I’ve been really enjoying a blog put out by the University of Colorado’s ASSETT (Arts and Sciences Support of Education through Technology) program.  They have frequent posts on technology that relates to higher education, and how it really impacts your classroom.

For example, connecting with students by Facebook; considerations, or whether to mentor via FB — tools like Evernote for organizing your own thoughts and to do lists — or creating a class website using Blogger.  Though it’s written for Univ. of Colorado faculty, most posts are widely applicable.  And they’re short and to the point!

No, of course not.  But to hear us education folks prattle on, you’d think that an instructor who lectures to their students is doing them a grave disservice.

Well, if all they’re doing is lecture, then their students could be getting more bang for their buck.  But lecturing is perhaps an indispensable part of class, especially in large college courses.  I’m reading a great article right now on how to make lectures more effective — here are some tidbits from that article (P.A. deWinstanley and R. A. Bjork, “Successful Lecturing:  Presenting Information in Ways that Engage Effective Processing,” in Applying the Science of Learning to University Teaching and Beyond).

Firstly, people need to be active in order to learn.

Toward achieving the goal of having students actually learn during lectures, it is important to remind ourselves of some fundamental properties of humans as learners. Learning does not happen, for example, through some kind of literal recording process. Rather, learning is an interpretive process: new information is stored by relating it to, or linking it up with, what is already known.

So, in lecture, we need to be able to spark the kinds of cognitive processes that actually help people learn.  For one, students’ attention can’t be divided if they’re to fully process what we’re trying to teach.  But Powerpoint and other tools require students to both attend to something visual (the screen) while they process something auditory (what we’re saying).  The end result seems to be that students think they understand, but can’t actually recall the material on the test  (Note the implications for students’ tendency to multitask during class!)  That’s horrible — students leave with the impression that they don’t need to study because they know the material, but they really don’t.

It’s also important that students, once their attention is directed, have a chance to interpret and elaborate upon what is presented in lecture.  New information has to be fit in with what a student already knows.  A graph, for example, isn’t easily memorized.  But once a student has determined what that visual information represents, and used it to answer a question, he will more likely recall the graphic or its message.

In order to remember information, it’s also important that students be given a chance to generate and retrieve that information.  The act of recall strengthens neuronal connections, creating learning.  That’s why it’s helpful to test oneself when studying for a test (and this is useful even if you aren’t given the answers about whether you’re right or not, though feedback is more helpful).  Producing information helps us learn more than being presented with that information.  Even something as simple as having to fill in missing blanks in a word (eg., “try to incorporate g-n-r-t-ng into your lecture”) results in better learning than reading that same word in bold (eg., “try to incorporate generating into your lecture.”)  Of course, the use of personal response systems (“clickers”) fulfills this end very nicely.

A few presentation tips from the article:

Space repetitions of information across lectures.  Long term recall is improved when information is spread out over time.  That’s why it’s better to study over several days, rather than cram the night before the test.

Show key concepts in several different ways. This is termed “encoding variability,” and gives students a chance to learn the material in more than one way, which helps them generalize what they’ve learned.

Provide structure. This is the goal of the ubiquitous outline we see in talks, lectures, syllabi, etc.  Some studies have found that students learn a lot from filling in an instructor-prepared outline of lecture notes (eg., headings and subheadings), rather than taking lecture notes on a blank piece of paper.  Concept maps are also useful ways of helping students see the big picture.

Use visuals and mnemonics. This is another way of increasing encoding variability, or the different ways in which students process the information that’s being presented.  Vivid examples and analogies can help, as can graphs, figures, or having students produce their own diagrams.  Enthusiasm and humor, well-placed, can also serve as a mnemonic.

Ask students questions. Ask students questions in class, and require them to give the reasons behind their answers.  Again, clicker questions are a great way to do this, and to make sure every student has a chance to explain their reasoning (at least to their peers).  To get the real benefit here, the questions have to be genuine questions, not rhetorical.  So many instructors ask a question, and then answer it themselves, lulling students into a certain passivity.

So, there are many ways to make lecture an extremely positive learning experience for our students.  But simple enthusiasm and clear explanations aren’t enough.

Here is the original chapter if you’d like to read it.

