Tuesday, February 01, 2011

Blended Algebra

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. This is a huge undertaking, Karl. Kudos to you for giving it a whirl. One "issue" I have philosophically with the strictly flipped classroom / Khan Academy video approach is one of appropriate pedagogy. Here's what I mean...if you want to students to construct a concept (let's say the idea that two perpendicular lines have opposite reciprocal slopes), it might be done more effectively in groups of 2-3 using a structured activity you design rather than watching some examples on Khan Academy. When it comes to algebraic ideas, Khan makes a lot of sense (follow these three steps...check for errors...), but when a relationship or concept come into play, a video may not be appropriate.

    Does that make sense? I guess what I'm trying to suggest is a flexible approach that changes based on the standard. You probably already knew that though. :)

  2. While I am not an experienced professional by any stretch of the imagination, why not use the same type of systems that I have experienced thus far in college. Most popularly teachers use an online class shell that contains important documents, links, and most notably a discussion board. This method has been fine in English, but in math it will require a bit of work on your part to think of creative assignments. Given your expertise and technological savvy, I believe that a simple system such as described above, in conjuncture with current technological trends for education, you could do something very inspirational and lasting for your students.

  3. I have some teachers teaching Chemistry in "flipped" fashion at my high school. They do it so the students can watch some instruction and have class time to ask questions and solve problems with the teacher experts there to help. This could be very beneficial in a math classroom, especially if you are not creating all of the sessions for the students to watch on your own. I'd like to see how it goes.

    I hope to see you when you come to Ohio in a couple of months.

  4. Matt - Yeah. With my current face-to-face Algebra class, that's how I'm doing it. I introduce/explore the concept in class, then they watch the step-by-step video for homework after exploring. (My videos, not Khan's, fwiw.)

    For what my district is asking me to look at, though, I'm not sure that's going to work out. We'll see.

  5. marleyfan601 - I'm curious, how does that work for you? Do you feel like it's just as effective, or even more effective, than a completely face-to-face class?

  6. Scott - If you're at that conference, try to find me and we'll talk.

    What you describe is more or less what I'm currently doing in my Algebra class (although I did create all my own videos). As I mentioned in my comment to Matt, though, I think this blended class may need to be a little more online and a little less face-to-face, not sure yet.

  7. here's what the kids created last year in an attempt to own their learning in algebra 2:

    here's a jing explaining it - esp how the cyclic grid worked:
    not mentioned in the jing, notice at the bottom of the grid - we had an expert tutor from india on call for those moments of - where is this in real life. highly recommend logging that as an open source collection. i know you do a ton of that already Karl.

    and then here's a doc explaining the philosophy behind what we did, how we got started etc: http://tinyurl.com/6f9b4m5

    and this ning is where we housed it all:
    it's morphed from the time the jing was made. on the right hand side if you go down a bit to a yellow strip labeled - it's right here - that takes you to the grid.
    below that is the updated version of most popular resources the kids used.

    the ning hasn't been touched much this year - as we have moved on to facebook.
    2 years ago we lived on moodle. last year i had the moodle and the ning available per their choice - everyone was on the ning by semester. this year i offered the ning or facebook.

    if any of this helps or interests you Karl, and you'd like to know more. give me a holler.

    bravo to all you are doing.

  8. I'm not an expert, but I have been playing with algebra since I was introduced to it more than four decades ago. I think your blended algebra plan can be a great combination of f2f practice/help and students using provided links and sources they find themselves to explore the concepts. The learning opportunities outside the classroom, such as the Kahn Academy and the links below, would help your students become self-directed lifelong learners.
    I wish you the best success in your endeavor!

  9. Carl,

    Since I became aware of your "Flipped" concepts, I have had the notion that you should connect to some local resources. Try some of these demos and see it applies in your paradigm


    Also, I am aware of an online Algebra resource that meets or exceeds current standards and SAT proficiencies.

