Khan Academy II: Discussions and "Khanversations"

"Khan Academy" style instructional YouTube videos could be more effective for introductory physics if they used a discussion model rather than a lecture model.

I had a fine time last week at the WNET Channel 13 Celebration of Teaching and Learning (which consisted of about 30% substance, 20% patting teaching on the back for doing "such an amazing job," and 50% advertising), and I wanted to follow up on the post I wrote about Khan Academy.

Over the course of the day, I saw Sal Khan (the Silicon Valley superstar shown in the camera-phone screens to the left) give his standard talk, and then follow it up with an hour-long question and answer session. In general, I came away convinced that Khan's heart is in the right place, and that Khan Academy strives to be far more than a YouTube channel. The goal of Khan Academy, he said numerous times, is to off-load a number of tasks traditionally done by teachers in order to free up the teacher's time to do more valuable things. During the Q&A, I got a chance to ask Khan essentially the questions that I posed in the last post: What is the role of an explanatory video when we know that clear and concise explanations can be counterproductive to student learning? His answer was basically that students should have access to whatever resources that might be helpful to them, and they're taking seriously their responsibility to measure the effectiveness of the videos to identify which ones aren't working. Here's a quote from his response:

When I think about my own learning, there are some times when I learned something through the experiential, where finally when I had to write a program when I was doing some computer graphics, trigonometry finally kicked in... But for some things, you know, especially when I was doing higher level math, it really sometimes was a friend in a coffee shop giving me a clear and concise explanation. And I was just like, "Wow, that really hit the spot. That was really much better than what was in the book, and that got me through my stumbling block."

I agree with what Khan is saying here, but this response reveals a slightly simplistic view of how learning works. I can't deny that clear and concise explanations from friends or teachers have gotten me through some tricky spots as well. However, I'd also suggest that hearing those explanations in clear and concise terms sometimes didn't actually help me as much as other approaches might have. Precisely because I was hand-fed exactly what I needed to fill in the gaps in my understanding at that moment, a few days or weeks later, those gaps sometimes returned.

When I think about what Khan Academy videos might look like if they were truly out to correct student misconceptions about, say Newton's Third Law, I imagine something more like the "dispute between students" prompts you find in Lillian McDermott's Physics By Inquiry books (see my previous post on this topic). In the Khan Academy model, picture a "Khanversation" between two voices, in which both individuals make arguments supported by diagrams to support a claim their view is consistent with observations in the natural world. This approach would provide opportunities to bring common misconceptions out into the open and model effective argumentation for students as they practice these concepts and skills in their classroom.

In a 2010 review paper in Science, Stanford School of Ed Professor Jonathan Osborne calls attention to a great irony in many science classes - traditional science teaching fails to develop the skills of argumentation and debate that are at the heart of the way science actually operates. Not only do student-centered teaching methods help to develop these essential skills, they also facilitate learning of science concepts far more effectively. Osborne writes: "Learning is often the product of the difference between the intuitive or old models we hold and new ideas we encounter. Through a cognitive process of comparison and contrast, supported by dialogue, the individual then develops new understanding. Consequently, learning requires opportunities for students to advance claims, to justify the ideas they hold, and to be challenged." We should be teaching our students first and foremost how to navigate their way through this process, as this is a skill that will be far more relevant to them than any science concept. (excepting, of course, Newton's Third Law...)

One of the most productive aspects of whiteboarding is that students are expected to formulate a verbal argument to support their answer, and present this argument to the teacher and their peers. Not only does this give a teacher instant access to their students' reasoning, but the students themselves are constantly exposed to effective and ineffective arguments. What role might other methods play in this process? I have tried to use handouts to structure and spur dialogue between students, but I've never gone so far as to upload such a dialogue to YouTube. At first glance, however, this possibility seems intriguing.

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What's to Learn from Khan Academy?

The video lectures on Khan Academy don't address the complexities of how people actually learn. What might these videos look like if they did?

I was lucky enough to secure a free ticket to the Channel 13 Celebration of Teaching and Learning this Friday in Manhattan. Sal Khan is giving a talk about Khan Academy, the series of YouTube tutorials that have been touted as a revolution in education. Here's an example of Sal Khan layin' down some knowledge about Newton's Third Law:

There's a healthy discussion in the physics teaching blogosphere about why these videos aren't the revolution to education that 60 Minutes might lead you to believe. Physics teacher Frank Noschese makes a very strong argument on his blog in this post and others (there is also a nice set of links to other blogs at the bottom of this page).