(P.A. deWinstanley and R. A. Bjork, “Successful Lecturing:  Presenting Information in Ways that Engage Effective Processing,” in Applying the Science of Learning to University Teaching and Beyond).

A good little post by Derek Bruff recently details his arguments why clickers are useful in college classrooms.  If you’re a skeptic, or trying to convince a skeptic, it’s worth checking out his post

We’ve also got a video that shows many of these same points — here that is.

Once again, here are a few very useful books on using clickers in the classroom:

Peer Instruction is the “bible” of clicker usage, including sample questions in physics. This text will change the way you teach! Derek Bruff’s new book Teaching with Classroom Response Systems comes highly recommended by Eric Mazur himself, which is high praise! Doug Duncan’s Clickers in the Classroom is a short and pithy gold standard of how to use Peer Instruction in the classroom.

I guess that I’m the last person to see this, but this YouTube video on digital technology and college education from Kansas State University made the rounds a while back.  It’s a very moving presentation of how distanced students feel from their own learning and the role that technology plays in that.

From a teacher’s perspective, there are some things that you can do to keep students on task and engaged in the classroom (and make that lecture more relevant to them).

On that note, I went to a nice presentation by Diane Sieber on “Facing Facebook” recently, talking about the challenges facing college instructors with the digital age.  How do you work with the technology instead of fighting it?

The results of a Pew research study in 2006 showed that, in class

• 80% of students access Facebook or MySpace
• 73% text message, IM or email
• 90% browse the web
• 45% read news or blogs
• 25% take notes
• 18% play online games

One thing that she does is to avoid Powerpoint at all costs.  Powerpoint just sucks the energy out of a room, she says, and students take it as a cue to tune out.  Powerpoint reduces complex ideas to simple slides, or at least students see them as reductive.  It also makes lecture scripted and linear — everything is in order and there is this “forced march” through the materials.  This kills any sense  that there’s a risk to not paying attention.  You might as well check your email and then download the powerpoints later.   She uses Mind Manager Pro to create a concept map of her lecture.

She didn’t encourage banning laptops, since that penalizes students.  Help students use their technology more productively, she says. There are some dirty rotten tricks, like using a “dummy” wireless router to draw wireless traffic from the main campus router to that non-internet connected router. You can also restrict laptops to the front row of class, but I’ve seen students still off-task with that method.

But more productively, she has the class create a social contract using an online wiki.  She uses the wiki throughout class, and the social contract is the first thing they do.  Then the whole class has bought in to the contract and enforces it.  That contract always ends up including something about the use of technology in the classroom.  After all, it’s distracting to other students if the student in front of them is surfing the net.

Just being aware, as an instructor, when people are looking at the screen and not touching the keyboard, can help.  Call students by name to draw their attention.  Walk around the class, beyond the first five rows.  Have “tops down” time when screens have to be down, signalling that this is an important topic, and breaking up the pace of class.  She even ran some performance correlations, showing that those students with laptops open during class had lower grades on the test –this was very surprising to students, and they changed their behavior.

These media can complement class activity, too, by assigning a student to googlejockey during class, or using tools such as ubiquitous presenter.

This is my second post in a series about using clickers in the upper division.

A lot of people have trouble imagining what kinds of questions you might ask at the upper division. The challenge is to make them tough, but not too tough. You want students to have to think and argue about them, but you don’t want to make them so hard that students are just stuck. Some example question types are:

• conceptual
• math/physics connection
• application of ideas
• step in calculation, proof or derivation

Here are some example questions from a few different courses:

Here is a video showing how one instructor used clickers in his upper division courses — this is a great little video, which really shows the thought process going into each question

Video: What kinds of questions do we ask in upper division? (2 min)

And while we’re on the subject of clickers, here are a few very useful books on using them in the classroom:

Peer Instruction is the “bible” of clicker usage, including sample questions in physics. This text will change the way you teach! Derek Bruff’s new book Teaching with Classroom Response Systems comes highly recommended by Eric Mazur himself, which is high praise! Doug Duncan’s Clickers in the Classroom is a short and pithy gold standard of how to use Peer Instruction in the classroom.

I recently gave a talk at the AAPT about how we’re using clickers in upper division physics, and I keep meaning to include this as a post here! I wonder, should I submit this to The Physics Teacher, perhaps?

