I just found out about a neat free service for science educators.  It’s mostly for those in Colorado, but those outside Colorado are welcome to use it as well.  It’s a free email servicer for teachers to ask questions directly of a science education expert, who will go out and find the answer for you.  How fabulous!

It’s called MAST WebConnect.

Here is some text from their site:

The Problem
Obviously the problem is not that the Internet does not contain enough math and science education resources, but finding quality resources can be an overwhelming task for teachers and students alike. Teachers often do not have the time to do a quality web search or seek experts in the field.

The Solution
MAST WebConnect will answer your questions and find high-quality web-based Internet resources personally for you! Supported by the MAST Institute and the University of Northern Colorado, WebConnect is staffed by math and science educators and professors with access to these resources and references.

How it works.
The idea is simple. We know that the Internet provides a wealth of information, but sorting through and filtering that information to find quality materials can be an overwhelming task.
That is where we come in. Contact MAST WebConnect with any mathematics or science question, and our coordinators will find the information either by contacting experts in the field, or finding high-quality Internet sites.
MAST WebConnect has a pool of available volunteer mathematics and science experts to help with more difficult inquiries. These include college professors and working scientists within Northern Colorado.


A free workshop for educators on December 9th from the National Science Digital Library:

This Web Seminar will focus on dynamic online resources you can use to teach your students about the chemistry of water through the NSDL Chemical Education Digital Library. Join presenters Dr. John Moore, W. T. Lippincott Professor and director of the Institute for Chemical Education, and Dr. Lynn Diener, Assistant Professor, Mount Mary College in Milawaukee, Wisconsin and guests Jon Holmes, Editor of Journal of Chemical Education Online and Dr. James Skinner, Chemistry Professor at the University of Wisconsin-Madison for this seminar for educators of grades 9-12.

Register for this free seminar

Learn more about NSDL NSTA Web Seminars

This is the last in a series of three posts on Dan Schwartz’s work on preparation for future learning, or helping students learn skills instead of rote facts so that they can apply their knowledge to new situations. All pictures in this post are courtesy of Dan Schwartz.

Contrasting cases

In the previous post, I showed Dan’s use of contrasting cases in helping students understand density and ratios. Why is it important to show students different cases, instead of the best single example of something? Well, he said, think about perception. Consider this circle:


We immediately recognize it as a circle. It is, after all, not a square.

untitled9But, in fact, it is many things. It’s a empty circle. It’s a circle created with a black line. It’s a largish circle. Here are a bunch of contrasts to this circle:

untitled11 untitled10 untitled81

We’re abstracting “circle-ness” from the single example, but that’s because we recognize circle-ness already. These contrasting cases would be important if we were first learning about circles.

Here are some contrasting cases of something familiar to us:


After all, what is the best way to teach Japanese speakers to say the sound “L,” which doesn’t exist in their language? Give them the purest example of an “L” sound that you can find? No, it’s to let them hear “R” and “M” and all the other sounds, so they know what the “L” is NOT in addition to what it IS.

But, this is what we do in instruction! We give students the purest example of something that we can. Consider, for example, this picture.

untitled13This is a perfect example of this breed. Now, tell me which one of the following is the same breed?

untitled14An expert will look at the width of the ears, the curve of the nose. But a novice can’t look at these pictures and see the immediate resemblance to the example picture. (I forget which one was the correct answer, but I think it’s the last one. The hair length is an extraneous feature, the ear shape is most important.)

It would have helped if, first, an expert had used the following picture with contrasting cases to help you learn about ear shape (what does “rounded” ear shape look like? How wide is “wide”?). You need to be oriented to understand the key structures in what you’re seeing. You can’t just look at the picture below and learn from it, though — a bunch of different examples are confusing to a novice. The expert’s role is to help them make sense of the different cases.

untitled15An example activity

Here, for example, is his activity where he asks students to invent a reliability index for a pitching machine. He gives them several different cases so they have to find a general solution which fits all these cases. This, after all, is what we do in science – to find a general solution that fits many cases.

untitled16In my previous post, I gave his activity for teaching density using clowns in buses.

