Graphing 'Fun'ctions!
Moving beyond the TI-84...
Grade 12 Applied Mathematics
Using technology as a tool, we attempt to solve problems and model many real-world situations.
One important area of focus is graphing and interpreting functions, including polynomial, exponential and logarithmic, and sinusoidal.
Established Tool
Used regularly in our school.
Familar Tool
Used within our division.
Familiar Tool
Used within our division.
TI-84 Graphing Calculator
Our main technological tool for the Applied stream has been the TI-84.
Reasons
- consistency with program, lessons, and units
- understanding of key strokes and general usage
- lack of access to computer labs and limited applications of current programs and/or apps
Issues
- Initial cost at approximately $130
- need for physical possession of the calculator
- risk of damage and/or theft
desmos
Accessibility
- can be accessed and/or downloaded on most personal devices
- online and app versions
- free to use (can save work with account activation)
- can create your own activities and share with class, along with an assessment feature
- a classroom activities section for resources
- very intuitive and/or user friendly, mimics the idea of using a phone app (simple)
Visual Representation
- viewable keypad along the bottom (can use on screen or your keyboard)
- icons on screen are familiar for app users
- screen size based on your device
- graphs appear in a variety of colours for differentiation
- clear and accurate animation of graphs
- option for visually impaired accessibility
Functions
- expressions can be easily entered and overlay pictures
- can move between an expression and table and graph with a click
- points of intersection/max/min... can be determined with a click
- zoom feature is seamless, quick drag to expand or limit coordinate plane
- animation of horizontal and vertical transformations, opened lines and parabolas to see the change in the values of a, b, c or d
Items of Note
- lends itself nicely to inquiry based learning (students discover relationships between the data, expression and graph), with that in mind, we also need to be sure that students understand the information they are working with and not necessarily just putting in numbers (although that could also be said for the TI)
- ability to include geometry in your graphing with a number of steps
- there are a number of additional units that fit well with our current use of the TI-84, including significant work on money (simple interest, compound interest, rate of return...), so the familiarity of one tool does have advantages, but tough to ignore the more in-depth possibilities of desmos
Geogebra Graphing Calculator
Accessibility
- easily accessed and/or downloaded on most personal devices, online and app versions,
- can be downloaded and used without internet access, free to use (can save work with account activation)
- can create your own activities and access on site materials, also have a community section for resources
Visual Representation
- viewable keypad along the bottom (can use on screen or your keyboard)
- screen and menu bars fairly easy to navigate and find
- screen size based on your device, graphs can be selected to appear in a variety of colours for differentiation
- clear and accurate animation of graphs with a few steps
Functions
- expressions can be easily entered and overlay pictures
- move between an expression and table and graph with a series of clicks
- points of intersection/max/min... can be determined with a series of clicks
- reset boundaries of coordinate plane easily, quick zoom features to expand or limit coordinate plane, expressions can be easily manipulated to see horizontal and vertical transformations, along with the change in the values of a, b, c or d
Items of Note
- also lends itself nicely to inquiry based learning (students discover relationships between the data, expression and graph), but does require some time and familiarity with the program
- ability to include geometry in a seamless manner, but other aspects are less fluid than desmos
- this version of Geogebra (as opposed to Classic) offers the ability to make the program exam compliant by turning off specific features
- again, there are a number of additional units that fit well with our current use of the TI-84, including significant work on permutations and combinations, so the familiarity of one tool does have advantages, but again tough to ignore the more in-depth possibilities of Geogebra
Conclusion
1st Place
- comfort of use
- high engagement
- in-depth learning
2nd Place
- variety of features
- user friendly
- pursue math concepts
3rd Place
- visually basic
- reliance on keystrokes
- limited exploration
Either digital tool, desmos or Geogebra, would be a better option than the TI-84 for our three function units. They provide an opportunity for students to be creative and learn independently, as opposed to being guided through all the steps. The learning is also much more visual, as instant feedback is provided with a slight adjustment to an expression and/or a graph. A slight advantage to desmos for the ability of a learner to jump right in and get to work... or better yet, get to play!
References
- Gonzalez, J. (2019). The Teacher's Guide to Tech 2019.
- Government of Manitoba (2014). Grades 9 - 12 Mathematics: Manitoba Curriculum Framework of Outcomes.
Winnipeg Free Press (March 12, 2020). 'Flatten the curve': The graph health officials say is key to managing COVID-19.