Last year I had a timid fifth-grader, Adriana, who took my “Math Attitudes” survey on the first day of school. “I hate math. It’s so hard. I don’t get it,” she confessed to me immediately. She wanted to like math, but it made her uneasy and confused. To her, problem solving meant looking for key phrases like “how many more” and “altogether.” She couldn’t always remember which operations went with what key words. She also had a hard time remembering the steps of long division. Worse, when she got her quotient, she had no idea whether her answer made sense. She only knew that when she multiplied to check her work she got two different numbers. “I don’t ever really get the right answer,” she admitted. Adriana is not unlike many of the students I have encountered over the years. Fortunately for her, and millions of students across the United States who share her struggles with math, perceptions of what it means to be “good” at math and strategies for teaching it are changing. As the Center for American Progress shows in a new report, the Common Core State Standards are changing the way I teach and reshaping attitudes toward math among students like Adriana.
Out With the Old
Before Common Core, math teachers like me didn’t foster discussion, encourage creative thinking and perseverance in solving problems or celebrate success without a right answer. Back then, my math lessons had two parts. First, my students memorized a procedure by practicing the same basic problem over and over with different numbers. Then they practiced “problem solving” by reading word problems in search of the key words and phrases that would signal which operation to use. There was only one right answer and one way to get there—using the process they had just memorized. For Adriana and students like her, the “old way” of doing math was confusing and unenjoyable. If you didn’t know the procedure then you really couldn’t do the math. Because everything was taught in isolation, students couldn’t easily draw on concepts and skills they already knew.
In With the New Lesson
Fortunately for Adriana, I had learned new ways of teaching before she arrived in my classroom.The Common Core has changed how I plan my lessons. When planning, I intentionally connect students’ prior math knowledge and skills with each new mathematical idea. Students “discover” problem-solving procedures, or algorithms, as they begin to understand and master new math concepts.For example, I now activate students’ prior knowledge of place value and powers of 10 before I teach them how to multiply decimals. To multiply decimals, students need to understand the value of numbers when compared to each other. They also need to understand what happens to numbers when they are multiplied or divided by powers of 10. Ensuring my students understand these ideas has increased their mathematical reasoning, improved their ability to explain their work and helped them better remember what they have learned.
Redesigning the Classroom
Common Core has also changed the landscape of my classroom. Students sit in groups, not rows, and the room can get very lively as they begin exploring new topics and talking about patterns they notice or “shortcuts” (algorithms). I am there to make sure their thinking is on the right track by asking probing questions. The goal is to have them understand what they are doing when they place the decimal in the product of multiplication, not just blindly count place and insert a decimal point. Through classroom observations, guided questioning and discussion I am able to differentiate instruction more effectively because I can pinpoint misconceptions and areas of weakness. My lessons and interventions are more structured for some students and more discovery-based for other students. How do I know it’s working? Students no longer just tell me an answer. In fact, the answer’s not the focus. They can explain what they did and why it made sense for that problem. They can show they understand math conceptually, in addition to getting an answer.About four months into the school year, Adriana said, “I love math now because of you. You’re such a good teacher. Thank you so much.” Five years ago, she wouldn’t have said that to me. Thanks, Common Core.
Lisa Caponigro is a fifth-grade math teacher and a teachers union leader in Revere Public Schools in Revere, Massachusetts.