    I'm more than glad to assist.
    Reid Cornwell

  10. The thing I found the most liberating about it was having a venue to express my opinion; even though the class was heavily discussion oriented, it was nice to be able to go online, view the text, and be able to give my interpretation. The only downfall was that everything was very basic as far as the technological aspect was concerned. Everything occurred within the class shell, but if the was a way to incorporate virtual activities into this scheme I believe it could be really fantastic because it provides an expressive outlet as well as a practical one.

  11. Karl,

    I read your post yesterday, but am just now getting back to it. The frost thought that i had was including in the virtual realm a video at the front end of each unit or top that illustrates some problem to be solved but the upcoming learnng, or some other application. Perhaps even solicit videos from leathers after the unit. I'm not sure this is possible, and there were certainly times in my life when I would have sworn that there was no possible practical application for algebra. But I'm older and more mature now.

    Another idea is that of including a virtual world as part of the virtual realm. This would not be a place to meet nearly as much as it would be a sandbox where leathers can actually apply their spends (algorhythms) to create objects that actually perform. I've done some building and scripting in Second Life and it's almost entirely about algebra.

    I know that Second Life would be difficult, but OpenSim should work the same way and they may even have better tools out ther now.

    2 penny's worth.

  12. Thanks everyone for the ideas. Thinking.

  13. I currently teach an Algebra class to 8th grade students and a few in 9th grade using this blended approach. My school is an independent study school that provides instruction two days a week. We usually cover 4-5 lessons from a textbook each week. In the past, I just covered several lessons each class period period and students did all homework assignments at home.

    Recently, I heard about the "flipped" classroom and was inspired to try this with my students. Most of my instruction is now on screencasts that students watch prior to coming to class. They also do a few simple problems at home.

    I created Cornell Note sheets with fill in the blanks and space for working out problems. During my screencasts, I am filling in the notes and my students are completing their notes while watching on their own time.

    I often make minor errors, because I'm recording so many screencasts in a short period of time, but instead of recording the screencast again, my students know that if they find an error and e-mail it to me, I'll award extra credit points to the first one to identify the error. It keeps them interested and watching carefully.

    When students come to class on the two scheduled days, I check their notes and they are expected to use them as we work on more difficult problems together and in groups.

    In addition, I offer online tutoring using Elluminate where students come for additional help once a week on a day when they work from home.

    Students have different roles in the class - experts: who understand and lead learning teams, scribes: who collaborate with one another and me to write additional notes that are posted on my class website, timekeeper: who let me know when time is running short for a specific activity, and List keeper: who keeps track of topics/questions that I'll address either online or on another day.

    My class website is a Google site and I use Google apps extensively. I've created quick checks using Google forms as well other online quizzes that my students take on their own.

    Recently, I created a Facebook page for my class. My hope is that I'll be able to quickly and easily communicate with my students. They are more apt to check FB instead of e-mail. I use e-mail to communicate with their parents.

    I have other aspects of my class that I am working on, but I've been very pleased with taking the lecture out of the classroom.

    You are welcome to look at my class website: https://sites.google.com/a/juliancharterschool.org/mrs-mckay-s-algebra-i/

  14. Have you looked at the work by the National Center for Academic Transformation. Here is what Carol Twigg said about teaching math using a blended model. "In mathematics, the Emporium Model has consistently produced spectacular gains in student learning and impressive reductions in instructional costs. The Universities of Alabama and Idaho, LSU, Ole Miss, the University of Missouri-St. Louis, Virginia Tech and Wayne State have all replaced class meetings with a learning resource center that features student use of instructional software supported by on-demand personalized assistance. We more or less assumed that subsequent new projects in mathematics would want to emulate this success. Boy, were we wrong!" http://thencat.org/RedMathematics.htm

    I have posted about his on my blog. I am a school board director and am advocating that our school district move toward this method of math instruction. It has shown good results in secondary education also.

  15. 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 http://grou.ps/bentongeometry/talks/c455959 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!

  16. @Mr. Knight - thanks for your thoughts, I really appreciate it.

    (Sorry, for some reason your comment got tagged as spam and I didn't notice it for a few days, so I just now published your comment.)