Final Reflections
IN THE BEGINNING
1. Ideology & Questions
In the beginning of the course, I was mainly focused on how the affordances and constraints of any technology device affects the quality of the learning; in particular, I was focused on Smart boards or tablets could be used more effectively to teach high school math and science. Since I have a humanities background, I was relying heavily on what I had observed in my own school in terms of how these subjects are currently taught. I was thinking that digital whiteboards could be used more effectively as they seem to result in transmission, and sometimes, demonstration teaching. I was certain this was not a best practice in these subjects, but I was not sure how else it could be done. From my learning in ETEC 512, 510, and 511, I was sure that there must be better methods for students to actively build knowledge.
2. Questions
The main question of focus for me when I started the course:
What are the best technology resources to teacher STEM subjects?
I wasn’t really sure what I would discover, but I expected to receive a number of applications for teaching particular concepts in math and science.
Khan Academy is a high profile site that is popular, so I thought that it may be a focus in this course. There are numerous online games, interactives and tools, and it is difficult to sort through what is useful and what is just distraction. I wanted to know how to use technology to motivate and engage learners in a meaningful way. Current science teachers in my realm are using technology to supplement the learning for initial teaching on a whiteboard or practice and reinforcement of concepts: for example, drill and practice, video or animation demonstration / explanation, and simulation experimentation (Gizmos). There is a desire to have a set of iPads so that students have a tool for accessing the internet, online learning objects, and science applications. Sabrina noted in our Framing Issues discussion that a great deal of time is wasted by searching for good, useful applications, and often more time is spent finding a good tool than the students spend using it!
As we explored questions we thought were important and completed our interviews, the following questions were prominent to me:
How can misconceptions in STEM subjects be prevented?
Is problem-based learning more effective for every student?
What is more important—software or teaching techniques?
Does technology use in STEM subject improve learning? (Samia, response to interview posting)
Can virtual experiences replace “hands-on” experiences? (Samia, response to interview posting)
Is there enough time to get through the curriculum and to allow for these rich opportunities for deeper learning and addressing misconceptions? (Janet, my framing issues posting)
EVOLVING PERSPECTIVE
1. Framing Issues
My approach to my framing issues paper on the effectiveness of computer-based math instruction as applied to eLearning environments was affected by my perspective of what I thought was important at that point in time. Since I teach (grades 11 and 12 college bound or workplace) math in an alternative education setting and I have an interest in becoming the eLearning Contact person for my school board, I wanted to learn more about effective online learning environments (LEs) that could be used in my context where students are working on different courses at their own pace or in an eLearning context. Currently, the materials and methods are very traditional whether it is eLearning or independent study booklets—read the content and examples, complete the practice questions, and complete the evaluated questions. In ETEC 500, I completed my research assignment on the effective use of multimedia in eLearning environments and discovered (not to my surprise) that eLearning has low success rates among non-academic (university bound) and male high school students (Kirby and Sharpe, 2010). These researchers highlight the need to determine why success is low and why? I hypothesized that the course formats are a significant factor since academic girls are more likely to accept traditional materials, but boys want a more engaging learning experience. Thus, I wanted to focus on research about various LEs to determine what is most successful.
There were some connecting observations noted from my literature review regarding effective LEs for teaching math:
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motivating and engaging students through real world problems (Bruce & Ross, 2009; Hubbart, 2000) and higher order thinking as opposed to drill and practice (Bos, 2008)
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interaction with peers as they solve problems is very helpful to learning (Hubbart, 2000)
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scaffolding complex concepts helps reduce misconceptions (Bruce & Ross, 2009)
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use of visual representations to make abstract concepts more concrete (Bruce & Ross, 2009)
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teacher pedagogy is more important that a well-designed LE (Cavanah & Mitchelmore, 2011) as the teacher is needed to guide the learning (Bruce & Ross, 2009; Hubbart, 2000)
2. Misconceptions
Initially, as mentioned, my thinking surrounded how we could prevent misconceptions; however, as we delved into this topic, I realized that exploration of misconceptions in STEM subjects can play a positive role in student learning. As Rebecca stated, “making mistakes and addressing assumptions may help students to be open to attacking their own learning from an objective perspective.” It is that process of remediation (Driver et al., 1985) that is needed to assimilate or accommodate new information (Posner, Hewson & Gertzog, 1982). Misconceptions are a natural and unavoidable part of learning (Gonen, 2008), and they occur at every level of education. As stated in my Conceptual Challenges posting, “a person’s understanding evolves as s/he matures and becomes capable of abstract thinking… (Posner et al., 1982, pg. 79).” STEM learning should involve a process of identifying and addressing student misconceptions.
