Getting started with LEGO Robotics – the book and the real thing.

This week I got a special early holiday present in my mailbox from my friend Mark Gura. Mark had invited me a couple years ago to be part of a book for helping teachers new to the field of LEGO robotics get started with their students. We had a great conversation one evening after school over the phone during which we discussed the educational goldmine that building with LEGO is for students.

Mark did this with a number of people with a range of LEGO robotics experiences, wrote up our conversations, and then combined them with a set of resources that could be immediately useful to novices in the book.

The book, Getting Started with LEGO Robotics, is published by the International Society for Technology Education. If you, or anyone you know, is just getting started with this exciting field, you will find some great stuff in here to help you work with students and get organized.

It was a particularly perfect time for the book to arrive because we have a new group of students at my school getting started themselves with building and programming using the NXT. My colleague Doug Brunner teaches fifth graders across the hall. He volunteered (or more realistically, his students volunteered him) to take on coaching a group of students in the FIRST LEGO League program for the first time. After building the field for this year’s challenge, today the fifth graders actually got their hands on the robots and programming software. I had the robots built from the middle school exploratory class available so the students could immediately start with some programming tasks.

We started with my fall-back activity for the first time using the software – program the robot to drive across the length of the table and stop before falling over the edge. The students were into it from the start.  I stepped back to take pictures and Doug took over directing the rest of the two hours. He is a natural – he came up with a number of really great challenges of increasing difficulty and wasn’t afraid to sit down with students to figure out how the software worked. By the end of the session, the students were programming their robots to grab, push, and navigate around obstacles by dead reckoning. It was probably the most impressively productive single session I’ve ever seen.

It’s always interesting to see how different people manage groups of students and LEGO. Some want to structure things within tight guidelines and teach step by step how to do everything. Others do a mini lesson on how to do one piece of the challenge, and then send the students off to figure out the rest. Some show by example that it’s perfectly fine to get something wrong in the process of solving a challenge by working alongside students. It was impressive to see Doug think on his feet and create opportunities for his students to work at different paces but all feel accomplished by the end of the day. It is also really unique to have to tell a bunch of students  at 5:15 PM on a Friday to go home from school, and yet this has now been the norm in the classroom for a couple straight weeks.

Having robotics in my teaching load means that I am thinking about these ideas interspersed among planning activities for my regular content classes. There’s no reason why the philosophies between them can’t be the same, aside from the very substantial fact that you don’t have to tell students how to play with LEGO but you do often have to tell them how to play with mathematics or physics concepts. It’s easy for these robotics students to fail at a challenge twenty times and keep trying because they are having fun figuring it out. The holy grail of education is how to pose other content and challenge problems in the right way so it is equally compelling and motivating.

Note that I am not saying making content relevant to the real world. One of my favorite education bloggers, Jason Buell, has already made this point about why teaching for “preparation for the real world” as a reason to learn in the classroom is a flawed concept to many students that have a better idea than we do about their reality. I never tell people asking about the benefits of robotics that students are learning to make a robot push a LEGO brick across a table now because later on they will build bigger robots that push a real brick across the floor. Instead I cite the fact that seeing how engaged students are solving these problems is the strongest level engagement I have ever seen. The skills they develop in the process are applicable to any subject. The self esteem (and humility) they develop by comparing their solutions to others is incredible.

This sort of learning needs to be going on in every classroom. I used to believe that students need to learn the simple stuff before they are even exposed to the complex. I used to think that the skills come first, then learning the applications. Then I realized how incongruous this was with my robotics experiences and with the success stories I’ve had working with students.

Since this realization, I’ve been working to figure out how to bridge the gap. I am really appreciative that in my current teaching home, I am supported in my efforts to experiment by my my administrators. My students thankfully indulge my attempts to do things differently. I appreciate that while they don’t always enthusiastically endorse my methods, they are willing to try.

