I’d like to begin this post with the coining of a new term: Pseudoteaching. This term was inspired by Dan Meyer’s pseudocontext, which sought to find examples of textbook problems that on the surface seemed to be about real world problems and situations, but actually were about make believe contexts that had little connection to the real world, other than the photographs that framed the problems.

After reading many of Dan’s pseudocontext posts, Frank Noschese and I had the idea of pseudoteaching [PT] which we have defined as:

Pseudoteaching is something you realize you’re doing after you’ve attempted a lesson which from the outset looks like it should result in student learning, but upon further reflection, you realize that the very lesson itself was flawed and involved minimal learning.

We hope that though discussion, we’ll be able to clarify and refine this definition even further. The key idea of pseudoteaching is that it looks like good teaching. In class, students feel like they are learning, and any observer who saw a teacher in the middle of pseudteaching would feel like he’s watching a great lesson. The only problem is, very little learning is taking place. We’re hoping that Pseudoteaching will become a valuable lens for critically examining our own teaching, and that the idea will spread to other teachers as well. Frank is keeping a collection of pseudoteaching examples at his blog, Action Reaction, on custom Pseudoteaching Page. We hope you’ll contribute some of your own examples of pseudoteaching as well.

## Scene: Hunting Monkeys and Pseudoteaching

My example of Pseudoteaching is super fresh. This week, I decided to do an exercise where we explored the famous monkey hunter problem. In case you haven’t seen it, here’s the basic setup. A monkey is hanging from a tree, a height $h$ above the ground. It’s a nervous monkey, and so it will drop from the tree at the same instant it hears any disturbing noise. You’d like to shoot a banana at the monkey (yes, this problem has been sanitized from its previous monkey hating roots), and you are a horizontal distance $d$ away from the the landing spot of the monkey. You wonder how you should aim at the monkey if you want to hit it with the banana. Should you aim at the monkey, below the monkey, or above it?

The unintuitive answer from physics is that you should aim at the monkey, since both are falling, even through the banana is traveling “upward” on its way to the monkey.

Being the masochistic teacher I can be, I thought this presented a great opportunity to dust off our algebra skills and prove, once and for all, that you should aim at the monkey.

So I drew this diagram on the board, and started by asking my students to tell me what the velocity of the monkey should be.

As I usually do, I asked the students to explain how to draw as many graphs as possible for these two objects. And we quickly got to the following velocity graphs.

From these graphs, I ask the students to write the equations for the x and y positions of these objects, assuming an origin at the starting location of the banana.

$\begin{array}{rcl} x_b&=&v_{b0x}t\\ x_m&=&d \end{array}$
and
$\begin{array}{rcl} y_b&=&v_{b0y}t+\frac{1}{2}gt^2\\ y_m&=&\frac{1}{2}gt^2+h\ \end{array}$

Then I ask what must be true if the banana is to hit the monkey, and the students tell me that the x and y positions must be the same at the time of impact, $t_i$. So we write

$\begin{array}{rcl} x_m&=&x_b\\ d&=&v_{b0x}t_i\\ \end{array}$
and
$\begin{array}{rcl} y_m&=&y_b\\ v_{b0y}t+\frac{1}{2}gt_i^2&=&\frac{1}{2}gt_i^2+h\\ \end{array}$

They also see that the last equation can simplified to
$v_{b0y}t_i=h$

Now we have two equations that relate describe the motion of the banana

$\begin{array}{rcl} v_{b0x}t_i&=&g\\ v_{b0y}t_i&=&h\\ \end{array}$

With some coaxing, my students see you can solve the first equation for t_i, to get $t_i=\frac{g}{v_{b0x}}$, and this can be substituted into the second equation to get

$v_{b0y}\frac{g}{v_{b0x}}=h$

Which rearranges to

$\frac{v_{b0y}}{v_{b0x}}=\frac{h}{g}$

We stop and puzzle here, since this seems to be relating the horizontal and vertical components of the velocity to the intial height and distance of the monkey. I say, “to a physicist, this says ‘aim at the monkey!'” How can we see this? I get them to draw a triangle for the initial velocity of the banana and its components:

Soon my students see that the ratio $\frac{h}{g}$ and $\frac{v_{b0y}}{v_{b0x}}$ are just the tangents of $\theta$ and $\alpha$ must be the same:

$\tan\theta=\tan\alpha$

And the only way this can be true is if $\theta=\alpha$, so you aim at the monkey!

## Breakdown: Why this is Pseudoteaching

After the lesson was over, I felt great. I’d basically run through this on the fly, and everyone seemed to be participating and understanding. I stopped along the way to make sure everyone was following the discussion, and to pick apart the particularly difficult parts. Courageous students asked good questions when they couldn’t follow, and I was sure that I’d made my former professors proud.