I learned first-hand that dispelling misconceptions is not as easy as it might first seem. My idea for teaching gravity using a vacuum experiment could still result in misconceptions because it is such a small dropping space. Learners may question what would happen from a higher fall which is not available to us without wind resistance. Thus, additional experiments are required to demonstrate the law. Air resistance experiments could be used to support the reverse by showing wind resistance is a definite factor. Several examples and counter-examples are needed.
3. Ideal TELE
My initial perspective of an ideal TELE was shaped by my study of multimedia (ETEC 500) and effective technology design (ETEC 510):
“An ideal TELE for the math or science classroom would be well-organized with an intuitive, clear design that is free of extraneous elements (distracting ads or visuals) and is focused on a particular task or purpose. Planned content would be scaffolded, and there would visual support (images, animations, films) for textually presented information. Students would be able to access as-needed content areas. They would also be able to do the following: share and compare data or ideas, annotate anything (for self reference), sort information in a variety of ways, collect and organize their artifacts, and create meaningful visualization. Finally, it would be engaging and rewarding to partake in the experience.” (Wagner, 2014, Ideal TELE Discussion)
I still agree with my ideal TELE definition; however, I believe it has become something more since studying TELEs in Module 2. The design concepts gleaned from Jasper, SKI, LfU and T-GEM, which have some commonalities, enrich this definition.
HOW I SEE NOW
1. STEM Learning
I began to see STEM learning differently when we examined the case studies. In reviewing the graphing calculator learning where students create pictures using the functions. It was quite obvious that the students were engaged in the task. There was an atmosphere of collaboration and they were very actively learning the concept. It was a great hand-on use of a technology. STEM learning should be an active process and not simply transmission, memorization, computation, and isolated word problems.
The Jasper Woodbury Problem Solving Series has several merits even though it is now somewhat dated in technology and appearance. As Mel noted, it was created to challenge traditional rote mathematics practices (Anchored Instruction discussion). Students become engaged in solving multi-step problems that have more than one potential solution; the instruction is anchored, “situated in realistic, problem-rich settings” (Cognition Technology Group at Vanderbilt (CTGV), 1992, pg. 78). Students work collaboratively with peers to determine a solution. The teacher acts as a resource or side-by-side learner with the students to help seek information that is not given or review skills that are needed to complete the task. Since lack of problem solving skills is a consistent problem personally noted and often mentioned by colleagues, these exercises are quite meaningful. The focus is on greater understanding as opposed to computational skills, and deeper learning occurs because of the active nature of learning. I appreciate the Jasper series’ constructivist origins, as stated in my Anchored Instruction discussion posting: “students engage in ‘generative rather than passive learning activities’ (pg. 67) that are more successful in overcoming their misconceptions (Confrey, 1990) because the more active process of using and refining their existing knowledge as they ‘attempt to make sense of alternate points of view’ (CTGV, 1992, pg. 67) results in deeper learning.
At this point, I was concerned about two things:
In pairing students, the weak student will over-rely on the strong student or the strong student may naturally dominate the work (Stephanie, Anchored Instruction discussion); pairing students of similar abilities could be a solution.
The process is time-consuming possibly without enough computational practice.
However, I believe that making problem-solving the center of the instruction was a key advancement of this TELE as becoming independent thinkers is crucial to mathematical understanding.
At this point, I reviewed the Scientific Inquiry steps and noted that they frame the following models that we explored: SKI, LfU and T-GEM. Each has cycles of inquiry built into the process that involves a variety of STEM learning TELEs.