Testing expected values using Geogebra

I was intrigued last night looking at Dan Meyer’s blog post about the power of video to clearly define a problem in a way that a static image does not. I loved the simple idea that his video provoked in me – when does one switch from betting on blue vs. purple? This gets at the idea of expected value in a really nice and elegant way. When the discussion turned to interactivity, Geogebra was the clear choice.

I created this simple sketch (downloadable here)as a demonstration that this could easily be turned into an interactive task with some cool opportunities for collecting data from classes. I found myself explaining the task in a slightly different way to the first couple students I showed this to, so I decided to just show Dan’s video to everyone and take my own variable out of the experiment. After doing this with the Algebra 2 (10th grade) group, I did it again later with Geometry (9th) and a Calculus student that happened to be around before lunch.

The results were staggering.

Each colored point represents a single student’s choice for when they would no longer choose blue. Why they chose these was initially beyond me. The general ability level of these groups is pretty strong. After a while of thinking and chatting with students, I realized the following:

  • Since the math level of the groups were fairly strong, there had to be something about the way the question was posed that was throwing them off. I got it, but something was off for them.
  • The questions the students were asking were all about winning or losing. For example, if they chose purple, but the spinner landed on blue, what would happen? The assumption they had in their heads was that they would either get $200 or nothing. Of course they would choose to wait until there was a better than 50:50 chance before switching to purple. The part about maximizing the winnings wasn’t what they understood from the task.
  • When I modified the language in the sketch to say when do you ‘choose’ purple instead of ‘bet’ on the $200  between the Algebra 2 group and the Geometry group, there wasn’t a significant change in the results. They still tended to choose percentages that were close to the 50:50 range.

Dan made this suggestion:

I made an updated sketch that allowed students to do just that, available here in my Geogebra repository. It lets the user choose the moment for switching, simulates 500 spins, and shows the amount earned if the person stuck to either color. I tried it out on an unsuspecting student that stayed after school for some help, one of the ones that had done the task earlier.

Over the course of working with the sketch, the thing he started looking for was not when the best point to switch was, but when the switch point resulted in no difference in the amount of money earned in the long run by spinning 500 times. This, after all, was why when both winning amounts were $100, there was no difference in choosing blue or purple. This is the idea of expected value – when are the two expected values equal? When posed this way, the student was quickly able to make a fairly good guess, even when I changed the amount of the winnings for each color using the sketch.

I’m thinking of doing this again as a quick quiz with colleagues tomorrow to see what the difference is between adults and the students given the same choice. The thing is, probably because I am a math teacher, I knew exactly what Dan was getting at when I watched the video myself – this is why I was so jazzed by the problem. I saw this as an expected value problem though.

The students had no such biases – in fact, they had more realistic ones that reflect their life experiences. This is the challenge we all face designing learning activities for the classroom. We can try our best to come up with engaging, interesting activities (and engagement was not the issue – they were into the idea) but we never know exactly how they will respond. That’s part of the excitement of the job, no?

A smattering of updates – the good with the bad.

I want to record a few things about the last couple of days of class here – cool stuff, some successes, some not as good, but all useful in terms of moving forward.

Geometry:

I have been working incredibly hard to get this class talking about their work. I have stood on chairs. I’ve given pep talks, and gotten merely nods of agreement from students, but there is this amazing resistance to sharing their work or answering questions when it is a teacher-centric moment. There are a couple students that are very willing to present, but I almost think that their willingness overshadows many others who need to get feedback from peers but don’t know how to go about it. What do I do?

We turn it into a workshop. If a student is done, great. I grab the notebook and throw it under the document camera, and we talk about it. (In my opinion, the number one reason to have a document camera in the classroom, aside from demonstrating lab procedures in science, is to make it easy and quick for students get feedback from many people at once. Want to make this even better and less confrontational? Throw up student work and use Today’s Meet to collect comments from everyone.

