Thematic E-Folio Analysis
My ETEC 533 Exploration
Effective Technology Use in the Mathematics and Science Classroom – Technology embodiment: A new ontology
Relevance
At the 15th Annual staging of the Jamaica Teachers Association education conference: ‘Mathematics Education in Jamaica: Conquering frontiers – Providing Solutions’ in Montego Bay Jamaica, the focus was on Mathematics Education.
The Keynote speaker, Dr. Huthcinson spoke of the alienation of students in Mathematics education because of poor learning processes. Dr. Hutchinson highlighted the January 2006 issue of Bloomburg Business week in which Mathematicians are employed and permeating untraditional math fields in: mapping advertising campaigns and with customers. She comments that “as more of the worlds’ information reduces to numbers…. It is a magnificent time to learn mathematics” so ‘Why are our students not excited to learn Mathematics?’ She offered the following reasons:
i. Classroom practices do not support problem solving in non-routine problems in which we can stimulate creative and critical thinking
ii. The learning environment is not conducive
iii. Weak pedagogical knowledge content (both teachers and students lack confidence)
iv. Lack of attributes to support the process (including tools for learning, not just physical tools but pedagogical models that scaffold and give diagnostic feedback).
Conrad Wolfram (2010) highlights these very issues with the solution that computers should be used in the Mathematics classroom to solve such issues. However, research has shown that computer aided/assisted instruction has shown little gains in enhancing student performance. What is the divide? The explorations within this portfolio put forward discourse, tools and experiences that prompt a more effective use of technology in the Mathematics and Science Classroom.
The tools versus the process
In January 2012 I enrolled in ETEC 533 with the desire to increase my knowledge of design skills in developing technology use in my Mathematics classroom. My timeline of technology experience and use, shown in my auto e-ography, reflects my interest in ‘creating/using simulations and for means of demonstrating abstract concepts in practical contexts’.
In my first point of exploration of what I considered were: technology, good technology and effective use of technology I kept honing in on the aspect that technology is not just a tool but should embody the essence of what Math represents and as such good and effective technology were those that: ‘facilitate inquiry, investigation, problem solving, testing and/or applying concepts/models within specific contexts or situations and analyzing results’. And were: ‘ interactive’ with and, should create, the environment in which ‘technologies and learning experiences in which students can use and apply concepts/areas of investigation in day to day experiences as well as global situations’. Are these assumptions correct, possible, relevant, and complete/incomplete?
A definition of technology ‘as a way of acting’ (Muffolleto, 1994) defines a multilayered concept of technology: ‘technology as a way of acting means not only the use of technology but also the thinking patterns associated with and/or influenced by its use’ (K Henry, ETEC 533, 2012). The cyborg, a seamless integration of ‘man’ with computers/machines/technology, emerges (Harraway, 1991).
So here we have man (students and teachers), machines, and technology integrated. The roles and place of ‘man’ and ‘technology’ (technology as a metaphor) determines effective use and effectiveness.
The Process
Let’s go back to Simulations and their role/potential. Simulations show great use and potential as seen in Jasmeet’s use of Food Chain. Diana comments on the highly interactive and dynamic interaction: “I really appreciated seeing the numbers change over years AND being able to see it visually in a graph”. Such dynamic visual representations offer concrete reference at some levels as seen in Mathematics simulations e.g. Parabola transformations. Simulations allow students to extend possibilities that are not offered in real classrooms without technology. They offer students’ knowledge integration and extrapolation that would not be possible without the technology. The latter was reflected in my interview with a colleague on the affordances of the use of Interactive Whiteboards in the Mathematics classroom. Students are also enabled to engage in learning that can ‘push’ human knowledge and capacity through technological affordances of opening a myriad of possibilities and removing many limits/boundaries . For this reason Conrad Wolfram encourages the use of computers as a part of Math education. Simulations and IWB offer visualizations and extrapolations but what of other elements? What is the point of Math education and the Math experience?
Getting the Math out
Dr. Hutchinson in her keynote address at the conference asked: “What do you expect your students to demonstrate after experiencing effective Math demonstration?” My answer to the question was that I was primarily interested in students being able to apply math thinking, skills and processes themselves and to also engage in that process. What is missing? As Darren and a number of other colleagues in our course discussions point out, having the technology does not mean it is effective as reflected in the viewing of the video case analyses, Learning Environment 1 with Teacher F (Mathematics Graphing Calculators) , in which ‘the lecturer noted that one issue was asking appropriate level questions that get the ‘Math out’ and not just the calculations’ (Video Analysis). In some cases in fact it is believed that a reliance on technology has reduced lecturers’ creativity. Jeffrey Young’s article about J. Bowen discusses When computers leave the classroom, so does boredom. Dean Bowen removed computers from classrooms in order to encourage teachers to use technology more effectively by going back to searching for more engaging and meaningful experiences for students. How do we ‘get the math out’ and how does technology effectively support this? In response to Jasmeet’s simulation Diana, while embracing its affordances, nevertheless linked it to a pedagogical model. “[it is ] a really good example of a computer simulation for younger students where we can employ the TGEM model”.
