Multiplication Problems

Normal 0 This week in class, we heard a presentation from a company called EdisonLearning. Their online learning model is very interesting, and I found it a fascinating real-world application of some of the concepts we’ve been talking about in class.

Edison’s strategy is to create highly componentized course modules, which allows the firm great flexibility to re-package lessons for various clients depending on the desired syllabus, learning goals, length of school year, etc. It’s an ingenious workaround for a difficult problem: educational needs and standards vary dramatically from state to state in the US. The issue extends well beyond the education world: I used to work with vendors of software for insurance companies, and insurers faced a similar problem with state regulatory frameworks. Clever vendors were able to design flexible systems that could bend to meet different legal demands, and Edison has done something similar—except that I think it’s quite a bit tougher to deal with shifting demands in a process as sensitive as designing a curriculum.

This got me thinking about the role of policy in the world of educational technology. With the Internet, information and education have the power to spread across borders with incredible rapidity and ease, and the dissemination of personal computers (in wealthy parts of the world, at least) allows for a unprecedented ability to scale up an existing product. On the other hand, legal frameworks and, of course, educational goals and standards are still very localized, which diminishes the potential to achieve economies of scale.

In the short term, this situation presents a challenge to creators of educational technologies, although certainly clever solutions like Edison’s can help tremendously. In the long-term, however, I wonder whether learning technologies could contribute to a slow convergence of statewide educational standards. The inefficiency of the United States’ patchwork testing system has frequently been noted. Technological solutions probably will not be widely adopted by public school systems unless they are shown to be cost-effective, but of course, much greater economies of scale can be achieved if such systems can be used in more states.

One might argue that a similar principle could be applied to textbooks, and to some extent it does. However, I think there is less incentive for school systems to clamor for similar standards to lower the cost of textbooks, because I think the differences will be less dramatic: even if textbook prices drop a little, books are still physical objects that need to be re-purchased every year due to wear-and-tear or the need to update the edition. With technology, on the other hand, the difference between two or twenty states using a system could make a great difference to the affordability of the system.

The longest distance between two points

In class this past week, we each presented on a research project we’d carried out about electronic tools designed to address a social problem. The presentations were all so wonderful and ingenious! Topics ranged from documenting vanishing cultures, to youth radio stations, to resources for ADD sufferers. Really cool stuff.

During the presentations, I couldn’t help but think how nice it was that our attention was being drawn to such a diversity of ideas, organizations, missions, and technologies. It seemed like some of the groups my classmates discussed might benefit from one another’s innovations. For instance, one student reported on a group in Africa called Naledi3d that maintains a database of virtual reality tutorials—on, say, farming techniques—which enables widespread users to view and use the lesson, even if they have limited literacy. Another student reported on groups in the US that aim to help the homeless find employment. It seemed like some of the US groups could adapt the notion of a tutorial database incorporating graphic content to the needs of their audience. The skills taught would be different—guides to service industry positions, for instance, rather than farming instructions—but the underlying concept seemed transferable.

These musings led me to consider the broader concept of intellectual cross-fertilization. What’s striking here is that these groups serve quite different audiences and in most situations wouldn’t come into contact. Oftentimes, it seems that good ideas emerge from just such happenstance—two apparently unconnected concepts happen to collide in someone’s head. The web makes it easy to search for the answer to a specific question. But what about when we don’t even know what the question is, or even that we should be asking one? Especially in distance learning environments, how can we provide time and space for such collisions to occur?

Well, one way for teachers of online classes to introduce that element of serendipity might be to take advantage of the various backgrounds of the students themselves, by, for instance, requiring them to write blogs and comment on one another’s ideas. Or teachers could rely on future events to supply surprises: for instance, students could follow current world leaders in the news and hold a weekly online discussion about the leaders’ adventures, which would no doubt allow for unexpected and interesting comparisons. Another strategy might be to assign traditional research projects, but to ask students to recombine them in unconventional ways, as sort of “research mash-ups”—for instance, a pair of students in an American history class who happened to research Harriet Tubman and Woodrow Wilson might be asked to think together about what themes or principles connect these two figures.

This still seems to me to be question worthy of further thought, because so often what we celebrate about technology is its power to streamline, to find the shortest distance between two points. Here, we’re looking for the opposite—for the meandering route that offers unexpected discoveries.

Geography lessons

This week I’ve been thinking a lot about “mind maps” or “concept maps”—web-like visualizations that represent ideas, words, or objects and the relationships among them. We used mind-mapping this week for an in-class group activity, via the website Mindmeister. Although I have friends who frequently use mind-mapping to brainstorm scholarly papers, research problems, etc., I’d never used the technique myself. To be honest, I felt a little skeptical; it felt so “gimmicky.” I preferred to brainstorm via stream-of-consciousness style notes. But after our class, I was intrigued enough to give it a try.