The most crucial thing that seems to loosen everyone up for this conversation is that we start out with a compliment. Not “you got the right answer”. Usually I tolerate a couple “the handwriting is really neat” and “I like that you can draw a straight line” comments before I say let’s have some comments that focus on the mathematics here. I also give effusive and public thanks to the person whose work is up there (often not fully with their permission, but this is because I am trying to break them of the habit of only wanting to share work that is perfect.) This praise often includes how Student X (who may be not on task but is refocused by being called out) is appreciative that he/she is seeing how a peer was thinking, whether it was incorrect or not. I also noticed that after starting to do this, all students are now doing a better job of writing out their work rather than saying “I’ll do it right on the test, right now I just want to get a quick answer.”

Algebra 2

We had a few students absent yesterday (which, based on our class size, knocks out a significant portion of the group) so I decided to bite the bullet and do some Python programming with them. We used the Introduction to Python activity made by Google. We are a 1:1 Mac school, and I had everyone install the Python 3 package for OS 10.6 and above. This worked well in the activities up through exercise 8. After this, students were then supposed to write programs using a new window in IDLE. I did not do my research well enough, unfortunately, as I read shortly afterward that IDLE is a bit unstable on Macs due to issues with the GUI module. At this point, however, we were at the end of the period, so it wasn’t the end of the world. I will be able to do more with them now that they have at least seen it.

How would I gauge the student response? Much less resistance than I thought. They seemed to really enjoy figuring out what they were doing, especially with the % operator. That took a long time. Then one student asked if the word was ‘remainder’ in English, and the rest slapped their heads as they simultaneously figured it out. Everyone enjoyed the change of pace.

For homework, in addition to doing some review problems for the unit exam this week, I had them look at the programs here at the class wiki page.

Physics

I had great success giving students immediate feedback on the physics test they took last week by giving them the solutions to look at before handing it in. I had them write feedback for themselves in colored pencils to distinguish their feedback from their original writing. In most cases, students caught their own mistakes and saw the errors in their reasoning right away. I liked many of the notes that students left for themselves.

This was after reading about Frank Noschese’s experience doing this with his students after a quiz. I realize that this is something powerful that should be done during the learning cycle rather than with a summative assessment – but it also satisfied a lot of their needs to know when they left how they did. Even getting a test back a couple days later, the sense of urgency is lost. I had them walking out of the room talking about the physics rather than talking about how great it was not to be taking a test anymore.

Today we started figuring out circular motion. We played broom ball in the hallway with a simple task – get good at making the medicine ball go around in a circle using only the broom as the source of force.

We then came in and tried to figure out what was going on. I took pictures of all of their diagrams showing velocity and the applied force to the ball.

It was really interesting to see how they talked to each other about their diagrams. I think they were pretty close to reality too, particularly since the 4 kilogram medicine ball really didn’t have enough momentum to make it very far (even on a smooth marble floor) without needing a bit of a tangential force to keep its speed constant. They were pretty much agreed on the fact that velocity was tangent and net force was at least pointed into the circle. To what extent it was pointed in, there wasn’t a consensus. So Weinberg thinks he’s all smart, and throws up the Geogebra sketch he put together for this very purpose:

All I did was put together the same diagram that is generally in textbooks for deriving the characteristics of centripetal acceleration. We weren’t going to go through the steps – I just wanted them to see a quick little demo of how as point C was brought closer to B, that the change in velocity approached the radial direction. Just to see it. Suddenly the students were all messed up. Direction of change of velocity? Why is there a direction for change in velocity? We eventually settled on doing some vector diagrams to show why this is, but it certainly took me down a notch. If these students had trouble with this diagram, what were the students who I showed this diagram and did the full derivation in previous years thinking?

Patience and trust – I appreciate that they didn’t jump out the windows to escape the madness.

_______________________________________________________

All in all, some good things happening in the math tower. Definitely enjoying the experimentation and movement AWAY from lecturing and using the I do, we do, you do model, but there are going to be days when you try something and it bombs. Pick up the pieces, remind the students you appreciate their patience, and be ready to try again the next day.

Presenting the MVT In Calculus w/ Geogebra…tech as a game changer.