TELE : technology and embodied pedagogy
A technology enhanced learning environment (TELE) links a technological process with pedagogical models, and learning theories and models. For example, “Learning-for-Use (LfU) was originally designed in part to try to meet the conflicting demands of content and process in science education. Too often students learn knowledge or content but cannot apply it in realistic situations”– Janet. WISE is and example of technology embodiment in that it incorporates all elements in one learning environment with the inclusion of reflection and metacognitive elements within the tasks themselves. Jasper uses multimedia and presentation tools that motivate and present anchored problem solving using real experiences but also to give students enough motivation to seek out additional information. The use of simulations as presented in MyWorld is also noteworthy in instructional design and delivery and was central to my experience exploring the benefits of/place for and/or use of simulations. Even though each model and technology used had positive impacts, particularly in promoting inquiry and discovery learning and extending classrooms, communities of practice and offering concrete reference some gaps; in others, such as MyWorld, gaps were seen in ease of use of interface, support for scaffolded processes and opportunities for reflection.
Kozma (2003), Wolfram (2010) and Rosalyn Kelly (2012) highlight additional issues in the representation, understanding and use/application of concepts: “Designers should provide students with environments that restructure the discourse of …classrooms around collaborative knowledge building and the social construction of meaning” (Kozma, 2003, p.9). While my explorations centred on real-world applications and experiences I neglected the navigation from real-world to abstract and from abstract back to real world, which is considered by both Wolfram (2010) and Kelly (2012) highlight this as the main skill that determine ‘expertise’ over ‘proficiency’ and sustained success in mathematics education. Both Wolfram and Kelly (2012) note the gap of transference and navigation between real world and abstract concepts: “In secondary school we are making the relationship between the abstract and the concrete making generalizations and proving things” (Kelly, 2012, Mathematics Education Conference). Wolfram (2012) proposes the process as:
i. Posing the right questions
ii. Going from the real world to Math formulatio
iii. Computation using computers
iv. Math formulation to real world, verification
The extended model: technology embodiment
Within my practical experience in teaching College mathematics and based on my interview and further extension with my framing issues assignment the steps that are most critical, particularly, for at risk adult learners are that of knowledge construction, and having an interactive means for observing and experiencing the phenomena and in applying understanding (the knowledge construction and knowledge refinement stages respectively) (Edelson et al., 2002).
Wolfram proposes that students use computers for step 3 and teachers etc. concentrate on steps 1 and 2 and 4 so Math is not equal to calculating but involves calculating. Here calculating becomes a means to an end. This is basically the philosophy held in the Video case analysis of the use of graphing calculators in supporting active Math in which the lecturer advocates for the teacher to spend more time on developing the ‘right’ questions to ‘get out the Math’ . Less time spent on teaching the calculation, more time spent on developing ‘expertise’ in modeling the real-to the abstract and vice versa. Wolfram proposes separating the basics of what you want to do from how it gets whereas I propose an extension in the ontology of technology embodiment with no separation of people, systems and processes such that “TELE should be problem oriented as well as theoretically oriented. Technology should look at solving problems as well as supporting theories” – Marc.
To achieve technology embodiment, an extended model of that proposed by Wolfram (2010) will infuse pedagogical models such as POE, to predict results prior to computation. It will also include an interactive process to computation, enabling knowledge construction using visual representations such as simulations, and scaffolding activities such as hints and feedback, in an integrated system such as WISE.
This involves technological pedagogical content knowledge TPCK Khan (2010): “TPCK … encompasses knowledge of: how different concepts can be represented using technologies, pedagogical techniques that employ technologies to teach content, what makes concepts difficult or easy to learn, students’ prior understanding and skill set, and how technology can help redress some of the problems that students face.” (p. 216)
What is agreed is to make math more practical and more conceptual. Wolfram suggests engaging in more programming and using real questions. For example, what happens when you increase the number of sides of a polygon, what is the- best life insurance you can get, mortgage payments. In her classroom Danielle uses such models with ‘manipulatives’ and hands-on tools as central to the process: “For many topics, real life application is a stretch. To combat this scenario, I usually make sure students have access to manipulatives (virtual and hands-on) so that they are able to make sense of abstract concepts.” By extension new digital technologies such as Virtual environments, field trips and interactions, offer an advantage in adding expert and real life contact for students, which is important in clarifying misconceptions and evaluating observations et al. as well as in contextualising, clarification and modification of knowledge.
