Princeton Review's formative assessment arm

-- CatherineJohnson - 02 Dec 2005

@Carolyn: I think you got a framework upon which to build a better understanding even in the 6th grade. The problem was in the details. When I went looking to confirm my understanding (there is no fact so basic that it cannot be gotten wrong; see "43"), I found out several things about specific heat that I'd not known previously. (Specific heat in a gas when holding volume constant isn't the same as the specific heat when holding pressure constant, for instance.)

All of which confirms the basic point — that when you are more expert you get information more efficiently.

-- DougSundseth - 09 Nov 2005

Doug, I suspected it was a simplification -- I didn't know the details. The point was that someone more knowledgeable can extract more information out of a piece of information that's given. Perhaps it's just as well that 6th graders aren't more knowledgeable, since apparently they'd be learning the wrong thing. ;-)

-- CarolynJohnston - 09 Nov 2005

when I did it again with Ben, I saw that, if true, it is an amazing formula. It says that the amount of energy needed to raise the temperature of a substance depends only on the substance, its mass, and the amount you want to raise it. In particular, it does NOT depend on the starting temperature of the substance, nor on its state of matter, nor on a billion other factors it COULD depend on. I know I didn't notice all that when I was in sixth grade; if it was explained to me, I didn't take it in.

What a great story.

I love those moments.

-- CatherineJohnson - 09 Nov 2005

"In particular, it does NOT depend on ... its state of matter...."

That part's not right. For a given state, the specific heat is very close to a constant value over temperature, but it can change quite a bit in different states. The most commonly seen specific heat values are those for water, most commonly given as:

Specific heat of water ice = 0.5 cal/g*(degree C)

Specific heat of water = 1.0 cal/g*(degree C)

Specific heat of steam = 0.48 cal/g*(degree C)

Energy required to melt ice: 80 cal/g

Energy required to boil water: 540 cal/g

I find this more interesting, actually. The last one is a major part of the reason that hurricanes and tornados are so destructive. When the water vapor column rises, it cools and condenses. The condensation releases a huge amount of energy (540 cal/g), which feeds the storm.

The second to last explains why the air sometimes feels warmer when it starts to snow, for the same reason.

-- DougSundseth - 09 Nov 2005

I think the expert-novice studies demonstrate this. Experts learn faster than novices.

Ben had a 'heat test' in science the other day, and we were talking about the fundamental formula in heat calculations, as his teacher gave it to these sixth-graders:

Energy needed to raise x kg of a substance by c degrees C = (specific heat of substance) x (x kg) x (c degrees C).

Ben was doing all he could just to remember it, which I am sure was also true of me when I was his age. And I probably have not thought much about this formula since sixth grade (if in fact I was paying attention that day at all).

But when I did it again with Ben, I saw that, if true, it is an amazing formula. It says that the amount of energy needed to raise the temperature of a substance depends only on the substance, its mass, and the amount you want to raise it. In particular, it does NOT depend on the starting temperature of the substance, nor on its state of matter, nor on a billion other factors it COULD depend on. I know I didn't notice all that when I was in sixth grade; if it was explained to me, I didn't take it in.

He is younger than I am, thus has more to learn and presumably more room to learn it in (whereas I have to push something out, it seems, for every new factoid I cram in), but in spite of all that I learned more from this one exposure to this formula. The difference is just that I have more hooks to hang new information on.

Age and wiliness beat youth and energy once again.

The main limiting factor now seems to be sheer memory loss.

-- CarolynJohnston - 09 Nov 2005

Their studies provide an insight into the paradox that you can successfully look something up only if you already know quite a lot about the subject.

I love it!

It's true.

-- CatherineJohnson - 08 Nov 2005

Once again it all comes back to the magic number seven:

From Hirsch's You Can Always Look It Up — Or Can You?:

For instance, there is a domain of cognitive science called "expert-novice studies." ... Their studies provide an insight into the paradox that you can successfully look something up only if you already know quite a lot about the subject. In these studies, an expert is characteristically a specialist who knows a lot about a field — say a chess master or a physicist, whereas a novice knows very little. Since the expert already knows a great deal, you might suppose that she would learn very little when she looked something up. By contrast, you might think that the novice, who has so much to learn, ought to gain a still greater quantity of new information from consulting a dictionary or encyclopedia or the internet. But, on the contrary, it's the expert who learns more that is new, and learns it much faster than the novice. It's extremely hard for a novice to learn very much in a reasonable time by looking things up.