Then the next day, I decided to see how well my students could do this same derivation on their own. So I gave them this:

View this document on Scribd

And as soon as they started working on it—I head the questions start rolling in:

“Wait, what are we supposed to be doing?”
“I don’t get it.”
“How should we begin?”

And boom—it hit me. Yesterday’s great lesson really wasn’t much more than me showing off my algebra skills. Students were saying the right things when I paused long enough and gave them enough hints to get to the right answer like Clever Hans, but there’s no way they were learning this to symbolically reason through a challenging problem, which was my goal.

Pseudoteaching rears its ugly head right in my classroom. Ugh.

## Resolution

This experience taught me a vital lesson. If I want my kids to be able to reason their way through difficult problems, using symbolic reasoning, I can’t teach it to them by walking them down the narrow road of my “enlightened” physics understanding. Since this is how almost all of my physics classes were in high school and college, and I turned out ok, I thought this would be a great way to learn from time to time. Of course, I forgot how poorly I understood physics when I graduated from college and started teaching. I didn’t figure out most of these things until I was forced to puzzle through them on my own as a teacher.

I need to make time and space in my teaching for students to take on challenges like with this, struggle with them, get lost, fail, and keep going until they get to the solution. So that’s what we did. My classes worked on this for more than half an hour. A few got right to the finish, and were able to then try to figure out how high off the ground the monkey would be when it got hit. Others really struggled to figure out how to interpret their graphs to get equations, but got there in the end, and a few never finished, and I need to find a way to give them more opportunities and scaffolding so that they, too, can see success.

I also need to find a way to assess this skill more. Goal-less problems are a great start, and I really like Kelly O’Shea’s exam design that gives students an opportunity to show synthesis.

Read more examples of pseudoteaching at Frank Noschese’s Pseudoteaching Page.

February 21, 2011 9:13 am

I felt a strong cringe of self-recognition reading this post. I think you and Frank are spot on about this idea of “pseudo-teaching” and that many teachers and department chairs are deceived by the apparent tidiness and fast pace of pseudo-teaching. This post and concept also remind me of Alan Schoenfeld’s article “When Good Teaching Leads to Bad Results: The Disaster of ‘Well Taught’ Mathematics Courses.” Though the points he makes are slightly different, that notion of seemingly good lessons not being educative is there as well.

• February 21, 2011 4:45 pm

Noah,
I shudder to think if I were honest and went back through this blog how many posts would have the fingerprints of pseudoteaching all over them. That’s also a great connection to Schoenfeld’s article. I read it long ago, but need to re-read it again.

2. February 21, 2011 9:27 am

Thank you for admitting that your understanding of physics was hazy when you graduated from college and that it didn’t become clear until you had to teach it. This is exactly what I experienced, and when I tell people this, I feel as if I’ve cheated the system somehow. I got a job without knowing what I was doing. I like this idea of pseudoteaching…keep up the good work of challenging your students to really learn and not pseudolearn.

• February 21, 2011 4:47 pm

Heather, you’ve inspired me to write another blog post. I think I took something like 19 physics courses in college (I was a nut—I think I took almost every class the department offered) and 10 more in grad school, but still I found myself struggling to explain basic things like Newton’s 3rd law. I think the temptation was to always go “deeper” by piling on more math and partial differential equations, without ever working hard (or being forced to) really explain what all the symbols in my pages of equations meant.

• February 21, 2011 6:46 pm

My experience about not understanding things fully until I taught them myself is similar to yours, but if you think that there will ever be a time where any of us manages to teach any subject to a kid in high school (or even college), where they will FULLY ‘understand’ what they are doing, then you are mistaken. That’s the nature of the beast, and it’s OK – really it is! Some will eventually work it out, most won’t, and that’s entirely appropriate and OK, too!

• February 21, 2011 7:52 pm

This is a great point. I think I do hold out a, perhaps naive, hope that all of my students will understand the aspects of physics I try to teach. It’s why I cover so much less material than I used to, and why I do much more to structure the class to help them recognize what they do not understand and how to improve. I think this is the most important lesson I want all my students to grasp—that they can understand science, if they are willing to put in the time and effort. In fact, I think Richard Feynman does a far better job of explaining this then I can.

So if you agree that Feynman is right (and I try not to get in arguments with physics gods), my job as a teacher mainly boils down to convincing my students that it’s worth getting interested in physics and putting in the time and effort to learn it.

