A Tale of Two Classes (and Two Choices)

Soon after our face-to-face COETAIL session for Course 3 I had the opportunity to learn a very cool movie-making software called Corel Video Studio.  This seemed serendipitous since one option for our project for course 3 involved creating a visual media presentation for the classroom.  With great energy and enthusiasm and armed with my new skills, I began to collect photos and video clips to use in my presentation.  However, as the project began to take shape, I paused and reflected … hmmm … Should I create this project, or should I take option 2 and instead of creating a presentation myself assign my classes to create a presentation?  Choices, choices!

Often we talk about the contrasts between digital natives and digital immigrants, and the imaginative and technologically creative talents of the natives.  So I made my choice!  I am going to learn from the natives!  The plan is to glean new ideas from my students while allowing them to review for their IB and AP exams through their presentations.  However, to make this a valuable learning tool for me as well as for them, I hope to include a post in our next course where I have enhanced my own presentation with the skills learned through observing my student’s process.

But now to make it interesting …  I have an AP Calculus AB class taking their final external exam in two weeks and an IB Higher Level Math class taking their final at the same time.  Do I want them both to do the presentation in the same way with the same set of instructions?  This was a tougher decision.  In the end I decided to use vastly different approaches so I could compare the results.

My IB HL class was given very general instructions.  We broke the topics of the course up and had each person sign up for two topics.  They had to prepare two small presentations: one for each topic.  The only requirement was that for at least one they had to use some form of movie-making software.  To reiterate this, we emphasized that at most one of the presentations could be done using PowerPoint.  The instructions they were given simply told them the goal of the assignment.  They were to create two presentations that would help both them and their classmates review key material for their external exam.  The specifics of what they should include and how they should do it were left open.  Also, of the two presentations they prepared, one of them would be presented in class; the other had to be able to stand alone so peers could go through it and use it for personal review at their leisure.  Both presentations had to be posted on the OLC.

For my AP Calculus class, I am part of a team of three teachers who teach different sections of the same course.  We all set the same review assignment.  For this group, they were given very specific instructions on what their presentation should look like and what it should include.  The rubric was included and each group was assigned class time to present their content.  The document is given below.


You have seen, studied, and excelled at many calculus topics throughout the school year.  Now it’s time to get ready for the final event – the AP Calculus AB Exam on May 4.  As you assume the role of teacher for the day, you will review the major topics and practice problems on the AP Exam. 


  1. Partner up!  
  2. Receive your topic.
  3. Limits, Continuity, and Differentiability (three ways to evaluate limits, when is a function continuous, when is a function differentiable, IVT)
  4. Derivative Rules (power, product, quotient, chain, implicit, trig, inverse trig, exponential, logarithmic, MVT)
  5. Derivative Graphs and Applications (extrema, concavity, EVT, linear motion with derivatives, related rates, optimization)
  6. Approximating Integrals (area, Riemann sums, trap method, average value)
  7. Integration Rules (definite, indefinite, u-sub, Fundamental Theorem)
  8. Integration Applications (net change, linear motion with integrals, area, volume)
  9. Grab Bag (exponential growth and decay, separable differential equations, slope fields)
    1. Develop a 20-25 presentation to highlight your topic using a 10-12 slide PowerPoint or similar program.  You will have two class days in which to plan together.  Remember, you are reviewing, not teaching, your topic.  Choose what to include carefully highlighting what is most important.  Be sure to include the following:
  • Title slide with topic and group members’ names
  • Main ideas, rules, reminders, and memory tricks
  • Meaningful images and examples
  • Accurate information
  • 2+ practice MC AP problems from Sample Tests III and IV with time worked in for the class to solve
  • A clear layout
  • 24+ point font
  • Citations for images and content from outside sources
  • Something to make us smile
  1. Submit your presentation to our shared folder by 7am on April 1.  If you need anything photocopied for your presentation, bring it to class on April 1 as well.
  2. Practice and present.  Speak slowly, clearly, and confidently.  Remember, you are the expert!    