Simon and others point out that one reason the novice has this difficulty is that the human mind is able to assimilate only three or four new items before further elements evaporate from memory. The expert had already assimilated most of the elements being looked up, and therefore needed to pay attention only to one or two novel features which could easily be integrated into his prior knowledge. In a famous experiment by de Groot, a chess expert could learn a complex new chess position after just a few seconds exposure, whereas novices could remember very little. That was because the novices had to remember ALL the unfamiliar positions (which the human mind simply can't do) whereas the experts had to notice only a few salient departures from a wealth of positions they already knew.

The analogy between the chess experiment and looking things up is quite apt. Imagine an expert and a novice looking up the entry "planets" on the internet and finding the following:

planet — any of the non-luminous bodies that revolve around the sun. The term planet is sometimes used to include the asteroids, but excludes the other members of the solar system, comets and meteoroids. By extension, any similar body discovered revolving around another star would be called a planet.

A well-informed person would learn a good deal from this entry if, for example, he was uncertain about whether asteroids, comets, and meteoroids should be called planets. A novice, even one who "thinks scientifically" would learn less. Since he wouldn't know what planets are, he probably wouldn't know what asteroids, comets, and meteoroids are. Even the simple phrase "revolving around another star" would be mystifying, since he probably wouldn't know that the sun is a star. Equally puzzling would be the phrase "other members of the solar system," since the term "solar system" already requires knowing what a planet is. An imaginative novice would no doubt make some fortunate guesses after a rather long time. But, looking things up turns out to have an element of Catch 22; you already need to know something about the subject to look it up effectively.

-- KDeRosa - 08 Nov 2005

I hadn't quite thought of it this way, but it's absolutely true.

Articles & books I used to struggle with are incredibly easy for me now, and it's entirely because I know much more about the subject going in.

-- CatherineJohnson - 08 Nov 2005

I find it much easy to learn today than when I was 15 becuase I have much more domain knowledge to drawn on. I understand more, so I pick up things much easier. I think the expert-novice studies demonstrate this. Experts learn faster than novices.

-- KDeRosa - 08 Nov 2005

formative assessment

Doug's comment reminded me that I'd pulled an OECD article on formative assessment to post:

Formative assessment – the frequent assessments of student progress to identify learning needs and shape teaching – has become a prominent issue in education reform. In fact, Studies have shown it to be among the most effective educational interventions ever reported.

Between 2002 and 2004, CERI examined exemplary practice of teaching and formative assessment in secondary schools in eight OECD countries – Australia (Queensland), Canada, Denmark, England, Finland, Italy, New Zealand and Scotland – and brought together literature reviews from English, French and German research traditions, relating all this to the broader current policy environment.

The resulting publication, Formative Assessment: Improving Learning in Secondary Classrooms, combines those elements to clarify the concept of, and approaches to, formative assessment and its relation to teaching strategies. The culmination of this study was a major international conference organised by CERI in Paris, on 2-4 February 2005. The conference highlighted international research and case study evidence from the CERI study.

CERI will co-sponsor a regional conference on formative assessment in Budapest, on 29 – 30 September 2005....

Beginning in 2005, the project has just started to look at assessment strategies for adult learners. The study will highlight the issues of why, what and how institutions should assess adult students, and implications for policy.

Being an adult learner, not learning that I can't learn was easy.

update

yes, indeed, I have done a bang-up job of not learning the bit about adult learners not learning, because the CERI web site, far from being the bearer of bad tidings about adult learners, is in fact the bearer of the Certain-To-Be-Correct observation that one can learn at any age. (pdf file)

In recent years, brain science has captured the interest of policymakers and educators. Many believe that new discoveries about the brain yield new insights into early childhood and adolescent learning. However, most of the brain science policymakers and educators cite is not new and even this “old” brain science tends to be oversimplified and misinterpreted in policy and educational contexts. Contrary to popular understandings about the brain, most learning is not limited to early critical periods in development. Furthermore, there is no simple relation between the number of neural connections in the brain and rate or ease of learning. What we do know, from psychological studies of the mind, is that rate and ease of learning depend critically on what one already knows, not on one’s age. We should attempt to use what we do know about learning across the lifespan to provide optimal learning environments for all our citizens.