IT Research Colloquium

Let me start this by developing a little bit on my response to these questions that I gave during the Colloquium.

As I said, I believe that the best way to learn something is to experience it firsthand. It’s all about the experience. If you can’t experience something firsthand (and for most things, that’s the case), the next way to learn it is through a simulation of that experience.

I think of every other kind of learning as some form of simulation, with varying degrees of fidelity in respect to the “real experience.” Someone telling you a story (direct instruction) is a low-fidelity simulation (forcing you to construct most of it in your mind). Learning from a book falls along similar lines. Visual instruction through pictures an film/video are higher fidelity, as they leave less to your imagination. Interactive 3D virtual reality simulations provide a much higher fidelity experience.

In support of my argument about the value of the experience as the best form of education, consider the following questions: who would you rather have piloting your next flight given these options — a pilot with 1000 hours of actual flying experience, a pilot with 1000 hours of experience in a realistic simulator, or a pilot with 1000 hours of studying flight manuals? Most people would choose the pilot with actual experience over the others, and given a choice between the pilot with simulator experience versus the pilot who just read manuals, most would choose the one with the simulator experience.

In this example we see the role of technology: it provides us the capability of bringing the learning experience closer to the “real thing.” In the case of math, what is the “real thing?” It’s hard for me to define, but I’m sure it can be defined in terms of an experience. The applications that Dr. Garofalo showed us (both during his talk and in the paper) give the student a much richer experience of math, and in most cases, an interactive experience. I see this as performing in a similar role as the flight training simulator in the scenario previously described.

I think many people would argue that this view of education can not be universally applied, because many topics are abstract in nature (and such abstractness prevents us from defining the “real experience” for these topics). I think it is possible to frame all abstract topics in a concrete experience, perhaps it’s difficult and may elude us, but I think the experience is out there waiting to be discovered.

I’ve recently been reading a lot about technological pedagogical content knowledge (see the TPCK wiki). And, although I agree that technology by itself can facilitate learning in some instances, I find it increasingly difficult (given my awareness of TPCK) to extract the pedagogy from the technology.

I’ll use Eddie’s pilot training example to illustrate my view. Like Eddie, I agree that there are “varying degrees of fidelity in respect to [a] ‘real experience’.” And, accordingly, I would prefer the pilot who has had the 1000 hours of actual flying experience. However, if that pilot isn’t available, the decision becomes more complicated. What pedagogy went into the development of the flight simulator? Do the controls in the simulator match the controls of the actual plane that will be piloted? What types of assessment were built into the simulator? Etc.

Thinking specifically about mathematics and Dr. Garofalo’s work, I think he’s been successful due to the fact that both the pedagogy and the technology were addressed together. Dropping a piece of technology on top of an instructional problem will do little to improve it and may even exacerbate it. But, understanding how technology, pedagogy, and content work in concert may provide opportunities for real improvements to both teaching and learning. As IT folks, we should even be prepared for solutions that don’t involve state-of-the-art technology - traditional instruction might just prove to be the most appropriate approach to a problem.

Eddie, you make a good point about all learning being some form of simulation. I don’t know if you have heard of Edgar Dale, but your reasoning is very similar to some of the theories he developed, especially the Cone of Experience. Some people argue whether or not he actually came up with the percentages or if those were added in later by those who built upon his theory. Like you, he believed that one of the affordances of technology was that it gets us closer to the actual.

I think most people will agree that technology shouldn’t determine our goals as teachers, but I believe as new innovations emerge, the opportunities they offer in the classroom will change the way teachers approach pedagogical problems. Many times, after I analyze the learning outcomes for my students, design the instruction and choose my materials to teach the lessons, I will actually go back and restructure the lessons because the technology facilitates activities I hadn’t thought of. In this way, the technology not only “fits” the teaching methods, but it also transforms them to some degree.

