Flipped Learning for Math Instruction (Flipped Learning Series) - Tapa blanda

Jonathan Bergmann was a classroom teacher for 24 years. He now works with teachers, schools and corporations to help them rethink educational practice. He co-founded the Flipped Learning Network and FlippedClass.com. He received the Presidential Award for Excellence for Math and Science Teaching in 2002.

Aaron Sams is an educational entrepreneur who co-founded the Flipped Learning Network and FlippedClass.com. He is adjunct professor at Saint Vincent College in Latrobe, Pennsylvania, and was a chemistry teacher in Colorado and California. He was awarded the 2009 Presidential Award for Excellence in Math and Science Teaching.

Chapter 4
flipping with interactive math resources
FLIPPIng A CLASS inherently provides a teacher with additional class time to involve students in more active learning. This may be a lab in a science class, a discussion of literature in an English class, or a public debate in a social studies class. What is the analogous activity in a math class? Fortunately, a large number of interactive activities are available for the math teacher. In addition to hands-on and participatory work, students can contribute to the collection of interactive material through the creation of their own content.
Math Manipulatives
Math teachers have been using manipulatives effectively for many years. Activities with manipulatives help students better understand and apply important math concepts by tactilely manipulating items that physically represent abstract mathematical concepts. A problem math teachers often face is a lack of time to use the power of manipulatives fully in class. Because the flipped classroom causes a drastic rethinking of how class time is used, teachers can take advantage of manipulatives more frequently. Missy Northingham, a sixth grade math teacher in San Antonio, Texas, flipped her class and uses the extra time with her students for a variety of activities, such as creating factor label cards that students use to convert units of measurement (Figure 4.1).
If virtual tools are more your speed, there is a library of virtual manipulatives at Utah State University that students can interact with online. Find the National Library of Virtual Manipulatives at http://nlvm.usu.edu/ en/nav/vlibrary.html.

Figure 4.1  after making factor label cards, students in Missy northingham’s sixth grade math class take the cards home and watch their teacher demonstrate how to use them in a flipped video. This accelerates students’ understanding of key concepts and it helps them ask specific questions the following day.

Interactive Simulations  and Tools
There are many online simulations for students that can take the place of direct instruction. These simulations serve as simple inquiry activities, where students explore mathematical concepts on their own or delve deeper into a particular topic. These simulations typically engage students with graphs, geometric shapes, and other realworld applications of math concepts, allowing students to interact with virtual objects and learn from them. Students are able to explore key concepts simply by changing variables and discovering for themselves what would occur. These types of simulations are very useful and can take the place of direct instruction through flipped videos. Students can learn more deeply through discovery, rather than just interacting with videos on the same topic. Learning through these simulations can also be faster than some inquiry labs because of how efficiently students can manipulate variables in a virtual environment.
Following are some examples of online simulations and other software that may be helpful for the flipped math classroom:

• Geogebra (http://geogebra.org) is not just for geometry. There are activities for all levels of math. You can also view teacher-created lessonsat http://geogebratube.org.
• Desmos (https://www.desmos.com) is an online graphing calculator that allows students to interact with mathematical concepts.
• PHET Interactive Simulations (http://phet.

colorado.edu) is a free resource made by a team at the University of Colorado that provides math and science simulations you can manipulate.

• Explore Learning Gizmos

(http://www.explorelearning.com) is a subscription service with math and science simulations.

• Many textbooks also include simulations that directly tie into the content teachers may already be teaching.

Manipulatives and simulations are ideal, though not necessary, for teachers who have access to an interactive whiteboard. Small groups of students can gather around the interactive board and collaboratively experience these simulations together. Many of these simulations also have guided activities that may be valuable in helping students make sense of the content.

Student-Created Content
Once students understand the content, it is valuable to have them demonstrate it through the creation of their own instructional or explanatory material. Crystal Kirch, a math teacher in southern California, has her students create their own videos as an assessment tool. She asserts this is important because “students need the opportunity to discuss math and speak in an academic way about the math. It becomes the teacher’s job to give them the appropriate guidance necessary to be able to discuss math.” To help students do this, she has them create a video for which they write their own word problems that are modeled after examples Crystal gives them. Students can collaborate by having a fellow student solve the problem, or evaluate the problem after it is solved. Students then work together to explain and record the concept using a simple whiteboarding app before posting it to a blog.
Another master of student-created content is Eric
Marcos, a middle school math teacher in Santa Monica, California. Eric has successfully established an afterschool math club, where students volunteer to develop and create math videos for their peers (November, 2012). Students use screencasting apps and take on fake names to preserve their anonymity.
Erin Richerson, an eighth grade math teacher in Olathe,
Kansas, features students in her videos as guest hosts (Figure 4.2). The students take on roles as guest experts and help her explain to other students the concepts they have mastered in ways their peers can understand. She also brings students in to participate in her “Hotspot” videos, which assist students who are struggling with particular math concepts. In these videos, she and a student think through and discuss certain practice or review problems without working out the entire solution.

Figure 4.2  Students from erin richerson’s eighth grade math class use a smartphone to video record an algebra tutorial.
Making math more interactive and participatory is one way to enhance your class time with students, but you can also use resources that are more traditional in a flipped class. The next chapter explores how the implementation of student choice and autonomy can enhance the use of traditional resources.