Since we’d worked with Mindmeister as a team in class, I hadn’t carried out much hands-on work with the tool, so my first step was to try creating my own mind map. As an example, I wanted to try mapping a topic around which I had few preconceived opinions or mental schematics. I chose the topic “health” and spent about ten minutes sketching out a map. Here is the resulting diagram.

To my surprise, the mind-mapping technique really did get my ideas flowing in a different way. For instance, if I’d been taking notes in my usual linear fashion, I think I would have name-checked emotional health and moved on; noting it as an idea-node weighted equally with physical health encouraged me to incorporate the concept of emotional health into my ongoing thought process, with the result that I added “stress management” to the “lifestyle” node.

Interesting. To further spur my thoughts, I turned to one of the recommended course readings, “The effects of a concept map-based information display in an electronic portfolio system on information processing and retention in a fifth-grade science class covering the Earth's atmosphere.” The focus of this study was not on creating concept maps, but on the merits of concept map-based navigation of electronic portfolio systems (in this case, for a fifth-grade science class) versus the traditional folder-based information display. The students who accessed course information via the concept map display were found to retrieve the information more quickly, score higher, and retain the information longer than their counterparts in a control group (although both groups found the activity fun).

For me, one of the most interesting parts of the article was the teacher’s remark that one of the students, who spoke English as a second language, repeatedly said he preferred concept maps to reading long paragraphs. It makes sense that a portfolio structure encompassing visual demonstrations of relationships, as well as pictures and video representations, would be more accessible to a non-native speaker. (Although here, we shouldn’t forget that different cultures may well choose to map the same concepts in very different ways!).

This remark also made me think about how concept map creation might be used in language learning. Most obviously, one could map out concrete vocabulary nouns (“Here are objects that belong in the kitchen. Here are objects that belong in the library,” etc.). More interestingly, one might ask students to map relationships among objects using connecting arrows, then ask the students to find suitable verbs for those arrows. Or to make maps of more abstract concepts, such as “community.” I’m sure there could be many potential uses I haven’t thought of yet…

Coming back to the technological aspect, I have to say that now I’m excited about mind maps, but somewhat less excited about online tools for building them (or at least about the one I used, Mindmeister). To me, Mindmeister doesn’t offer the flexibility of a whiteboard, or of pen and paper; for instance, I found I couldn’t combine a web with a Venn diagram in my “Health” map. Of course, online tools do boast other advantages, such as the ability to share a map with the whole web or upload photos. But it would be nice to have the best of both worlds. Still, I do think that the technology will reach this point in time.

Thinking about thinking

In this week’s class, I was interested by our discussion of “meta-cognition,”—loosely defined as thinking about one’s own thinking. For example, reading a novel would simply be classified as cognition; musing “Why did I enjoy that novel so much?” would be meta-cognition.

The sheer power of the artificial intelligences that reside in today’s computers poses interesting meta-cognitive questions to learners. The example that springs most readily to my mind is the Perseus Project, an online library that hosts virtually all the most famous works in Ancient Greek and Latin—Caesar, Catullus, Homer, etc. Every word in the text is hyperlinked to a dictionary entry and various other statistics such as the frequency with which it appears in that text, frequency in other Greek texts, etc. Classics classes in literature are typically very translation-heavy, and Perseus can be an incredible timesaver to the busy student. This is especially true when it comes to Ancient Greek, in which verbs can change their morphology quite a bit, forcing the student to waste lots of time flipping through a dictionary looking for the right root form.

Whether to use Perseus or not is something of a debate among Classicists. It seems easy to dismiss the time wasted in long dictionary searches as useless. However, many professors and some students say that the process of searching forces the student to learn the various forms of difficult words, especially common ones, as well as the related words that will tend to show up in the dictionary next to it. It’s all too easy to click on a hyperlink, write down a definition, and move on—which will leave the student in poor shape when it comes time to take the unassisted final exam. A student who owns up to using Perseus will often sheepishly add something like, “Yeah, I know it’s evil, but…” Thought of in terms of Bloom’s Taxonomy, Persues is a shortcut past the boring-but-fundamental memorization—the “knowledge”—to the fun bits, the translation and analysis.

So is Perseus really evil? Myself, I like to advocate a third, technology-enabled way: the tool also allows you to easily sort the Greek words in a text by frequency. A word that recurs several times in critical passages is most likely worth memorizing; some strange word for an herb or a type of shoe, probably not.

So here—and I think the lesson is applicable to other cases, as well—technology does allow us to study smarter. But it forces on us a certain type of discipline that wasn’t at issue before: there’s less gruntwork, but a greater meta-cognitive investment is demanded of the student, who has to honestly assess his or her own learning process. By and large, I think we come out ahead. “Know thyself”…no matter how you translate him, Socrates had a point!