ISTE1 Triggering question: How can I, as a high school Math teacher, utilize technology to both enhance student learning and create genuine opportunities for creative thinking and problem solving?
Traditionally, the mathematics classroom has been a space where teachers lecture and students take notes followed with some practice. This is especially true of the higher level classes such as calculus. In my quest to increase engagement and rigor, I decided to work to finding ideas of how I can use technology to help my students' understanding and problem solving. I am not interested in introducing technology for the sake of using technology. As, Merzenich states that, "simply adding computers to conventional teaching strategies is an unsophisticated approach that, it is not surprising, adds very little to students' experiences in the classroom" (as cited in Robin, 2008, p. 221).
In order to create genuine opportunities for learning and investigation I have used some programs such as ST Math and Think Through Math that are adaptive to students' needs. I have found that these resources are less than ideal. I have also used the graphing program GeoGebra to render graphs for practice and such in the classroom. I had not thought of using GeoGebra for learning opportunities using applets as suggested by M. Hohenwarter, L. Hohenwarter, Kreis, and Lavicza in their article Teaching and Learning Calculus with Free Dynamic Mathematics Software Geogebra (2008). The use of GeoGebra in a class such as calculus was not an obvious connection that I made, but Hohenwarter et al., found that this tool may be used to "help students to better understand their algebraic manipulations of functions, to visualize characteristics of certain types of functions, and to improve their skills of sketching graphs of functions and their derivatives" (2008, p. 4). Students can certainly learn about calculus the "traditional" way via lecture and practice, but may reach greater depths of understanding working with the reasons why certain properties and theorems work (effectively learning the why, not just the how).
Here is an example applet that lets students discover information about derivatives.
An article found by Sonja Ostling, Metacognition and the Influence of Polling Systems: How do Clickers Compare with Low Technology Systems, informed me further by suggesting the use of clickers or an app or website to poll students on their understanding (Brady, Seli, Rosenthal, 2013). This use of technology was one I did not realize until I read this article and saw the potential uses for formative assessment with this type of information gathering. The traditional use of hands up or down, or thumbs up or down, in response to a teacher asking who understands material may result in students being influenced one way or the other by their peers providing me with flawed information.
The combination of using GeoGebra with my calculus class and using clickers, or a viable alternative, with all classes may result in more engaged students who are learning the information with greater depth and greater retention, as well as, providing me with valuable, real time information about students' understanding, respectively.
Brady, M., Seli, H., & Rosenthal, J. (2013). Metacognition and the influence of polling systems: how do clickers compare with low technology systems. Education Technology Research and Development, 61, 885-902. http://ezproxy.spu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&AuthType=ip&db=eric&AN=EJ1040689&site=ehost-live
Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. Proceedings from TSG 16: Research and development in the teaching and learning of calculus. ICME 11, Monterey, Mexico. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAAahUKEwjo4sq7vbvIAhVCXIgKHXt9DWY&url=http%3A%2F%2Fwww.geogebra.org%2Fpublications%2F2008-ICME-TSG16-Calculus-GeoGebra-Paper.pdf&usg=AFQjCNEMCFCRQaEgMnVOzLF5g6F-H1kgFw
Robin, B. (2008). Digital storytelling: a powerful technology tool for the 21st century classroom. Theory Into Practice, 47, 220-228. https://canvas.instructure.com/courses/972604/files/36977374?module_item_id=8061854
KC, you make an excellent point with the quote from Merzenich - adding computers doesn't automatically improve instruction, and that's important to keep in mind as instructors when we look for ways to integrate technology with traditional teaching methods. With GeoGebra and its applets, I think you have found a way to genuinely enhance student learning in your calculus class! The visualizing aspect of GeoGebra would have been very helpful for me as an additional to lectures and worksheets. I'm glad you found a use for clickers; I hadn't realized it could be used across so many subjects!
ReplyDeleteKC, I really liked your introduction with the quotation from Merzenich. Your focus is on creating genuine experiences for creative thinking and problem solving, rather than using technology for the sake of using technology. I like that assertion. You even continue to say that students can learn new calculus concepts through the "traditional" method of lecture and note-taking, but students can grasp more through GeoGebra and gain a deeper understanding. You don't seem to be interested replacing their learning method, but enhancing it, as you said. This was a great read and I think you explained your intentions well. Great job!
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