During our warm-up activity today, we looked at a function and identified critical points, relative, and absolute extrema for this function:

It was kind of neat talking about this and the extreme value theorem from last time. Since the domain is not defined over a closed interval, the EVT doesn’t guarantee the existence of an absolute maximum or minimum value. The students seemed to really get the idea this year that this function specifically has no absolute maximum over the domain because it is an open interval – last year there was a lot of confused faces on this idea. There were a couple really insightful comments about whether there would be an open interval domain over which the function did have an absolute maximum, even though the hypothesis wasn’t satisfied. The theorem just tells you whether or not you are guaranteed to find one, not that there isn’t one at all. Really good stuff, and I’m proud of the way everyone was chiming in to talk about what they understood.

The most important thing was that this led perfectly into introducing the idea of an existence theorem. This idea is different from other theorems (especially in comparison to geometry) that students have learned because the information it gives you is not as specific as “alternate interior angles are congruent” or “the remainder of polynomial P(x) upon division by (x – c) is P(c)”. All it does is tells you whether you can find what the theorem says is there. I didn’t plan on having this discussion today, but it was perfect for then introducing the mean value theorem, and I will definitely repeat it in the future.

I then gave my students this geogebra applet to play with today.

Download link here.

The students understood pretty quickly what they had to do, and didn’t seem to have a hard time. It was kind of interesting to watch them rediscover the concept of forming a tangent line using two points, as that concept has been a bit overshadowed by other things as we looked at derivative rules before the test they took last week. Some students moved P and Q so that they were tangent, and then adjusted the domain using C and D to find a domain over which the tangent line and line AB were parallel.

From this, I showed them what the slope of line AB represented (average rate of change over the interval) and came up with the right side of the MVT. We then talked about what the slope of the tangent line they identified represented – a couple immediately referenced the derivative of the function. What is the relationship between parallel lines? What would make it so that you couldn’t find this value? Ideas of continuity and differentiability jumped out. There it was: the entire mean value theorem.

Last year I presented the students with the MVT, and then we drew graphs to represent what it was saying. They kind of got it, but it wasn’t a sticky idea. I was doing all the developing. This approach today started with something visual that they were doing, that they could understand intuitively, and then that intuition was applied to develop an abstract concept out of that understanding.

I continued doing what I had done last year – answering some multiple choice questions about the MVT (See here for today’s handout) analytically, and I immediately lost a couple students. So I showed them how to throw the new function into Geogebra and adjust the domain to match the problem. They could then solve the problems graphically – they immediately located the points to be able to answer the questions.

The group is a mix of AP and non-AP exam bound students. I will introduce them all to the analytic ways of identifying these points, and we did some of it today. It was really nice that the moment things got a bit too abstract, I could push students to identify how the question being asked was the same as the idea of the MVT, and they were then able to solve it.

Without the technology, these students would have been done for the rest of the period. Those that could handle the algebra, would. Those that couldn’t would spend the rest of the period feeling like they were in over their heads. Introducing how to use the technology to really understand what was being said by the abstract theorem enabled many more students to get in on the game. That made me feel all warm and fuzzy inside. The rest of the class focused on definitions of increasing functions using the derivative, something that was made incredibly easy by referring back to the activity at the beginning of the period.

We’ll see how well they remember the ideas moving forward, but it felt great knowing that, at least for today’s lesson, everyone in the room had a way into the game.

The museum in your classroom – exploration, discovery, play, and authentic learning

I was visiting the Great Lakes Science center with family during high school. I was busy reading information printed on a horizontal rotating triangular prism – the three sides had facts about the phenomenon being demonstrated at the exhibit, though I don’t remember what the exhibit was about. While I was reading, a younger student came along and stood in front of me to view the exhibit. He barely paid any attention to me; his attention was piqued when he placed his hand flat on the prism and it rotated slightly under the weight. He then proceeded to flick the prism as hard as he could to see how fast he could make it turn. That was how he spent a couple of minutes while I looked on, flabbergasted by both his lack of interest in the flashing exhibit in front of him and the fact that all the exhibit inspired him to do was to challenge himself to a spinning competition. Once he was satisfied that he had peaked in the spinning task, he went off to a new exhibit.

