Two local teachers in Colorado (Jon Bergmann and Aaron Sams)  just put together a wonderful little video about how they completely transformed their high school chemistry classrooms, so that students would actually master the material.  In the video, two dynamic presenters show and talk about how they used video podcasts to make better use of lecture time by taking the non-interactive part (lecturing) out of class time and putting the stuff that kids were struggling with (homework and problem solving) into class, to improve their mastery. I didn’t think I’d want to watch a 20 minute video but I was utterly charmed by these two teachers, and their explanation of their journey along this transformation is very compelling. Their website has more on their approach to using vodcasting in the classroom.

Watch the video



Here is a long description in text of what they’re doing in case you don’t have time to watch the video (but you should watch it, you’ll get it much more, and they’re fun folks).

Peer into Jonathan Bergmann or Aaron Sams’s classes and you will see something exciting happening.  What you will observe are students taking responsibility for their own learning.  Students conduct experiments, watch video podcasts, work on assignments, interact with the class Moodle site, have one-on-one discussions with their teacher, and get tutored by their peers and cadet teachers.  This is mastery learning at work.  Students work at their own pace through science curriculum.  When they complete a unit they must demonstrate that they have learned the content by taking an exit assessment that includes both a lab and a written component.  If students score less than 85% on these exit assessments, they must go back and re-learn those concepts they missed and retake the exam.  Grades are no longer determined by a percentage but rather how much content they have mastered.

What Caused Us to Change?
We discovered software that would capture our lessons and simplify distribution over the internet.  Then we began to record our lessons and post them for students who missed class.  This was very successful in our rural school where students frequently miss class for sporting events and other school activities.  Then we realized what students really need from their teachers is not to hear us talk and “do the sage-on-the-stage thing,” but rather, to get help when they get stuck.  This prompted us to dramatically change the way we teach.  In the 2007-2008 school year we began to have students watch video podcasts at home and then use class time to do directed problem solving, more experiments, and generally get the help that they needed.  This was highly successful and the scores of students made dramatic increases.
Then it struck us.  Now that we had a library of instructional podcasts, students no longer have to all receive the same instruction on the same day.  So, in the 2008-2009 school year we implemented a mastery teaching method.  In this method students have a check-list of things to master in each unit of study.  The list includes the required video podcasts, experiments, one-on-one demonstrations with the teacher, and appropriate Chemistry problems to solve.  When students have completed ALL of the assignments and labs, they must pass the exit exam with a minimum of 85%.  If students do not score 85% or better they retake the exam as many times as needed to pass.

Implementation of Mastery
Our classrooms now resemble three-ring circuses.  Students are in various places in the content on any given day.  Lab stations around the room are set up so students can complete the experiment that is next on their check-list.  This poses some safety issues in a Chemistry class, however, with the proper training, the students have quickly adapted to this method of experimentation.  Before each lab we spend time with a much smaller group of kids and discuss the main points of the lab and safety considerations.  This makes for a more intimate learning experience for each student, giving each student far more one-on-one time with their teacher.

All Students are Successful
A huge benefit of this teaching paradigm is that ALL students are leaning.  This is the ultimate method of differentiation.  Slower students are given the extra help that they need to master the content.  Advanced students are allowed to learn on their own, which ultimately helps them to become more independent learners.

Learning Outcomes from Podcasting
In the 2006-2007 year, we gave common assessments. We agreed to use the same tests in 2007-2008 as we did in 2006-2007 and compared scores after every unit.  In addition, the math pre-requisite for chemistry was lowered from Algebra II to Geometry, thus our students came to us with lower math skills.  In addition, enrollment in the course increased by 80%.  The average scores of the students on identical science tests given before and after implementation of the podcasting model were nearly the same, showing that the podcasting model gave equivalent results with students of a lower mathematical ability.