Khan Academy lectures seem to me to be a new type of textbook for a sort of curriculum that has been around for ages. The problem is, we've seen that this curriculum just isn't effective. The idea that YouTube lectures can be useful to students isn't flawed in itself, but video resources for more effective pedagogical approaches just aren't posted on Khan Academy. Rather than bashing Khan, let's think about what types of videos might be used as part of more effective curriculum, like Modeling Instruction.

Modeling isn't about lecturing, of course. It doesn't matter whether the lectures take place in a classroom or on YouTube, lecturing just doesn't work. So, what video resources would be effective in a Modeling course? Much of the most valuable student experiences in a Modeling course can't be replaced by videos - hands on lab work, interpreting unique data, discussions with other students, presenting a whiteboarded solution to the class. Somewhere in the midst of all this I imagine there's room for, say, example problems worked out using language and representations specific to a Modeling course, but how would you prevent such concise explanations from interfering with a student's natural struggle to build their own understanding? Perhaps, as Derek Muller suggests in this video, students might benefit from watching a conversation between students as they gradually work toward a correct understanding of a concept or problem.

For me, the takeaway from Khan Academy is simply how easy it is for individuals to make simple instructional videos that are available to a very wide audience. There's still a ways to go in thinking about how such videos might supplement progressive pedagogy, but the method is there for the taking.

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Whiteboard Everything

 Whiteboards should be central to any inquiry-based approach. Whether students are asked to present their solution to a problem, their interpretation of lab results, or anything else that requires them to think independently, whiteboards are an ideal tool for this process.

The more I observe, it seems, the more opportunities I see for effective applications of whiteboarding. Whiteboarding is simply a highly effective way of getting students' thoughts out of their heads and into the classroom, where they can be critiqued and discussed. There are other ways of doing this, of course (simply asking students to raise their hands is one such way, "clicker" response systems are another, higher-tech approach), but whiteboards have unique flexibility and versatility. When a group of students works together to prepare a whiteboard for presentation, the peer discussion that goes into this activity is the first step toward correcting individual students' misconceptions. Plus, whiteboards are extremely economical!

On a recent visit to a school teaching Physics First, students in a rather large class were asked to present their results from a lab experiment. Each student was given one or two poster-sized pieces of sticky paper, and wrote out a summary of each section of a conventional lab report (hypothesis, procedure, results, analysis, etc.), which they then stuck to the wall for the class to see. This was a challenging task, and some groups took much more time to complete it than other groups. When everyone was done, the teacher then asked each group to present their posters, in turn. The room was rather restless, and during each group's five-minute presentation students in other groups found it hard to sit still. To save time, the teacher asked latter groups to skip the parts of their report that were essentially similar to things other groups had already spoken about. When the period ended, most of the groups in the room hadn't had a chance to present their posters at all.

Imagine the same activity done with whiteboards. The whiteboard is too small to record all the information in every section of the lab report with a big, bold dry erase pen, so the activity would have to be broken down into pieces. For each section of the report, a few groups would present what they'd recorded on their whiteboards and other groups would look on. Each of these presentations would be less than a minute long, and even the most restless students would find it easier to pay attention to their peers for this short time. The teacher would have the opportunity to focus closely on the aspects of the activity that differed most from group to group (in this case, the data and analysis), and could spend more time discussing with students the significance of these differences. Since each group's presentations were only a minute long, every group in the room could be assured an opportunity to present at least once, and the threat of being called on to present again would encourage all students in the room to stay alert.

On another visit, I witnessed a very successful application of whiteboarding that faltered a bit when many students in the room had made a similar mistake in the free body diagrams they'd recorded (the whiteboard pictured here doesn't show this mistake...). What followed was a lengthy, lecture-style instruction about how to correct this mistake in the students' diagrams. In talking with the teacher of this class later in the day, we agreed that one might instead make up a new free body diagram problem on the spot designed to hone in on this common mistake, or perhaps even refer to a database of problems specifically designed for this purpose. Students would be asked to set their original whiteboards aside and solve the new problem for class discussion on a new whiteboard. Rather than lecturing about how to correct the common mistake, the correct solution would arise out of this group discussion.

My Modeling workshop leader, this past summer, mentioned that whiteboarding is so entrenched in his current teaching that he wouldn't know how to teach any other way. If he was asked to teach a European history class, he would teach it using whiteboarding. I'm starting to see what he means as I begin to appreciate the power of creative whiteboarding in physics class!