I was pretty annoyed as a sixteen year old science enthusiast. How dare he not take the time to read what was printed at the exhibit? Not even try? There was so much good knowledge there to be learned – why bother coming to the museum if you weren’t going to try to learn something new? The best part for me was coming and playing with the exhibits and then seeing what science principle was being demonstrated. This was (as I understood it at the time) what science was all about.

For me, this was not something that was limited to museum visits. I had a pretty good arrangement for doing investigation at home as well. I was always able and encouraged to go outside and explore in the woods, burn stuff with magnifying glasses (not of course while doing the previous activity), and do experiments mixing things in the kitchen. I am incredibly grateful that my mom allowed me to do these experiments in spite of my frequent habit of rushing away afterwards without cleaning up. I didn’t realize at the time how unique it was that she let me do some of the things I did, and probably would have cleaned up myself more often  if I had. (I did do so marginally more often after a particularly stern chat about the difficulties of removing hardened candle wax from the good silverware. She clearly explained that the experiments would stop if I didn’t do this sort of cleaning myself.) The other major time I realized I should be grateful was when I accidentally removed the gold coating on a fork during an electroplating experiment. (Sorry mom.)

One that sticks in my mind was after I first learned about objects from space reentering the atmosphere and burning up.  I didn’t understand how metal objects could burn – I had seen metal melt before on TV, but could it really burn? I took a penny and some cooking tongs to the gas stove and held the penny in the flame for a long time. I was able to see the penny get hot and ultimately glow. I had a bowl of cold water there to drop the penny into afterwards. The colored patterns on its surface reminded me of a picture in a magazine that showed the oxidation patterns on a sample of material that had survived reentry. I also tried wires and aluminum foil in the flame, and the way both materials twisted around themselves and changed both in appearance and material properties gave me some insight into what it meant for metal to burn.

Was there a goal? Not really. I didn’t write up a lab report or keep a notebook recording my observations. These were just experiences in which I explored what I could do with the stuff in front of me. I did get the sense that this sort of thing was distinctly different from what I was doing in school because there was no assessment. I don’t know if she ever talked to others about her son “playing on the stove” as she called it. At the time I objected to her calling it that because I thought it made it sound like I was being reckless. I had a purpose to my experiments. I was creating meaning on my own as I had done throughout my Montessori elementary education. And I was careful when carrying out these investigations.

Years later, I have a different understanding the role of play in learning. I really like this TED talk by Stuart Brown that talks about some of the reasons why play is important. Much of what I have learned about building with LEGO is in the context of playing in an unguided way. Another major influence on my philosophy on play was K.C. Cole’s book Something Incredibly Wonderful Happens, which I heard about during the summer before teaching biology for the first time to ninth graders. The book describes physicist Frank Oppenheimer (brother of Robert Oppenheimer) and the full story of his life as a father, rancher, teacher, and ultimately creator of the world class Exploratorium.

I have visited the Exploratorium twice. There is no other museum in the world that has influenced me in such a visceral way as that museum. as I can still picture numerous things at that museum and what I learned from doing the exhibits. Reading about Frank and his process of seeing the museum as vital was really important to defining something that I think I hadn’t officially acknowledged in the preceding six years I had been teaching.

First, some Frank Oppenheimer quotes from a speech he gave upon receiving an award from the American Association of Museums, along with my thoughts:

Many people who talk about the discovery method of teaching are really talking about arranging a lesson or an experiment so that students discover what they are supposed to discover. That is not an exploration. The whole tradition of exploration is being lost for entire generations.

There is a role for discovery in our classrooms. This is not, as is often thought, the expectation that students will spontaneously figure out Newton’s laws or the quadratic formula. These are instead carefully designed activities through which students arrive at an idea. Our world needs more interactivity. People, not just students, are spending less time constructing their own understanding, and more time (since we are all inherently busy) hoping that others can explain things to us since it will invariably be faster this way.

If one of the things, however, we want to teach students is how to construct their own understanding, this is not going to come from giving them information and then telling them how to use it. Any way we can engage students to interact with the material actively instead of merely receiving content moves us closer to that goal.