The way he uses these in the classroom is to have students explain their classmates’ solutions to each other. That means that each student’s solution has to be written clearly enough so that someone else can understand it. This act of public “publishing” of the results gives students a bit more motivation to come up with a good solution. On the other hand, the goal of this task is NOT to come up with the “right” solution! It’s to prepare students to understand the expert solution (in this case, the idea of variance) when it’s presented.

Expert blind spot

As experts in a subject, we know an amazing amount. What we’ve learned has been compressed into a bunch of huge steps. We don’t recognize the huge number of things that we’re doing when we do what seems to us to be a single step (such as computing a ratio). We need to decompile our knowledge for the novices. In order to do this, it’s good to have an intelligent novice around — someone to ask us a bunch of questions at every step so that we can see what it is that we are doing in any task. Once you’ve discovered some key, fundamental idea that is needed to solve the problem, that’s a great place to put an invention activity. Examples are density, vectors, variance, and other fundamentals.

What these activities are not:

  • Not just brainstorming
  • Not puzzlers
  • Requiring a flash of insight to solve
  • Not pure “discovery” tasks
  • Not to replace standard instruction

What these activities ARE:

  • Students make answers for one case, and recognize it doesn’t generalize to the others
  • Learning is incremental
  • Students don’t have to find the right solution to benefit from them
  • Students should start to notice the variables that matter
  • Students are told to invent a form of representation
  • They are visual
  • These activities are used strategically to communicate fundamental key ideas (like density). Not used for everything.
  • Prepares student for standard instruction

To make these cases yourself:

  • Think about your own knowledge to isolate key concepts
  • Think of each case as an experimental treatment to isolate a key variable
  • Or, think of formulas or units and make sure they contrast for each case
  • Have some sense of likely misconceptions so you can create cases that will highlight probable “traps” students might fall into
  • Make them approachable. You don’t have to be as frivolous as the clowns example, but it should be done in a context that’s different from what you want students to learn (like physics). Then you can help students map it into the new context.

What about assessment?

Dan’s main point is that our assessments need to change in order to use this kind of instruction. If we value students’ showing that their learning is adaptive, we have to give them a chance to demonstrate this on a test, to demonstrate an expert level of perception.

What do I mean by expert level of perception?

What do the images below say to you?

untitled17 untitled18

The novice answer (“car,” “bird”) is not very precise.

The expert answer (“2007 BMW X5” or “indigo bunting”) is much more precise, and relies on deep recognition of various features. We should test students on this more broad ability to apply their knowledge. For instance, geology students should be able to extract some important features from this picture of a landslide:


This doesn’t have to be a perceptual test — in the previous post, the “green people” vs. “blue people” example relied on students ability to recognize the variability in a data set.


I think this stuff is incredibly powerful. Let me know of any more activities that you come up with or you know about!

In my last post, I wrote at length about Dan Schwartz’s work about teaching students how to learn by having them create a solution to a problem before you give them the standard lecture about how to solve that kind of problem. I wanted to give you an example of this kind of “Preparation for Future Learning” activity, in addition to the batting machine example in the previous post. All images are courtesy of Dan Schwartz at AAA Lab.

This one is to help students learn about density. The task is below.


And here are the graphics for the task.


The key to notice here (and in the previous batting example, though I only showed you one example of the batting machines) is that he uses contrasting cases to teach this concept. There are different buses with different amounts of clowns. These cases are chosen carefully so that the student must come up with a solution that satisfies all these different cases. For example, the number of clowns in the bus does not distinguish between the very first and very last cases shown on this sheet (for which the answer would be “2” for both cases, which are clearly different).

He found that those students who first invented this density ratio were better able to then use this knowledge to understand spring constants (another ratio) than those were were just told the formulas for density. That data is shown below.


More on how to write your own preparation for future learning activities in the next post….