• February 23, 2011 9:46 am

quantumprogress – EXACTLY! Who would have thought it was so difficult to understand Newton’s laws of motion?! It’s among the first things we learn in an undergrad physics degree. I was utterly humbled when I began teaching and realized that my understanding of things was still fuzzy. As you mention, I was so focused on the equations and the math that I sometimes forgot the concept. For my first teaching position, I was assigned to teach Conceptual Physics (little to no math) and AP Physics. This was the perfect mix for me. The Conceptual Physics students did not let me hide behind math. We had REAL discussions about physics every day. This led me to structure the AP class so that we had real discussions also…and not just math discussions. One thing that frustrated me in high school was kinematics…it seemed like you just had to pick the right equation to get your answer. I never understood why. I tried (probably not always successfully) to help my AP and Concept students see how the equations were based on the physical world…and not just made up by someone. I am sure a lot of what I did would be considered pseudoteaching as well. I only hope we did some real learning as well!

I’d also like to give my two cents on the other conversation happening here. I truly believe every person can learn physics and math if given the right environment and if he or she puts forth the effort to learn. Other factors such as breakfast in the morning or a math fear instilled early in school get in the way. Yes, students have diverse talents. Yes, not every student will attain the level of a Nobel winning physicist. But, everyone has the capacity to understand basic science. Anyone who is interested enough in science to put in the effort can become a scientist. My favorite story about this is a college acquaintance who was not interested in science. He took a 100 level physics class for non-majors called Atoms to Galaxies to meet gen ed requirements. He fell in love with physics and decided to change his major. But, he didn’t have the math background to enter the physics classes for majors. He had to go back and take high school level math classes to catch up. He did that and eventually completed his physics degree and now works at a physics lab. I was always amazed at his perseverance.

• February 23, 2011 8:36 pm

Many physics teachers write me that they graduated from college with a degree in physics and didn’t learn it well. Their low scores on the Force Concept Inventory, on the first day of their summer Modeling Workshop, are evidence.

Last week a physics teacher wrote, ” I am a new science teacher, working at a new charter school in — that has whole-heartedly adopted the modeling method and is seeing great success with it in the classroom. I studied Physics both in college and high school, though never with the modeling method–now I wish I had. After my three week course in the E&M Physics workshop, I gained a more thorough understanding of electromagnetism than I did after six years of college-level physics instruction.”

Modeling Workshops will be offered in 25 states in summer 2011. Info is at
http://modeling.asu.edu/MW_nation.html
Jane Jackson, Co-Director, Modeling Instruction Program, Dept. of Physics, Arizona State University, Tempe.

• February 23, 2011 8:38 pm

Right on Jane. I’ll vouch for Modeling Instruction having taught me an incredible amount of physics.

3. February 22, 2011 7:04 am

Actually John, I completely disagree with Feynman. You cannot teach a Golden Retriever to do Calculus! It ain’t happening. Children have talents that are diverse, and some of them do not have the either the capacity or the correct skill sets (and never will, even through extensive teaching and instruction), to conquer some of this stuff – and that’s OK, they will be entirely productive citizens without that knowledge.

• February 22, 2011 3:26 pm

First, I’d say there’s a big difference between a golden retriever and a high school student, but we physicists are hubristic enough to think that you can teach Quantum Mechanics to your dog, anyway. While it my be true that not every student can make a nobel prize winning discovery (again, it would seem Feynman disagrees), I do think every student, especially those afforded the tremendous advantages children at independent schools have been afforded, like starting with breakfast every day, can learn high school physics or chemistry. And I’m fairly certain if there’s any chance for this to be true, it must begin with me having unwavering conviction that my students can learn.

Secondly, I’d disagree that no harm comes to society from us having a populace ill-informed of science. Besides the obvious go-to topics of global warming and evolution, I’d say that there’s a real danger that a lack of understanding of biology and stem cells might disrupt research into cures to many diseases, any one of which might affect me, just like a lack of understanding of vaccinations has lead to many needless deaths, and can pose some risk to the health of my child. Finally, at independent schools like mine, that pride themselves on developing the leaders of tomorrow, I would hope that an proper understanding of scientific thinking is a part of their education, so that in the case that they do end up being a leader, they’ll be able to properly evaluate the role science plays in so many of the decisions they’ll have to make.

Just recently, I read a post on Morning Coffee Physics that does a much better job of explaining this than me: Science is a Life Skill.

• February 22, 2011 6:14 pm

You can have (relatively) informed citizens, who can make (relatively) sensible comments about some scientific things WITHOUT them needing to understand quantum physics (that’s what ‘science literacy’ is), but I think you are forgetting the role politics plays the big issues like global warming, alternative fuels, stem cell research etc. Much of this is colored by politics on the right AND the left, and is not subject to being permeated by science in the public arena! Your optimism is commendable John, but……….

