Calculus Activity: Determining Instantaneous Speed of Usain Bolt as He Crossed the Finish Line

In order to bring Calculus to life for my students, our AP Calculus team are implementing different labs to get students to apply the actual concepts they learned to  real life situations. One such example was to find the instantaneous speed of Usain Bolt as he crossed the finish line when he beat the world record in Berlin (2009). We had provided students with the video of the race and they were allowed to use other online resources. Below is the instruction of the assignment, quick footage of students working on the lab and a sample of one group’s work that was submitted. 

Assignment Instructions

1. Work in pairs. 

2. Download the video file.

3. Goal is to look at the video in iMovie, using frames, to calculate the instantaneous speed of Usain Bolt as he crosses the finish line by using more and more refined, successive values of delta distance and delta time, with minimum 5 iterations. (eg. 100m, 10m, 5m, 2m, smallest possible)

4. Write up like a lab report, answering following questions.
    a) Objective
    b) Plan of action
    c) Process and Calculations
    d) Conclusion and validity of result
Include screenshot of pictures to help explain your process.

Footage of Students Working on the Assignment

Sample of Student Work

Assessment Tools for Student Created iBooks

I believe iBooks are a great way for students to find creative ways to share their learning, as I have talked about in my blog post My Relationship with iBooks Author. Some teachers would find it hard to implement digital tools for learning as it’s hard to find ways to assess them. Here are some rubrics I have used for assessing students’ iBooks for different tasks.

1. Precalculus Conic Sections    This was my first attempt to use iBook as a student project. This was a once off major project. Below is the instruction sheet given to students and the assessment rubric. We have also taken a class time for peer assessment which I modified the below rubric for simple student use.

Conics iBook Project Instructions

Conics iBook Project Rubric

2. AP Calculus AB Limits Activity    In our AP Calculus classes we had decided to utilise the iBook throughout the year to log the learning that happens with the activities we do in class. Following was done for researching different aspects of the use of limits. Instructions sheets and assessment rubric is given below.   

iBook Limit Activity Instructions

AP Calculus iBook Limits Activity Rubric

3. Calculus Year Long Project    In my Calculus class, I use the iBook for the year long project for Student-Led Project Based Learning (details in my Piloting Student-Led Project Based Learning post). Below is the rubric that I use to assess each of the iBook chapters student submit.

Calculus iBook Chapter Rubric

Feel free to download and use any of these documents as you see fit.

Piloting Student-Led Project Based Learning

I had been a flipped classroom teacher for two years when I had the privilege of being accepted as Apple Distinguished Educator, class of 2013. As I talked about in my previous post, this is where I came across iBooks Author and how it became part of my life.  It is also where I felt like what I was doing with my students was not enough. I wanted to make learning a different experience altogether for my students by making them take more control over their learning process to empower them. It was soon after the ADE Institute that I started thinking about how I could implement a Project Based Learning in my classes. By this stage, all my classes have been flipped, so I was done making all the screencasts, meaning, I could shift my focus from having materials ready for my students, to new way of learning, using the resources which I've already created. After brainstorming with a colleague, I decided to approach my principal to ask permission to pilot it in my Calculus class in the new school year. The reason why I chose the Calculus class was because of the following.
1) It is the only class that I am completely autonomous. I am the only teacher who teaches this class and only one section of it exists.
2) Calculus class, unlike the AP Calculus class, isn’t bound by any external exams and students who take Calculus would need to take Calculus in college again anyway.
3) Calculus class is mainly composed of students who don’t really like math and they take Calculus because they don’t want to take Statistics. So, I thought trying new things would actually be more fun for this group of students.
Thankfully, my principal gave me the green lights to go ahead.

The basic idea was to have an iBook as a year long overarching project where their learning will be logged. Each unit of the course will be a chapter of their book. It will contain the concepts of that unit, their learning activity for the unit and a personal reflection of their learning process. The three basic questions they need to address are : What is it that I need to learn? How am I going to learn it? and How will I show that I have learned it? The book will serve as a digital portfolio of their learning in Calculus.

So, I had to come up with a concrete structure. It all seemed great as an idea, but how would the day to day running of it look like? I was feeling overwhelmed at the thought. It wasn’t until days before school started for the new year, that I sat down to plan out the structure.  I realised the first step was to think about what my gradebook would look like. What did I want to assess? What are the things I valued as a learning process for my students?

Following is an excerpt from my Calculus Syllabus that outlines the structure.

