Mobile Phone Cameras in Teaching and Learning

My latest “Teaching with Tech” column for MAA Focus just published this week.

Phone Cameras Handle Information in a Snap!

Teaching with Tech: Phone Cameras Handle Information in a Snap!

 

Here are the general topic areas:

  • Carrying a library of “good problems” with you for topics you are teaching.
  • Transfer an application problem to the computer/projector in your classroom.
  • Share your lecture notes from class (from a blackboard, whiteboard, or document camera).
  • Keep notes from a meeting.
  • Make a copy of a handout or meeting agenda.
  • Share student work for discussion about good methods or errors in thinking.
  • Answer emailed questions easily.
  • Tips for Conferences

Phone Cameras Handle Information in a Snap!

Archive of Teaching with Tech Columns

 

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Collecting Learning Notebooks in an Online Course

In a prior post, I discussed how I’m using Learning Notebooks to encourage students to carefully think through the mathematical steps and notation for solving problems.

I promised that I would explain how students complete this assignment in an online course, so today I’ve made a video, Collecting Learning Notebooks in an Online Course to show you the process I’m using inside of Instructure Canvas.  The process should be similar for other Learning Management Systems (though it may not be quite this easy).

Here’s the process.  Students still complete their Learning Notebook exactly how they do in a traditional class. I encourage them to keep a Table of Contents so that they can quickly find their assignments and make sure they are complete. Again, this was discussed in a prior post. The turning in part is a bit different for an online course.

I want to collect ten random problems from the students. So first, I create a Question Bank (or test bank) of 18-20 problems.  The problems look something like this:

Example problem from the Question Bank. [click on image to enlarge

In the actual assignment, I tell the Quiz to pull ten problems at random from the Question Bank.  This is a timed assignment, and I figure that 45 minutes should be plenty of time to take 10 photos or scans and upload them, even on cruddy Internet like mine.

How do students take their photos?

  • Digital cameras
  • Webcams (I required them for this course)
  • Scanners
  • Multi-function printer/scanners
  • Cell phone cameras

How do they get the image to the quiz?  They have to get the image to their computer screen and then use Jing to create a URL for the page they want to share.

Here are a few examples [click on the images to enlarge]:

Handwritten student work shared with a camera.

Handwritten student work scanned and shared with Jing.

Handwritten work shared with a webcam and Jing. (permission granted by student to share photo)

Then I grade the quizzes. Done!

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Learning Notebooks for Online Math Homework

After teaching math at a community college for 10 years (and using online homework for at least 7 of those), I have noticed that my online math students don’t seem to have the same grasp on notation and the steps to “prove” the solution to a problem as when they did old-fashioned paper & pencil homework.  I have also found that the students who use online homework have become much more unorganized, and are unable to find the work for the problems they have questions on.

 

Example of student work in a Learning Notebook

This last year, I’ve been experimenting with what I call a “Learning Notebook” – where students keep an organized notebook of the handwritten work for selected problems from the online homework system. In these Learning Notebooks, the students have to show the steps required to complete the required problems (including all necessary graphs and proper notation).  They don’t have to keep a record of every problem, since some questions can be answered by inspection alone. For the Learning Notebook, I typically choose problems that would require me to show steps in order to complete it with a reasonable confidence in my answer.   The online homework, graded on accuracy, is worth 20 points per unit.  The Learning Notebook, showing sound mathematical thinking and notation for required problems, is worth an equal weight of 20 points.

The student is responsible for keeping the notebook organized, including a Table of Contents and page numbers (these help me to find assignments when I go to grade the notebooks).  While this may seem like busywork, keeping a notebook has several benefits to the student:

  • When studying for an exam, the student can find the work associated with each problem quickly.
  • When there’s a question on a specific problem, the student can quickly find their version of the problem and what they tried.
  • Repetition of the use of proper notation leads to better outcomes on the exams (since they don’t “forget” to include the notation there when they are required to have it in their notebooks).
  • Thoughtful reflection on the problem steps may be more likely when they slow down to write the steps down instead of trying to do too much in their head.
  • Students get points for showing their work, which can act as a slight padding of their grade when the tests are hard (which they inevitably are).
One of the additional benefits of the Learning Notebooks is that it gives me a “place” to collect additional assignments that can’t easily be covered by online homework.  For example:
  • Sketching the graph of a function given a list of properties
  • Explaining the transformations of a graph in multiple steps
  • Proving that a series converges or diverges
  • Explaining all the properties of a rational function

A collection of Learning Notebooks on exam day.

For my traditional classes (that include an in-person meeting) I grade the Learning Notebooks while the students give the exam. I select ten problems at random to check for completion, notation, and supporting steps.  I typically give a 2-hour exam, and I can grade the notebooks for 15-25 students by the end of that time.  This is when it becomes vitally important to me that the students include a Table of Contents and numbered pages.  Without those, I would spend a lot of extra time searching for assignments.  I use a 0-1-2 point scale for each of the ten problems.

  • 0 points = the problem cannot be found, there was only a problem and answer,  or there was no reasonable attempt to solve the problem
  • 1 point = some reasonable attempt to solve the problem, but details missing or problem is incomplete
  • 2 points = problem is completely solved, with all appropriate details included
After I have worked through all 10 problems, I give the student a score out of 20.
To help you understand the process a little better, I asked a few students to let me share their notebooks and the grading process.  They agreed, so here’s a little video explanation of how the process works.