A TELE designed according WISE principles has the following elements: student collaboration through pairing, well-planned content areas, dialogue with peers to evaluate and critique work, scientific inquiry, and individual reflection. A WISE project begins with an inquiry question that frames the learning; then students move through the content to get background knowledge about the topic; next, they engage in data collection within the environment; in response to the data collection, the students propose explanation based on their learning and current understanding; then they critique each other’s models; and, finally, they modify their initial explanation.
The WISE TELE seemed an improvement over the Jasper series; however, experimenting with existing WISE environments demonstrates that it is rigid in terms of what it accepts as answers and the multiple choice understanding checks are not as revealing as a short written answer. The ‘basket’ for collecting ideas is a useful feature as students can track their own understanding development.
The WISE system does allow for inquiry learning without the teacher being put in a position of ineffectively dealing with questions (Furtak, 2006) as students are redirected back to the content to strengthen their understanding; however, one can reach a point of frustration with being redirected to the content area repeatedly when having difficulty. The main point of the WISE project system is to confront students’ misconceptions and to result in deeper, lasting understanding (Linn, Clark & Slotta, 2003).
The Learning for Use (LfU) model (Edelson, 2001; Edelson, 2002) is a goal-directed process with experiences for the students to construct, assimilate or revise knowledge. The Technology – Generate Evaluate and Modify (T-GEM) model’s three step cycle which can recycle indefinitely as learners add new understanding to their mental models (Khan, 2007; Khan, 2010) is quite similar. All the inquiry-based TELEs we studied are concerned with students learning concepts deeply and not simply memorizing content; there’s a social learning aspect in terms of getting students to work and learn together, to benefit from a dialogue in pairs and then in large group to build or modify their understanding; they are all rooted in constructivism and there is an element of meta-cognition. SKI, LfU and T-GEM are focused on life-long, ongoing learning. Even though these examples were focused on science concepts and teaching, there is value in using this approach for teaching math as well.
The focus on embodiment (Winn, 2002) introduced another aspect of teaching STEM subjects with a consideration for socially situated learning. The body is an important aspect of the physical dimension that can help learners understand their physical world and thus gain knowledge. We use our bodies to solve problems, so “cognition consists of the constant, reciprocal, interaction between the mind and the environment” (pg. 11). When the learning is embedded in a real world situation that involves active discovery, the learning is more memorable, and adaptation in thinking occurs. There is a connection with this concept and the TELEs we have studied because they are focused on using real data and applications to make the learning more meaningful; it’s embedded in the activity. The adaptation in thinking is knowledge building or modification of current understanding.
Finally, participatory simulations are demonstration applications that can show STEM concepts visually with computer software (Colella, 2000). Complicated concepts can be demonstrated quickly, for example the spread of disease or the rate of burn for a forest fire in NetLogo. It’s even more meaningful when students can play a role within the system which is a sort of embodiment even though it is digital. Such applications could be incorporated within an inquiry-based learning model for students to hypothesize, experiment, and modify their understanding.
2. New Questions
My questions have evolved as a result of this course. Even though I had been told many times that we should be putting learning in the hands of the students, that it is not how much content we teach but students learning to learn (or the quality of what we do with less content), and that we should not be transmission teaching, I have been really at a loss for what that actually looks like in the classroom or how to plan for this kind of teaching. It’s not the way I was taught and it’s now the way I was trained to teach either, so I really wasn’t comfortable moving far away from teach and practice methods. Also, even though I had experienced some learning in this program about constructivist learning, I envisioned building content on a wiki or blog as opposed to a learning cycle that fits within the scientific inquiry model.
Here are some of my current questions:
How can I use a LfU or T-GEM model to teach senior high school math? In an alternative education setting? How can I get students to be less autonomous in this setting and working in pairs?
Can such a model be used in an eLearning context?
How can I incorporate embodiment in math for my students who have never developed a solid understanding of many basic math concepts? What kinds of physical activities and/or applications could be used to bring embodied meaning to a mathematical concept?