Class Structure and Policy

In this Calculus class, we are implementing Student-Led Project Based Learning. A year long, ongoing project is an iBook of your learning process. Each unit will occupy one chapter of the iBook and that chapter will be assessed at the end of each unit. A clear rubric will be given for the assessment of the iBook. Within each unit, learning teams will form and decide what learning activities they will take on to master the content of each unit. Screencasts of all the lectures will be available for you to view to help with the learning process. You will no longer be given a unit test to demonstrate your understanding of the content, however, quizzes will be given to test your mathematical skills. Following is the breakdown of each assessment component.

Daily work/Activities

• Daily work and activities grade is based on successful completion of the deadlines set by students, individually or in learning teams.
• There will be a pool of points from which one point will be deducted for each missed deadline. A larger deadline for the unit completion will be set by the teacher.
• At the beginning of each unit, learning teams will present a proposal of what learning activities they will take on with mini deadlines they have set to the teacher.
• Same type of learning activities can be used maximum of two times throughout the year.
• For each unit, you must form different learning teams. You may work with the same person maximum two times throughout the year. You may have maximum of three people in each learning team.
• All your daily work and learning activities will be included in your iBook.

Quizzes

• Quizzes will be testing your actual mathematical problem solving skills.
• Quizzes will be given three different times within the unit. You may choose to take it anytime you like and as many of the three times that you like.
• The best scoring quiz will be your final score of the quiz which will be uploaded to Powerschool.

iBook Unit Assessment

• iBook chapter of the unit needs to be completed according to the rubric given.
• Each student will submit their own iBook chapter.
• Each chapter needs to include: introduction of the concepts covered, learning activities you have taken on to learn the concepts, demonstration of understanding that came from the learning activity, and finally a reflection piece of your learning process.
• Due date of the chapter will be given by the teacher and you will be penalized 10% for one calendar day, 20% for two days late, and no credit beyond that.

Class Participation/preparation

• Students are expected to participate in class discussions, oral presentations, group work, and projects.
• The class participation/preparation grade consists of a pool of points from which one point will be deducted from when participation or preparation is not fulfilled.

Final Exam

An exam will be given at the end of the semester which will include the content of all the units covered throughout the semester. It will in a traditional exam format.

Grading: The following components will be used in the evaluation process. Each of these areas is

is compiled to reach a cumulative grade for the semester.

• Class Participation/preparation   : 5%   
• Daily Work/Activities : 15%   
• Quizzes : 25%   
• iBook Assessments : 40%   
• Final Exam : 15%

I stand by the philosophy of each educator needing to find the method and structure that works for them. There is no single recipe that works for everyone. Teacher’s personality, demographic of the student body, dynamics of the classroom all play a part in it. I encourage you to try implementing few different things until you find what works for you.

My Relationship with iBooks Author

I was first exposed to iBooks Author when attended the Apple Distinguished Educator Institute in Bali, March 2013. I spent forever being utterly confused as how the program worked and what was the point of it all. It wasn’t until I started creating my own iBook that I actually saw its full potential as a learning tool. My first class, first day back from the institute, my students were taking a test. Normally I’d be, “woohoo, kids taking tests… quiet time for me to do some work” but not this time. I sat there feeling angry and was thinking what was the point of all this. Yes, my students were taking a test but it hit me that a test was a terrible way of showing their learning. Things needed to change. After spending the day in anger and frustration, I decided to approach my team. You see, because there are multiple teachers teaching the same course, we need to have common assessments. So unless we come to an agreement on our assessment, there was nothing I could do.

My precalculus team were receptive in trying out the iBook as a project for our students. Soon after that, I was able to set up a department iBooks Author training from one of our Ed Tech members (Tim Bray). Students were also very receptive to the project. The product of their efforts were astonishing. Their books could easily be used as a textbook. They demonstrated their understanding of the topic clearly and were able to use a lot of creativity to make the book interesting. After the iBooks were completed, we had a peer assessment class where they viewed and critiqued each other’s books. During that time, I would frequently hear “whoa, that’s so cool!” They blew each other away in the way they presented the topic. The iBooks Author project was a success! Here are few of the statements made by students when I asked them to reflect on the project.

"I personally enjoyed doing the iBooks author because I can create a book of my own using the knowledge I know. Compared to other projects, I was interested in my own project for the first time."

"Wow, what a fun project! The project was fun; I learned to use iBooks author, a new program! I think that my book was very creative, and that a lot of my classmates had very creative and sophisticated projects. The peer assessment was also very beneficial because I got fresh eyes to look at my project. This type of project is beneficial to our learning, and I hope that we do more of these in the future"

"I really enjoyed the ibooks project. It was my first time to write a book and I was surprised how easy it is to write a book because I am not that good with computers."

It was from this that I thought about a year long iBook project as their digital portfolio. My next post will be about how I used this idea to pilot my Student Lead Project Based Learning class.

Below are some screenshots I have taken from various student created iBooks from my classes.