We had a visit from Stanford education researcher Dan Schwartz last week, and what he told us about how people learn just rocked my world. I always enjoyed his work (and it was a real pleasure to tell him how much he’s influenced my thinking about education), and have blogged before about his A Time for Telling paper. Still, spending many hours with him over two days was a transformative experience for me. Let me try to tell you why.

All images in this post are courtesy of Dan Schwartz. His research website is here.

This is a problem of transfer (or so we say).

For example, students can learn how to do permutation problems using, say, cars or marbles as examples. But when you ask the marble-trained students to answer a question using cars, they struggle. Similarly, we see our own students do well on homework and chapter-level tests, but not on the final. They know the formulas and ideas, but don’t know how to apply them. This has been called a problem of transfer from one domain to another.

But, he argued, how is it that we could fail to transfer what we know? After all, we learn something at home and we bring it to work, or we learn something at home, and we bring it to school. We seem to transfer all the time. And, as my colleague Noah Finkelstein has argued, in order to believe in transfer, we have to believe that there is some thing to be transferred. What is transferring? Some static little packet of knowledge? There’s no tangible chunk of knowledge that we can bring from place A to place B. Knowledge is about skills and process and understanding, it’s not a static thing.

Efficiency over Adaptation

So, Schwartz argued, it’s not really a problem of transfer. The problem is that we’ve trained people to do things quickly – efficiently – not to adapt to new situations. We train people to recall lists of words quickly, or take timed tests, or tell us what causes the seasons when asked on the street. So we’ve trained efficiency over adaptation. While efficiency is important for routine tasks, experts readily adapt their knowledge to a new situation.

Preparation for Future Learning

Schwartz did a fascinating study to see what helps students learn to adapt to new situations.

  1. One set of students read a chapter and then hear a lecture about it
  2. Another set of students analyze and graph data, deciding what they think is important to graph
  3. A third set played around with graphing the data and then heard a lecture about it.bar-chart

So, how did they each do on assessment? On a traditional factual test, group 1 (reading and lecture) and group 3 (graphing then lecture) do equally well. Group 2 (graphing only) did very poorly — without some expert guidance they didn’t really learn much from just playing around. Those data are to the right.

OK, so does that mean that it’s equally good to have studentsbarchart2 read and hear a lecture as to play around with the data before hearing the lecture?

Nope… he then gave them all a test that required them to use their understanding in a new situation, and those data are to the right here. Those who first played around with the data and then heard the expert lecture did much better on that test. They were approaching adaptive expertise more quickly than the others! The differences in performance on this test, above, are stunning — these students (who, he argues, were prepared to be able to learn during the test by the instruction they were given) did more than twice as well on this test.

So the message here is that there is a time for telling (ie., lecture) — just not too soon!

This is particularly appropriate to remember in math and science. Math, for example, is usually presented as an efficient way to solve problems. What if, instead, students found that math helped them understand science and manage complex problems? For example, he took a class of 9th grade students and taught them statistics by asking them to find a way to rate the reliability of pitching machines. Below are two examples of student approaches to this problem.


This forced them to create ways to deal with variability in data before being given a formula for computing variability (eg., standard deviations). He found that, even a year later, these students did better than college students in understanding formulas for variability, and were much better able to understand variability in data and its importance. Below is the task that he gave these students — those who had struggled with variability before hearing the lecture were able to recognize that the IQ scores of the green people had more spread, even though the IQ of the blue people was higher, on average.


He argued that this emphasis on efficiency is very American. We train people to become expert at routine tasks, but what we need to emphasize instead is innovative experiences. Let go of what you’re told, and try something new. For one, when students innovate a solution first, then they have a context for what they’re learning. When given the solution first, they don’t have a context for it. Telling people the answer works if they have a lot of prior knowledge (and that’s why talks at conferences, for example, can still be decent ways to get a lot of information across). But when you’re learning something new, don’t tell too soon!

You can find out more about Dan Schwartz’s work here.

