John T. Sieben Texas Lutheran University Creating and using videos in support of modeling in differential equations course work John T. Sieben Texas Lutheran University

Video + Class ? Often the first thing people think of is Video + Class= Flipped

March 2014 Creating Videos using iPad and PC Reza Abbasian John T. Sieben Texas Lutheran University, Seguin, TX

Four Important Bullets You may not need to make the video. You might want to spend your energy creating for your students a viewing sequence of the best of the thousands of video lessons that are already available on the web. http://www.learnerstv.com/Free-Maths-video-lecture-courses.htm Making a video is easy. That said, you will get better with practice. Don’t forget the in class projects. Exercises from the book will probably not be sufficient.

Salman Khan The Khan Academy

A video from Sal Khan

Steps (the C, R, P s) Create a story board Create a script Rehearse Record Review Rework Redo Produce (render) Publish

Making an instructional video Keep it short Script the video To keep concise To organize your thoughts To be sure you have necessary materials No need for a personal appearance, stay out of it Use your handwriting, don’t type. This is a tutorial model, not a lecture model

SmoothDraw3.2.11

Camtasia Recorder Resolution is set in Windows Control Panel Recording Area (Dimensions) are set within Camtasia Recommended Resolution 1024 x 786 Recommended Dimension no larger than 800 x 600 BUT, you can record with larger Dimension and save smaller The reverse doesn’t work well (shrink, don’t stretch)

But there are other ways videos can be a great aid to teaching and motivating students of differential equations If we are to model using differential equations we must first convey the model

How do you convey the model? Words A simple pendulum is defined as an object that has a small mass, also known as the pendulum bob, which is suspended from a wire or string of negligible mass. When displaced, a pendulum will oscillate around its equilibrium point due to momentum in balance with the restoring force of gravity.

A picture is worth 10 3 words

A video is worth 24 pictures per second

Many interesting experiments are difficult for faculty and students to set up and run in a classroom or a residence hall living space. Torricelli’s Law is a good example. The setup involves containers, flowing waters, timers, etc. This would be messy for a classroom or bedroom.

A video can solve the problems of difficult setup, expensive or unavailable equipment, and people with multiple thumbs on each hand, etc.

With usual assumptions my students solved a Differential Equation that described the water level at time t. 𝑑𝑉 𝑑𝑡 =−𝑘 𝑦 𝑑𝑉 𝑑𝑦 =𝐴 𝑑𝑉 𝑑𝑡 = 𝑑𝑉 𝑑𝑦 ∗ 𝑑𝑦 𝑑𝑡 =A* 𝑑𝑦 𝑑𝑡 𝐴∗ 𝑑𝑦 𝑑𝑡 = −𝑘 𝑦 𝑦 𝑡 = (− 𝑘 2𝐴 𝑡+ 𝑦 0 ) 2

Then they collected data from this video

Finally they compared their observations and predictions.

Look at us, we solve real problems! Comparing their particular solution to their observations adds an element of reality to the class Look at us, we solve real problems!

Recent Tools

This was done in July 2015 at a SIMIODE workshop in Montana

Action in a VIDEO

Another Example With video

And using Video Physics we collected data on two springs from a video

These are but a few of the opportunities to enhance modeling with differential equations using video. There are many other products and applications that can be found on the Internet I am confident you will discover more applications on your own

Thank you for allowing me to share these thoughts with you John T. Sieben Texas Lutheran University Seguin TX