### By Catherine Freeman, mathematics teacher at Sage Park Middle School in Windsor

*You’ve heard from Catherine Freeman before—in her op-ed and in a previous blog—talking about why Common Core has made her classroom a place of deep learning for both her and her students. Today, Cay will tell you a little more about how Common Core specifically helps her students in math.*

**What exactly are the Common Core State Standards?**

The Common Core Standards for Mathematics are an outline, a clear set of specific skills and mathematical concepts that students should know by the end of each grade level. The Common Core is NOT a curriculum. Although the standards do set rigorous end-of-year learning goals, districts have the freedom to determine how to help their students get there.

In fact, each state or district has the independent right and responsibility to take the Common Core Standards and develop or adopt a curriculum that outlines how much time to spend on each topic, and identifies age-appropriate materials and resources to be used. Curriculum specialists and teachers in each district decide how to lay out the sequence of big ideas and smaller learning tasks to reach the end goal of developing critical thinkers and problem solvers. They also develop regularly scheduled check-ups on students’ progress so that students who are behind can receive intervention and support as the year progresses. There should be an ongoing cycle of developing lessons to teach the standards, going back to revisit and revise them as we become experts on these new standards, and discussing how to best help our students reach deeper levels of understanding and lasting skills.

**Common Core Creates Deeper Understanding of Content**

The Common Core Standards are written to encourage students to solve real-world problems. As a math teacher, I see these standards built with greater focus–with fewer standards than before in each grade, but with the potential for a truer and more lasting understanding. Instead of giving students a cursory survey of many math concepts, we work on building lasting conceptual understanding of the really important concepts. This translates to higher-level learning with more opportunity to teach critical thinking skills.

Previously, students were taught the procedures to solve a math problem with an often tangential explanation of the conceptual understanding behind the process. I look at the work that I used to give my students, and I see how I used to teach skills in isolation, without context. I was teaching my students how to get the answer, instead of how to understand the math. I am throwing out my old worksheets, which listed 40 problems of a single type on each page. I’m not going to use these anymore because this isn’t how students will be presented with math in real life. Instead of teaching, “Here’s the process for finding the answer to a ratio problem. Now solve it 40 times,” teachers must now ask their students to demonstrate that they understand ratios and can use them to solve real life problems.

The Common Core Math Standards certainly still emphasize computational fluency, but now it is not enough for students to be able to solve a problem without being able to articulate why their solutions makes sense. As explained in the Common Core State Standards for Mathematical Practice document, *“Students who lack understanding of a topic may rely on procedures too heavily.”*

Common Core helps me to build real understanding in my students. It’s actually a much more interesting way to teach, and to learn.

**Common Core Creates Continuity Between Grades **

The Common Core Math Standards are also designed with strong coherence: there is a clear sequence of skills and conceptual understandings that are developed in each grade level, and then built upon and developed in subsequent grades. Students will learn concepts in a more organized way, both within a school year and across grades.

In a classroom that has a curriculum fashioned around the Common Core, students spend most of their time learning only the material that will build the foundation needed for future learning. For example, students in grades K-2 focus on developing strong number concepts and fluency, in addition and subtraction; grades 3-5 focus on multiplication and division of whole numbers and then fractions; grades 6-7 extend the work with fractions to focus on ratio and proportional reasoning; and grade 8 uses this foundation to explore linear algebra. In this way, the grades within a school and between schools have continuity so that a student builds the foundation in math this year that he will need to understand math next year.

When I was in school, I was considered a good math student, but I never saw the connections between math topics. I think about how much more sense math would have made to me and to many of my peers if we were taught to see connections between concepts (e.g. how understanding the division of whole numbers can help solve division of fractions).

**Common Core is Difficult for Teachers to Implement**

These new standards are certainly a challenge both to teach and to learn because they represent an increase in rigor compared with Connecticut’s prior math standards, and they definitely require a whole new way of teaching math. But the promise inherent in these higher-level standards is worth the effort. They have the potential to truly transform our math classrooms into high-energy centers of problem solving. I know that in my classroom, we are all thinking and learning with new energy and purpose; my teaching has been transformed, and my students are finding new ways to approach challenging material. This is the promise of the Common Core Standards.

*Stay tuned for a piece from Cay about the Common Core habits of mind in math, which can help students to develop the types of skills that they’ll need to be great at math in any grade. *