Review Assessments:

  1. Homework from Review Book and past AP problems
  2. Daily Quizzes on previously reviewed topics.  You can drop your lowest two review quizzes.
  3. PowerPoint and Presentation for Test Grade

PowerPoint and Presentation Rubric 

  • Content                                                                                                          _____ /30
    • All main ideas, rules, reminders, and memory tricks covered
    • Meaningful images and examples
    • Accurate information
    • 2+ practice MC AP problems from Sample Tests III and IV with time worked in for the class to solve
    • Citations for images and content from outside sources
    • Something to make us smile


  • Format                                                                                                           _____ / 15
    • Title slide with topic and group members’ names
    • Clear layout
    • 24+ point font
    • Slides are easy to read and understand


  • Delivery and Coordination                                                                        _____ / 15
    • Use a clear and confident voice
    • Speak with your face, not your back, towards the class
    • Summarize material effectively and avoid reading line for line from your slides
    • Interact with other students – ask questions and solicit feedback
    • Show evidence of organization and partner coordination
    • Submit work on-time

      Total:  _____ / 60 

Before I give you my comments on the final products, let me share one presentation from each class.  The first is a project from my IB HL class covering half of the Statistics and Probability topic.  The student chose to use MovieMaker for his stand alone portion.  He also posted it on YouTube.  When he was determining what would be most helpful for his peers to review, he chose to primarily focus on formulas.  Rather than have an audio track where he explained ideas, he chose to use a music track with everything else presented as text.

YouTube Preview Image

The second project is from my AP Calculus AB class covering integration applications.  This partnership chose to present their material in class using a combination of PowerPoint and Prezi.  They opened both documents before class and then just switched between them during their presentation.  Since it is difficult to instruct another person on exactly when and how to switch from one part of the presentation to the other they combined the two sections together using SmartRecorder.  Unfortunately, they began the prezi portion of the presentation on the wrong slide.  This will be posted on the OLC for their classmates to use for review.  Since they are presenting in class, they do not have an audio track either.

TC and DH Applications of Integration

If I was to give this assignment to a class again there are a number of things I would do differently.  Firstly, on the day the assignment is given I would talk about the benefits of images and how we remember information.  I would also spend a few minutes talking about PowerPoints and what makes a PowerPoint presentation effective.  Though the IB presentation above has all the key information, I would recommend that the content be presented with more visual prompts such as the Venn diagram and graphs and that the material be given in more practical terms or at least connected to the IB exam.  For example this may mean that they include some IB style questions which focus on a particular topic.  The AB group had more visuals that they used to their benefit in front of the class, but they needed to make sure each screen was still readable.

When assigning the project I would also try to give them an example of a good project, especially highlighting a project that uses a different mode of presentation (rather than just PowerPoint).  In AB, out of the seven groups only one used Prezi, the rest just did PowerPoints.  In the IB class, I was regularly asked if they had to do a movie and repeatedly explained why they could not just do PowerPoints.  Students are comfortable with PowerPoint and consider it the easy option.  To encourage more creative work, I would change the rubric to include a creativity grade.

Next time I would definitely give more specific instructions and rubrics to both classes.  Though the quality of the IB work was good, it lacked consistency.  One student presented a PowerPoint where the formulas did not have key subscripts, making the information useless.  Before posting it on the OLC, those details needed to be corrected.  The IB class was also less likely to include examples because it was not written up in a rubric.  Also, the value of audio for some topics would be addressed here.

Finaly, I want to try this out again on a topic that they have not been taught.  Preparing an engaging review session is very difficult.  It would be interesting to see how they do when they are coming up with new material.

Despite some of the unexpected pitfalls that were encountered, I believe this was a valuable learning experience for both the students and me.  I will definitely do it again and improve using the lessons learned here. 

I am attaching a third presentation here because the student did a great job at bringing humor to his presentation and thinking through how he could present his concepts in a visual manner.  Unfortunately, there are a few notation errors which influence the effectiveness of this particular presentation as a review tool.   Great creative thought though!

Stanley’s Vectors

Old School Manipulatives and High Tech Tools

A constant issue that arises in discussions with math teachers is whether technology is enhancing the learning environment.  Do students understand concepts in a deeper manner because of the technological tools they are utilizing?  For me, there is one Calculus topic in particular where I feel technology has improved student understanding because of the animated visuals that they can manipulate as they learn.  This topic is calculating volume using integration.