First off, you can download my powerpoint, as well as the accompanying videos, here. There are a whole bunch of different resources on clickers (clicker banks, videos in progress, useful links) at that website as well (http://STEMclickers.colorado.edu) and on my YouTube channel.

Clickers in the Upper Division 

Some people disagree with the use of clickers at the upper division (or even in the lower division). We find them incredibly valuable as a tool to engage students so they get (a) to talk to their peers, (b) get feedback on their performance in a private way, and (c) the instructor gets instant feedback on what the class is understanding. We typically ask a question, then ask students to discuss it with their neighbors to convince each other of their answer. They click in and we discuss the question as a class. I’ll write a post in more detail about clickers later, but if you want to know more, go to Derek Bruff’s blog, or take a look at his excellent book Teaching with Classroom Response Systems: Creating Active Learning Environments. He also has some resources posted here.

You can see more recommendations on books on clickers at my sciencegeekgirl picks page.

Using clickers in the upper division is a little bit controversial. Many faculty disagreed with our choice to use clickers at this level, and still do despite the data showing that it was an effective way to teach. There is a sense that clickers are “babying” the students, or not serious.

The history of upper division clickers at CU

We’ve been using clickers in the upper division at CU since 2004 in classes from Stat Mech, to Classical Mech, to E&M and Quantum, plus one graduate course (AMO) — a total of 26 classes and 10 courses. This hasn’t just been the work of Physics Education Research (PER) faculty — it’s been a real mix of PER and non-PER. One thing to note is that, with just two exceptions, faculty had taught an introductory course using clickers before they used it in the upper division.

We’ve been working on transforming two of our courses in particular, to be more interactive — junior level Quantum I and E&M I. Let’s look at Quantum I. This is typically taken by 2nd semester juniors, and is currently in its third semester of transformations. It was co-taught by a PER instructor (and expert clicker user), Steven Pollock, and a non-PER instructor (new open-minded clicker user), Oliver DeWolfe, this last semester.

Let’s see how this looked in action — here is a video showing Steve using clickers in this quantum class, students talking about what they got out of it, and Oliver discussing whether he thought clickers were a good thing.

Download this video as a .mov

Coming in future posts this week — what kinds of questions we ask in the upper division, what students think, and tips for success!

There was an interesting discussion on a college level email list recently about classroom management, where an instructor was trying his darndest to create a group learning environment in his classroom, but ended up with a bunch of rowdy off-task students.  A whole plethora of responses flooded in with personal experiences on classroom management and tried-and-true tips for getting these active learning strategies to work in practice.  Here are some snippets from that conversation.

The original question (from Paula Engelhart) was:

The pedagogy works great and the students really seem to get a lot out of it but…. what I’m having difficulty with is controlling the amount of social interaction that is occurring in the second semester class.It wasn’t very difficult to keep them on task the first semester in part because they wanted to know the answer to the activity.  Moving into the more abstract ideas of the second semester they don’t really seem to care as much and also many of them were together last semester and know each other.  Some days I have a very hard time getting them to stop talking at the beginning of class to get class going.

Julie Libarkin had similar problems in a large (275 student) class.   She felt the group work was very useful, but had trouble getting them to stay on task during the activity and then struggled to bring them back together afterwards.  She posted a query to the Chronicle of Higher Education and got some useful suggestions:

1) Establish a standard routine for group work. For example, always let the students know before group work begins what the purpose of the work is, tasks they should plan to do during the activity, and products they should expect to have completed or close to completion at the end of the activity. Set a time limit for the activity – you can always add more time if the class wants it. Write everything on a slide that is displayed during the group time.  For longer group work, have some mechanism for grabbing attention about mid-way through the activity, like a clicker question geared towards the first part of the activity or a brief discussion of common problems you have observed cropping up in groups.

2) For me, the hardest thing was getting students to settle down when it was time to finish up the activity and have a class discussion. I got this great advice: Have a slide (mine has cartoon images that move randomly around) start playing 2 min before groups should be done. Have a countdown clock on the slide. This worked like magic for my class, especially since I told them about it ahead of time, and we even practiced the whole quiet down thing. If your class is really hard to settle down, you can also have music that plays and which gets louder and louder as the end time approaches.

