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Update 2: The Graphing Calculator & a modern version, Desmos
I am using this opportunity to discuss the two different versions of the graphing calculator. I love our hand-held TI-whatever –version graphing calculators and I think they are great tools. I wouldn’t consider them “new” by any means, but I do think many teachers think they are using technology by using them. When forced to write up lesson plans, I even admit to putting graphing calculators & SMART Board as my technology use for the class period. We require them for our Honors Algebra 2 course and most students use them all the way through Calculus and beyond.
I love using them and many students enjoy and appreciate them as well. I just introduced basic features to students the other day and they thought it was so cool that they could graph functions and it graphs it for them. Ah ha! The key to efficiency – a tool to do everything for the student. I find that the graphing calculator mostly just helps us move class along, so that every time we have to graph a quadratic, polynomial or rational function (or a plethora of others), the students don’t take several minutes to do it themselves. It allows us opportunities to talk about key parts of the graph and what that means more effectively. However, I do not believe that all students truly understand what they are looking at or why graphs look the way they do. I think with the use of graphing calculator, they are starting to miss out on the reasoning behind the math. I also find that the graphing calculator often just enhances the lecture and just allows us to cram more into the coursework. It is easy to create an activity with the graphing calculator and disguise it as “an investigation” because students are making their own conclusions, before we move along in lecture. Realistically, we determine what conclusions the students will make, and the students don’t determine what or how to manipulate the functions.
Enter in: Desmos!
I love this resource. While it is a graphing calculator, it has many more features that allow students additional visuals and additional manipulations. I have started to explore the use of the teacher resources that are pre-created, but now we can also make our own modules. We can include text and imbed directions, hints, short answer responses/student justification with the graphs and module. Students on their own devices can work at their own pace, and if all have a device or computer, they all have to be engaged through it. One of the best features of this, is I can see all student work and answers, and can pick and choose things to post for the whole class to see. On some screens students can also see others’ work, after they have input their own ideas. I have also used Desmos for a project where students create their own art, while requiring them to use specific mathematical functions. Many students have loved this project as it allowed them to explore different transformations, different functions and key features of them.
Many of these modules in Desmos are still very guided and have a very specific end target in mind. I also wish there was more opportunity for student-student interaction (some modules do link peers up). However, I think it is a much better alternative to the handheld calculator and lends itself better to the “New Learning” model. It does allow for maybe a tad bit more natural exploration as I think it is a little less cumbersome and possibly easier to manipulate the graphs. As more districts move 1:1 or 1:4, this might be a better use of classroom time and engagement. Although, as long as an SAT or an ACT will be required for university entrance, most students will still have to know how to use their trusty old graphing calculators.
Interesting post. Not being a math wiz, I cannot relate to what your students are learning but I think you bring up a great point in how they are learning.
I do not believe that all students truly understand what they are looking at or why graphs look the way they do. I think with the use of graphing calculator, they are starting to miss out on the reasoning behind the math.
I think this statement you made sums up most people's frustrations with technology.
In my profession, it is required to have a working knowledge of sound physics and oceanography. Back in the day, old-timers used to hand calculate and graph propagation paths of sound through water to determine the probability of detecting a particular class of submarine. In my era, we were introduced to computer software that only required environmental and target data to be inputted and a nice colorful graph would be produced, providing the output that would take the hand calculations 10x more time to generate. Although it is obvious that this software provided a tactical advantage, it required less depth of knowledge from its operator. A relative novice could produce more accurate and reliable predictions in the fraction of the time as a master level technician of the olden days. When put in those terms it seems like a ridiculous notion to ignore the ubiquitous technologies that we are surrounded by today. However, I think the role of the teacher is more important than ever to explain the background theory behind how the technology works in order to create new master level technicians. Being able to do something quicker and better is always good but knowing why and how is the key to future growth.