• February 22, 2011 8:06 pm

I don’t think I want them to understand quantum physics. That isn’t my goal at all. In fact, if pushed, I think all the s,p,d,f orbital stuff, octet rule, etc in chemistry is really hard to teach to kids with any level of understanding given that kids can possibly grasp the real meaning of quantized orbital angular momentum as 10th graders. Instead, I want them to understand all those fuzzy “science process skills” I want them to know that we can determine that vaccines are safe for exactly the same reason in chem lab, you can determine the molecular formula of an unknown compound. And while I think you are right that politics definitely does its part to muddy up the waters, there are lots of things, like vaccines, people falling prey to homeopathy, or purchasing powerbands to improve their balance that have nothing to do with politics, and in my dream world, these things would go away once everyone got a decent grounding in science and the art of BS detecting.

• February 23, 2011 6:59 am

John – OK, let’s forget global warming and take a look at ‘powerbands’. Having agreed that fighting ideology (i.e. politics) with science is largely pointless and a battle that will never be won, now you want to take on marketing (i.e. capitalism)!? Don’t bring a knife to a gunfight!

My point is that there are colossal numbers of kids (i.e. future adults) for whom external drivers like ideology and marketing will always supersede the laws of logic and reason. It’s not palatable, but it’s inevitable; this is why I concentrate on achievable, tangible goals like SAT and AP scores and feel that lofty goals of ‘across the board science literacy’ whilst desirable, may not be the best way to go about things.

• February 23, 2011 7:48 pm

Well, I would say science won a huge battle against powerbands, when they were forced to admit the bracelets are a sham. Science is the tool that invented the knife, the gun, and the nuclear bomb, so in properly trained hands, it’s the only weapon you need.

And I appreciate your point about achievable goals. I want (and am trying) to find ways to make my goals more achievable and measurable. And this isn’t a fully formed thought by any part, but what if the standardized tests we have today aren’t contributing to these larger goals of teaching students the real process of science? What if they are reinforcing the idea that science is a bunch of facts to be memorized, equations to be plugged into, disconnected from the real world? Would it still be worthwhile to pursue excellence in these tests, if it comes at this high cost? There’s at least some question out there about how well AP even prepares kids for college level math/science classes.

• February 24, 2011 10:58 am

>What if they are reinforcing the idea that science is a bunch of facts to be memorized, equations to be plugged into, disconnected from the real world?

A fairly significant portion of science NEEDS to be that IMO! Especially at the level we are talking about. I really dislike the whole, “We can look up any factual information on the web and therefore don’t need to teach it”, philosophy. Kids SHOULD be drilled we (some) stuff.

I guess in my judgment and experience, there is no “high cost” that you speak of.

• February 24, 2011 6:41 pm

I’m definitely not arguing for the kids looking everything up, and I do agree there are things that are good for students to just know. But I am concerned if they focus too much on knowing what the formulas, facts or procedures are and manipulating them, they might lose sight of how we came to know those facts, formulas and procedures, which I think is the essential point of science.

4. February 24, 2011 8:21 pm

On the “bunch of facts” meme: I thought the whole point of physics was to reduce the necessary facts to memorize to an absolute minimum. Of course, to deal with more complex systems (like in chemistry and biology) you have to use approximations, which often require memorizing empirical formulas, but the point of physics is to eliminate memorization in favor of computation or mathematical derivation.

• February 24, 2011 8:30 pm

Definitely. This is how I try to teach physics, and I find the modeling curriculum does this nicely. But there are a few “facts” that are very helpful. One example would be the value of gravitational field (often mistakenly called acceleration due to gravity) near the surface of the earth, which almost every kid has memorized before getting to my class as $9.8 \frac{\textrm{m}}{\textrm{s}^2}$. In fact, I often find students have little trouble memorizing facts and formulas in many cases, that’s what the game of science has been all about for them. They struggle much more when trying to explain why to use a particular formula, or why a particular procedure in the lab works.

5. February 25, 2011 4:59 pm

The trouble with the idea of pseudoteaching is that you usually don’t know if it has happened or not.

• February 25, 2011 10:50 pm

This is why formative assessment is so critical. We need to develop ways to measure student learning before the test, and use the information we learn to shape our teaching. A great example of this is the 20minwms experiment that a number of my colleagues and I are participating in. Also, I think the the act of discovering ones own PT and reflecting on it is very beneficial, even if you only discover it far after the fact.