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Analyzing Aspects of Difficulty

Physics teachers have a lot to gain by analyzing what factors contribute to the difficulty of the course they teach. For students, the priorities of the course are dictated by these factors, whether or not these priorities are intended by the teacher.

Conceptual understanding of physics is an important facet of a student's physics education, but this is not the only thing we strive to teach in our classes. Aspects of student learning could be categorized as conceptual (e.g. applying Newton's 3rd Law to an analysis of forces), mathematical (solving a quadratic relationship to find the time aloft for a projectile), skill-based (plotting data with error bars), and knowledge-based (knowing that g on earth is 9.8 N/kg), and we could certainly identify other categories as well (problem solving, scientific reasoning). Any physics teacher makes choices to emphasize certain of these aspects over others, based on their own personal priorities and priorities dictated by others (through a standardized test or curriculum or through administrative or departmental influence). How can we use these distinctions to inform decisions about what priorities to set in our curriculum?

I believe that a physics course should be difficult. I also believe that we have a responsibility to our students to examine the "difficulty" of the course we teach through the lens of categories like I mentioned above. In other words, if a task or problem is difficult for our students, why do they find it difficult? Do the concepts being studied conflict with misconceptions? Are students being asked to use unfamiliar math techniques or analytical skills? Are they having trouble recalling or accessing necessary knowledge?

To illustrate a distinction between conceptual and mathematical difficulty, for example, consider the diagrams to the right, depicting two varieties of the "modified Atwood machine." As part of a discussion of Newton's 2nd Law in a high school physics course, students might be asked to, "Find the acceleration of the hanging block."

In my experience, either of these problems would present a challenge for a ninth grade student. It's a challenge to recognize that the acceleration of the two-block system is affected by both masses, though the force of gravity on the large and small masses affects this acceleration in different ways. However, the problem on an incline would present a significantly greater challenge to an average ninth grader. Why is this second problem more difficult? Does it require a require a more sophisticated conceptual understanding, or does it simply require more knowledge of math?

Well, I'd say it requires both*, but I'd also argue that the added difficulty of the second problem in this case is overwhelmingly due to the trigonometry involved in the solution. If we choose to include this problem in our course, it should be because we want to increase a student's familiarity with trigonometry, not because we assume that this trigonometry is inseparable from the physics concepts. Of course, a student's understanding of physics concepts is often connected to their facility with the relevant math (though the connection between math and physics is less direct than we sometimes assume), but we physics teachers have some degree of flexibility to include only the pieces of the "whole story" we deem to be age-appropriate. We don't shy away from discussing gravitational field in a typical algebra-based high school course simply because our students can't compute the line integral required to show that this field is conservative.

In making choices about how to teach and what to teach in our courses, there's a lot to be gained by analyzing how the activities we include in our course develop both skills and understanding. In a Physics First course, our task is twofold (at least!): we are teaching physics and introducing students to high school science. In determining how best to accomplish these parallel tasks, we can continuously ask ourselves what conceptual, mathematical, skill-based, and knowledge-based aspects of physics our course is prioritizing.

*To clarify, it seems to me that vector analysis of the forces on an object on an incline is mostly a conceptual (or perhaps skill-based) task. However, I'd argue that the added challenge of applying this analysis to a calculation of acceleration is mostly mathematical in nature.

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Programming as Problem Solving

Computer programming provides an ideal environment for young students to develop the cognitive skills required to solve a problem gradually through trial and error... and error, and error, and error.

At a New York City public school with a focus on science and math, I observed ninth grade students in a class called Engineering, devoted mostly to introductory computer programming. Students had spent much of the beginning of the year working in Alice, a simple-to-learn 3D programming environment, but had moved on to a text-based, open-source language called Python. Python is rapidly developing a huge following in both the programming and teaching worlds, in part because of its simplicity, readability, and diverse and dynamic library of resources.

Many of the students in the class were working on a coding a guessing game in Python, an assignment written by Tim Wilson as part of a public library of Python-related materials.  In this game, the computer selects a random number between 1 and 100, and the user enters integers until they guess the number correctly. I've included below a few examples of observations I made while watching students make their way through this challenge:

In developing a method of comparing a user's guess to the computer's selection, one student had written a guess test consisting of the following code:

    if guess = computernum:
        print 'You got it!'

This student was busy running the program and trying out different numbers, but was getting increasingly frustrated that the computer just sat there silent whenever he entered an incorrect guess. 