3) For engaging the class in discussion: I assigned my students to group numbers, mostly as a mechanism for handing back assignments. Each group has a folder which they pick up and return themselves at the start/end of class. Even though my groups are not formal in the classic sense, the group numbers help with discussions. If I ask a question about the activity, and no one responds, I shout out a group number. Someone from the group always pipes up. If no one from that group is in class that day (happens occasionally), then I write it down. I don’t actually do anything with this information usually, but the rest of the class is empowered to speak up if they think not speaking up is somehow detrimental.

Melissa Dancy shared this advice (which was seconded by Chandralekha Singh)

One thing I’ve found that does help is to walk up to a group that is not on task and start asking them questions to force them to engage in the material.  This works if the class is small enough that I can visit each group regularly but for my larger class the time it takes me to get from one group to another means they can spend lots of time off task.

This is a good use of Learning Assistants — a model created at the University of Colorado (where I’m at) where good undergraduates are given the job of helping to facilitate peer discussion by circulating the room during lecture.  They help students learn, get good experience themselves, and can also help with these classroom management issues.

I recently gave a talk at the AAPT about how we’re using clickers in upper division physics, and I keep meaning to include this as a post here!  I wonder, should I submit this to The Physics Teacher, perhaps?

First off, you can download my powerpoint, as well as the accompanying videos, here. There are a whole bunch of different resources on clickers (clicker banks, videos in progress, useful links) at that website as well (http://STEMclickers.colorado.edu) and on my YouTube channel.

Some people disagree with the use of clickers at the upper division (or even in the lower division).  We find them incredibly valuable as a tool to engage students so they get (a) to talk to their peers, (b) get feedback on their performance in a private way, and (c) the instructor gets instant feedback on what the class is understanding.  We typically ask a question, then ask students to discuss it with their neighbors to convince each other of their answer.  They click in and we discuss the question as a class.  I’ll write a post in more detail about clickers later, but if you want to know more, go to Derek Bruff’s blog, or take a look at his excellent book Teaching with Classroom Response Systems: Creating Active Learning Environments.  He also has some resources posted here.

You can see more recommendations on books on clickers at my sciencegeekgirl picks page.

Using clickers in the upper division is a little bit controversial.  Many faculty disagreed with our choice to use clickers at this level, and still do despite the data showing that it was an effective way to teach.  There is a sense that clickers are “babying” the students, or not serious.

Clickers in the Upper Division at CU

We’ve been using clickers in the upper division at CU since 2004 in classes from Stat Mech, to Classical Mech, to E&M and Quantum, plus one graduate course (AMO) — a total of 26 classes and 10 courses. This hasn’t just been the work of Physics Education Research (PER) faculty — it’s been a real mix of PER and non-PER.  One thing to note is that, with just two exceptions, faculty had taught an introductory course using clickers before they used it in the upper division.

We’ve been working on transforming two of our courses in particular, to be more interactive — junior level Quantum I and E&M I.  Let’s look at Quantum I.  This is typically taken by 2nd semester juniors, and is currently in its third semester of transformations.  It was co-taught by a PER instructor (and expert clicker user), Steven Pollock, and a non-PER instructor (new open-minded clicker user), Oliver DeWolfe, this last semester.  Let’s see how this looked in action — here is a video showing Steve using clickers in this quantum class, students talking about what they got out of it, and Oliver discussing whether he thought clickers were a good thing.

 

Download this video as a .mov

Coming in future posts this week — what kinds of questions we ask in the upper division, what students think, and tips for success!

There’s been a quite interesting (and sometimes vitriolic) exchange of ideas on the usefulness (and cost) of clickers in college classrooms, in which I recently took part.  A “clicker,” for those of you who haven’t heard of them yet, is just a little device which lets an instructor take a real-time poll of the class.  Each clicker has 5 buttons labeled A through E, corresponding to answer choices to a question posed by the instructor.  A real-time histogram is created showing the class response. In itself, clickers are no magic bullet, they’re just a tool.  But we’ve found them to be incredibly effective tools for learning when we use them in conjunction with Peer Instruction (as coined by Eric Mazur).

