Standard 12 - Teaching with Technology, Module 2

Module 2 Triggering question: How can I utilize contemporary, adaptive learning tools to maximize and evaluate students’ learning of mathematics?

Adaptive learning tools have been a recent addition to the curriculum in my school district. We have access to two programs in which students are able 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. 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.

"Teachers rarely have the capacity to design curricula and assignments that uniquely cater to every student" (Johnson, Adams Becker, Estrada, & Freeman, 42). I have found it increasingly difficult to individualize my classroom with students who are ready for Algebra 1 and beyond in the same class as students who have not passed a math class in several school years. The ability to successfully utilize an adaptive math program has been on my mind for several years, but I have not really understood what elements are necessary to make a program effective. The article I found did not answer how to utilize math programs, but it did enlighten me on what aspects should be present for one to be as supportive to students as possible. Cognition, metacognition, and affect were the main categories presented as necessary when utilizing an effective program in a math class (Arroyo, Woolf, Burelson, Muldner, Rai, & Tai, 390). These areas are seen as critical to support student learning and allowing teachers to see how and where student understanding is thriving or faltering. In looking at some of the aspect or Wayang Outpost, the specific program they researched, I realized that the cognitive aspect was something that is already in place with the particular programs our district has available. It is in the metacognitive and affective aspects that the programs fall short. The metacognitive aspect described in the article were evaluated by looking at "1) open student models that scaffold the self-regulatory process, encouraging reflection and informed choice at key moments of boredom, 2) progress charts and tips that encourage good study habits, and 3) interventions supporting help-seeking behavior in order to improve self-monitoring and evaluation" (Arroyo, et al., 404). This look into how students are seeing their learning is important for both my students and myself to help us understand how they each learn. The affect aspect of learning was also very interesting to me especially with respect to using a computer program. The emotions of the learner can be very influential in the overall learning experience, "affective states and traits (e.g., frustration, boredom) can bias the outcome of any learning situation" (Arroyo, et al., 412). Since these affective traits can be so influential, regular check ins with students must occur.

An idea formed from reading the article 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 small quizzes (which could effectively be check ins regarding affective and metacognitive states). One possible avenue for creating quizzes that could help streamline the process for information gathering is a resource like Quizlet (as presented by Sonja). 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.

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. Retrieved from http://link.springer.com/article/10.1007%2Fs40593-014-0023-y (Links to an external site.)

Johnson, L., Adams Becker, S., Estrada, V., and Freeman, A. (2015). NMC Horizon Report: 2015 K-12 Edition. Austin, Texas: The New Media Consortium.

www.quizlet.com

Standard 12 - Teaching with Technology, Module 1, ISTE Standard 1

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

Initial Reflection for Accomplished Teaching

Something I really want to improve on is my ability to differentiate instruction.  I feel fairly comfortable working with students with varying levels of prerequisite knowledge, but being able to plan for and incorporate strategies to allow access to all students, regardless of their comfort with the material, is something I am very eager to improve. The reality of teaching in my school and content area (as I am sure in many other schools and content areas) is that many students come to my Algebra 1 class without having passed math the previous year, or maybe over several previous years.  This creates a massive disparity in the mathematical understanding of the students in my class.  Additionally, this necessitates me to be very good at differentiating instruction to the point where I need to have my tasks be accessible to students with little prerequisite knowledge to those who are fully prepared for success in Algebra 1.  Further developing and strengthening this ability is my present priority.

Welcome!

Welcome! You have found my bPortfolio for the Seattle Pacific University's Master's in Teacher Leadership program.