Koala at Australia Zoo by N. Connor

There are three main applications of integration that we cover in our high school Calculus course:  calculating motion in a straight line, determining area (which is 2-dimensional), and finding volume (which is 3- dimensional).  Of these application topics, the one I most enjoy is integrating cross-sectional area to find volume.  We know that if we take the equation of a curve and integrate between two x-values, we get the area under the curve.  And if we then integrate area, we get volume.  Integration allows us to find the volume of shapes beyond the standard geometric shapes which we study in lower and middle school.  Rather than finding the volume of a sphere, a cone, a rectangular prism, or a pyramid, we can now find the volume of a vase, a light bulb, a baseball bat or even a koala.  In fact, we could approximate the equation of any curve and find the volume of almost any shape.  Pretty cool!


Before calculating volume, we look at calculating the area under a curve both by hand and  using a calculator.  Generally students grasp this idea quickly and have little need for any tools other than their calculator or graphing software.  For example, to find the area under the curve y = (0.3x – 1)(0.35x + 2) x between x=-3 and x=4.5 we can use our calculator.  The calculator shades the area being considered and gives students a satisfactory visual representation of what they are finding.

Area under a curve

Area Under a Curve

However, once we move into three dimensions, the regular graphing calculator becomes less effective for visualizing the expected results.  Fortunately, there are many tools on the internet that help students to understand the particular formulas being used for these three dimensional calculations.  For both AP Calculus and IB Calculus, we look at calculating volume using the following approaches: cross-sectional area, the disk method, the washer method and the shell method.  To aid student understanding of the choice of formula to use for each of our different methods, I have some physical models that we examine in class.  However, these physical models used in isolation are not enough.  They can only develop student understanding to a certain point.  For students to really understand the process of calculating volume and the choice of formula for each of our particular methods, animations from the internet become essential.  There are many sites that demonstrate this concept, but the internet sources I have found most useful are the Math Demos Site, the Visual Calculus Site and the animations prepared by Steve Egge.  These are supplemented with the Calculus in Motion resources developed by Audrey Weekes.  Test out some of these sites to get a great visualization of how we calculate volume.

Don’t Make Me Listen to that Song Again!!

Over the past two days, my Algebra 1 classes have been learning the quadratic formula.


The derivation of this formula involves a rather dry process of completing the square.  Though I was not able to figure out a way to turn this portion of the lesson into a digital, visual masterpiece, I did turn to YouTube at the end of the lesson to help students remember this challenging formula.  We looked at four videos.  Of the four, one could be classified as an attempt at digital storytelling.  In this video, the hero is brutally murdered after saving the killer from the stress of dealing with a parabola by applying the quadratic formula.  Betrayal and violence … a true hollywood blockbuster!!

YouTube Preview Image

Another video showed that it is not only Math teachers with no life that post math videos.  This rap performed by Adam and Braley Branson brings out a number of key math topics, including the quadratic formula for determining x-intercepts, the discriminant for determining the number of solutions to a quadratic equation, the idea of symmetry and inverses, and the process for combining rational expressions.

I am not sure that listening to this rap would validate the statement by Patricia Deubel  in “Web 2.0 in Instruction.  Adding Spice to Math Education”  that a “math class would certainly be spiced up with math raps” but at least it is a start.  Though these two videos provide entertainment and valuable mathematical content, I think the final two videos will prove the most effective for actually recalling the quadratic formula.  In these two videos, the quadratic formula is sung to the tune of “Pop Goes the Weasel,” which is one of those tunes that gets stuck in your head … and has the potential to drive you crazy!  The first video has some “geeks” singing.  However, in case students tried to say that they were not good at memorizing or that the formula was too hard, we watched one final version:

YouTube Preview Image

The question is though, was it the visual images connected with the song, or the tune itself that helped students remember the formula?  Regardless of what caught their attention, the YouTube videos served another purpose.  They got students talking about math.  They critiqued the videos I chose, picked their favourite, and talked with their parents about the song.  At the beginning of the next class they were still talking about the songs of the quadratic formula.  Some students even started to write their own song.  It is this interest that is most meaningful.  At the conclusion of our YouTube viewing, it was also entertaining to hear students humming “Pop Goes the Weasel” as they wrote out the quadratic formula in preparation for solving a problem.

