Making mistakes causes your brain to grow.
I am moving the blog portion to http://noblemath.net. I will slowly move some of the content over. I just felt that things were getting too messy and I wanted a better blog name than “MrMathTutor.”
Here is my first attempt at creating an Explore-Flip-Apply type lesson. These are basically all in draft form. I would like to be able to do this EVERY DAY. Not 100% sure that is going to happen. So far, I have created the first unit, which consist of about 5-6 lessons on solving equations. Any feedback would be greatly appreciated. I plan on posting 1 lesson per day for the next few days while I work on Unit 2 (graphing). I have tried to source pages that inspired me.
Class: Elementary Algebra
Class Time: 55 min, 3 days a week for 15 weeks
Topic: Order of operations, exponents, & the distributive property
- Negative Numbers Squared: http://mathforum.org/library/drmath/view/61633.html
- Order of Operations is (morally) Wrong: http://www.youtube.com/watch?v=y9h1oqv21Vs&sns=em
- PEMDAS vs GEMS:
Comments: I struggled with this one. Sometimes when the concepts are very simple, I am tempted to just TELL THEM. But I know from experience that they always mess up the order of operations. So I want them to realize that we need to have some sort of order, else we get different answers. I want them to see how this relates to evaluating polynomials (degree > 1). I want to point out the tricky problems that are actually just poorly worded problems (e.g. Evaluate 5÷xy for x = 2, y = 3). No self-respecting mathematician would every write something like this due to the ambiguity it presents. I decided against providing a broader application context. I did not want to obfuscate the simplicty of how we combine terms mathematically.
With regard to the distributive property, I am trying the “Area of a rectangle approach for the first time. I am including “Extension problems” for some of the lessons. This is for groups who finish early. I try to show where this topic is used later in this course. NCTM Illuminations has a lesson on this that extends to factoring that might help. Factoring is the last unit of the term and I may consider going in this direction later.
I have tried to link these to my Google Drive. I have the comments function open if you want to comment directly on the document, feel free. You may, of course, leave comments below.
I find that I kind of cave on the “Flip” part of the lesson. I bassically digress back to direct (Khan-like) instruction. This is the longest video in the first unit. Most are under 20 min. I have embedded a quiz (using Camtasia Studio 8). When I do this, I get a report sent to me about how they did and how much of the video they viewed.
Here is my initial model as I go through the process of reorienting my class to inquiry-based learning. I am sure there are some flaws. Each topic will begin with Explore. This should take 20-30 mins. Some Explore lessons may be significantly shorter. The intent of the explore is to spark a student’s curiosity. Some recent research suggests that students should do an in-class activity before watching the out-of-class video. Showing the mechanics (e.g. solving a linear inequality) is pushed outside of class (i.e. the Flip). These will most likely be a short (<20 min) video that gives some standard (direct) instruction. Currently I use Camtasia Studio 8.1 to do this and a Dell Latitude XT2, which is perilously close to burning out.
When students return to class, they will begin the Apply phase. Now that they have been given some of the tools, we will either finish the “Explore” problem we worked on previously (maybe a 3-Act problem) or they could just apply their skills at solving some problems (anything wrong with that?). Most all of the in-class time will be spent in groups (or at least pairs).
We use a Pearson online product (MyMathLab) as an LMS and for them to do “homework.” My current strategy to implement this is to have optional homework problems for them to practice. I will also have a very short online quiz (3-6 questions) in which they will get multiple attempts.
I will post some initial iterations for the first unit (Linear equations, Inequalities, & Problem Solving) later this week. I still have not nailed down everything. Any feedback would be greatly appreciated.
While I have been doing the “traditional” flip since 2006, I am exploring ways to improve it. I am going to attempt to keep a record here of my journey, including sources of inspiration, any support research, and even some sample lessons. Dan Meyer and Ramsey Musallam are two educators who are are on bleeding edge of technology and pedagogy, yet from slightly different camps. Dan Meyer, the rock star of high school math teachers who is now finishing his doctorate at Stanford in Math Ed, has an amazingly active blog. His 3 Act math lessons, which are growing in number weekly, seem like the new standard in teaching math. Act 1 is the hook. Something to get them interested. Perhaps its a video of someone stacking a bunch of pennies in large pyramid, or maybe it is a video of someone filling a tank with water. The teacher then probes the students to find out if they have any questions they want resolved (e.g. how much money is the pyramid worth, or how long will it take to fill up the tank). The teacher can then probe a bit to get some buy in from the students. Ask students to give a maximum and a minimum: What is the most amount of money you think there is in this pyramid? What is the least? How much do you *think* is there? Even students who are timid with mathematical calculations have some sense of this. Act 2 is where the teacher gives the students the tools to solve the problem. However, unlike the text book, the teacher asks the students what they need to solve the problem. They might want to know the dimensions of the square base of the pyramid. They would want to know the flow rate of water being poured into the tank. Only then does the teacher furnish them with the tools. Act 3 is the resolution. Hopefully this has been figured out in class and students are wanting to know if they are correct.
Ramsey is a high school chemestry teacher who has been flipping his class for a number of years, but most recently has transformed a traditional flip (just placing the lectures you would have done in class online and having those done as homework, then working what would have been done at home during class) into a type of pedagogy where the simple word “flip” does not do it justice. His method, while certainly not new, comes in a nice package: Explore-Flip-Apply. So, rather than the students’ first exposure to the material coming outside of class as a full 20-30 minute video lecture (which is what I did), the teacher first has students explore some topic. They explore this topic without any new knowledge–only prior experience. Most, if not all, students should struggle with this part–this is a good thing. The teacher should not give away too much here. There is an intentional withholding of information.
My plan is to (somehow!) blend these two paradigms–Meyer’s 3 Act and Musallam’s Explore-Flip-Apply–into an algebra class here at MTSU. Meyer has stated that the 3-Act approach and the flipped approach are mutually exclusive. Perhaps with the hybridization of these two, I can make it work.
I have been reading through Presentation Zen by Presentation Guru Garr Reynolds. I plan on making many changes to how I communicate my ideas, specifically on the flipped classroom. Base on some of the suggestons from Zen and others, here is what I hope to do:
1. While I am still (reluctantly) going to use PowerPoint, 95% of the text is going to be omitted and/or replaced with images (not cheesy clipart if it can be avoided). (Seth Goden recommends no more than 6 words per slide-Ever.) Much of this has revolves around the cognitive load principles. Sweller is the researcher credited with initiating much of this.
2. I am going to try to invoke my storytelling abilities rather than presenting a checklist of the process.
That’s it for now. I will post BEFORE and AFTER samples after it is done.