We ask students a challenging question and then ask them to talk to their neighbors about the question.  In this way, the clicker isn’t a quiz, but rather it focuses the class on a particular conundrum in the physics (or biology, or what have you) material being taught, and they get a chance to wrestle with it and teach each other.  Their answers are anonymous (at least to their peers), so there’s no embarassment if they raise their hands for the wrong answer.  If they’re not sure of the right reasoning, their peers can often help them better than the instructor, who is a long way past his or her own struggles with the material.  And then the instructor gets a snapshot of whether the class is following his or her (brilliant) lecture  — both by seeing the histogram, and by eavesdropping on conversations that students have with each other. It can be a fantastic tool.

But here’s the “controversy” (in quotes, because I’m not so sure that both sides are really arguing about the same thing).  In a recent issue of the Chronicle of Higher Education, Michael Bugeja, argues that clickers are the product of successful marketing by companies who want to make a buck, at the expense of our students and academic integrity (see “Classroom clickers and the cost of technology“).  He argues this not just for clickers, but for technology in general (see “Could you be a Hoopla-dite” in the Chronicle).

He says, for example (from the article in the Chronicle):

Clickers, or “audience-response systems,” were designed in the 1960s in Hollywood to test unreleased movies, commercials, and television shows. A decade later, a retired planner at IBM, Bill Simmons, developed a rudimentary response system to simplify boring business meetings. Soon the business world commercialized and adapted audience-response systems to augment consultations and presentations.

Then, in one rhetorical stroke, manufacturers substituted “student” for “audience,” introducing clickers into education.

…

. Institutions have much to learn from students about the cost and effectiveness of technology. Chief information officers need to be consulted before departments invest in expensive for-profit consumer technologies. Professors need to realize that technology comes at a price, even when advertised as “free.” Finally, administrators need to double their efforts at cost containment, demanding assessment before investment, especially in schemes that bypass mandated accountability standards.

Otherwise business as usual will continue to disenfranchise our students, who will hold their debt-ridden futures in their clicking hands.

There have been, of course, many responses to this, such as Richard Hake’s very complete and referenced online response, a detailed post (and response by Bugeja) on Derek Bruff’s blog, as well as several letters to the editor which appeared in the January issue, including one by myself, and one by Doug Duncan (also at CU-Boulder).  Those are online at the Chronicle but only available to subscribers.  Derek Bruff commented on those letters as well.

Derek Bruff responds to Bugeja, in part:

I agree with some of Bugeja’s takeaways from his institution’s experiences with clicker vendors.  He argues that students should be involved in decisions about instructional technology, that chief information officers should be consulted by departments making such decisions, that faculty adopting technologies should be aware of not-so-obvious costs of using these technologies, and that administrators should be prudent when conducting cost-benefit analyses of new instructional technologies.

Those are all very sensible points.  However, I see some problems in the ways Bugeja uses clickers as an example in support of these points.  The fundamental weakness of the essay is that Bugeja seems to be doing a cost-benefit analysis on clickers without paying much attention to the benefits portion of that analysis.  As well-referenced as the cost portion of his analysis is, he fails to consider any of the research looking into the impact of teaching with clickers on student learning.

In kind, here is a portion of Doug Duncan’s response to Bugeja:

Most of the practices [Bugeja] describes are what our research shows to be worst practices. We see them fail, too. When instructors use clickers as part of peer instruction and explain to students that they will attend class more, work harder, learn more, and be rewarded for that, peer instruction and clickers produce learning gains. When instructors ask low-level memorization questions and don’t explain why they are using clickers, students call them dumb and worthless.

And here is my response in its entirety.  (Here is a a PDF including Duncan’s whole response).

Based on years of extensive systematic surveys, observations, and peer-reviewed research on personal response systems (“clickers”) we strongly disagree with many of the points raised in Mr. Bugeja’s December 5 article “Classroom clickers and the cost of technology.”  This simple tool, when used well, can result in a remarkable transformation of a university classroom, increasing how much students learn and enjoy a given course through increased interaction and engagement with their instructor and peers.  We have found no other single tool that achieves as many benefits for such low cost.

