Flipped Algebra 1 Class Description
Arapahoe 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 Taxonomy
Arapahoe’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 Practice
What we do each day varies, but here’s what a typical lesson cycle might look like in this class.
Class typically begins with “openers” – a few problems that review something we’ve just learned and/or leads into the new topic (example
Then if it’s our first day on a topic, we’d begin with some inquiry around that topic (this is the “inquiry” phase). This might include students doing an experiment, gathering some data and trying to form a conclusion (example
pdf), or it might be some guided inquiry around a mathematical idea (example
pdf). The initial inquiry portion might last just one class period, or it might last several, but it’s designed to have the students begin to develop an intuitive feel for the concept and begin to construct their own understanding of it.
After the initial inquiry phase in class, students then might watch a video at home (“explain” phase). These videos (example
) replicate what a typical lecture in class might have looked like several years ago (albeit somewhat shorter). Each video is composed of three parts (often referred to in education as “I do,” “we do,” and “you do.” First is the explanation phase, where I explain the topic step-by-step with examples (“I do”). Second is the guided practice part, where students are guided through several examples to solidify their understanding (“we do”). Finally students do a self-check section (“you do”), where they are given several problems, asked to pause the video and work them out on their own, and then resume the video to see the worked out solutions. All of the videos are available via YouTube
or for download
Students then return to class where we continue to practice and apply the mathematics (“apply” phase). They will also have additional practice opportunities outside of class via various online or print sources should they need it, and they of course can always come in for help or receive help from me electronically (email, Skype, chat, text, etc.).
The Technology We Use
We 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.
: LPS Google Mail
(any modern web browser, Chrome works best). LPS provides a Google Apps account for all students.
For Homework and Pre-Assessments
: LPS Moodle
(any modern web browser).
Optional: Students can use things like Skype to contact me (webcam, microphone), and if they have a text-capable cell phone we can communicate via text as well.
Moodle 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).
When 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.)
Other 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.
Students will occasionally have other short assignments on the Moodle, sometimes a couple of homework problems or perhaps a reflection or explanation problem.
Everything 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.).
Initial assessment is done in class. Students are assessed over the essential skills
in Algebra I. Because Algebra is skill-based, the class uses a modified form of standards-based-grading (modified because there is still an overall grade for the class). Students are assessed frequently with short assessments over discrete standards. Each skills assessment is scored using the following five-point scale:
5.0 = Demonstrates thorough understanding
4.5 = High level of understanding, but with small errors
3.5 = Demonstrates understanding, but with significant gaps
3.0 = Shows some understanding, but insufficient to be successful
2.5 = Attempts the problem
Because Algebra is skill-based, it is essential that students master the skills as we go along and not get behind. Therefore, if students do not score proficient on the skill (4.5 or 5.0 on the scale), that grade is temporary. They will have multiple opportunities to get help from various sources and then re-assess over that skill, and the improved score replaces the previous score in the grade book. Students may re-assess as often as once per day, by appointment
, for the next five school days (for a possible total of up to five re-assessments). Students, however, must do the work necessary to come to those re-assessments prepared. If a student needs help, they can come in, but they can’t re-assess that same day (otherwise students can memorize how to do something just long enough to pass the assessment, but perhaps not truly understand it).
If they score a 2.5 or a 3 on the original assessment (given in class) it will not get put in the grade book. Instead, the assessment will show as missing (with the score noted in the comments) until the student comes in at least once and re-assesses. If they should still get a 2.5 or a 3 on a re-assessment, then that will go in the grade book, but they need to make at least one attempt to improve their score (and their understanding) before it goes in the grade book. They can re-assess up to five times, no matter what their original score, until they get at least a 4.5 (preferably a 5).
What Type of Student Will Be Successful in a Flipped Algebra Classroom?
In general, successful students will need to be fairly independent, self-directed learners. This class only works for students if they watch the videos and complete the online pre-assessments outside of class, participate fully in class, ask for help when they need it, and generally take charge of their own learning. While this is true of all classes at Arapahoe, it is even more important in the Flipped Algebra class as the productive use of class time depends on students having watched the videos and completed the online pre-assessments for homework.
If you decide you’d like to enroll in Flipped Algebra, then you’ll need to enter in course #354013.4 (1st semester) and course #354014.4 (2nd semester) as electives in the online course registration. Please note that the course title will say Extended Algebra I/II on the course request screen (with a note about it being Flipped Algebra in the description field) simply for scheduling reasons, but the course will show as Algebra I on the student’s schedule and transcript. Please also note that all students are pre-populated into the traditional Algebra I so you’ll see two sets of Algebra courses on there after you add Flipped Algebra as an elective (we’ll remove the other one before scheduling).
Thank you for your interest,
Arapahoe High School