I strongly agree with Eddies’ view that more actual experience you get, then easier you learn. Most of the curricula are actually abstracted from the real world experience in order to teach student in the school environment—which is a very economical way to deliver knowledge and to build skills, however, there will be tradeoff in the abstraction process. Students usually encounter difficulties to acquire abstract knowledge and skills which are not really practiced. Technology provides us a great way to make the abstract knowledge visible and vivid, and also provides students with numerous opportunities to practice.

As I address to Eddie’s first questions, I have similar concern with Dennis on utilization of technology in the classroom. It was not easy for me to integrate technology with learning content to achieve intended learning goals. In many cases of mine, the “technology supported class or lesson” is used more for presentation to parents or others rather than for effective instruction to students. However, Dr. Garofalo’s work has shown the successful adaptation of technology in mathematic education. I agree with Dennis’ attribution of the success to “the fact that both the pedagogy and the technology were addressed together.”

And then, what the model of Dr. Garofalo provided students for better understanding on subjects? Unlike Eddie & Jie, I thought the matter of learning styles and meaningful input. For me, the visualization of some math software is another format of input. That is to say, students may have deeper understanding on subject-matter through various experience-input types (visual, audio, psychomotor, or high order thinking). The math software added a vivid visualization to abstract reasoning. It also related with learning style. One of the reasons the teacher should provide various learning experience is to meet the variety of learning styles among students as well as to connect learning to various experience within a student (meaningful input).

What do we consider in adopting technology to provide various learning experience? Depending on the characteristics of subject-matter the affordance and constraints of technology may differ. In case of mathematics, it highly depends on abstract reasoning. Visualization may increase understanding a complex math rule. In younger classes, nuts are used to enhance add-subtract math skill in a similar context (Kinetic, visual, and tactile input). Simulator training will be the most effective model for psychomotor domain of learning. However, how to install technology in instruction is more important than what technology will be placed. So, we, ITer, need to understand well on contents, pedagogy, and technology to make them synergic.

Looking back my school days, I had a bad learning experience on Math. I depended on rote memorization of the formula without conceptual understanding of it. In Korea, it is highly competitive to get into the university. Most high schools teachers are didactic.
Pressure and concerns on SAT scores, curricula tend to focus on drills and practice rather than higher order thinking.

I was impressed by the excellent feature of Skechpad. Technology in deed enhances visibility by connecting abstract concepts to multiple representations. I think it is a useful tool to promote student’s learning of abstract concepts.

Just out of curiosity, how widely software programs such as Sketchpad distributed in Math class in public schools in the States?

Extending on Dennis’s comment that it is increasingly difficult to extract the pedagogy from the technology, it seems to me that Dr. Garofalo did not explain how different pedagogy was used in incorporating technology in math class as opposed to traditional class. Pedagogy changes as technology is applied in the instruction. How can we conclude that improvement of student’s learning result from only use of technology?

Some really interesting discussion here! Here are some of my thoughts in response…

Eddie introduced some of his thinking about simulation fidelity, and makes some useful and important points. (I’m a huge fan of experiential learning and feel that in general I learn best by doing and know many others do, too.) But, in the spirit of encouraging discourse, let me add some other ideas…

- I’m not well-versed in the research data from simulation research, but recall an AECT conference symposium in which I heard David Merrill (well-known IT theorist) describe research conducted on military simulations). While acknowledging the value of simulations for encouraging skill development and transfer to future situations, Dr. Merrill suggested that there is a point of diminishing returns–that the highest fidelity in military simulators hadn’t always led to better performance.

- There are benefits associated with the investment learners make when they are engaged in imagining. Think of the different experience attached to reading a novel and then seeing a movie based on the novel. Sometimes, we’re disappointed at the impoverished experience the movie supplies, relative to the rich experience we had conjuring up the characters and their challenges in our mind… And that richer, imagined experience might tend to stay with us for longer because of the greater mental investment made.

- Would I rather have a pilot with actual flight experience or simulated flight experience? Good question! I want both! The simulator can provide pilots with a wider range of flying experiences, including simulating the more uncommon and most dangerous weather patterns, plane malfunctions, etc. Certainly this is the “richer experience” that technology promises.

