 Hello and welcome. I'm Robert Talbert of the Mathematics Department at Grand Valley State University, and this video is going to discuss what I hope is a reasonably detailed and complete description of the conception, construction, and use of a lesson for a university math class that uses flip learning design. The purpose of this video is to give instructors who are thinking about investing in flip learning an example of flip learning design from the beginning conception all the way up through deployment in the classroom. I hope that experienced flip learning instructors can also find this example useful as well. So the lesson I'm going to describe here is for a basic introductory calculus one class in which students are learning the limit definition of the derivative function. Now at Grand Valley State we use the textbook Active Calculus by Matt Balkans and other members of our math department. This is a free PDF download at the link that you are currently seeing on your screen. So download it and follow along if you like. To map this into other popular textbooks this would be section 2.8 in the Stuart Early Transcendental's book and section 2.3 in the Hughes-Hallit book. For more context, GVSU is a 26,000 student public university in Michigan in the United States with most of our students coming from the state of Michigan and a large plurality of them being first generation college students. We offer between 10 and 15 sections of calculus each semester at each at around 30 students and mostly these are students in the STEM disciplines with a strong portion of those being engineering majors. Our calculus course is four credits and classes usually meet four times a week for 50 minutes or twice a week for 100 minutes. Additionally, we are currently piloting a fully online 12 week version of this course that has no synchronous meetings at all. So the overall design process in constructing this lesson consists of seven steps. I'm not going to step through those one at a time. Step one of the design process is arriving at learning objectives for the unit or section that I'm going to teach. In forming this list of learning objectives I'm answering the question what would constitute acceptable evidence that a student has mastered this material? I'm going to answer that question by going through the section itself and identifying key tasks that students should be able to perform with fluency if in my professional judgment they truly have mastered the material. The section in this example is chapter one section four of the active calculus book. When I studied this section carefully I came up with these learning objectives. Now again I got these just by going through the section in the book carefully and identifying the key concepts and the tasks that are involved with them and by writing them down in order of appearance. Now it's important when writing learning objectives to use concrete action verbs like state and compute rather than something like understand which refers more to an internal state than a concrete action and this is because eventually I'm going to need students to provide the evidence of mastery that I'm seeking and they can only do that if given a concrete task. So that's step one. Step two in the design process is to take that list of learning objectives I just made and put the tasks in order of increasing cognitive difficulty from the least difficult all the way up to the most difficult. Now sometimes possibly most of the time when you're listing the learning objectives from a section of a textbook in order of appearance they will also be in order of difficulty because textbooks tend to go from the simplest ideas to the most advanced but that's not always the case. Some remixing may be needed. A handy tool for doing this kind of remixing if it's necessary is Bloom's Taxonomy. This is a hierarchy of cognitive tasks that has been around in the research literature for quite a while. You might have seen this pyramid picture before. What it depicts is a structure of cognitive tasks with the simplest ones at the bottom like remembering and understanding and increasing in complexity as you go up the pyramid all the way up to the top levels. Now I can take a list of learning objectives and then sort it using Bloom's Taxonomy as a filter. For example if I have learning objectives that involve stating definitions which could be a very important learning objective for your lesson those would go at the bottom of the pyramid. Objectives involving applications would go higher and then those involving judgments and analysis even higher. So the learning objectives from section 1.4 in the active calculus book I think are actually in the correct order in terms of complexity but again this need not be the case for other units and some so some reordering might be necessary. So at this point what I have after steps one and two is a list of learning objectives that appears in order of increasing difficulty. Now what happens next is very important. As you know flip learning is predicated on the idea that the learning activities typically done in class are now done before class and then the resulting class time is used on harder more complex more creative activities that are best done in groups. So while it may be tempting at this phase to start figuring out what students need to do before class to get ready for class, step three of the design process is actually to look ahead into what activity I want students to be doing in class. In class we're going to focus on the hardest and most challenging tasks and concepts of the unit being covered. Now in my own professional judgment the hardest concepts from this unit are two things. First of all they're sketching the graph of the derivative given the original function. Historically I just know that students have a hard time with us and then secondly using the limit definition of the derivative to calculate a derivative formula especially with a view toward getting all the notational syntax correct throughout the computation and then using the definition on functions and aren't just second-degree polynomials. So these two ideas are not exactly earth-shatteringly creative applications but for beginning students in the opening weeks of an introductory course on calculus these two ideas constitute a big stretch from this purely computational world that most of them have lived in during previous math courses. So what I have in mind for our in-class work is a couple of problems. One of them will be a problem in which students work in small groups and are given a randomly selected functions graph and they're supposed to draw a graph of the derivative to scale and then explain to the entire class or at least do their group mates why their graph has the features that it does. The second problem will be a computational problem where they are supposed to work out the derivative formula for some non-standard kind of function like a cubic or a square root or a reciprocal or maybe all three of those. Those two problems the graphing problem and the harder computational problem and their debriefing will easily take up 35 minutes if not more in my experience. So I'm not going to flush out the details of this in-class exercise just yet all I want and what I have now is a basic high-level idea of what I'm going to do that I can flush out later. Now we're moving on to step four the design process. Having gotten an ordered list of learning objectives and having roughed