Copy of the following analysis as a Word Document: e-Folio Final Analysis
As I reviewed my e-folio for this course, a strong central theme emerged in Module A and stayed consistent throughout the remaining two modules. This theme centers on using technology to facilitate a change in teaching style. At the start of the course, I was chiefly focussed on moving towards constructivism. Towards the end of the course, I started to look at how different learning theories can complement each other and how these relate to the integration of technology. In the following analysis, I will detail the evolution of this theme in my e-folio, how it ties in to the courses content, and how it has impacted my current teaching practice. Finally, I will look at what questions have arisen and where these questions might lead in the future.
Module A – The Theme Unfolds
The activities in Module A were designed to help us explore our assumptions about the use of technology in mathematics and science education and to look at examples of how technology is currently being used in educational settings around us. For example, the Unpacking Assumptions activity provided me the opportunity to reflect on my current views as well as some of what I have learned in previous courses. In this activity I wrote, “The more I learn about using technology in class, the more I think that it isn’t adding technology that is important, but rather, it is changing the way I teach that is important.” This statement reflects the idea that methodology is tied to pedagogical theory and that using technology should flow from how the course or lesson is designed, rather than adding in the technology and trying to make a lesson work with it. I stopped randomly looking for technology that could be used in class and started focussing on asking myself what exactly it was that I wanted the technology to do – for me and for my students.
This shift in mindset necessitated some introspection and reflection on how my pedagogical theory and philosophy have changed throughout the MET program. The Video Case analysis and the Interview activities each shed light on this gradual change in philosophy. In my Module A Journal, I wrote:
“I was struck in both of the videos that I analyzed how both of the teachers were using technology to allow the students to create their own knowledge. With the graphing calculators, the assignment … was at the heart of the change in learning style, but the technology allowed the students to do the assignment – pedagogy/methodology and technology in a symbiotic relationship to improve learning.”
By the Interview Discussion Synthesis, my thoughts on methodology had crystallized into the primary focus of “Using technology to move towards a more constructivist teaching methodology.” I find the emergence of constructivism to be important is because it is a learning theory that I struggled with in earlier courses in the MET program. As I have learned more about constructivism, I have developed a better understanding of what it means and that scaffolding and teacher direction are necessary. Students construct their knowledge, but not just haphazardly. Mathematics lessons built upon constructivism need to be planned carefully and designed with enough guidance to lead the students to correct understandings, but with enough latitude to allow for exploration and discovery. This gradual understanding on my part lead to this entry in my Module A Journal, following the Interview Discussion Forum.
“I am finding it somewhat ironic that the biggest change in pedagogical thinking that I have undergone during the MET program is not directly about technology. The biggest change for me is that I am finding myself more and more buying in to the whole idea of constructivism. I still think that there needs to be a balance in methodologies … but my skepticism of constructivism, specifically in mathematics, is definitely being replaced by a grudging acceptance and recognition of its power and technology’s ability to facilitate constructivist approaches.”
Module B – Examples of Constructivism and Technology
Recognizing a pedagogical shift to embrace constructivism during Module A made the activities in Module B particularly appropriate and timely for me. Investigating the Technology-Enhanced Learning Environments (TELEs) and the accompanying readings were activities that provided me with the theoretical knowledge and background upon which to build my developing learning theory. Throughout each activity, reading and discussion forum, the idea of using technology to encourage or facilitate constructivism appeared repeatedly.
In the discussion forums for Module B, a number of people commented on the constructivist approach employed by the TELEs that we investigated. For example, in a response to a post on the Jasper Woodbury Series, one class member commented that,
“I agree that, “The biggest change was the move to constructivism and collaboration” The Jasper series uses strong constructivist principles that facilitate meaningful learning through collaborative problem solving. I think that the shift from the teacher as the transmitter of knowledge to student construction of knowledge collaboratively is a whole pedagogical mind shift that promotes independent thinkers.” (Post by VW, private discussion forum, February 10, 2012)
I chose to include this post because it sums up and reinforces the shift in my personal mindset. This shift was also strongly affected by the articles and activities related to T-GEM (Khan, 2010; 2007). T-GEM stands for using Technology (T) to help students Generate (G) relationships between variables, Evaluate (E) those relationships and Modify (M) them if necessary (Khan, 2007). I found these readings particularly relevant on a number of levels.
