I decided to analyze Case 2. To summarize, case 2 described a classroom in which the teacher suggested the use of graphing calculators as a way of engaging students in a grade 11 math class. The videos showed different ways the teacher used the calculators, and also gave some insight into the students’ experiences with the devices.

**What are the underlying issues and why are they issues?**

The first issue that always arises with the use of graphing calculators are their prohibitive cost. Texas Instrument has held a monopoly over the graphing calculator industry for the better part of 2 decades now and have charged a premium for a device that is outdated, and in today’s smartphone proliferated classroom environment, quite unnecessary. Desmos calculator for example, is an app that is available on smartphones that performs the same graphing functions as a TI 84, but is also free. Cost is an issue because it acts as a barrier of entry for students who cannot afford the devices. Although the summary of the case suggested that a number of calculators were purchased by the district and the school, how would these calculators help students outside of the classroom?

One other issues exist that prevent programmable calculators from being used in post secondary settings: How do you stop students from programming the calculator with information or programs that allow for academically dishonest activities? Short of checking everyone’s calculators before the test, this is pretty much impossible. That is why graphing calculators are typically outlawed in post secondary exams.

Some other issues described by the videos suggested that some students preferred to use traditional pencil and paper to problem solve before diving into the calculator because they thought it helped them better understand the concepts that needed to be learned, which could lead to problems for some students as some would move right onto the calculator before attempting to conceptualize the ideas that needed to be learned. Another issue that I have seen in the videos, and from my own experiences working with graphing calculators are their ease of use. In many cases, the number of buttons and functions that needed to be used for some students could prove to be a challenge.

**What further questions does the video raise for you?**

The videos were not dated in this case, but I am thinking they are likely from 2000-2010. Would the teacher have a different opinion of graphing calculators today with the abundance of smartphones that most students own? Furthermore, given Desmos calculator (an app available on their smartphone), would they choose this over a TI 84?

**How would I explore a response to this issue?**

I have explored the alternatives to the graphing calculator in my own classrooms by essentially eliminating all problems that required the use of a graphing calculator on tests. While there is value in using graphing technology in the math classroom, I have instead allowed students to use Desmos to solve problems in various assignments as another way of assessing their ability to use graphs to problem solve.

**How might the issue that is raised exacerbate or ameliorate a conceptual challenge held by students?**

As with the use of any calculator, giving students free reign to use technology before they have understood the fundamental concepts would allow students to solve problems without understanding the concepts, as a result, the graphing calculator has the potentially to exacerbate ANY numerical, or graphical misconception by giving students a free pass to avoid spending time learning the concepts at a high level. For example, adding numbers like 1/2 + 3/4 is very easily on a calculator, and giving students these devices at an early age allows them to bypass the need to understand how to add fractions, by giving them a way to solve the addition problem that does not require an understanding of fractions.

On the other hand, by simplifying the process of graphing, students have greater access to visual information that could be useful in unlocking concepts that are best understood with visuals. For example, graphing a straight line on a graphing device may help bridge the concepts of intercepts and why one would need to substitute 0s into an equation to determine their values.

Gary

I like the fact that you organized your post with headings … easier for me to find what is supposed to be covered. Thank-you. I also, like the fact you noticed that some of the videos are dated. It is difficult to keep up with technology. I had one digital media course where I spent hours, days and weeks creating lessons on how to use Flash, Dreamweaver and other software and then Adobe came out with new versions of the software and many of my video capture videos were outdated overnight. Now my lessons are concept based in that course and the students can use any software they wish.

I wonder if students have lost the skill of graphing. I remember in high school (Lord Byng) where we spent hours learning to create a “proper” graph with pencil and paper. Do you think this a skill that students should know?

A good next step might be to explain the alternatives to the graphing calculators.

Christopher

I have taught Pre-Calculus 12 3 times now and I am now coming up with the same question myself. It takes significant time (3-4 weeks) to go through the Transformations chapter, and a lot of it is spent teaching students how to transform a template graph into a new graph, a process which can be done on a device in about 5 seconds. If the point of the unit is for students to be able to read equations and understand how the graph of one equation could be different from another, then I am starting to believe that we are spending way too much time on teaching concepts that are quite irrelevant given the power of technology. This is something I plan to change the next time I teach that particular unit.

Currently I stand behind the growing movement to try to dethrone Texas Instrument as the monopoly holder over graphing technology, and I champion the use of Desmos graphing calculator. (www.desmos.com/calculator) in my classes. The graphing calculator can be accessed as an app on most smartphones, and essentially turns a phone into a graphing calculator, while also making graphing on a device much easier to learn. Desmos has been discussed in the news in the past:

http://money.cnn.com/2017/05/12/technology/ti-84-graphing-calculator/

http://www.cbs58.com/news/digital-calculators-replacing-ti-84-graphing-calculator

Graphing calculators for sure can be powerful visual tools, to help picture written concepts on paper, though students might become lazy since much is automated and done for them. For sure, they still need to understand what calculators are plotting, along with mathematical analysis but as always balance is key. To chime in on Chris’ response, even graphing calculators are becoming more out dated, with ipads and other mobile devices providing even more functionality and accessibility.

Andrew

At the end of the day, the graphing calculator is still a “calculator”, and there will be very strong resistance from a lot of teachers in adopting the alternative, which is clearly the smartphone and tablets/laptops. The problem is that mobile devices are still very difficult to manage in assessment situations, and thus the incumbent graphing calculator remains locked in as the status quo.

This has changed recently though, as Desmos was used on some standardized testing scenarios: https://www.edsurge.com/news/2017-05-08-desmos-passes-the-smarter-balanced-test-and-hopes-to-save-math-students-100 . I am very much looking forward to the day where the change is complete and graphing calculators become a thing of the past.