3. Future Practice
The problem-based learning of the Jasper series was novel to me, and I decided to give it a try with a few of my students who were taking the same course. I purchased a book recommended by Janet Galbraith called Hands-On Math Projects. They completed a buy a pet project that would be similar to a Jasper problem as there wasn’t one right answer to the problem of choosing as appropriate pet based on their own living and financial situation. They had to research and choose a potential pet, complete an initial cost spreadsheet to determine the start up cost, another spreadsheet of the monthly costs, and reflection questions. It was quite successful. The students learned how to use Excel better than they had before, calculated costs (sale prices and with HST), and made a final decision regarding whether they could afford their chosen pet. I would definitely use this approach in the future, and it was quite easy to incorporate into the learning. They will be completing another in the future as if they are a band going on the road for a concert tour. They will have to calculate travel distances, gas mileage, expenses, and income.
I have come to a new perspective on Khan Academy. It is a impressive database of transmission demonstration videos that are more often than not well-constructed and clear explanations. The short nature of the videos is manageable for my students to digest an idea and the practice questions help to reinforce their understanding; however, it falls short of inquiry-based learning which I believe is far more valuable. In my teaching context though, with the materials I have been given to deliver and the large number of courses for which I am responsible in a semester, it has been a great help to me. For example, I have a few students who should know fractions and exponent laws as prior learning, but they are still struggling with the concepts; thus, I had them go through the lessons on Khan Academy and they had a much better understanding when they finished. It lacks the demand to problem solve except on a small scale of answering individual questions with precise answers accepted in a particular format. I will continue to use this resource as I attempt to gradually transform the delivery of the math courses.
I was impressed with the following resources that I plan to use in math or science in my alternative setting to reinforce the concepts outlined in the course booklets: Chemland, NetLogo, Desmos, Geometer’s Sketchpad, and Phet (Colorado University). Although it is not what I would like to achieve in the long run, there is only so much time to perform course revisions when responsible for about 15 different courses in a semester.
CONCLUSION
Overall, I have found this course to be quite challenging to me since I am an English Specialist teacher; I performed well in high school and first year university math, but I avoided science like the plague. I did not enjoy the subject matter or classroom experiments as it seemed like an exercise of memorization in the way it was taught in my time. Currently, though, I feel more of an interest to learn Chemistry. I also want to instill in my students the desire to understand as opposed to how to get through the questions in the booklet (regardless of whether I learn anything). I have been having an interesting journey with them as I learn how to teach math and make discoveries I did not see before. Finally, I expect to incorporate inquiry-based learning in other classes as well. I see the value in using the T-GEM cycle, for instance, to complete a social studies inquiry on any number of world issues. We hypothesize on the subject, review evidence in the form of credible sources, modify our understanding, and then ask new questions. These inquiry models have merit in other non-STEM subjects.
References:
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Bruce, C. D. & Ross, J. (2009). Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence. Electronic Journal of Mathematics and Technology [online serial], 3(1).
Cavanagh, M., & Mitchelmore, M. (2011). Learning to teach secondary mathematics using an online learning system.Mathematics Education Research Journal, 23(4), pp. 417-435. DOI: 10.1007/s13394-011-0024-1.
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Kirby, D., and Sharpe, D. (2010). HIGH SCHOOL STUDENTS IN THE NEW LEARNING ENVIRONMENT: A PROFILE OF DISTANCE E-LEARNERS, The Turkish Online Journal of Educational Technology, 9(1), 83-88.
Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87(4), 517-538.
Posner, G. J., Strike, K. A., Hewson, P. W. & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Sci. Ed., 66, pp. 211–227. doi: 10.1002/sce.373066020.
US Board of Science Education. (2000). Inquiry and the National Science Education Standards. National Academy Press: Washington, DC.
Winn, W. (2002). Learning in Artificial Environments: Embodiment, Embeddedness and Dynamice Adaptation. Tech., Inst., Cognition and Learning, 1, 1-28.
Media Credit:
dan. (2009). Reflection Tree Stock Photo. Freedigitalphotos.net. Retrieved April 10, 2014 from http://www.freedigitalphotos.net/images/Trees_and_Shrubs_g75-Reflection_Tree_p9187.html.