To begin with, they provided a useful and practical technique for creating more constructivist lessons on a daily basis. Even when a teacher is lecturing, it is possible to build in time for students to generate hypotheses and relationships, share and evaluate them and modify them if necessary. Technology is incorporated by using it to provide data to the class as a whole or through the use of simulations or graphing calculators. Asking the questions needed to get students to generate their own ideas is one step in helping students actively engage in lessons and to begin to construct their own understandings.
T-GEM is a practical approach to incorporating constructivism that is based on research. Khan (2007) found that students experienced increased engagement in science, reported that they felt they understood the concepts covered using T-GEM, showed evidence of conceptual understanding and developed enriched mental models for abstract chemistry concepts. Khan (2010) also looked at how the teacher’s pedagogical views impacted the use of T-GEM and technology. This research was done using the Technological Pedagogical Content Knowledge (TPCK) framework. It reinforced for me the idea that our use of technology should be purposeful. This idea is stated in my TELE Synthesis:
“T-GEM and LfU increase our TPCK by helping teachers to reflect and engage in metacognition while planning activities and lessons and how best (and when) to integrate technology into the learning environment. They can be guiding principles or templates to help teachers move towards that constructivist environment that is so highly sought after.”
The final paragraph of my TELE Synthesis e-folio entry sums up what I learned from my interactions with the four TELEs in this course.
“Valanides and Angeli (2008) present a study of professional development for in-service teachers in which they state that, “the effective design of computer-enhanced science learning should greatly depend on aligning inquiry-centered pedagogy with the inherent features and affordances of computer tools to transform science content into pedagogically powerful forms” (p. 4). When it comes to incorporating technology into the classroom, I believe that the power of technology-enhanced learning environments lies in their use to facilitate change from traditional transmissive methodologies to constructivism. Jasper provided examples of how this might work, WISE provides a platform within which to construct lessons and LfU and T-GEM provide guidelines for teachers to follow in constructing these lessons.”
Module C – To Constructivism and Beyond
In the third Module of the course, my focus remained constant, but broadened to include learning theories and approaches beyond constructivism. For example, the online opportunities for information visualization reminded me that visual representations of concepts, made possible through technology, can enhance student understanding of the concepts. However, it was the theory of embodied learning that had the largest impact.
Embodied learning involves actively using our whole selves in learning. I see this as very complimentary to constructivism. When one is constructing knowledge and understanding, the more senses that we involve, the deeper we understand and can remember what we have constructed. The saying that once you have learned to ride a bike, you will never forget, is an example of this. When learning to ride a bike, we use our minds, our eyes, our ears and our sense of feeling. Our construction of knowledge is made more complete because it is made with our whole being rather than just our minds.
The readings on students using gestures and other semiotic means to communicate mathematically resulted in another “aha” moment for me. I have always valued discussion and collaboration in my math classes. It made sense to me intuitively that having students verbalize their thoughts and discuss them would result in deeper learning and help them construct more accurate mathematical knowledge. Radford (2010, 2005) provided me with some rationale to back up these intuitive suppositions. In my Module C Journal, I wrote:
“Both of the articles by Radford (2010, 2005) that I read reinforced the idea of embodied learning in math class. Both of his articles remind me of the importance of writing in math – and in talking and collaborating. Putting thought into words or symbols or gestures makes it more concrete and helps the learner figure out what they are thinking. Gestures explain things that we cannot put into words. Radford (2005) identified the idea that multiple semiotic means are used when students discuss math. Often, one semiotic system is used for one aspect of a problem, and another for a different aspect of the problem. We have to look at them together in context to understand what is going on in the students’ learning process.”