Jaeho suggests that, “One of the reasons the teacher should provide various learning experience is to meet the variety of learning styles among students …” There has been significant interest in our field, in matching instruction to the learning style of the student and technology promises to offer this flexibility. As instructional designers, I believe we can go a long way toward encouraging student interest by embedding a range of learning styles, deepening the experience (what I think Jaeho is suggesting) and offering students a chance to improve their learning skills with less familiar modalities. However, there are some alternative points worth considering:

- Research does not provide strong support for “aptitude-treatment interactions” (ATI) — matching the instructional treatment to student aptitudes. Several decades of research suggest no particular benefit for going to the trouble of assessing student aptitudes and doing the matching of instruction to suit. There could be a variety of reasons for this: aptitudes may shift over time (development of aptitudes) and across tasks (different aptitudes are employed for different tasks), and so be difficult to reliably and validly, measure; instructional treatments could be confounded, with more than aptitude-related changes being made between them, etc.

- UVa psychology professor (and Associate Director for the Center of Advanced Study of Teaching and Learning - CASTL), Dan Willingham wrote a very readable review of the research on learning styles: Willingham, D. T. (2005). Do visual, auditory, and kinesthetic learners need visual, auditory, and kinesthetic instruction? American Educator, Summer, 31-35, 44.
http://www.aft.org/pubs-reports/american_educator/issues/summer2005/cogsci.htm
In short, Dan suggests that learners may prefer different learning styles and we might make instruction more attractive to them by calling upon the preferred sytles, but research doesn’t indicate that this is more effective–it doesn’t lead to better student outcomes. Instead, Dan points out, there is one (or more) optimal learning style(s) for a given instructional task, and that better performance is attained when that style is called on within the instruction.

I hadn’t intended this post to achieve book length, so will stop here!

I agree with Eddie that bringing a learning experience closer to the “real thing” facilitates the learning process and technology can assist with this. I also think that what made Dr. Garofalo’s examples so pertinent was their grounding in “real world” experiences. The example that comes to mind is the illustration of matrix multiplication that Dr. Garofalo demonstrated. I think most of us felt that we never really understood this abstract concept prior to activity, but had a strong understanding after the activity. The factor that made this activity so powerful was not necessarily due to the technology (at least for me), but due to its grounding in an authentic problem. I could see the same activity being just as powerful using pencil and paper and I could also see the technology-enhanced version having little effect on learning if the examples (menus, pizza restaurants, class needs) were removed. As Dennis explained, this is an example of pedagogy and technology working together to solve an instructional problem. Without the pedagogy, the technology would not have been effective.

For the teachers, technology such as sketchpad, can save them lots of time of drawing, especially for some teachers who are not good at graphing. With the help of technology, when they are preparing for the class, they can spend much more time on considering how to make appropriate lesson plans and how to improve pedagogy of the lesson.
For students, taking geometry for an example, sometimes, the inaccurate graphics would influence their understanding for the problem. In addition, using some software, dynamic shapes of some graphics can be shown to students, which can develop students’ spatial thinking skill, and help them to understand the abstract questions.
As for the technology and pedagogy, sometimes, it is hard to say which one is more important. I know in China, some experienced teachers are not good at technology, and in some poor areas, they have little technology appliance, and some teachers in the poor areas just use the chalks, and the students just have paper and pens. However, they can still learn Math very well compared with the school which is full with technology.

I agree with several of the points that have been brought up in the previous responses with respect to learning through “authentic activities and experiences.” Others reading this blog with K-12 teaching experience, however, will probably agree with me when I say that finding and/or creating real, authentic, learning activities that incorporate technology are VERY rare. In addition, once they are found it can be difficult to implement them at the right time of the curriculum.