out the main idea for what we're going to do in class I'm going to go back to my learning objective list and split it into two parts the objectives that I want students to master before class and the objectives that students will master during and after class. So what I'm going to do here physically is draw a line that separates the learning objectives for pre-class focus away from the learning objectives for in and post-class focus. I'll call the first group the basic learning objectives and the second group the advanced learning objectives. I'm doing this for two reasons. First of all this lightens the cognitive load for students. I made the mistake early on of giving the entire list of learning objectives to students as part of their pre-class work and they understandably took this to me that they were expected to master all of the learning objectives for the unit before coming to class. Now this was super stressful for students and it's not at all what I intended so I learned that by specifying that they're only expected to attain some of the most basic learning objectives before class and then the other stuff will be addressed during and after class. It made them much more comfortable and open to doing the work that I asked them to do and it's also closer to what I meant. Secondly this list of advanced learning objectives serves as an agenda for your class meeting. If students know that the class meeting is going to be used for addressing those advanced objectives and nowhere else for those advanced objectives be met they are a lot more likely to come and participate knowing that they'll be on their own if they don't. It also helps students to have a reference point for why they are doing the activities that they're going to do in class because those activities map clearly back to specific learning objectives. So now we have a double list of learning objectives and a rough idea for an in-class activity. Step five of the design process is to go back and just finish the in-class activity. Now it's important to remember that the most important part of a flipped lesson is what happens during group meetings not what happens before group meetings so that's why we're going to focus on that here. Now the way I designed our class meeting which again I'm assuming a 50-minute class meeting I broke up that time and devoted the first five say to eight minutes of class to open question and answer time. Just open Q&A time on anything from their pre-class work that they have a question about. I'll describe how that particular slice of time is structured in just a few more minutes. I reserve the last two minutes of class for wrapping up usually in the form of some kind of metacognitive activity like a one-minute paper which of course takes two minutes in real life. That leaves something like 40 minutes in the middle of the class for those two activities that I talked about earlier. Now I could definitely see 10 minutes for students to actually work on each of those two activities the graphing activity and the computation activity with five to seven minutes sandwiched at the end of each of those for discussion. So I won't go into the mechanics of designing the in-class activity itself because this is not necessarily anything specific to the flipped classroom but rather I'll just show the finished product here for the most recent instance of the class that I taught. Again realize that the idea in class is to focus on the biggest and most complicated ideas and the most difficult concepts of the unit while we are all together in a class that can help each other out. Now we're down to step six of the seven step process where we're going to design the pre-class activity. Now we waited this long to get to the pre-class activity because the main purpose for the pre-class activity is to get students ready to engage productively with the in-class activity. The pre-class serves the in-class and not vice versa. Now the model that I've been using for several years is something that I call guided practice. Each guided practice is a pre-class assignment that is designed as follows. As I talk about these different elements of the design of guided practice I'll be showing you on screen the actual assignment that students received. First of all in a guided practice assignment I'm going to write down for students just a little overview of the content that's in the unit they're going to learn explaining in simple terms what we're going to be learning why it's important and how it relates both to what they've already learned and what they will be learning. Second I'm going to give students that list of learning objectives that I made up earlier. With that list of objectives in front of them students will have a clear sense of what they're expected to know how to do and when they should know it. The list provides a target and a key element of flip learning is that students are responsible at this pre-class stage for determining how well they're hitting the target. Third in the guided practice I'm going to provide students with a set of resources that will help them attain those basic learning objectives. Now you might have been wondering where the video content was this entire time as we've been talking about flip learning. A lot of times when flip learning is discussed the focus somehow stays on the videos and how to make the videos and where they should be posted and so on but in fact video content is not really even necessary for flip learning. You just need to ask what primary sources will help students get up to speed with the basic learning objectives. For my students this worked out best to have a relatively small but diverse list of resources for learning. I usually assign a reading from the active calculus book and then we have a YouTube playlist of videos that we made in the department to go along with the book and I usually assign some of those but I also stress to students that these are just recommended resources not required resources and they can use them as little or as much as they want or use alternative resources or no resources at all if they're already familiar with the material. We don't track students to make sure they watch the video or read the book and we never will. All we care about is whether they master the basic learning objectives. The consumption of reading and viewing material is not the same thing as mastering learning objectives it's not always even a necessary condition for mastering them. So the resources are there to serve the students not the other way around and we found it's much more important to give students choice in how they wish to learn about those learning objectives rather than to force something upon them. Fourth in the guided practice having listed those learning objectives out and given resources for learning we're going to give students some simple exercises that will help them practice and learn those objectives. The active calculus textbook has many of these exercises written in. This time I decided to make my own as you can see one of them is review it's just computing f prime of three using the limit definition and that was actually covered in the previous section. In the subsequent exercises I'm trying to engage the students in a little computational thinking by decomposing this problem of finding a formula for the derivative into a process of finding a bunch of derivatives at specific points then looking for a pattern in the derivative results and then making