It is, therefore, more important than ever that museums assume the responsibility for providing the opportunities for exploration that are lacking for both city and suburban dwellers. It would be fine, indeed, if they would, but it will take a bit of doing to do so properly. If museums are too unstructured, too unmanageable, people get lost and simply want to get back to home base. On the other hand, if they are too rigid, too structured or too channeled, there are no possibilities for individual choice or discovery.

It may be useful to note that these quotes are from 1982. Certainly these issues are no different nearly thirty years later. If lesson activities for students are too unstructured, they may have no idea of the learning goal, what they are supposed to figure out, or how to get from one point to another. They get lost. They get cranky. They would rather just be told information. This, however, is the opposite extreme. While some students demand the structure, there are serious limitations to the quality of learning experiences under a classroom model that is too rigid.

Exploring, like doing basic research, is often fruitless. Nothing comes of it. But also like basic research, as distinct from applied or directed research, exploring enables one to divert attention from preconceived paths to pursue some intriguing lead: a fragrance, a sight or smell, an interesting street or cave, an open meadow encountered suddenly in the woods or a patch of flowers that leads one off the trail, or even a hole in the ground! Often it is precisely as a result of aimless exploration that one does become intensely directed and preoccupied.

A museum that allows exploration does not have to be disorganized either physically or conceptually. It does, however, mean that the museum must contain a lot of which people can readily miss, so that discovery becomes something of a surprise, a triumph, not so much of personal achievement as of personal satisfaction. It is the kind of satisfaction that invariably leads me to tell someone about the experience.

When people in a museum find something that engages them, that moment of engagement is what justifies the museum’s existence. That may be what the visitor remembers about their museum experience. It may also be the sort of experience that causes the visitor to come back, and ideally, bring a friend or child. A well designed exhibit involves its visitors in its operation, tries to engage them, and along the way provides interesting information in the off chance a visitor is interested. A good museum has many of these experiences.

Here is the key idea that changed the way I decorate my classroom, organize my lessons, and structure my time with students:

You cannot entirely control what your students will get out of their time with you.

I have spent lots of time designing what I thought were perfect lessons only to have students remember the fact that I used colors in my handout, even months later, because that was what stuck with them.

You can tell them what you want them to get out of an activity. You can assess that they got out of the activity what you wanted them to get out of it. You can also try to tell them why something should be interesting to them. (Not recommended) None of these work well, at least authentically well when it comes to evaluating our use of an activity to reach specific learning goals.

What you can do is provide a range of activities, approaches, and experiences for your students. Providing students a chance to play in your classroom is one of the most powerful tools in our tool chest. You can’t play incorrectly. You can’t get playing wrong. Play is one of the few times when the only judgments being made belong to the individual that is playing. In the world of math education where students still see math as a class where there is always a right answer, and that right answers are inherently worth more than wrong answers, we need play more than ever.

What does play look like? Not like the majority of lessons I do, admittedly, but I’m working on that. The real reason this doesn’t happen as often as I want it to is that it doesn’t necessarily feel productive. I force myself to push through this because I’ve had the idea of clear learning goals and measurable objectives drilled into my head from the moment I started teaching. The problem is that real learning doesn’t look like this. When we figure things out, it isn’t with the end goal in mind. Unstructured time to just be in the presence of an idea that motivates itself is enough to get students to think as they do during play.

The biggest tool that we have at our disposal though is the use of technology. I’ve seen students discover by accident that when you hit the equal sign on some calculators, it repeats the previous operation with the answer. What do most students do when they discover this after multiplying? They hit it a bunch of times until the calculator overflows. Sometimes they will do the same thing with multiplying a decimal, and the number of zeroes to the right of the decimal point increases. Is there a lesson on place value or exponential functions there? Sure. The moment you tell them that though, it suddenly ceases to be exploration and starts becoming Math Class.