Proof of Success with Mastery
Now, in the 2008-2009 school year, under the master model, every student is now required to master the content before progressing, and ALL students are learning.  This has been magical!  Students of all ability levels are really learning!  As much as we were excited about the 2007-2008 results, mastery learning has been an even more positive experience for our students.  Now, EVERY Chemistry student demonstrates proficiency on EVERY topic in the class, which far surpasses the level of understanding of prior student success.

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….

tt_icon_170I had the great pleasure to work at the Exploratorium with a wide variety of master teachers, each with their own unique style.  I learned something new from each one of them.  What I learned most from Modesto Tamez —  who taught K-12 science with aplomb for 18 years — was about how to work with kids to get the very best out of them.  One thing he always talked about how to use kids’ particular quirks to help you manage your classroom — for example, the loudmouth who always caused trouble would become his personal assistant and get the attention he was craving in a productive way.  Modesto is a master at reading people and getting them genuinely engaged in the lesson.  One way he did this was with what he called “Provocacion”.  This spanish word doesn’t have a perfect equivalent in

Modesto Tamez

Modesto Tamez

english — it means to “provoke”, but not in a negative way.  Rather, it means to spark the interest, get the kid engaged, curious, interested, afraid, or whatever is needed to hook them into your lesson.  I just posted a new episode of my Science Teaching Tips podcast — Hey neat!  The importance of “provocacion.” Give it a listen and hear Modesto talk about how he uses this technique in classes.

Here is a nice video about how MIT has transformed their undergraduate physics classes using group work. This has been a very successful approach, though not without its critics. You can see my previous post on
Twisting the Ivory Tower to see more about reforms in undergraduate courses, including this SCALE-UP approach. I have another post on how it can be challenging for professors to give up center stage in the classroom.

Watch the video here

“A Time for Telling” is the title of one of my favorite papers of Dan Schwartz (Professor of Education at Stanford). In it, he argues that lecture isn’t all bad. We complain that lecture (or “direct instruction” in ed-speak) doesn’t result in a lot of learning for our students. This has been shown again and again, in a lot of studies. But it’s pretty hard to completely eradicate lecture from our universities (or high schools, etc.) — it’s a pretty efficient way of communicating information. But if students first struggle with the ideas and concepts, then they’re prepared to learn from it. This is called Preparation for Future Learning.

For example, you could imagine (and it’s been shown) that students who first invent the idea of density (by being given the task of coming up with a way to describe how many clowns there are per square foot at a circus) will be better able to answer a question about the density of water than, say, a student who was just given the formula for density and shown a worked problem using gold. And a recent study by Schwartz shows just that, that those students who first invented the solution were better able to transfer the idea to a new situation. He writes:

Direct instruction is important, because it delivers the explanations and efficient solutions invented by experts. To gain this benefit without undermining transfer, direct instruction can happen after students have engaged the deep structure, per the Invent condition. [The students who invented the solution on their own] performed just as well on a subsequent test of word problems about density and speed. Direct instruction becomes problematic when it shortcuts the appreciation of deep structure. Across conditions, students who encoded the deep structure of the clown problems were twice as likely to transfer. It is just that fewer students in the Tell-and-Practice condition encoded the deep structure, because they had received direct instruction too soon.

Similarly, he later cites a study that found:

For example, college students learn more from lectures and readings when they first work with relevant data compared to when they write a summary of a chapter that explains the same data .

In some instances, he says, it is useful to just receive direct instruction because the goal is to build rote, routine skills. But in math and science, this isn’t the case:

In math and science, instruction cannot exhaust all possible situations. Transfer and adaptation are important. Although automaticity is important for some facts such as “2 x 3 = 6,” real situations rarely come with formulas attached, so students need to learn to recognize the relevant deep structures. Moreover, the cumulative curricula of math and science mean that students should build a base of knowledge on deep structures from which future learning can grow and adapt.

But teaching this way brings up the problem of assessment:

In the current milieu of high-stakes testing, standardized assessments largely measure routine expertise; namely, efficient recapitulation. If educators want students to become adaptive, innovative citizens who keep learning through changing times, current assessments do not fit. A better fit would map students’ trajectory towards adaptive expertise. Ideally, assessments would examine students’ ability to transfer, particularly for new learning. Such assessments would include resources for learning during the test (for example, a simulation that students can freely manipulate).