Another student was trying to print the number that the computer had guessed, to make it easier to debug her guess-comparison code. Another student tried to help by suggesting that she include the code "print computerchoice" but any time she ran the program she got an error message:

Traceback (most recent call last):
     File "/Users/Documents/Python/guessinggame.py", line 10, in <module>
        print computerchoice
NameError: name 'computerchoice' is not defined

Another student had successfully completed the necessary code for making and checking a guess, and he was trying to expand his code to allow for multiple user guesses, in sequence. He copies the section of his code that checks the guess and pastes it below the first "guess-checking" section, but he is puzzled when he sees the computer's emphatically repetitive response:

What is your guess?56
56
ha ha you got it wrong
ha ha you got it wrong 

An introductory course in programming is, above all, a course in problem solving. The world of programming plays by consistent rules, and solving problems within this environment means learning those rules. Large tasks can be broken down into discrete, testable chunks, and incremental progress is rewarded with immediate feedback. Creativity and collaboration go hand-in-hand, and successful and unsuccessful approaches are identifiable by the program they produce. Any differences of opinion on what approaches might work are best resolved by simply trying things out - as recently quoted by our nation's youngest billionaire, "Code wins arguments."

We physics teachers like to paint the universe as a place that operates by a few simple relationships, but demonstrating the simplicity of these relationships can sometimes be a little complicated. When faced with a complex problem, developing a successful solution takes a organized approach based in the assumption that a system is doing what it's doing for a reason. Rather than simply saying, "it's not working..." a successful problem solver admits "It's working... It's just not doing what I want it to do. Why is it working this way and how can I change it?" Programming is an ideal venue for practicing this skill. As each of the issues I described above were resolved, students were rewarded with a more sophisticated understanding of the "unsuccessful" program they'd written, as well as the modification that brought the program closer to completing the task at hand.

Later in the course, students are exposed to a 3D graphics module called Visual, which allows for fluid 3D programming within Python, or as it's referred to when used with this module, VPython. All students at this school take physics in ninth grade as well as engineering, and one of the later assignments in the course is to use VPython to program a 3D simulation of a projectile moving in two dimensions. What better way to help students arrive at an understanding of the rules nature uses to determine the position of a projectile than to ask students to code these rules themselves?

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The No Relationship Relationship

Students often have a difficult time interpreting data from a graph of two variables when the relationship between these two variables doesn't exist. Teachers should approach these situations with care, and use them as an opportunity for direct discussion of what "no-relationship" means in a scientific investigation.

On a recent visit to a New York City public school, I saw ninth graders complete a classic pendulum lab. Students measured the period of a pendulum at various different angles of initial displacement, and then measured the period for various string lengths. Students then graphed their results and posted them on the walls of the room for everyone to see. Though not many groups looked around the room at their classmates' graphs, if they had they may have been surprised at the diversity of results! I've included a sampling of some student graphs showing their results concerning the relationship between period and amplitude.

These graphs illustrate how challenging it is for students to accept the no relationship relationship. (Before you take me to task about the amplitude-dependence of the period of a pendulum, keep in mind that for the maximum amplitude measured here, the actual period deviation from a small-angle approximated pendulum is less than 5%...) Young people who have been graphing results in science class since elementary school are so used to seeing a trend in the relationship between two variables that they go bonkers when the relationship between those variables doesn't jump out at them.

Watching students carry out this pendulum lab was fascinating. Nearly every group doing the lab expressed doubt and dismay when they noticed they were getting approximately the same value of period for every amplitude. (At least one group decided to do something about it: if they didn't get a result that was sufficiently different from the last angle they measured, they went back and did the run again.) One member of the group that made the correct graph shown on the upper right apologized that they "did the experiment wrong." The assumptions students brought with them to this lab led to quite a few discussions with the teacher about why they were so sure that their measurements were wrong, but I didn't get the impression that these conversations resulted in much self-reflection. (We could find out, of course, by asking these same students to examine the relationship between period and mass...)

This period-amplitude relationship was just one piece of the entire pendulum lab, and students' graphs showing the relationship between string length and period were more successful than the period-amplitude graphs I've shown here. But, applications in torture aside, it seems like pendulum's most promising role in a Physics First course is in encouraging students to examine their own role as scientists. With a little bit of restructuring to this activity, the widely varying results shown in these graphs could provide the fuel for quite a sophisticated discussion about experimental design.

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Active Physics and Inquiry

An independent school in New York City provides an excellent example of a successful application of the Active Physics curriculum, but aspects of Modeling Instruction could have potential to make the course even more dynamic.