Mr. Bugeja argues that “manufacturers substituted ‘student’ for ‘audience’” when adapting clickers from audience-response systems in Hollywood.  We do not find it interesting to hypothesize about intentions of manufacturers or their profit motives, but rather to adapt their tools for our needs. As a familiar example, computer manufacturers’ goal is profit, yet nobody doubts the utility that the personal computer has as a tool towards accomplishing great things.  Or not (think Tetris). And so, as with any technology, a clicker is simply a tool, and depending on the hands of the craftsman, it can either be an expensive toy or a vehicle for classroom transformation.   Here at the University of Colorado (CU) at Boulder we use iClickers campus-wide, which are designed to be technically simple and robust.  Students buy the iClicker, once, for about $40 ($20 used), and use it in multiple courses. That’s it.  And from there, it’s up to the instructors.

Now, if instructors substitute “student,” for “audience” then there is a problem.  In fact, that already is the problem.  Decades of research on learning and cognition show that students learn more when they are engaged interactively .  But it’s hard to change university classrooms to encourage active learning, given a myriad of institutional constraints such as fixed stadium style seating.  Clickers, however, offer an easy, cost-effective way to engage students in the material, by the following process:  (1) asking students a question that’s challenging, but not too hard, (2) giving them adequate time to discuss with their neighbors before they give their final vote and (3) asking students to explain their answers, including why the wrong answers are wrong.

Using this method of clickers and peer instruction (modeled after that of Eric Mazur at Harvard), research at CU and elsewhere  has shown that student learning increases compared to traditional lecture, across several disciplines. Additionally, several studies ,  show that, after talking to their neighbors, students gravitate towards the correct answer, and the experience of talking to their neighbors substantially contributes to learning.  In addition, clickers give students a chance to practice communicating their thinking to their peers, a skill that they would not achieve while passively listening to a lecture.  Classes that use clickers to ask simple quiz-like questions without peer discussion aren’t achieving these full benefits.

Obviously, teachers don’t need clickers in order to ask students thoughtful questions and have them discuss the answers with each other.  But clicker technology itself provides several key benefits that promote active engagement, namely:  (A) focusing the class clearly on a question, (B) having students commit to an answer, instead of retroactively deciding that they would have answered correctly, and (C) allowing the safety of anonymity. Mr. Bugeja quotes Ira David Socol claiming that clickers are “no more sophisticated pedagogically than raising your hand.”  Come now.  If most people are raising their hands for answer “A”, will you still bravely raise your hand for “B”?    And once you know the answer to the question, your own reasoning process has been short-circuited.  And lastly, clickers offer (D) the computer tabulation of responses, giving both instructors and students real-time systematic feedback about student understanding.
Mr. Bugeja hypothesizes that students would vote against the use of clickers because the costs outweigh the benefits.  Research suggests otherwise.  In our own large introductory physics courses, 95% of students stated that clickers were helpful to them in learning the material .  Studies in other disciplines suggest that students are more likely to value clickers when they’re used to promote discussion, rather than to ask simple questions or take attendance.
Sure, clickers cost students money.  But students are paying thousands of dollars to sit in your classroom.  Clickers can make this experience more educationally productive, for a marginal additional cost.  Let’s not concern ourselves with the business of the manufacturers.  We’re in the business of supporting the development of thinking minds.

Dr. Stephanie Chasteen (Physics Department) on behalf of the Science Education Initiative of the University of Colorado at Boulder

http://www.colorado.edu/sei

Stephanie Chasteen
Research Associate
Science Education Initiative
University of Colorado at Boulder
Boulder, Colo.

Note that Bugeja was not given the opportunity to respond to these letters in the Chronicle.  You can see his unpublished reply here. I was saddened to see that he still didn’t address the pedagogical usefulness of the tool.  He focuses on the cost ($20-40 for an item that can be used in multiple classes, unlike hundreds of dollars worth of textbooks good for a single semester).  On the other hand, those of us who advocate clickers and see their pedagogical usefulness are arguing for that. Bugeja is arguing on basis of cost.  Are we comparing apples to oranges?  We advocates don’t want to tax students unnecessarily for their education.  We do the cost benefit analysis and see the benefit far outweighing the cost.  Does Bugeja see no benefit, and thus the cost benefit analysis focuses on the cost?

For the record, at CU we like the i>clicker system a lot!

“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).