There was an interesting post, and comment thread, over at Built on Facts — on How to Be a Good TA. I’ve been wanting to respond to it for two weeks and have been too busy. It is interesting that this discussion came up just as I was forwarded a great article about TA Training — Growing a Garden without Water: Graduate Teaching Assistants in Introductory Science Laboratories at a Doctoral/Research University (Luft et al, Journal of Research in Science Teaching, vol 41, pp 211-233, 2004). That article delves into the dearth of training giving to graduate TA’s, who bear a large brunt of the work of communicating science to undergraduates [I’ll send you a copy if you ask]. They write:

In the past 3 decades there has been a rising concern about the instructional support afforded to Graduate TAs, and an acknowledgment by faculty that expertise in teaching does not occur instantly in higher education.

No kidding. Even faculty don’t often get this kind of training. And then they’re supposed to teach the next generation of worker bees. (One of the exemplary training programs is called Preparing Future Faculty). TA’s are called on to make all sorts of decisions about their courses (curriculum, what concepts to emphasize, how to evaluate students) and faculty aren’t guiding them very much. Faculty aren’t often well-informed about undergraduate education reforms, anyhow, which suggest that there are better ways to teach and assess students how we were traditionally taught.

The blog post from Built on Facts, in some ways, exemplifies these problems. I have no doubt that Matt is a great TA. He understands that it’s important to engage students in the process of learning. But many of his comments suggest that being a great TA is just about doing traditional instruction the best that you can. Here is what Matt said about his extensive experience as a graduate TA:

What (students) need in recitations is only so much theory as is needed for an understanding of the concept, with lots of worked example problems. Lots of them. Do them as interactively as possible, so that instead of just working through the problems yourself in front of sixty glazed-over eyes the students are actively involved in figuring things out. …

Put real thought into how you present your lectures. What seems beautiful and elegant to you might be obscure and overly complicated to a new student. Try to be clear with concepts and buttress each new idea with a concrete example problem. A real one, not a toy problem that’s orders of magnitude easier than what they’ll face on the homework.

He also suggests giving students extra practice in working problems by giving quizzes and review sessions.

I think a lot of these methods would work if there was good evidence that lectures work. But so far, the evidence suggests that students don’t learn by telling, they learn by doing. As long as you’re up there in front of the blackboard, you’re stuck in a classroom structure where information is supposed to travel from teacher to student. I don’t think that’s the best approach, based on the evidence. Get the students talking to each other, working through problems, discussing and arguing. Then act as their “guide on the side” (not the “sage on the stage”) to help them learn. You can’t teach anybody anything.

Now, I’m really not slagging on anything that Matt’s saying (or any of the other good suggestions in the comments of his post), just that the initial structure of the teaching environment he’s using is flawed. For instance, I can’t argue that it’s good to give clear explanations, to think about your lectures in advance, and to give example problems. I love his suggestion of giving quizzes — research shows that the act of trying to recall information increases your memory of it (even if you don’t get the answers), so taking as many tests as you can is a really good thing. But the “good lecture” techniques only go so far. Students plead for us to give them example problems often because they want to see something that “looks like” the homework so that they can follow it as a recipe.

The comments to Matt’s post suggest that at least the better students don’t want those boring example problems, though — like Matt says, they want “real” problems — interesting, tough problems that get them engaged in solving it. I’ve seen that desire in our physics majors here as well. What would be great is if we could really model to students how we go about solving such a problem — taking wrong turns, thinking back to worked examples, looking at limiting behavior, etc. But that takes a very long time, and is hard to do justice in front of a class.

