Archive for the ‘Chris’ Reflections’ Category

Quadratics in our Lives


The next time someone says to you…when am I ever going to use this in real life…point them to some of the pictures that my grade 11 students took as they wandered through the school looking for quadratic shapes to model with equations.  They had 15 minutes to go take a picture on their cell phone or iPod and email it to me.  Here’s what we got back:

There’s a great variety of ideas that we can talk about here.  Stretches, domain and range, rotations, axes of symmetry, vertices…not to mention how excited the students were to go out and find parabolas in the school.

Within that same period, I collected the photos in my email and pasted them into a tns file to send out to the students.  Their task was to model some of the images with an equation and state the domain and range that made sense for their model.  Here’s what it looked like on the calculators:

CAS a Moral Imperative?


In thinking about why information visualization is important and useful to students, as well as the ways in which certain technologies enhance the learning of students, I decided to investigate graphing calculator software and online manipulative representations.

My students often struggle to make connections between the graphical, the numerical and the algebraic.  When I ask them to move from one form to another, for some reason they often don’t see that they are at all related.  Perhaps it’s a function of the silos (strands) that we place mathematics curriculum into in elementary years, or perhaps it’s a lack of true understanding of the concepts.  Texas Instruments graphing software allows students to emphasize connections between mathematical concepts (CTL, 2007) by seeing the dynamic changes that take place in all three forms of visualization of the data when you change a parameter in any one of the visualization forms.  Their ability to see what happens when you change the function, or change a y-value in a table of values helps them to make connections and see the bigger picture.  It tells a story about the mathematics that is facilitated by the use of technology.

In the United States in particular, there is hot debate about the use of CAS (Computer Algebra Systems) on standardized testing.  There is an interesting commentary about the connection to standards and practices recognizing that the calculators should not replace student learning (Roschelle and Singleton, 2008), but rather supplement it.  The fear is that students will offload the cognitive load onto the technology and be worse off for it. Zalman Usiskin, director of the University of Chicago School Mathematics Project delivered a thorough and thought provoking lecture on the ethics of CAS in mathematics education.  He suggests that we not only should use CAS in educating our students, but we have somewhat of a moral imperative to do so.  His argument is based on an interpretation of the NEA (National Education Association) Code of Ethics and is rather convincing.  He goes on to argue that restricting our students from certain points of views and learning opportunities is unethical.  As an extension, restricting our students from using and learning through CAS is therefore not an ethical practice according to the NEA.

By using the TI Nspire CAS handhelds and teacher software, I am able to engage my students in learning activities that are both math related, and relevant to their everyday lives.  Using photos from around the school to determine if ramps or stairs are built to code or whether a skateboard park is safe is both engaging and authentic to students.  Those tasks are possible without technology, but far more efficient and powerful when facilitated by the integration of graphing calculators in math class.

These arguments provide me with refreshing support of my pursuits to integrate technology into my teaching practice.  A practice that I will endeavour to continue and grow in as I gain experience in the profession.


Center for Technology in Learning (2007), “Why should a teacher use technology in his or her classroom?” Research Note 8, Menlo Park, CA

Roschelle, J. & Singleton, C. (2008). Graphing Calculators: Enhancing math learning for all students. In J. Voogt & G. Knezek (Eds.) International Handbook of information Technology in Primary and Secondary Education, Springer, 951-959

Usiskin, Z, (2012). The ethics of using computer algebra systems (CAS) in high school mathematics. University of Chicago School Mathematics Project.

A week after Jennifer Wilson


It’s been about a week now since I attended Jennifer Wilson’s presentation on TI Nspire Navigator for Networked Clients.  Jennifer is a teacher from Jackson, Mississippi who uses an old laptop cart in her classroom.  She shared both features and teaching techniques with the group crowded into a make-shift computer lab.


The ability to allow a resubmit on sending out a quick poll.  This is handy as students realize that they had mis-typed or mis-understood the question having read it quickly and trying to respond before their friends.  It’s not a race…it’s a journey.

