Flip your instruction so that students watch and listen to your lectures… for homework, and then use your precious classtime for what previously, often, was done in homework: tackling difficult problems, working in groups, researching, collaborating, crafting and creating. Classrooms become laboratories or studios, and yet content delivery is preserved.  Jonathan Martin

PEDAGOGY: The Flipped Classroom concept
Baker and Mentch, 2000
The utilization of a flipped classroom will afford the opportunity spend more time in the classroom immersed in mathematics. Instead of having students sit at home, isolated, struggling to do their homework problems, they will be in a classroom environment where they can work with others, discuss the mathematics, and delve deeper with the teacher as a facilitator. Students could spend time in class doing practice problems, problem solving, modeling or building a wiki study guide for the class material. A secondary benefit of the flipped classroom is that students will have the videos in a digital format where they can access the lecture and class content at any time and play it as many times as they need to while learning foundational skills.
In Effective pedagogy in mathematics, authors Glenda Anthony and Margaret Walshaw, associate professors at Massey University, highlight researchbased strategies that engage learners and lead to desirable outcomes. The concept of the flipped classroom allows for the implementation of several of those practices on a much larger scale than the traditional setup due to the amount of time freed up for interaction between students and between student and instructor. Four of the practices listed are especially ripe for development in the flipped classroom environment. They are listed below.

Pedagogical Best Practice #1
Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas.
When making sense of ideas, students need opportunities to work both independently and collaboratively. At times they need to be able to think and work quietly, away from the demands of the whole class. At times they need to be in pairs or small groups so that they can share ideas and learn with and from others. And at other times they need to be active participants in purposeful, wholeclass discussion, where they have the opportunity to clarify their understanding and be exposed to broader interpretations of the mathematical ideas that are the present focus (Anthony and Walshaw, p 9). Prominent learning theorists John Dewey and Lev Vygotsky dedicated a large degree of their work to the social nature of learning. The acknowledgement that learners are social beings and, by default, belong to social groups is key to the development of any learning environment. Learners have parents, siblings, teachers, peers, and fellow learners, wtih whom they communicate and interact, and receive guidance and stimulation. Any account of learning that gives short shrift to these diverse social factors to some degree must be deficient (Phillips and Soltis, p 53). Jonathan Bergmann and Aaron Sams, two forerunners in the flipping world testify that "...we notice the students developing their own collaborative groups. Students are helping each other learn instead of relying on the teacher as the sole disseminator of knowledge. It truly is magical to observe. We are often in awe of how well our students work together and learn from each other" (Bergmann and Sams).
Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas.
When making sense of ideas, students need opportunities to work both independently and collaboratively. At times they need to be able to think and work quietly, away from the demands of the whole class. At times they need to be in pairs or small groups so that they can share ideas and learn with and from others. And at other times they need to be active participants in purposeful, wholeclass discussion, where they have the opportunity to clarify their understanding and be exposed to broader interpretations of the mathematical ideas that are the present focus (Anthony and Walshaw, p 9). Prominent learning theorists John Dewey and Lev Vygotsky dedicated a large degree of their work to the social nature of learning. The acknowledgement that learners are social beings and, by default, belong to social groups is key to the development of any learning environment. Learners have parents, siblings, teachers, peers, and fellow learners, wtih whom they communicate and interact, and receive guidance and stimulation. Any account of learning that gives short shrift to these diverse social factors to some degree must be deficient (Phillips and Soltis, p 53). Jonathan Bergmann and Aaron Sams, two forerunners in the flipping world testify that "...we notice the students developing their own collaborative groups. Students are helping each other learn instead of relying on the teacher as the sole disseminator of knowledge. It truly is magical to observe. We are often in awe of how well our students work together and learn from each other" (Bergmann and Sams).
Pedagogical Best Practice #2
Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests, and experiences.
An affordance of the flipped classroom is that teachers have much more facetime with students and have the opportunity to engage in discourse about the mathematics. Identifying inconsistencies and alternate conceptions in students' understanding aid teachers in structuring future learning activities that address such conceptions. Effective teachers take misconceptions (or alternate conceptions) and use them as building blocks for developing deeper understandings (Anthony and Walshaw, p 12). Instead of trying to fix weaknesses and fill gaps, they build on existing proficiencies, adjusting their instruction to meet students’ learning needs. Such teachers are responsive both to their students and to the discipline of mathematics (p 11). Bergmann states that "...since the role of the teacher has changed from presenter of content to learning coach, we spend our time talking to kids. We are answering questions, working with small groups, and guiding the learning of each student individually (Bergmann and Sams).
Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests, and experiences.
An affordance of the flipped classroom is that teachers have much more facetime with students and have the opportunity to engage in discourse about the mathematics. Identifying inconsistencies and alternate conceptions in students' understanding aid teachers in structuring future learning activities that address such conceptions. Effective teachers take misconceptions (or alternate conceptions) and use them as building blocks for developing deeper understandings (Anthony and Walshaw, p 12). Instead of trying to fix weaknesses and fill gaps, they build on existing proficiencies, adjusting their instruction to meet students’ learning needs. Such teachers are responsive both to their students and to the discipline of mathematics (p 11). Bergmann states that "...since the role of the teacher has changed from presenter of content to learning coach, we spend our time talking to kids. We are answering questions, working with small groups, and guiding the learning of each student individually (Bergmann and Sams).
Pedagogical Best Practice #3
Effective teachers understand that the tasks and examples they select influence how students come to view, develop, use, and make sense of mathematics.
Whether students are problemsolving, modeling, or building wikis of classroom content, effective teachers ensure that all students are given tasks that help them improve their understanding in the domain that is currently the focus. Students should not expect that tasks will always involve practicing algorithms they have just been taught; rather, they should expect that the tasks they are given will require them to think with and about important mathematical ideas. Highlevel mathematical thinking involves making use of formulas, algorithms, and procedures in ways that connect to concepts, understandings, and meaning (Anthony and Walshaw, p. 13). If students are going to "make sense of problems and persevere while solving them" as stated by the Common Core State Standards for mathematics, it needs to be a part of their regular routine. In my version of the flip, students will build wikis or create calculator programs that demonstrate and apply the concepts that we are learning and that strengthen students' ability to thinking logically. Both of these activities support this best practice and engage students in higherorder thinking.
Effective teachers understand that the tasks and examples they select influence how students come to view, develop, use, and make sense of mathematics.
Whether students are problemsolving, modeling, or building wikis of classroom content, effective teachers ensure that all students are given tasks that help them improve their understanding in the domain that is currently the focus. Students should not expect that tasks will always involve practicing algorithms they have just been taught; rather, they should expect that the tasks they are given will require them to think with and about important mathematical ideas. Highlevel mathematical thinking involves making use of formulas, algorithms, and procedures in ways that connect to concepts, understandings, and meaning (Anthony and Walshaw, p. 13). If students are going to "make sense of problems and persevere while solving them" as stated by the Common Core State Standards for mathematics, it needs to be a part of their regular routine. In my version of the flip, students will build wikis or create calculator programs that demonstrate and apply the concepts that we are learning and that strengthen students' ability to thinking logically. Both of these activities support this best practice and engage students in higherorder thinking.
Pedagogical Best Practice #4
Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.
Effective teachers use assessment for evaluating students’ progress in learning and for planning curriculum improvements, not just for generating grades. Good assessment includes data from many sources besides paperandpencil tests, and it addresses the full range of goals or intended outcomes (not only knowledge but also higherorder thinking skills and contentrelated values and dispositions) (Brophy p 29). In the course of regular classroom activity, they collect information about how students learn, what they seem to know and be able to do, and what interests them. In this way, they know what is working and what is not, and are able to make informed teaching and learning decisions (Anthony and Walshaw, p. 17). Assesment can take on many different forms in the flipped classroom. The teacher, as observer, can gather anecdotal data as (s)he monitors the class. For more about how I see assessment playing out in the classroom click here (scroll down to the middle of the page).
Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.
Effective teachers use assessment for evaluating students’ progress in learning and for planning curriculum improvements, not just for generating grades. Good assessment includes data from many sources besides paperandpencil tests, and it addresses the full range of goals or intended outcomes (not only knowledge but also higherorder thinking skills and contentrelated values and dispositions) (Brophy p 29). In the course of regular classroom activity, they collect information about how students learn, what they seem to know and be able to do, and what interests them. In this way, they know what is working and what is not, and are able to make informed teaching and learning decisions (Anthony and Walshaw, p. 17). Assesment can take on many different forms in the flipped classroom. The teacher, as observer, can gather anecdotal data as (s)he monitors the class. For more about how I see assessment playing out in the classroom click here (scroll down to the middle of the page).