By NCTM President Linda M. Gojak

NCTM *Summing Up*, October 3, 2012

Over the last three decades a variety of instructional strategies have been introduced with a goal of increasing student achievement in mathematics. Such strategies include individualized instruction, cooperative learning, direct instruction, inquiry, scaffolding, computer-assisted instruction, and problem solving. A recent strategy receiving much attention is the “flipped classroom.” Innovative use of technology to enhance student learning makes flipping possible and motivating for students and teachers. Simply stated, flipping is a reversed teaching model that delivers instruction, usually at home, through interactive teacher-created videos, while moving “homework” to the classroom. Teachers who have begun to flip their classrooms claim that this approach allows more one-on-one time with each student and increases student motivation, at the same time that students take greater responsibility for their own learning.

I am often asked what I think of the flipped classroom. I do not have any firsthand experience with flipping, so in addition to checking it out online, I have been thinking about it in the context of how mathematics teachers make decisions about what strategies to use when teaching mathematics. What is the potential of the flipped classroom, or any other strategy, to support our decisions on how to teach to ensure student learning?

Teaching is a complex activity. Student needs, teacher content knowledge, conceptual understanding vs. procedural skills, district curriculum, teaching materials, and standards must all be considered as we plan instruction. The Horizon Research Report, *Looking into the Classroom*,* *concludes that effective lessons are distinguished from ineffective ones by whether they—

• engage students with the mathematics content;

• create an environment conducive to learning;

• ensure access for all students;

• use questioning to monitor and promote understanding; and

• help students make sense of the mathematics content.

I believe that we need to go further. As we consider effective instruction that leads to student learning, we must remind ourselves of the characteristics of mathematically proficient students. We find these highlighted in the Process Standards identified in *Principles and Standards for School Mathematics *(problem solving, communication, connections, reasoning and proof, and representation), which are the foundation for * *the Standards for Mathematical Practice in the Common Core, and the strands of mathematical proficiency* *from the National Research Council’s influential publication *Adding It Up*. What is so compelling about the Process Standards is that they provide a critical vision for mathematics instruction and student learning. Rich mathematical tasks provide students with opportunities to engage deeply in mathematics as opposed to a lesson in which the teacher demonstrates and explains a procedure and the student attempts make sense of the teacher’s thinking. Communication includes good questions from both teacher and students and discussions that develop in students a deep understanding by wrestling with the mathematical ideas.

Considering some questions about process can be helpful when deciding how you will structure and present a lesson:

- Is this instructional approach appropriate for the grade level of students at this time?

- Can I adapt this strategy so that my lesson incorporates the NCTM Process Standards and encourages students to make sense of the mathematics?

- Does this lesson build from a rich mathematical task?

- What questions can I ask students that will encourage them to think more deeply about the mathematics that I want them to understand?

- How can I encourage rich discussions with and among students as they develop understanding and apply the mathematical ideas in a variety of contexts?

- Will my instruction help students to reason and make sense of the mathematics in the lesson?

- In what ways do I anticipate students will represent their thinking about the mathematics?

- How does the mathematics in this lesson connect to previous concepts as well as future concepts?

Although the flipped classroom may be promising, the question is not whether to flip, but rather how to apply the elements of effective instruction to teach students both deep conceptual understanding and procedural fluency. Flipped lessons that simply demonstrate how to do a procedure do not encourage understanding, do not ensure that students will remember the procedure, and do not promote adaptive reasoning. A single instructional approach is unlikely to have a major impact on student achievement once the novelty wears off. A combination of well-thought-out strategies that consider student needs, incorporate the characteristics of effective instruction, and develop understanding of mathematical concepts will have the greatest impact on student achievement.