It’s also easy to create a Geogebra sketch of a quadrilateral with measured angles and tell students to “play” with it for five minutes. The goal is not to have them discover the sum of the interior angles is 360 degrees, though they might observe that. The goal is instead to give them a chance to interact with a mathematical object and have an experience that is all their own. Then start the lesson. See what happens. This is exactly what Noah Podolefsky from the PhET physics simulation project at the University of Colorado recommends students be allowed to do for 5 – 10 minutes before telling students what you want them to use the simulation to do.

The other aspect of this is in decorating my classroom. I don’t want so much on the walls that students will be continually distracted. I do want things that create interesting learning experiences without much effort. I hung a spring between two corners of the room as an example of a catenary curve – students don’t care about that. They do walk by it all the time and make it bounce up and down. Sometimes they see how long it takes for the vibrations to die down. Sometimes they hang things on it to see how it changes the droop in the overall spring. I have a bicycle wheel that normally is used as a demonstration of conservation of angular momentum. Students have instead spun it and observed that it stays upright like a top on the table. I have a checker board with checkers, the game Set, little metal puzzles, and a bunch of other things that don’t require a whole lot of explanation to be interesting. It’s amazing to see how the students use their down time to interact with these objects and with each other – it makes my classroom the same safe learning environment of a museum. The dream is to create this environment during every single lesson.

Looking back, the kid that stepped in front of my at the Great Lakes Science Center wasn’t learning what the exhibit designers intended him to learn. He was, however, constructing his own knowledge when he spun the prism as fast he could. He might have gotten some notion of what feels different about a force and a torque. He might have seen that the rotation only increased in speed while his hand was in contact with it – an intuitive concept related to Newton’s 2nd law.

Or not. It was pretty hypocritical of me to judge and potentially hamper his learning process when so many others (including my mom, who had many good, flammable reasons to do so) did not. He wasn’t using the museum wrong – I was. He was just doing what came naturally.


Entirety of Frank Oppenheimer’s speech to the American Association of Museums, 1982 can be found here.
I also find myself going back to this article written by Oppenheimer about teaching as a quick reminder of all sorts of important ideas.

Your students might not be cursing at you…

One of the students I had the pleasure of teaching in AP physics in the Bronx started with quite a reputation. As a student that spoke Chinese and little English in the 9th grade, he was placed in the entry level math class. It took only a short time for his teacher to notice that, given his background and obvious mathematical skills, this probably wasn’t the right place for him. He was quickly moved up the sequence of courses until he ended up in a Math B course that included trigonometry as I recall.

This was not just a case of this student having memorized mathematical concepts from his time in China, though he had seen a lot of math by the time he arrived at Lehman. In his junior and senior years, the quality of his insights and ability to predict, comprehend, and connect ideas in both math and physics were truly impressive and indicative of a strong talent. As his teacher in physics, the greatest challenge I had was not in teaching him how to solve a physics problem, but to write down his line of reasoning that scattered together with frightening speed in his head. My favorite teaching moments with him came on the rare occasion when he had an actual misunderstanding and I witnessed the exact moment of his realization of what he did not get; the physical change in his face was unforgettable.

I was brought back to a story I heard a while back from colleagues about his early times in the classroom. He had a tendency to mutter to himself during class. On an occasion when a student made a comment that was an oversimplification of a concept, this student started saying at a noticeable volume something that sounded like ‘bull-shit’.

The teacher, clearly shocked by this, reacted softly with a word after class. Given the student’s limited English ability, the message had little chance of making it across. The outburst happened again under more unlucky circumstances when the assistant principal and principal were both in the room observing the teacher – this time, the consequences were a bit more serious. The fact was that, given his personality and the directness associated with translation into a second language, it didn’t seem completely out of character for him to call out a teacher on glossing over a math concept. He saw past the simplification for the sake of his classmates. Calling a teacher out publicly like that, though clearly inappropriate to all of us, might have just been a side effect of being in a new place with new people.

If math was the only language he understood well, and he witnessed math being communicated in an way that was not fully clear to him, of course those moments would attract such a reaction. Over time, we learned to react constructively to these reactions and counsel him into more appropriate ways to ask questions or address his usually correct abstractions of the ideas presented in class.