The ability to blast out any type of document with NC to the student computers…then the ability to collect those documents (even in something as foreign to TI as a Word Document.  What a fantastic feature for expanding the scope of what we use the networked Navigator Stystem for.  The alternative formats were only able to be sent out via the Class Tab.  You’re not limited to sending files either.  You can send whole folders of data.  A very handy feature for projects or for activities taken from the TI Exchange.  I can send out both the student instructions as well as the .tns file in one folder.

When collecting .tns files, students don’t need to know it’s going to happen, but when collecting alternative formats such as Word Documents, students must save their work first.  Student First name and Last name are appended to the filename on collection which would save me a ton of time as I currently have students email me and I often have to rename the files as I detach them from messages.

There is a toggle feature to show TI Nspire Work Area Only or to see the full screen space of the students.  This is handy if you are working in multiple applications (or just for classroom management if the activity is not engaging enough to take care of that for you).

Class Capture (Gallery View) has moveable windows which allow a teacher to group student responses by idea, topic, or process.  It’s a digital bandshow of sorts.

There is a data view to see graphs of all functions sent in from students in response to a poll at  the bottom right of the teacher software.  The frequency table and ability to individualize student graphs (responses) by color were very impressive.


Jennifer shared a quick poll that she uses with her students.  It differed from a standard question in that the display was split.  On one side was the traditional question about transformations of a quadratic in vertex form.  In the response box, as you input your answer, the right window pane automatically graphed the equation that you were editing.  The ability to drag the graph was disabled, so the student was required to do the translations algebraically, but they had a preview of what the numbers meant.  I saw this as good in a sense that students can definitely see the connection between algebraic and graphical.  It’s similar to what I’ve been studying with the use of FluidMath.  There is a downside to this technique though as well.  I had to ask myself whether this example was testing knowledge of the mathematics or their ability to use the technology.

I managed to snag a screen capture of what I was learning.  Here’s the video:

Data capture is something that I need to do more with myself.  Jennifer demonstrated how to collect captured data then copy those data points from a spreadsheet collected from students into a new doc.

T3 International in Chicago (Teachers Teaching with Technology)


I just got back from the T3 International Conference in Chicago.  It was an international gathering of mathematics educators that teach with technology, specifically the Texas Instruments calculator technology as they were the key sponsor of the event.

It was a fantastic learning opportunity.  I attended sessions about Computer Algebra System use in Scotland, a lecture on the ethics of allowing students to learn with CAS and how that related to the standards of practice in the United States.  I attended workshops on engaging students through open-ended questions using technology to drive the inquiry.

Some of the sessions I attended were focused on emerging technologies such as the LUA programming language for simulations right on the TI handheld.  Another was on the Networked Computing version of the teacher software and the features that allowed for quality formative assessment.

All in all, it was a fantastic learning opportunity and a chance for me to participate in professional dialogue about and with teachers teaching with technology from all over the world.

I’ll blog more about my learning in the coming days.  I just need to get back on my feet and out from under the pile of stuff I left undone while I was away.

Collecting responses … one student at a time


One of the downfalls of collecting student responses on an assessment using the Navigator System is that students all have to be done before you can collect from the class.  There’s always one or two students that wait till the end, take forever and a day, or ignore the instructions and need to go through and do it again.  This makes it difficult at exam time when students are able to leave as soon as they finish the exam.  I can’t tell them to hold  out for another hour until Johnny is done so I can collect everyone’s responses.  Imagine the pressure on Johnny.

Today I discovered that you can collect files from an individual or select individuals in your class without interrupting the rest of the students working.  Simply right clicking on a student from Classes view, selecting Collect From, choose the file (usually the most recent sent), and then selecting individuals you want to collect it from.

