Tuesday, February 1, 2011

Blended Algebra

(cross-posted on The Fischbowl)

I need your help again. I'm currently in the brainstorming phase of trying to figure out what a blended learning high school Algebra class might look like in my school. We're defining a "blended" class as one that is designed with both virtual and face-to-face components, with a significant portion of the class taking place in a non-school setting.

(Note: "significant" does not indicate a certain percent, it just means that this is not a "regular" face-to-face class with an online component. A "significant" portion of the content/learning will be delivered/completed/happen outside of  a traditional brick-and-mortar classroom.)

Since this is very much in the beginning of the brainstorming phase, it's pretty wide open in terms of how it might be structured. At this point, the following are the only parameters that we can't change (and I may be assuming too much even with these):
  1. We have to teach our current Algebra curriculum. See the skill list from my current Algebra class for an idea of what we have to "cover." So this is not the time or place to have the discussion of whether we should be teaching Algebra.

  2. We have to assign grades, and those grades have to be kept in our student information system and available on our portal for student/parent access at any time.

  3. The class is time-bound to our school year, so students need to start at the beginning (mid-August) and finish the course by the end of our school year (late May). (And the course might have to be time-bound to our semester schedule, so they have to finish the equivalent of first semester Algebra by mid-December - not sure of this yet.)
Other than those three restrictions, the rest at this point is open. Here's my Google Doc with some notes (not editable, also embedded below) and the brainstorming wiki page (editable, please do edit). You can comment on this post, edit the wiki page, or start/contribute to a topic on the discussion tab of the wiki page.

You can see from my notes that I am making a few assumptions in addition to the three non-negotiables above, with the most significant one being that this will be a "flipped" or "reverse" classroom, with the traditional lecture component delivered via online video outside of face-to-face time. While these assumptions are where I'm leaning, they still are subject to change.

You can also see that one of the huge questions that is still up for grabs is whether this class just teaches the Algebra skills, or whether we try to teach the skills and have the students try to go deeper, exploring the mathematics (perhaps through a project/problem-based approach, perhaps not). While it's probably no surprise that philosophically I prefer the latter option, this pilot course may not be the place to try this.

So, I'd appreciate any feedback/brainstorming you'd like to contribute.


  1. You’re definitely on the cutting edge of innovating with the “flipped classroom” approach. I see a lot of logistical challenges to making it work, but that doesn’t mean that it can’t or shouldn’t.

    Where I’ve seen the “flipped classroom” approach work is in the high school sciences: students learn at home from videos put together by the instructor(s) and then can have the classroom time for longer and more frequent labwork.

    What exactly is the benefit you’re hoping to gain from flipping a math classroom? It wasn’t clear from the blog post or documents whether you’re hoping to spend the in-class time on projects or full day practice sessions or something else. If it’s projects, I’m wondering if you could create a project or two that could take the place of a test for some units.

    I think the main ingredient needed to make this work is extremely high student self-motivation and the one thing I see missing is what you will do if you get students who end up not watching the videos: because in a regular high school algebra class, the ability and motivation levels tend to be all over the range.

    Like I said, it’s an intriguing idea and I appreciate your sharing your development process so openly.

  2. Thanks Paul. I'm currently doing this in my Algebra class and most of the students are watching the videos most of the time (this is with them walking in not knowing what they were walking into). Pretty similar to any Algebra class where some students do the homework (more traditional homework) and some students don't.

    For this Blended Algebra class students would know what they were signing up for in the first place, and part of that would be a descriptor of what qualities would help them be successful (able to work independently, able to keep to a schedule, willingness to ask for help when needed, etc. etc.).

    As far as what we're doing in class, that's the crux of my dilemma at this point. I think I can easily make this work with a "skills only" approach, where class time is simply practice, practice, practice (with guidance when necessary) and assessment opportunities. But I'd like to figure out a way to make it more than just a skills approach, and that's where I struggle.

  3. I like capstone project learning, where the students take what they’ve learned and take it to the next level. This could be having them work in groups on an AMC 10 competition problem after they’ve spent some time on factoring quadratics, such as solving a system of equations like


    (1/x) + (1/y) = 1/2

    or it could be giving the students a group test where the problems take thinking to the next level and where there’s no way one student can solve the test without their group’s involvement. Here’s a link to a good video on group testing in action:

    You could also spend class time in the computer labs doing Geogebra explorations when you get to graphing, which is something I wish I had the time to do. Mimi at “I Hope This Old Train Breaks Down” is doing such an exploration on graphing with her precalculus kiddos this week and is planning to blog about it, so you may get some good ideas out of that:

    You could also do some graphing calculator explorations, since they may not get that experience from the Khan videos. Tom Reardon has a nice video on working with at-risk students with graphing calculators and authentic instruction:

    But with the state end of course exam pressures and all, you may have to use the in-class time only for practice. To make it more fun, you may want to mix it up with some of the review games from Kate Nowak and others:

    Hope some of this brain dump is of use!

  4. PS: I have no idea how to imbed links into comments on Blogger, so I re-posted the above review games and activities to my blog with active links to make things a little easier.

  5. Hi Karl,

    I realize that you have posted this information a long time ago, but I would like to give to you my thoughts and opinions on the subject. I sadly have not been able to research many people with my hectic schedule and finally, I was directed to your blog and found this very interesting.

    I think that the idea you have is very innovative and very realistic. It is hard to get away from the traditional style classroom, especially for mathematics. Some people say it is not possible to go from direct instruction to an student-centered classroom with complete exploration. I do have to disagree with those individuals, due to my experiences over the last year in my Geometry classroom.

    Something that I tried to create inside my classroom is a project-based learning type of atmosphere. These projects were mostly small, but the emphasis was on 1. Getting to know the basics 2. Applying the basics to something simple 3. Taking what you know and directing it to real-life 4. Hopefully synthesizing that information with future information to come.

    The students did all of their projects online and really did not have to be inside the classroom for any of the information. Although the students in my district are required to be inside the classroom, I did individualized instruction with this information and facilitated the learning rather than direct the learning. A lot of my students did not need assistance in the process, rather they just need a little guidance or clarifying questions to help them along the path.

    Here are my thoughts on your blended situation:

    - I do not think that a face to face meeting is necessary, unless you need a periodic check-up with a students. Or a student is falling far behind and they need required assistance (as stated by your classroom structure).

    - You mentioned Khan videos that were created for a variety of topics. I think that Khan's videos are okay, but they lack the personality aspect of what you get when you have your own teacher. I think self-made videos that help with the burning questions that your students have and embed them on your website, would be a better idea than using Khan's. This way the students know that you are there to answer their questions, rather than directing them to a place where someone else can answer for them.

    -My thoughts with having some sort of pre-prescribed program for your students like Khan or Catchup math, takes away from the individual prospering that your students can do. With project-based performance the students can turn their projects into something personal and you can see them prosper in their own light. If you allow them to follow one standard and just focus on the math, I believe that the students will get bored and lose interest, as well as, learn a way to beat the system.

    Those are my thoughts on the subject and I do not know if I have helped you in any way, shape or form, but I think that you have an excellent idea. The following is my website that the students and I used to create our projects I made most of the assignments and have used them to complete all of the standards set-forth by the state. You are more than welcome to look through any of these and I will be happy to discuss things that might be helpful to you.

    I am no expert and I do not want to come off as one, I am just telling you what I know and have learned and maybe the knowledge that I have gained could help you. Thanks Karl!