Some of the shifts will be seen in the mathematical content as topics move among and expand across grade levels. For example, multiplication and division of whole numbers will move up to higher grade levels after students have been exposed to these operations at more conceptual levels. The idea is to teach the algorithm after the student gains understanding of the concepts. Similarly, operations with integers are delayed until well into middle grades.
Some topics will also expand across fewer or more grade levels. Addition and subtraction of whole numbers will be addressed over a period of five years to better ensure that students gain fluency and understanding of these foundational topics.
Other topics will receive increased or decreased emphasis. Though algebra has been a K-8 topic in California under the previous state standards, it is not emphasized in the K-5 grades in the Common Core State Standards for Math. On the other hand, we will see a greater emphasis on understanding mathematical properties and data analysis than was encountered in previous frameworks.
The greatest changes we will encounter are not in the area of the content of the mathematics but rather in the process of how mathematics is presented. These are the mathematical practices.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Students not only will be required to do math but also to understand what they are doing. Thus we will see a significant emphasis on these eight practices. In geometry for example, students will work at level three of van Hiele geometric thinking instead of level one. That is, they will use inductive reasoning as opposed to simply recognizing shapes or learning area formulas.
While the changes in mathematical content will require some adjustments, the introduction of the mathematical practices will necessitate a much greater redirection in our teaching approach. We will be teaching students to think differently. Change is always both challenging and time consuming, but ultimately this will be a good move for us. We will be creating a generation of students who can reason mathematically and are better prepared for a leading role in a technologically advancing society.