Tag: curriculum

From novices to experts

Socrates teaching (from Wikimedia Commons).

The primary role of an instructor is to transform a novice into an expert within a given subject area. – Cooper (1990)

The above quote comes from a paper on instructional design by Graham Cooper. I don’t quite agree with it entirely since it does not seem to allow for a well rounded view of a student as an individual, or the Socratic ideal, but it does seem applicable to the more strictly academic areas in the middle school curriculum.

In order to figure out what distinguishes experts from novices, cognitive scientists have spent a lot of time observing the two groups. Their key finding has been that as you become an expert on a topic, you construct mental pictures (or schemes) of the shapes of problems, so when you encounter a new problem you can just fit the new problem to the mental pictures you have and see which best fits. It’s a bit like learning rules of thumb that apply to different situations. When a problem comes up, the expert can quickly whip out the right rule of thumb from their mental back pocket while the novice, though equally smart, needs to figure out all the steps with some degree of trial and error.

This is a nice perspective when it comes to teaching something like solving equations, but I think one important distinction of the Montessori philosophy is the belief that adolescents should also be learning flexibility, and be capable of dealing with novel problems. Because adolescence is when students are just becoming able to think abstractly (at least according to Paiget), and abstract thinking needs to be practiced, it is necessary that students encounter novel, challenging problems on a regular basis.

Pangea breakup in reverse (adapted from image in Wikimedia Commons).

A lot of creative and problem solving thinking comes from hashing out new problems. In a globalized world, where technology is capable of dealing with routine tasks, be they constructing a car or solving a series of equations, creative problem solving is becoming a more and more valuable skill. Especially now that “The World is Flat“.

The importance of thinking about thinking

Know thyself - Socrates (and others) from Wikimedia Commons.

Personal World is the time for introspection. Every day students get a chance to think about themselves and, hopefully, about how they think. Thinking about your own thinking is called meta-cognition, and there is growing scientific evidence that it is an important life skill that leads to better decision making.

According to Jean Paiget’s theory of cognitive development students only begin to develop the capacity for abstract and meta-cognitive thinking in the middle school years. However, further research has shown that only about 30-35% of high schoolers actually develop the skill (it’s called “formal thinking” or “formal operations“). The brain develops the capacity for formal thinking in early adolescence, but people do not naturally move into that stage; school and the right environment are important.

For formal operations, it appears that maturation establishes the basis, but a special environment is required for most adolescents and adults to attain this stage. – Huitt, W., & Hummel, J. (2003)

The requirement that students spend some time in introspection is one key way that Montessori adolescent programs try to promote formal thinking.

Finally, Jonah Lehrer, a journalist who writes a lot about how people think and makes decisions, points out the importance of metacognition in the qualities that make for a good president.

some studies suggest that when confronted with a complex decision – and the decisions of the president are as complex as it gets – people often do best when they rely on their gut feelings …
However, it has also become clear that listening to your instincts is just a part of making good decisions. The crucial skill, scientists are now saying, is the ability to think about your own thinking, or metacognition, as it is known. Unless people vigilantly reflect on how they are making an important decision, they won’t be able to properly use their instincts, or know when their gut should be ignored. Indeed, according to this emerging new vision of decision-making, the best predictor of good judgment isn’t intuition or experience or intelligence. Rather, it’s the willingness to engage in introspection” – (Lehrer, 2008; emphasis mine)

Other sites linking to this post

    Mind-Mapping software (Free)

    VUE mindmap

    I recently received a tip about the VUE mind-mapping software. It’s free from Tufts University and it’s open source, though you do have to register to download the software. A quick test that produced the image above shows that it’s pretty easy to use and can easily incorporate images.

    Free software. It’s better than coupons.

    Rock band and the choice of poetry

    Popular music lyrics have been used to introduce students to poetry (Brenda Guerra has a nice lesson plan on the subject). We recently had an overnight at the school and the students elected to play Rock Band. It was clearly indicated that the songs they played would have to have language acceptable to the Middle School. Among the song choices they made was Bon Jovi’s “Living on a Prayer”.

    I’d considered “Living on a Prayer” as one option for poetry reading but rejected it because I wasn’t sure that lines like, “she brings home her pay for love” would be quite appropriate. What I found most interesting was that even though they sung the song, they did not actually know the words. The game appears to only require them to make sounds of the right length and maybe pitch. So the singing sounded like, “Tommy used to blah blah blah blah.”

    So now I think I’ll use the song, but I’m curious to see the response. Will the fact that it’s something they are aware of and play in a game make it more interesting to them? Or will it work the opposite way? We’ll find out.

    This song also introduces issues of unions and the way the arts reflect society, both overtly and, in this case apparently, hidden in the music.

    Seeing temperature, kinetic energy and color

    We read that temperature is the average kinetic energy of a substance but you can (especially if you’re a visual learner) nicely internalize this from simple videos or animations. UCAR has a little animation with their definition of temperature. I however, adapted an interactive, 3d animation that I think does a nice job, and also introduces a couple of other interesting concepts too.

    I’ve also used this model, at different times, to show:

    • The relationship between temperature and color emitted by objects. The main way we know the temperature of stars is because blue stars are hotter than red stars. Blue light has a shorter wavelength than red light, and things that are at higher temperatures emit shorter wavelengths.
    • Absolute zero (0 Kelvin) – where (almost) all motion stops and the objects stop emitting light.
    • Pressure in a gas – you really get a feel for the force exerted by the particles on the side of the box (although it might be even more interesting once I figure out how to add sound).

    It is an interactive model, but it’s pretty simple because the only control is a slider that lets you set the temperature.

    Finally, in the age of 3d movies, like Avatar, the models can be easily shown in 3d if you have the glasses (redcyan).

    The model is easy to install and run on Windows, but you have to install the programming language VPython separately on a Mac (but that isn’t very hard). I have this, and a bunch of other models, at http://earthsciweb.org/GeoMod/.

    A sailing game that explores the trans-Atlantic triangular trade

    Discovering America

    Wind patterns over the North Atlantic Ocean had a huge effect on the colonization and history of the Americas because, after all, all they had were sailing ships. The circular, clockwise winds meant that it was easiest to sail south and west from Europe, and when you did, the first place you arrived at in the New World was the Caribbean or the northern edge of South America. This helps explains the first settlements of the Portuguese and Spanish, and why the latecomers, like the British, ended up further north up the coast of North America.

    Using wind data from the University Corporation for Atmospheric Research (UCAR) and Google Maps I created an online sailing game I call Mariner AO. The game is pretty simple (basic instructions are here), you tell your ship which direction to go, starting off near Lisbon in Portugal and sail the Atlantic. What makes it interesting is that you can go wherever you like and make your own objectives. All that limits where you can go is the fact that you can only sail within 90 degrees of the wind. It’s very Montessori in that you have choice within limits.

    The game is most interesting, I think, if you set objectives like trying to sail the triangular trade route, Europe (Portugal) to Africa (Dakar) to America (Charleston) and back to Europe again. The general clockwise wind pattern is persistent throughout the year, but sometimes you need to wait until the wind changes to be able to reach your objective.

    Alistair Boddy-Evans has a nice article on the triangular trade of European manufactured goods to Africa, African slaves to the Americas, and plantation crops back to Europe.

    I really like this game because it integrates so much. Atmospheric circulation, slavery, colonization, and even the physics of sailing if you can and want to get into it. In fact, I think it’s enough to base an entire cycle of work around. I’m still taking comments about how to improve the game.