Through this week’s reading, I was able to conjure a new way to teach quadratic functions, and equations going forward that incorporates technology. In the following sequence of planned activities, I plan to incorporate a greater amount of collaboration between students, more opportunities to physically manipulate the information they are working with, and focus more on an inquiry based approach.
Learning about the graph of the quadratic function using graphing software
One of the major concepts students taking Pre-Calculus 11 need to learn is the quadratic function, and how the equation of the function determines various attributes of the graph such as its direction of opening, the location of the vertex, and its width. In teaching these different concepts, I plan to utilize Desmos Calculator to have students play around with different forms of the quadratic formula using the calculator’s slider function: http://support.desmos.com/hc/en-us/articles/202528919-Sliders
This Desmos activity I plan to create will leverage the “interdependence” of embodiment, embededness, and adaptation” (Winn, 2002) as students will physically manipulate the artificial environment I have created to learn, and adapt their knowledge about parabolas. An activity of this sort would also promote collaboration between students on a “mixed reality” type software where students have the opportunity for “physical interplay” of the graphs, which, according to Lingren (2013).
As for the choice of using Desmos Calculator over a standard graphing calculator, I am making the choice partly due to my own experiences with Desmos, but also to avoid many of the misconceptions related to quadratic functions pointed out by Powell (2015), many of which involves incorrect equation entry, and may be due to the standard graphing calculator’s small screen.
Relating quadratic equations and the graph of the quadratic function
Students frequently have difficulties connecting the concept of solving quadratic equations and working with the graphs due to their failure of seeing the relationship between the two concepts. To solve this problem, I would utilize another activity using the Desmos calculator. This time, I wish to use the calculator to showcase the relationship between the solution to the equation of the form 0=(x-a)(x-b), and the graph of an equation in factored form: y=(x-a)(x-b), vertex form: y=a(x-p)^2+q, and standard form: y=ax^2+bx+c. I would again utilize an activity involving sliders. I believe an activity utilizing sliders again in this instance, would allow me to reap the same benefits as the previous activity.
My questions for colleagues:
1. What are your experiences learning Mathematics with technology? How has graphing technology (whether it is on a graphing calculator or not) helped you with learning?
2. What do you see to the biggest problem in Mathematics education today?
3. What misconceptions in Mathematics have you struggled with in the past? How did you manage to get past them?
- Lindgren, R., & Johnson-Glenberg, M. (2013). Emboldened by embodiment: Six precepts for research on embodied learning and mixed reality. Educational Researcher, 42(8), 445-452.http://www.move2learn.education.ed.ac.uk/wp-content/uploads/2015/04/Lindgren-2013-Embodied-Learning-and-Mixed-Reality.pdf
- Powell, J. (2015). Solve the Following Equation: The Role of the Graphing Calculator in the Three Worlds of Mathematics. Interpreting Tall’s Three Worlds of Mathematics, 52(2), 11. Read one of the chapters from: https://scholar.google.ca/scholar?as_ylo=2013&q=embodied+learning+and+graphing+calculators&hl=en&as_sdt=0,5
- Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114. Full-text document retrieved on January 17, 2013, from: http://www.hitl.washington.edu/people/tfurness/courses/inde543/READINGS-03/WINN/winnpaper2.pdf