The readings from Module C have led me to incorporate a broader picture into my personal learning theory, which in turns affects the methods that I choose to employ in class. Constructivism plays a central role, but using activities involving information visualization and trying to incorporate embodied learning enhance how knowledge is constructed and answer some of my concerns with constructivism.
Where do I go from here?
Early in the course, my focus was on using technology to facilitate a practical paradigm shift to constructivism. The theme has remained consistent throughout the course, with a developing openness to including information visualization techniques and embodied learning. Constructivism is a powerful pedagogical mindset and theory, but no one theory encompasses every situation, subject or setting. In a perfect world, students would have time and the self-motivation to engage in constructivism while having access to technological affordances such as information visualization applications and the tools to participate in embodied learning while constructing their own knowledge. However, I do not teach in a perfect world. My questions have changed from “How do I know which technology to use?” to “How can I use technology to change the way I teach?” to “How can I use the technology I have available now to impact my lessons today, and how do I get my students to buy in?”.
For my framing issues assignment, I researched the use of blogs in mathematics as one possible aspect of a blended learning environment. I want to place the technology in the hands of the students, but in my setting, computer availability is low, so a blended learning environment involves the students using computers outside of scheduled class time. To this end, I recently started using an asynchronous discussion forum hosted in a Moodle shell and I plan to continue to research ways to implement blended learning, asynchronous communication and writing in mathematics.
Within class time, I am working towards my goal of developing a more constructivist design by actively incorporating T-GEM as a model even in planning notes and lectures – building in time for students to generate and evaluate ideas, in small groups and as a class, often using graphing calculators. I want to spend time developing more role-playing activities, with an eye towards embodied learning. I am also planning to take a summer institute workshop offered by Texas Institute on using graphing calculators effectively in class, as a direct result of this course.
Finally, I am reminded to use technology purposefully and that it is most powerful when linked with intention to pedagogy. JV put it perfectly in her post: “Theory needs to come before technology and I am starting to think that professional development should be about pedagogy [constructivism] and would not the technology just follow by itself?” (Post by JV, private discussion forum, February 28, 2012) My professional development lies along that road. How I want to use technology is becoming clearer as I identify what it is that I want to accomplish and why. Understanding the pedagogy behind different activities helps me to understand how to incorporate the technology, and which affordances of technology I want to use.
Conclusion
“The aspect of technology that I am finding MOST important is how it can allow us to change the way we teach – to teach students how to learn for themselves instead of just trying to transmit knowledge to them.” (Barker, Module A Journal, 2012)
This statement embodies the theme of my e-Folio for ETEC 533. The course started with me identifying the issue and recognizing that I wanted to create a more constructivist atmosphere in my classroom. The four TELEs that we investigated provided me with examples of how to create this atmosphere and how technology can play a role in that pedagogical shift. I have started using a class website, T-GEM (Khan, 2007), information visualization via exploration with graphing calculators, simulations and YouTube, and an asynchronous discussion forum. Helping students to engage in embodied learning, both with and without technology, is a new shift in my thinking that I feel compliments and enhances constructivist activities. Developing activities that embrace embodied learning and continuing to develop my own personal learning theory, based on sound pedagogical research and experience, that incorporates, but is not limited to, the tenets of constructivism are ongoing goals.
References:
Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.
Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.
Radford, L. (2010). Signs, gestures, meanings: Algebraic thinking from a cultural semiotic perspective. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello, F. (Eds.), Proceedings of the Sixth Conference of European Research in Mathematics Education (CERME 6) (pp. XXXIII – LIII). Université Claude Bernard, Lyon, France.
Radford, L. (2005). Why do gestures matter? Gestures as semiotic means of Objectification. In Helen L. Chick, Jill L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, University of Melbourne, Australia, Vol. 1, pp. 143-145.
Valanides, N., & Angeli, C. (2008). Professional development for computer-enhanced learning: a case study with science teachers. Res Sci Technol Educ 26(1): 3 – 12