I was concerned about trying this out on an exam as I once blew up the process by trying to collect a file from class twice or something…right in the middle of a test and ended up marking everything by hand that day. :)  It worked out today.  I was daring and it paid off.  Sometimes learning something new means taking a bit of risk.  Hey, what a great thought…maybe we should be sharing that with our students, encouraging them to take risks to learn. :)


Another colossal flop and learning opportunity


It’s Exam time.  I thought…what better opportunity to let the Navigator system really shine than to have my students write their exam right on the calculator.  Now there’s usually a short multiple choice section on each of my end-of-unit tests (unless we do a performance task for that unit instead), followed by full solutions.  The exam followed that same format with multiple choice, a few short application problems, then the full solutions.

I knew that collecting and monitoring student responses via the Navigator for the multiple choice would work swimmingly as I’ve done that before.  I decided to try it for the application problems.  What a disaster that turned out to be.  I began a list of students that were either struggling to keep up, or who had incorrectly input answers in the open-response type boxes.  I set a “correct” response and even added some prompts on the file such as (accurate to two decimal places) when dealing with money etc.  The class average (over 20 questions including abcd type stuff) was about 47% with many scoring a full 0%.

I spent a good 2 hours preparing the file, ensuring I typed in all of the questions, importing the graphics so nobody would get lost in the tns file wondering what question they just answered.  Then another hour or so cross-referencing actual responses to the solutions to see how well it worked.

My conclusion…the Navigator is great for closed-response questions and gathering feedback, but don’t try to evaluate open response questions by assuming you’ve provided enough hints on formatting issues.  My biggest downfall was the negative sign.  Unfortunately many students would put -1 rather than (-)1  where (-) is the negative sign and – is the subtract sign.  The system didn’t know enough to say that they were the same and I couldn’t input multiple right answers.

It was worth the time and effort to try it out, and now I have a better understanding of how the whole exam / self-assessment module works on the TI Navigator.

TLLP Project Video


I’ve finished “cobbling” the video together as Tom describes it.  We as a team are happy to share some of our work with you our faithful reader(s).  :)

Tech can’t replace the Teach


I’ve been out a few times this week working on our project video and compiling some of our learning artifacts.  In the time that I’ve been out, I’ve been using youtube and other digital means to ensure that my students are learning in a consistent manner, using the same routines and content as if I was there in person.

While I’d like to say that my next TLLP application will be to sit in the living room with my 9 month old and teach from home next semester, it just isn’t going to happen just yet.  There have been technical challenges with setting up the projector/speakers/laptop, with the students not being able to ask questions, and with the students eventually disengaging from the lesson.

It would be interesting to do another study on how to effectively use tools like youtube in a mixed environment where I can be present to answer questions, but to also use digital resources so that students can work at their own pace.  The other ball that needs to be juggled in this setup is the inquiry based learning approach.

For now, I’m going to need to try and minimize my time out of class so that my students get the most consistent and stable learning environment.

Spying on Assessment


My grade 9 class is writing a math test as we speak. They have a multiple choice component in order to get them used to the idea of multiple choice in preparation for eqao. Tom created and shared a file with me that allows students to answer their multiple choice questions on their TI Nspire. While on it’s own, it’s kind of a nifty trick, the real benefit to me is that I can spy on their progress as they work through the assessment.

I try to stay out of the way when they write a test, so I’m not always looking over their shoulders to see how they’re doing.  Now I can finally see who is struggling with the pace of the assessment, what they’re spending most of their time working on, and really get a feel for the “process” that they went through to come to a final answer.

Often I’ll get a paper back and be trying to figure out how that person came up with that answer.  This gives me a little window into their thinking as they are being assessed.  This stuff is gold!

Exiting Press-to-Test


Tom has graciously provided us with a video synopsis of how to exit Press-to-Test mode. It was actually a little demonstration he did for our math department at the meeting this evening, but I thought it was worthy of sharing on our blog. Tom thought it was worthy of me sharing on our blog to, so it’s going under Chris’ reflections. :)