Conclusions
When technology is thought of a more than just the tools but also the process, people and systems then instructional design is such that strong pedagogical models are integrated and tools offering concrete reference, extrapolations, and visualizations and representations, are included in the design of effective TELE as seen in models, in varying degrees, such as: Jasper Adventure, MYWorld, LFU and WordlWatcher, WISE, and TGEM and Chemlab; and in classroom practices such as IWB integration, the use of graphing calculators and mobile technology in constructivist classrooms. All have valuable elements that should be included in the design of effective technology use in teaching and learning. For example, the use of anchored instruction and real-life problems, as found in Jasper, support scaffolding, practice, feedback, revision, reflection, community learning (distributive cognition), divergent thinking/ instruction (the what if scenario) and the inquiry process/discover learning. Understanding how people think is an essential element to the foundation for the Jasper model (Pellegrino & Brophy, 2008). Formulation of problems and sub-problems occur here. At this point the technology can be integrated in an extended Wolfram model to have students manipulate real world problems into equations, employ POE, enter equations into the technology to create simulations and/or visualizations and solve. Translate back into a real world scenario to verify and compare results with predictions in POE. Students then explain occurrences and extrapolate. The process is pedagogically sound employing POE, steps in LFU (Motivation , Knowledge Construction and Knowledge refinement) (Edelson, 2001). At the stage of simulations, visualizations and solving of problems it should still be an interactive one in which students are prompted within inquiry utilizing naturally embedded hints (scaffolding), feedback and reflection, as seen in WISE. In this way we have embodied technology, as people, systems and processes as seen in the integration of: the student/user, the content, the pedagogy, discovery learning, knowledge construction, embodied cognition, distributed cognition, knowledge refinement (discussion and reflection) and the math process. The use of new technologies such as virtual worlds and mobile technologies in the technology infusion stages present opportunities for further embodiment and representation of knowledge and visualizations that also allow for increased engagement, extrapolations, collaboratories, extending classrooms, removing boundaries enabling and deepening cognitive affordances, desired inquiry, direction, independence and ownership and most importantly ‘Gets the Math out’ and supports ‘mastery’, ‘application, ‘transference’ and ‘flexibility of use’.
References
Bayaa, N. & Daher, W. (2009). Learning mathematics in an authentically mobile environment: The perceptions of students. International Journal of Interactive Mobile Technologies, 3, 6-14.
Bell – Hutchinson, C (Dr.). (Apr, 2012). Keynote presentation. Unpublished paper presented at Jamaica Teachers Association Education conference: Mathematics Education in Jamaica: Conquering frontiers – Providing solutions, Montego Bay, Jamaica.
Drijvers, P., Kieran, C., Mariotti, M-A., Ainley, J., Andresen, M., Chan, Y., Dana-Picard, T-D., Gueudet,G., Kidron, I., Leun, A., Meagher, M., & Leung, A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J-B LaGrange (Eds.)
Drexel Island on Second Life (2007). Drexel University http://drexelisland.wikispaces.com/
http://slurl.com/secondlife/Drexel/216/209/24
Mathematics Education and Technology-Rethinking the Terrain, 89-132, Springer.
Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385. http://onlinelibrary.wiley.com/doi/10.1002/1098-2736%28200103%2938:3%3C355::AID-TEA1010%3E3.0.CO;2-M/abstract
Edelson, D. C., Salierno, C., Matese, G., Pitts, V., & Sherin, B. (2002, April). Learning-for-Use in Earth science: Kids as climate modelers. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, New Orleans, LA. http://www.worldwatcher.northwestern.edu/userdownloads/pdf/LFU_PF_NARST02.v3.doc
Bell – Hutchinson, C (Dr.). (Apr, 2012). Keynote presentation. Unpublished paper presented at Jamaica Teachers Association Education conference: Mathematics Education in Jamaica: Conquering frontiers – Providing solutions, Montego Bay, Jamaica.
Kelly, R. (Apr, 2012). Conquering Algebra. Unpublished paper presented at Jamaica Teachers Association Education conference: Mathematics Education in Jamaica: Conquering frontiers – Providing solutions, Montego Bay, Jamaica
Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.
Kozma, R. (2003). Technology, innovation, and educational change: A global perspective, (A report of the Second Information Technology in Education Study, Module 2). Eugene, OR: International Association for the Evaluation of Educational Achievement, ISTE Publications.
KWL charts http://olc.spsd.sk.ca/DE/PD/instr/strats/kwl/ Retrieved March 4, 2012
Mathscard – http://www.mathscard.co.uk/
Math Ref – http://itunes.apple.com/us/app/math-ref/id301384057?mt=8
The POE modelhttp://www.slideshare.net/TRENTON/technology-and-best-practices-in-science-learning-using-the-poe-model Retrieved March 4, 2012
Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303. http://ezproxy.library.ubc.ca/login?url=http://dx.doi.org/10.1007/978-0-387-76898-4_14
USC mobile apps http://campustechnology.com/articles/2012/02/06/usc-launches-mobile-apps-for-online-graduate-programs.aspx Retrieved 29 February 2012
Virtual Field Trips – Field Trip Earth
http://www.fieldtripearth.org/index.xml
Wolfram, C. (2010, July). Conrad Wolfram: Teaching kids real math with computers. [Video file]. Retrieved from http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html