Active Physics is a project-based curriculum with a conceptual focus, designed to be used with ninth graders. Active Physics groups concepts by themes, such as "Communication," "Sports," or "Home," in an attempt to make the physics more relevant to students' daily life. The work done in each unit culminates in a "Chapter Challenge," where students must apply their knowledge to solve a real-life problem. One independent school in New York City has been using the Active Physics curriculum since 1994 as the foundation of a physics course for all ninth graders. When I visited this school, students were studying the efficiency of various methods of heating water, and were just about to begin the "Chapter Challenge" of selecting appliances to meet the basic needs of an average family, capable of being powered by wind-generator with an output of only 2400W.

When class began, students were seated in lab groups, discussing a question from their textbook: "Are high-efficiency appliance worth the added cost?" Students' responses reflected a common misconception - conflating the efficiency of an appliance with an assessment of its overall quality: "Well, yeah they're worth it... they're better." "They're more durable, work faster, and just work better in general." When students were asked to present the results of their discussion, only one group in three appreciated the more subtle implications of the concept of efficiency, stating, "A higher efficiency appliance will make up for its cost with less power used over time," but even this group was confused by the difference between the terms "power" and "energy." The stage was set for an inquiry-based activity to root out the would root out these misconceptions and lead students to a more sophisticated understanding of the concepts of energy, power, and efficiency.

The lab activity for the day consisted of heating up a beaker of water on a hotplate. The procedure steps outlined in their textbook were summarized on a projector: "Measure: 150mL of water, initial and final temp of water, measure time appliance is on (increase temperature by 20˚C)." After a brief discussion of how to use the equipment, students got to work carrying out these steps. They made a few potentially problematic procedural choices along the way (measuring water volume with a beaker rather than a graduated cylinder, plugging in the hotplate before starting their stopwatch, resting the thermometer against the bottom of the beaker, for example), but the teacher caught most of these and gave suggestions for improvements when he felt it was necessary to do so. In class discussion, students struggled with how to use the values they'd measured to make the required calculation of efficiency, but the teacher coached them through the process (partly by referring them to a similar activity done a few days earlier with immersion heaters):

Teacher: "Who remembers how we calculate the thermal energy gained by the water?"

Student: "Was that the thing that was 4.18...?"

Teacher: "Yes, we need the specific heat of water. Anything else?"

Over the course of the discussion, each group eventually arrived at calculations that basically agreed with one another, confirming an efficiency of about 10%.

While watching students carry out this activity and discuss the correct method for calculating efficiency, I tried to imagine what the same basic procedure would look like using a whiteboarding approach. Students might start the lab by brainstorming steps they'd take to to collect whatever data they felt were relevant to a calculation of efficiency, then writing these steps on a whiteboard and presenting them to the class for discussion. Once students had carried out these steps with their lab group, they could attempt a calculation of efficiency (again, on a whiteboard), and discuss as a class whether the calculations they'd made were relevant to the central question of the efficiency of appliances. Different groups could even use different methods of heating the water: an immersion heater, a hotplate, a microwave...

I emailed a prominent advocate of Modeling Instruction to ask about crossover between Active Physics and Modeling Instruction, and she told me that "Active Physics and Modeling Instruction don't go well together." Modeling Instruction is about developing basic models for the most fundamental interactions in physics, whereas the projects in Active Physics tend to highlight more complex applications of these concepts: efficiency of electric appliances, acoustic properties of instruments (watch your ears...), how to build a DC motor or generator, etc. Both of these approaches have merit, and it seems to me that there's a lot to be gained in exposing students to aspects of both. That is, a whiteboarding approach might have avoided the more "cookie-cutter" aspects of this particular lab activity on heating water (and probably brought misconceptions to the forefront more effectively), and a project-based "Chapter Challenge" in a Modeling course might give students a better appreciation for how even the simplest models they develop can be applied to their daily life.

In my observations, I've noticed a trend among teachers of Physics First: in the absence of a single universally-accepted ninth grade physics curriculum, teachers tend to pick and choose aspects of various programs that appeal to them. This dynamism is healthy and exciting, but there is something particularly thrilling about the momentum that has been building around Modeling Instruction. A lot of aspects of Modeling just feel like the right way to teach physics: whiteboarding, student-designed experiments, modeling phenomena with multiple representations, and it's tremendous to see the Physics First movement marching forward hand-in-hand with Modeling Instruction. Still, we'd be wise to keep in mind the potential benefits of a diversity of approaches and try to maintain some of the freedom and flexibility that characterizes so many ninth grade physics classrooms.

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