One of the great travesties of this nation, I think, is the complete lack of logic in how we treat criminals. Our criminal justice system sucks people in and makes it very hard for them to reintegrate back into society. We stick them in jail, where they lose their connections to community and become enmeshed in criminal culture. When they get out, it’s very hard for them to get a job, and much easier to cycle back into jail. Most incarcerations nowadays are actually due to parole violations rather than new crimes. I found out about this when I did a piece on prisoner recidivism (“Life Beyond Bars“) for Science & Spirit (a neat magazine focusing on the intersection of science, religion and life). Here is an excerpt from that article:

The United States has the world’s highest incarceration rate, with one of every seventy-five American men in jail or prison. There are more U.S. inmates now—2.1 million—than at any other time in history. This increase isn’t due to a crime wave; crime rates have actually fallen. Instead, criminals are serving longer sentences, and many return to prison to finish those sentences when they violate their parole. Two-thirds of parolees are rearrested within five years of their release. Most are rearrested within the first year, some within days. The end result is a huge surge in the prison population—a twofold increase per capita over the past twenty years.

There are also more prisoners being released than ever before: More than 600,000 will come home this year, the equivalent of the city of Boston being turned out onto America’s streets. The majority will have had no access to education, job training, or drug rehabilitation. They will exit the prison gates with a bus ticket and a few hundred dollars in gate money, and maybe a list of apartments or shelters. Most will return to crime-rich neighborhoods, and while they will likely be released into some sort of supervision, they won’t get as much help as in the past. Many parole officers act more like cops than social workers nowadays.

In 1984, Reagan eliminated Pell Grants for prisoners. Since this was the primary way that prison education programs were funded, this effectively ended all higher education opportunities for prisoners, making the road to reintegration really difficult (read more here). So instead of funding education and other programs to keep prisoners out of jail, we’re spending huge amounts of money on housing and feeding prisoners, to the tune of $32K per year.

Anyway, in the course of writing that article, I found out about a unique program in the country, the Prison University Project at San Quentin. A shoestring operation, it provides college courses as an extension of Patton University in Oakland. It’s the only degree-granting higher education program in all of California state prisons. All instructors are volunteers, and I volunteered for a few semesters as a math tutor. What an experience — to go through a half-hour of security clearance every time you entered, and classes could easily be canceled for a security lockdown.

Two inmates in the Prison University Project

Two inmates in the Prison University Project

Once inside we were in a room of, frankly, primarily Latino and African-American men, trying to teach basic arithmetic skills so that they could go on to take pre-algebra. I tried to teach fractions, and it was hard. We used fraction tiles (which are a physical representation of the different fractions, using pieces of squares or circles to represent 1/3, 1/4, etc.) I was impressed by these mens’ determination to learn, and willingness to be humble. They often wanted to be able to help their kids with their homework when they came to visit them at the prison. We didn’t know what it was that they had done to be sentenced (and were not supposed to ask), but the men in these classes had to earn it as a special privilege. These were well-behaved prisoners, and this was their only chance to do something intellectually challenging during their day — the rest of which was filled with a full-time job. Night classes for them were just as tiring, if not more so, as for the rest of us working stiffs who take night courses.

I write this because I just got a copy of the latest newsletter of the Prison University Project and, as always, they are in need of funds. They get no state or federal funding and rely entirely on individuals and foundations for support. I know times are tough, but if you are able, I highly recommend any small gift you can manage. It’s a wonderful program, and just it takes just $1000 to educate a single student for a year. Or, if you know of a private foundation that may be interested in this endeavor, please let us know! You can donate directly here, or email director Jody Lewen at info(at)prisonuniversityproject.org.

Richard Hake (of Physics Education Research fame) has just posted a very nice list of 32 education blogs, fully annotated with useful descriptions of the content and author of each blogs. Includes blogs on eLearning, how people learn, mathematics education research, and more.

UPDATE 12.1.08  Hake has now posted an updated list of 60 education blogs.

Note my earlier post on a list of education blogs from the Nat’l Science Digital Library.

And also a list of 5 mistakes to avoid when using blogs with students.

And another post on Why let our students blog