Standard 12 - Teaching with Technology

Standard 12 - Teacher leaders will evaluate and use technology for teaching and learning.

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 AP Statistics and AP 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).

Beginning the program, I decided to find out how to create genuine opportunities for learning and investigation math. Whether that means using programs such as ST Math or Think Through Math, both are adaptive to students' needs. Or, utilizing free technology such as GeoGebra or Desmos to help students gain a different perspective. An article by M. Hohenwarter, L. Hohenwarter, Kreis, and Lavicza, suggested the use of GeoGebra in an upper level class such as calculus. This was not an obvious connection, 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 upper level math 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).

Additionally, my school district has added adaptive learning tools to interact with math in different ways. One, ST Math, looks at math in a non-equation way showing pictures and game-like activities to teach the basics associated with Algebra, Geometry, and all pre-high school level classes. The other, Think Through Math, looks at math in a more traditional way utilizing various feedback including live tutors and immediate feedback. I have had the opportunity to utilize both with various classes over the past several years and have found my use of them with my classes to be less than successful. So, I decided to research how I can best utilize either with my classes if I should choose to do so.

An idea formed from reading an article by Arroyo, Woolf, Burelson, Muldner, Rai, and Tai is to use journaling as a supplement to regular program use.  I believe that journaling is one way in which students can record their affective traits and thoughts about what and how they are learning the material. An additional supplement to the software could be regular information gathering around via formative quizzes. One possible avenue for creating quizzes that could help streamline the process for information gathering is a resource like Quizlet. I could use Quizlet or a similar technology to have students reply to questions based around what they learned, how they learned it, what information they required help on, and how they felt throughout the process of using the program.

Throughout the Teaching with Technology class, I wanted to discover what it means to be a technologically innovative math educator. Research by Sherman (2014), I read outlined two vital aspects of technology use that are necessary to deepen students' mathematical knowledge. The first category used in the article is the use of technology as an amplifier. The article states that the amplifier use, "supports a shift in the focus of students’ mathematical activity and thinking from drawing and measuring to looking for patterns and making and testing conjectures” (2014, p. 223). I am currently using at least one amplifier in my classes, the graphing calculator. This resource has allowed my students, while working with transformations, to get past worrying about making a table, and remembering rules to make a graph and allows them to get to the inner workings of transformations. The second category used is the reorganizer. The reorganizer "has the power to affect or shift the focus of students’ mathematical thinking or activity" (2014, p. 223). In reflecting on my practice, I realize that I do several things associated with either the amplifier or the reorganizer, but very few of them rely on technology right now. To move toward being an innovative educator, I will need to work on incorporating technology tools as a means of moving toward deeper learning.

Additional research by Starkey, offered some other interesting points of reference in determining the efficacy of technology including collaboration and connection to prior learning. These areas are very important in being learners with technology as they allow students to process the information gathered or learned. When students are collaborating, they can process new learning together which gives students the potential for multiple points of entry. These multiple points of entry are vital to putting their learning into their own words and style of understanding. Similarly, connecting their learning to other areas of knowledge, especially to previous knowledge, allows students to deepen their understanding and connect different issues. Both these aspects can help to strengthen any new learning and better student’s problem solving abilities, both of which elevate their ability in math.

We further learned about the legal ramifications of technology use in the classroom and what to look out for as teachers. There are many laws surrounding the expectation of privacy for students in public school systems, especially regarding the use of technology. Unfortunately, these rights to privacy are not always easy to enforce or ensure with the prevalence of technology use in today's school environment. Research by the Center for Educational Privacy and Law at the University of San Diego (CEPAL), revealed one of the most interesting concerns for privacy that schools face is called householding. "Householding allows data collection to occur across devices regardless of whether or not they are owned by a district or owned privately by a student" (CEPAL, 2015, p. 6). This rather sneaky method for data collection is strong enough to pinpoint usage across devices at any time, so students are not immune to data collection whether working on school work at school or home. The many laws that protect student autonomy are not much of a deterrent to this sort of activity. The Family Educational Rights and Privacy Act (FERPA), Protection of Pupil Rights Amendment (PPRA), and Children's Online Privacy Protection Act (COPPA), are limited in what they have jurisdiction over and the depth to which online information is protected. For example, FERPA does not have any consideration for third party application operators, the PPRA has made considerations for protection, but does not include any currently, and COPRA only protects children up to the age of 13, so is very limited once children are out of the primary grades (CEPAL, 2015, p. 10). Furthermore, the only real protection that seems to be available to parents is opting out of the use of technology devices provided by schools and districts. This brings up other, very real implications concerning the equity of technology availability, especially at high poverty schools where many, if not most, families do not have reliable access to the requisite technology. A product from this portion of the class is an infographic we created that would allow us to share some of the concerns that may affect students online.

Lastly, we created a webquest that allows students to do research about a topic relevant to the content of our classes. For my webquest, students are asked to research about the history of math. The students are researching and then creating an argument to show that the mathematician chosen is the best mathematician in history. This project allows students to look at a different aspect of math and get into the lives of mathematicians (which, believe it or not, are often quite intriguing). Being able to figure out how to incorporate technology into our classes in a genuine way to deepen understanding or appreciation for our subjects is a great way that will help us connect with our students throughout content areas.

Arroyo, I., Woolf, B.P., Burelson, W., Muldner, K, Rai, D., Tai, M. (2014). A multimedia adaptive tutoring system for mathematics that addresses cognition, metacognition and affect. International Journal of Artificial Intelligence in Education, 24, 387-426.

Gunn, T. & Hollingsworth, M. (2013). The implementation and assessment of a shared 21st century learning vision: a district-based approach. Journal of Research on Technology in Education, Vol. 45 (Issue 3), p201-228.

Johnson, D. (Sept. 2013). Good technology choices: a team effort. Educational Leadership, Vol. 71 (Issue 1), 80-82.

Sherman, M. (2014). The role of technology in supporting students’ mathematical thinking: Extending the metaphors of amplifier and reorganizer. Contemporary Issues in Technology and Teacher Education, 14(3), 220-246.

Center for Education Policy and Law (2015). Legal Implications of Using Digital Technology in Public Schools: Effects on Privacy. San Diego, CA: University of San Diego.

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.

Robin, B. (2008). Digital storytelling: a powerful technology tool for the 21st century classroom. Theory into Practice, 47, 220-228.

Starkey, L. (2011). Evaluating Learning in the 21st Century: A Digital Age Learning Matrix. Technology, Pedagogy and Education, 20(1), 19-39.