IntroductionArapahoe High School will be offering one section of Algebra 1 next year that will be taught using a “flipped classroom” approach. This class covers the same curriculum and standards as every other Algebra 1 section at AHS, but the way class time and homework are structured will be different. Instead of the more typical math class where the lecture is presented in class and then students do practice for homework, this class will use class time for inquiry and practice and have the students watch the lecture for homework. This is the third year we have offered this class, but since there has been a lot of press around Khan Academy lately (60 Minutes
 , TED Talk), we wanted to explain what our class looks like (it’s similar to Khan Academy in some ways, yet different in some important ways).In a traditional math classroom approach, a teacher might briefly go over the previous night’s homework, lecture for a good part of the class period, and then students would be assigned 15-30 homework problems. Students might have some time to get started on those problems in class, but then the rest would need to be completed as homework. This works very well for many students, but the flipped approach works in a slightly different way.
The idea behind this approach is pretty simple. For some students, listening to a lecture in Algebra class and then doing homework at home is somewhat problematic. If they get home and are struggling with the homework, there is often no one there who can help them. As a result, they can spend a lot of time on the homework, often reinforcing misunderstandings of concepts and frequently getting very frustrated. But now, because of the technology available to us, we can “flip” the traditional classroom model. Students can now watch the lecture at home (typically an 8-10 minute video, one to two videos per week) as homework and do the traditional “homework” at school.
Here are some reasons that some students might find this approach better. First, students have more control over the time and place that they watch the lecture. If watching the lecture right after school when they get home works best for them, great. If watching it at school during an unscheduled hour works for them (with headphones), then do it then. If the best time for a particular student to work on this is at 10:00 pm, then more power to them. They can choose the time and location that works best for them.
Second, students have much more control over the pace of the lecture. They can pause the video at any time to study what’s on the screen, and they can replay part or the entire lecture any time they want. So a student that typically “gets it” the first time they hear it can move on to other things and not have to listen to a teacher repeat various parts of the lecture for other students in the class. On the other hand, students that need more time to process, or need multiple repetitions of examples, can control that without the teacher needing to move on to other topics. (Depending on the Algebra topic, your student might be both kinds of students at different times.) And all students can go back to videos they’ve already watched if they need to review a particular topic.
Third, students are no longer practicing in isolation. They now have the opportunity to do the traditional “homework” practice problems in class, where they have the teacher and other students available to help them. If they don’t understand something they no longer have to struggle with it on their own at home and possibly get frustrated because they know they can’t get help until the next day (if the teacher has time). Now they are practicing together, in class, with the support of the teacher.
Finally, this approach also frees up class time to not only practice but to explore mathematics. Teachers often feel pressed to cover the Algebra curriculum in the time we have. By shifting the lectures to outside of class, it frees up class time to practice mathematical inquiry. It allows us time to explore, question and investigate the mathematics, which is not only more interesting for students but leads to a deeper understanding.
Inquiry-->Explain-->Apply and Bloom’s TaxonomyArapahoe’s Flipped Algebra class follows an inquiry-explain-apply cycle.
 This is an attempt to leverage technology to address some of the shortcomings of the traditional approach. For years educators have worked to move students to higher levels of thinking on Bloom’s Taxonomy
. Here is the revised taxonomy:
Typically students have spent much of class time at the lower levels of Bloom’s taxonomy, concentrating on remembering, understanding and perhaps applying. If they ever get the chance to move to the higher levels of analyzing, evaluating and creating, it has been done on their own time. The flipped classroom approach tries to “flip” this as well. We try to leverage the technology to allow students to concentrate on the remembering, understanding and a bit of applying outside of class, and then utilize our time together in class to work more on analyzing, evaluating and creating. (That’s not set in stone, though, we do some of each in both settings.)  What It Looks Like in PracticeWhat we do each day varies, but here’s what a typical lesson cycle might look like in this class.
The Technology We UseWe use a variety of technologies in this class, and each student will use a variety of their own technology. There is no specific hardware requirement for this class (other than a scientific or graphing calculator which is true of every AHS Algebra class), but students must have high-speed access to the Internet at home. It doesn’t matter whether they have a PC or a Mac (or other), desktop or laptop, brand new or relatively old computer – as long as it works reasonably well and can access the Internet at reasonable speeds.
MoodleMoodle is an open-source course management system that allows me to “collect” homework from students and to pre-assess them online without having to use valuable class time. While Moodle is very powerful, we use just a small portion of it and it’s pretty straightforward for students. Here’s a screenshot of the main course page in Moodle to give you an idea of what it looks like (students each have an individual login).  Video HomeworkWhen students watch a video and complete the two or three self-check problems in their notebooks, they then login to the Moodle and simply enter their answers.
This allows me to quickly see that the student is completing the video without using valuable class time. (Since the video completely works out the self-check problems, this is graded on completion only.)
Pre-AssessmentsOther than the midterm and the final exam, each assessment in Flipped Algebra is over one concept at a time (this is often referred to as standards-based-grading – see assessment/grading below). At least two class days before each assessment students will take a short online pre-assessment on the Moodle (as a homework assignment). This pre-assessment is typically only two or three questions (just enough to show me if they understand the various nuances of the particular concept). After they submit their answers they will see the problems fully worked out, including steps and explanations.
These pre-assessments are graded on completion only, and students can take the pre-assessment as many times as they like. This gives students a great idea of what they understand – and what they don’t – before taking the actual assessment, so it gives them time to get help before taking the graded assessment.
Other Students will occasionally have other short assignments on the Moodle, sometimes a couple of homework problems or perhaps a reflection or explanation problem.
Class BlogEverything is organized through the class blog (2011-12 version). Each day class meets a blog entry is posted that summarizes what we did that day (you can subscribe via email or RSS). We have a Smart Board in our classroom so the openers and the lesson we do each day are captured and posted as PDFs. Then whatever homework they might have is listed (could be completing a video, or a pre-assessment, or preparing for an assessment, etc.).
Assessment/Grading
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