represent real situations.
5. Choose and use appropriate tools in mathematics.
6. Be precise in how you use words, symbols, pictures, and numbers.
7. Look for connections among ideas, pictures, and numbers.
8. Look for patterns in the ways that you solve problems, and use them.
Every mathematics teacher, at every level, should have the Standards for Mathematical Practice visible to students at all times and include them as part of teaching and learning every day.