One idea that I’ve found really compelling is called Preparation for Future Learning. The idea is that sometimes there is a time for telling (for the “theory” part of the presentation, tying things together, giving out facts), but it is after a student has already struggled with the ideas. One way to do this is to give them a canonical problem and ask them to come up with the solution. For example, ask biology students to come up with a strategy for eagle conservation. That’s a huge, open-ended problem (they don’t have to be that unstructured) but after students come up with a bunch of (poor) strategies, they are better equipped to hear and understand a lecture about conservation techniques.

TA’s aren’t well-trained and teaching is undervalued

But when would a TA learn these kinds of techniques to teach?  The article I mentioned at the top of this post (about TA training) argues that it’s not enough to know the content (in this case physics) — you also have to have Curricular Knowledge (instructional methodologies) and Pedagogical Knowledge (how to take the content of your particular discipline to the learner).  And graduate TA’s are taught neither of these — they’ve been prepared for research careers, for the most part.  Teaching is often seen as a lower-tier calling than research.  Thus, TA’s aren’t rewarded for working on their teaching, and their faculty mentors aren’t well prepared to help them in these endeavors.  TA’s feel that teaching is important, but an interest in teaching doesn’t really help their professional development as scientists.

Here is a faculty’s comments on the lack of importance of teaching for a TA, from that paper:

Sydney did think that teaching  was important, but there is a reason that it is not emphasized. He goes on to add that at the graduate student level it is perceived as being more prestigious to hold an RA appointment instead of a TA appointment. At the faculty level, research productivity is important in the yearly reviews, not teaching. Faculty may talk about the importance of teaching, but during the department reviews the focus is on research and funding. At the national level, grants are funded for research and not teaching. When grants are funded, they pay more for RAs, not TAs. Sydney pauses again and states that it is clearly a cultural thing.

TA training is poor

In keeping with these cultural expectations, TA training meetings aren’t sufficient to teach such a complicated and difficult task as teaching. Here is one TA’s comments on the usefulness (or lack thereof) of weekly training meetings, from that paper:

The staff meetings address what the lab is about. They are necessary, but are not done well.
Some TAs just like to talk and so we listen to them and they take up so much time. I just
don’t get a good view of what the lab is about from the staff meetings. I’ll ask a
question . . . and the laboratory coordinators can’t answer the question and I get frustrated.
I know that they try really hard, but it’s not exactly what I would want. I guess I need
more clarity than the other TAs and the 2-hour staff meeting is just not an efficient use of
my time. I end up going to Monday lab before I teach my sections to really get a sense of
the lab.

TA’s are left on their own

One other quote reminds me a lot of what Matt said about his teaching, since it sounds like he was pretty much on his own as he decided what to cover in recitations:

The lack of faculty involvement was also evident when GTAs discussed their preparation for teaching each laboratory. No GTA indicated seeking out the assistance of faculty members or even the laboratory coordinator when planning for their classes. Instead, as Samie stated, she often “. . . read through the laboratory manual, making sure that I understand the order of things
and what it’s asking. I interpret the lab, reword things, make the objectives clear, and think
of ways to introduce it to students and think over what I want to lecture on in the
laboratory. “

These sorts of decisions are fairly complicated for a beginning teacher to make!

The article concludes quite strongly:

In this study, GTAs and laboratory coordinators who were involved in preparing GTAs had limited opportunities to enhance their instructional abilities. The constraints of the working environment often led GTAs to make intuitive decisions, or decisions based on their own experience as students; thus their practices were often disconnected from the literature base in education.

The title of this article, ‘‘Growing a Garden without Water,’’ represents the expectations and  potential of GTAs in the absence of adequate support to facilitate their growth. GTAs have an  essential role in universities and colleges, but without proper instructional support they may not  achieve their potential. Furthermore, it is estimated that by the year 2014, 500,000 new professors  will be teaching American college students (Jones, 1993). Many of these professors will have served as GTAs. Improving the education of future students depends on the thoughtful, careful, and purposeful training of future faculty members. To meet the needs of the community, the garden must be properly tended by involved caretakers, and it will yield its fruits.

They say that rewards and incentives should be given for good teaching, and TA training programs should draw on the research base in education that informs us how we best learn to teach science.