an abstraction. This addresses the first two basic learning objectives that students are expected to attain. For the third learning objective about identifying derivatives from a list I made up a geogiber applet where students are supposed to examine several candidates for the derivative of a function and guess which one is right and then explain why. So students work on these exercises and then enter their responses into a google form that I have set up here. Now the way google forms work is that they take students responses and dump them into a google spreadsheet. Students are supposed to turn their work in no later than one hour before class time and prior to class I look through the spreadsheet of their responses and I look for patterns particularly misconceptions or large-scale wrong answers and if anything seems noteworthy I'll make it an agenda item that we need to address during that first five to eight minutes of class if there's no other questions. Before I move on here just a couple of notes about time expectations and about grading these guided practice assignments. We expect students to be spending two to three hours outside of class for every one hour of class meeting time and that is the timeframe we have for these guided practice assignments. We're pretty vigilant about keeping the running time of the videos down to about 30 minutes or less total so as not to create the class and a half syndrome. In this instance the running time is only about 15 minutes total. Now I estimate that a reasonably close reading of section 1.4 in the book might take 45 minutes to an hour then maybe one hour additionally is needed to complete the exercises. So that adds up to about two hours spent on guided practice. Possibly the time required is going to be a whole lot less than this. In practice when I've asked my students about their own preparation habits with guided practices they'll tell me that they don't always read the entire reading from the book just parts of it and then go through and selectively watch the videos to bolster those parts that gave them trouble and that's perfectly okay. Anyway the expectation is that each guided practice assignment should take no more than two hours to complete and again usually it's a lot less than that and if not if it consistently takes longer than this then students are instructed to get help and they're held responsible for getting the help that they need. Grading wise I grade these assignments on a pass-fail basis with a pass meaning that the student has made a good faith effort to give a correct and complete response to each item. Actual mathematical correctness is not factored into the grade here. We don't want to hold an expectation that students will get everything right when learning things for the first time because that's unreasonable and it causes undue pressure on the student. This also means that students might show up to class not actually having mastered the basic learning objectives but in practice we found that students will do better in the long run when they are not under the pressure of getting everything right upon first contact and they're going to use that five to eight minutes at the beginning of class to great effect in getting their misconceptions fixed when they know that they have a question coming in. By and large almost every student has the basic objectives mastered by at least the time they finished the class meeting if not earlier. Now because the guide to practice is simple structured and it's welcoming of initial failures literally the only way to fail this is to leave things blank or put in a response like I don't know or something else that indicates incomplete effort. We have had no systematic problems getting students to complete these things on average the completion rates for guided practice are usually in the high 90% range and most of the time students are acquiring the basic objectives perfectly well through their independent work. So that's how the learning objectives in class activities and pre-class activities are put together and how they connect with each other. Now we're down to the final step step seven in the design process and that's thinking about what students will do after the class meeting is over. Post-class activities can look like a lot of different things. Some post-class activities might be homework that further solidifies the lower level skills like computation for example in our calculus classes at GVSU we assign online homework that gives students practice on rote computation. Sometimes we do this in class which is possible with a flipped structure but primarily it's done outside of class or as a post-class activity you could address some of the highest level cognitive tasks in your unit that you may not have time for during class or which need further development than you have time for in class things like a project an extended application problem or even a proof assignment. These kinds of assignments are dependent on context and you might choose to give none of these or a combination of these. Anyway they are not particular to flipped learning but in a flipped learning design class the in-class meeting is so heavily and intentionally focused on higher level cognitive skills that students should be well positioned to work on further problems post-class once their own in-class experience is done. So let me end here by giving a quick recap of the seven steps that we've discussed in flipped learning design. Step one is to come up with a list of learning objectives in order of appearance of the unit that you're going to teach. Step two is to then remix or reorder those learning objectives to put them in increasing order of cognitive complexity perhaps using Bloom's taxonomy as a filter. Step three is to then look ahead and do a rough design of the in-class activity you want that's going to address the most advanced ideas of your unit. Step four is then to jump back and split the list of learning objectives into basic and advanced basic being the objectives you want students to master prior to class and advanced being the objectives that you want to address in class. Fifth is to then go and do a detailed design of the in-class activity that you have in mind. Step six is to then jump back again and do a design and construction of the pre-class activity possibly using guided practice as a model or possibly doing one of your own design. And then seventh and finally is to jump way ahead and think about the design of your post-class activity if indeed you want to have any post-class activities. Let me end here by addressing what I haven't discussed in this video. I haven't talked about the human element of the course such as getting buy-in from students getting students to be happy and productive or handling classroom management situations and I also haven't talked much about technology. I've done so in the interest of keeping a very long video as brief as possible here but in a moment I'll be putting up my contact information and you are very welcome to contact me with any questions you have about these or other items. So I hope this example of a flip design of a unit has been helpful. There are probably lots of improvements that can be made here in this workflow and my way doesn't necessarily fit your classes. So take it with a grain of salt but I hope that it's useful and it generates good thoughts about flip learning design as you seek to apply it to your own students. Thanks for watching.