Next year rather than simply have students view the work of others, I may have them create their own video to post.  This process of creation will both aid their recall of the formula and hopefully can also be designed to deepen their understanding of the use and derivation of the formula.

The worst part of this … having listened to these songs about the Quadratic Formula in multiple classes over two days, I keep waking up with these songs on my mind!  “x equals negative b plus or minus the square root of b squared minus 4 ac all over 2a!”

Cherry Blossom Paradox

As I sit here in my luxurious Kyoto hotel looking at the deer grazing on the nearby forested hillside dotted with the pink hues of the cherry blossoms, it is hard to believe that 600 kilometers to the north a myriad of people are fearing for their health and safety and a few sacrifice for the benefit of many. It all seems surreal. Yet the graphic images viewed across the globe of the triple disasters to hit Japan on March 11, 2011 are still fresh in my mind. The paradox is hard to reconcile, as are the contrasts between the photos shown in this post that were taken on my recent trip to the YouTube footage from such a short distance away.

YouTube Preview Image
The implications of the devastation in northern Japan will be felt globally for many years to come. The environmental and economic issues will be slowly played out on the world stage while the human implications will primarily be experienced on a personal level, one individual at a time; for some it will be the pain of deteriorating health, for many the grief of losing loved ones, for others the fear resulting from the loss of their feeling of security. For each of us we deal with the reminder of our own mortality and the fragility of life.

YouTube Preview Image 

Beauty in the Cherry Blossoms, Path of Philosophy, Kyoto by N. Connor

As a defense mechanism against the overwhelming emotions associated with these tragedies, let me shift to the subject at hand: visual literacy. Though the ultimate focus of this course is on visual literacy in the classroom today, I want to start by focusing simply on the power of visual media to positively influence our world.

The rapid revelation of unfolding events in Japan was evidence of the power of visual media to disperse information. The images and videos posted on the internet of the effects of the earthquake and the resulting tsunami in Japan brought the situation to a world audience in a graphic and heart-wrenching manner. Through the posted images we felt the buildings shake and watched in horror as the wall of water covered the countryside wiping out everything in its path. Images like this had not been seen before. The wireless coverage in Japan combined with its digital and mobile nature allowed people to capture events on their digital cameras or cell phones and practically simultaneously share them with the world. Images were viewed around the world as they happened from a variety of different perspectives.  This demonstrates what a powerful tool digital media is for the timely dispersal of information. But is that all it can do … share information?


It was as I was sitting in my Kyoto hotel at the end of an exhausting yet exhilarating day of

Fushimi Inari Shrine, Kyoto, Japan by N. Connor

 sight-seeing and cherry blossom viewing that the true power of visual literacy and images was revealed. In a twist of irony, I was reading a newspaper in the old-fashioned paper form when the power of visual media to instigate global and

individual response was seen. In the “World News” section of The Global Edition of the New York Times there was an article by Martin Fackler entitled “From shadow of damaged plant, a cry for help.” The article on the internet has a different title but can be viewed here. The article begins by saying, “It was a desperate plea for help, spoken into a small digital camcorder by the mayor of this seemingly forsaken city, and posted on the Internet like a bottle tossed into a digital sea.” Fackler goes on to describe how the mayor of Minamisoma, Mr. Katsunobu Sakurai, posted a youtube video begging for help as he described the plight of his town, located a mere 25 kilometers from the damaged Fukushima Daiichi Nuclear Power Station.

He spoke from his heart and the world responded. Phone calls and “hundreds of boxes of food and other supplies from individuals, and truckloads of relief goods from non-profit organizations” came flooding in. More important than the actual volume of supplies was the realization by the residents of Minamisoma that though they were locked in their homes, they were not forgotten; the world cares about their plight. Can you imagine any other way that this plea could have been sent out to such an extensive audience in such a short period of time? There was no time for fancy editing of the video or Hollywood-style special effects, just an ordinary man reaching out to the world on behalf of his community. Seeing the face of the mayor as he describes the dire straits of the residents of his town was a far more powerful tool for touching the hearts of others than a written request could ever be. The visual images revealed the human suffering and gave a personal face to the tragedy while also providing people around the world with a practical method of response.
What dramatic proof that images can make a difference. The challenge now is to harness these tools for the benefit of student learning.