Video: Learning Notebooks for Online Math Homework

Here is a Sample Table of Contents and Sample Notebook Check for the Learning Notebooks.

Because they have to keep a Learning Notebook, students know that they shouldn’t cut corners when they work through problems.  At first, many will try, rushing through the online homework (probably with the aid of calculators and WolframAlpha) with the belief that they will just “take a few minutes to go back and write up the steps.”  For this reason, you shouldn’t be surprised if the grades for the first set of Notebooks are pretty bipolar (half will be great, half will be awful).  It turns out that to actually think through and write the math takes time, time that some of these students have been cutting corners on ever since online homework was first introduced.

I’ve been using these notebooks in Math for Elementary Teachers, College Algebra, Calculus I, and Calculus II over the last year, and have seen an improvement in mathematical thinking, use of notation, and study habits for those students that keep good notebooks.  I don’t have any scientific evidence, but overall, I feel like these Learning Notebooks are helping improve my students’ success.

NOTE: In about a week, I will share how I’m using the same strategy in my online classes.  I want to get all the way through the process of collection once before I write about it.  Hint: It involves webcams and cell phone cameras.

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Custom Stamps for Grading in Adobe Acrobat

Many people have asked me to give a tutorial on creating custom stamps in Adobe Acrobat for paper grading.  There’s no reason why you couldn’t do something similar in other programs by pasting images into files, but there’s no doubt that the ease of one-click access to custom stamps is a nice feature of Adobe Acrobat.

Step One:  Create the content of the Custom Stamp

You can use any program on your computer to create the content: MathType, LaTeX, Wolfram Alpha, Mathematica, Maple, Sage, Word, Journal, etc.  Write the content and try to make it somewhat compact in width (aim for a square or squarish-rectangle rather than a long skinny rectangle).

Step Two: Capture an image of the Content

Use any screen capturing program to capture an image of your content.  You want to use one that has a “snipping” feature so that it’s not a screen capture of the entire screen.  Just capture the content you want in the stamp.  I usually use Jing or SnagIt to do this, although there are certainly many other options.

Step Three (optional): Make a Border

If I am making a longer comment, I like to put a border around my “stamp” content to make it clear that this was something that was added in the grading and not part of the original content of the exam or assignment.  Even free programs like Jing have the ability to add a rectangular “border” box on the image.  Save the file.

Step Four: Create the Custom Stamp

In Adobe Acrobat, open the stamp menu and choose “Create a Custom Stamp.”  Browse to find the image file you’ve created (Adobe defaults to finding PDF files, but you can use the drop-down menu to choose from other file formats).

 

 

You’ll find it helpful to have stamp categories (Limits, Derivatives, Integrals, Exam 2, etc.) to make stamps easy to find.

Step Five: Use the Custom Stamp (over and over and over and over)

At this point, you should be able to use the stamps by choosing them from Comments & Markup Tools –> Custom Stamps.


Once the custom stamp is inserted in a PDF document, it can be resized and moved all over the page.  You can use a custom stamp multiple times in the same document.

And now that notation error that requires you to explain in a lengthy comment is not such a burden to correct anymore.  I use custom stamps to explain the difference between d/dx and dy/dx, to insert missing limit notation, to explain the difference between a derivative and a differential, to explain how to rewrite an improper integral … once you can just stamp the comments, the explanations can be as clear as you want them to be.

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Shifting Assessment in a World with WolframAlpha

I let my students use Wolfram Alpha when they are in class and when they are doing their homework (um, how would I stop them?).  Because of this, I’ve had to shift how I assess on more formal assignments.  For the record, it’s the same adjustment you might make if you were using ANY kind of Computer Algebra System (CAS).

The simplest shift is to stop asking for the answers to problems, and just give the students the answers.  After all, they live in a world where they CAN easily get the answers, so why pretend that it’s the answers that are important?  It’s the mathematical thinking that’s important, right?  Giving the students the answers turns problems into “proofs” where the evaluation (grade) is based on the thought-process to get from start to finish. It also eliminates the debate about whether to award points for a correct answer with no correct process.

Here are two examples of problems from a recent Calculus exam (old and new wording).

I wish I had thought to do this years ago, because students who insist on just doing the “shortcut” (and not learning what limits are all about) now have nothing to show for themselves (the answer, after all, is right THERE).

Again, a student that knows the derivative rules might get the right answer, but the right answer is now worth zero points.  The assessment is now clearly focused on the mathematical thinking using limits.

Another reason that I really like this is that it allows students to find mistakes that they are capable of finding “in the real world” where they can quickly use technology to get an answer.  They are now graded solely on their ability to explain, mathematically, the insides of a mathematical process.

Wolfram Alpha also allows me to pull real-world data into my tests much faster.  Here’s a question about curve shape (the graph is just a copy/paste from W|A):

If you haven’t begun to think about how assessment should change in a world with ubiquitous and free CAS, you should.  You don’t have to change all your problems, but I think some of them should change.  Otherwise, we’re just testing students on the same thing that a computer does, and that doesn’t sit well with me.  If you can be replaced by a computer, you’re likely to be replaced by a computer.  Let’s make sure we’re teaching students how to think mathematically, not how to compute mathematically.

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