As a high school math teacher, I constantly tried to find ways that I could implement these types of activities, but I found that even with some of the most interesting applications or cover stories, some students were still apathetic. Additionally, certain students would engage in the activities, but lacked “mathematical focus”, rather focused on the activity as form of entertainment or as a game. The reason for this apathy or lack of focus could be attributed to several possible causes. First, it was clearly evident that some of the activities that I found online or from other sources were clearly not developed by someone with mathematics content knowledge or teaching experience. Consequently, while the materials where visually appealing or entertaining, the actual content did not address the necessary standards that were to be taught. This example fits in nicely with the TPCK points that Denis brought up. In this instance the creators of the activities has the “T” part down, but lacked the foundation in the “P” or “CK” to build effective technology lessons. At times classroom management issues arose or student engagement was not at a high level. I learned this the hard way my first year of teaching. Another reason is that what might be a genuine, authentic, rich experience for one student, might be completely irrelevant for another. Invariably, each student’s personal interests are going to be different. To try and combat this problem, however, Carnegie Mellon is in the process of creating a morph generator for mathematics word problems. So students can select a topic of their choice such as music, sports, movies, etc. and the problem will automatically generate a cover story more applicable to individual interests.

During my experiences in the classroom I found it difficult to try and cover all of the state standards and at the same time implement fun, authentic technology. However, as a result of Dr. Garafolo’s presentation, coupled with this discussion, I am becoming more optimistic that effective, authentic, technology-based mathematics applications are out there. It is our job now to locate the good ones, and continue to develop technology-based materials that include all aspects of TPCK.

I like that in the math-oriented technology bits, we got to see things that very clearly couldn’t be done as easily without a computer. In language arts, the clarity of this is not as present. But showing the 3-D images and the measuring-under-the-curve program for calculus, was just plain cool. Last semester we saw a great animation that demonstrated the sine curve that was equally obvious in its practical use. The tables/layout of the pizza example was another example of how the visualization and animation process can make things clear.

What stood out the most was the way technology could be integrated in such small doses. Any one of those things could have taken anywhere from 30 seconds to 5 minutes to show. In language arts, I have come across no such thing. Typically, technology comes within a bigger project that goes on for between a few days to a few weeks. This distinction is interesting to me and has gotten me thinking about ways i might integrate technology in smaller chunks…thanks!

I agree with Pat’s astute reasoning as to why some of his students remained apathetic and lacked focus. However, before actually reading his reasons, my immediate response was, “Students are apathetic and they lack focus because they are being held captive in the classroom and they don’t want to be there.” But that issue is an elephant in the parlor, isn’t it?

I was going to leave my cynical self in Mt. Pleasant, but I felt compelled to comment here as I read maggie16’s comments about high math performance coming out of the poor, low/no-tech areas of China. I wonder whether we’re not failing to adequately account for the dynamics of broader sociocultural conditions. Here’s my thought–maggie16, please correct me if I’m off-base here–I suspect that in low-end China, instruction is very didactic and there is little tolerance for non-compliance and poor performance within the classroom, which is no more tolerated by the society at large. In the US, our education system is based on a similar, father-knows-best, approach. Unlike the Chinese, however, we seem to lack the appropriate follow-through for this approach. In other words, we don’t have a problem forcing students into classrooms for years on end and subjugating them to standards, but we fail to follow through with the logical extension of this approach, that is, to coerce all students into producing desired performance outcomes through direct behavioral conditioning within a context of societal conditions that reinforce such a system.

We drop the ball at this point not because it slips out of our hands, but because modern western sensibility tells us that coercion is less desirable, and that there’s more to the story of life and learning than what might be achieved through rote memorization. So, we let up and begin to infuse the system with more individualistic and humanistic elements. Unfortunately, we end up simply trying to mash the round pegs of progressive pedagogy into the square holes of the old school. The result is a frame that doesn’t sit well on it’s foundation, and now we’re stuck wishy-washy between oldschool and newschool. In the end, we don’t do oldschool very well, we don’t do mainstream progressive stuff very well, and we don’t even come close to newschool. For those of you who don’t know me, or for those of you who haven’t already surmised, to Michael, newschool = unschooling & free schools. And yes, I did wake up on the cynical side of my bed, this morning ;o)>>>

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