They love using it, and I get immediate feedback on how many students understand what we’re learning, and how many need some extra practice. It works with smartphones as well as laptops.

1. Less time at home spent doing problems (they only need to watch a 6 – 15 minute screencast)

2. I’m available to answer questions while students work on an assignment.

3. Class time is freed up for more hands-on activities that are more memorable than plowing through worksheets.

4. Students can work at their own pace – some of them are two to three days ahead of the course syllabus.

5. All of my lectures are archived for use when it is time to review for exams.

My tentative steps into this teaching method last year were so successful that I began this year’s Honors Precalculus course with 100% flipped classes. After one semester, I asked my students for feedback. Here are the initial responses:

   I really like it because it gives us the opportunity to work through problems as a group, and ask for help if needed. Its way more time efficient to be able to ask a question right when we have it, instead of having to wait a day or two. The screencasts are also nice because if you didn’t understand something the first time, you can always rewind it.

   I really like it because it gives us the chance to try to learn the material on our own and then come in with any questions.  Also, I have the most questions when I’m working problems as opposed to taking the notes, so its helpful to be in class when these questions come up. Thanks!

   Here is my opinion:
Though it took some getting used to, I like the “flipped” classroom style. It is a lot easier to do homework in class because the teacher is right there to answer questions. It is also nice learning at home because students learn at different paces, and I can pause the teacher whenever I need to process something without bothering other people in the class. I am not a huge fan of the online homework because I prefer to use books and think it is easier to work out math when everything is written down. However, it is very helpful having the answers easily available and being able to redo the homework multiple times for practice before a test.

   I have loved the flipped classroom idea. It allows me to get ahead when I know I am going to have a busy night of homework. It also allows for me to be able to pause and rewatch a certain concept I may not understand clearly the first time. Then if I am still struggling after rewatching a few times, I am able to come to class with my questions already prepared.

Hope this is helpful. See you in class.

   I think that the “flipped” classroom learning technique allows for students, especially girls, to individually manage their time when taking notes and understanding the material. This is extremely helpful because not all students learn at the same pace, and this technique allows for them to each cover the same material but in their own way. I have also found that if after the lesson, I still do not understand the material, at least I already have information in my notebook to refer to when I go in to ask questions. It is very useful!

   I’ve really liked the flipped classroom technique.  I’ve had so much less homework and it’s been much more efficient.  The only drawback would be that we fly through the chapters pretty quickly and sometimes I feel like I don’t get to really absorb the material until I try to cram for the test.

   I like and dislike aspects of the reverse classroom technique, but one thing I didn’t like was the fact that if some girls worked ahead it made the rest of us rushed because there was no need to cover the material and less time to answer or ask questions. I do like how we can work on our homework in class and how you come around checking on each of us. I am also not a huge fan of the screen casts. Because they can’t be too long, sometimes I have a hard time understanding certain concepts. But with the reversed classroom, this problem basically fixes itself because even if we are confused from the screen cast, we can come in to ask questions while we are working.

   I really enjoy the flipped class technique.  It allows us to be exposed to the material/learn the material before we come in for class. This gives us the time to more in depth questions and begin our homework while you are still there to help us.

   Having “reverse classes” is like always having a teacher present! When we watch Mr. Wert’s screencasts at home we can take notes and write down questions. Then when we get to class we have both the opportunity to ask questions on the note-taking and broader part of a topic. Also, we then get to really dive in and be able to take risks and explore mathematics when working on homework because of the confidence we are given with having a teacher always available during class. The chance to do homework in class is very relieving and reduces the stress of tough homework (which discourages many from trying again). Instead of giving up on a seemingly-impossible problem, I can work extremely hard and collaborate with other classmates (because they are siting right beside me in class) because I know that Mr. Wert is available to help us out along the way. It is also positively helping our solving skills, because unlike normal class where the answer to a homework problem is just given the next day in class; because Mr. Wert is available he can give us little hints and advice as we are working the problem out. I feel more accomplished and educated when a teacher can help me along instead of giving me the correct answer and look at my work in retrospect. Also because of experience I know sometimes I ask, “what was I thinking when I did this homework?” Now when I am at home alone I can just write down something that is directly given to me and challenge myself during school amongst others so I will never get lost in a problem I am doing and will not have to ask the dreadful question of, “Where was I going with this?” Having witnesses and almost 16 times the help in a class like mine makes all the difference. I love reverse classes.

   I like the flipped math system because it allows me to get ahead on work if I finish my assignments early. I also concentrate better when reading notes in the comfort of my home, so I enjoy that feature very much. Having all of the notes via screencasts is also great  when studying for tests, just in case I forget to write a certain point or if I wanted to re-do an example problem.

By having our lectures on a screencast, I get to set the pace of how fast or slow I want to take my notes. Also, if there is something I don’t understand, I can watch it multiple times. While studying for tests, I am able to re-watch lectures at my disposal instead of having to guess what I wrote (or left out) in my notes.

 

I also like doing the practice problems and homework in class because I am able to ask questions on the spot instead of having to wait till the next day to understand a problem.

So what can we conclude from these positive responses? I think online tools have become easy enough to use, and accessible enough for students, that almost all teaching and learning should have an online component. Beginning next year, ALL of my courses will be taught using the reverse classroom technique.

See? That wasn’t so scary, was it? Now watch my latest screencast to learn more about these misunderstand numbers.

Julia sets were first calculated by the French mathematician Gaston Julia. They are the result of iterating the the function f(z) = z^2 + c, where c is a complex number. Depending on the value of c, the iterations lead to “prisoner points” that stay close to the origin, “escaping points” that increase to infinity, or points that lie on a boundary between the prisoners and the escapees. The points on the boundary are the Julia Set. Until the advent of modern computers, we were unable to calculate Julia Sets with much accuracy. Now, however, we are able to see them in a matter of seconds.

Here’s my explanation of this very useful law:

I haven’t had a chance to really explore all of FluidMath’s features, but I am so excited about it, I wanted to share a screencast showing some of the basic things it can do. It’s really amazing!