Fast forward eight yearsto when I was with my ninth graders on our class trip to Shandong province a week ago. As a reward for a hike up thousands of stairs the day before, we spent the final night of the trip visiting a hot springs pool. While the students were splashing around, our tour guide was having a conversation with one of the other tourists in the pool. I was relaxing my eyes staring out at the rocks around the pool when I heard something strangely familiar in their conversation.

“Bu shi…Bu shi…”

I knew both of these words now with my limited experience, but had never thought of them together before. The character bu (不) negates whatever comes after it, and shi (是)is essentially the verb ‘to be’. Putting it together in my head while getting prune fingers at the time, I realized that the phrase bu shi must then mean ‘isn’t’. I confirmed my reasoning with the guide: she was saying that something the tourist was saying wasn’t true.

There I was, seven thousand miles away, realizing long after the fact that this student we all came to admire was probably not cursing at us. He was just saying he thought something he was being taught wasn’t entirely true. It’s the sort of thing we hope our students are thinking about during lessons, questioning their understanding of the content of a lesson. I’ve had students do this in English and never felt threatened by it.

There are many different lessons to take from this. I have been cursed at as a teacher, and I knew it was happening when it was happening because, well, it’s pretty hard to ignore it when it’s happening to you. The fact that this student was having a fairly normal reaction when something wasn’t making sense to him was overshadowed by our misunderstanding of what HE was saying. We assumed he was being out of line. He was innocently saying what was on his mind.

How often do we assume we know what our students are saying without really listening? I’m guilty of wanting to hear an answer that moves a lesson along, but it’s not right, especially when the understanding isn’t there. My students in the Chinese student’s physics class would say an answer they thought was right, and I would on occasion fill in the gaps and go on as if I had heard the correct answer I wanted to hear, even though what the students actually said wasn’t even close to what I wanted. Over the years since they called me out on that, I’ve worked to make that not happen.

In an international school like the one at which I am now teaching, there are languages on top of ideas on top of personalities in my classroom that mix together every day. It is incredibly important to make sure that with such a complex mix of factors, you really know what your students are saying to you and each other.

How China Keeps Me Learning: Part I

Ever since moving to Hangzhou, China in August of 2010, I’ve been amazed at the number of ways it has forced me to use my own problem solving and critical thinking skills. I’ve remarked inwards that talking about these experiences would help greatly in describing the sorts of experiences I want my own students to have, as well as the factors that have helped me be successful as I’ve explored. Now that I am taking the time to write about my experiences, I think this theme is a good one to return to from time to time to describe how these experiences I have relate to my classroom.

Hangzhou has a number of truly incredible places within its city limits. Some are incredibly beautiful. A few of them, however, are incredible for how they address my geeky-tinkerer side.

This building is one of two that sit on opposite sides of the road in the North-east section of Hangzhou. Inside are rows and rows of little booths that each sell electronic parts. Some specialize in motors or solar cells. Others have all different electronic components from resistors to circuit boards to jumper wires, all on display.

I’ve been to this place several times to get parts, other times just to wander around and gawk at the amazing quantity of raw materials there for projects not yet materialized. This week I returned for a different reason. My parents decided to take a big step and visit my wife (Josie) and I here in China, so they have been on numerous adventures with us for the past week. Another post on that is imminent, so stay tuned.

My dad is an engineer and was the first person I thought of when I walked into the building for the first time and saw what was there, so I knew I had to take my dad there for a visit. I also had a vague goal for what I wanted to get while I was there: sensors. Whether for robots or for upcoming units in physics, I knew it would be good to see what was available there so I had more available for experimentation in the classroom and to think ahead.

One other thing to be aware of: I don’t speak Mandarin. I know some basic greetings and scattered vocabulary, but don’t know ‘sensor’, ‘resistor’, or even ‘electric’ either in symbolic or spoken Mandarin. On every visit to the market, I have always had to resort to sketches and diagrams to communicate. This, however, is the most entertaining and enriching part of these trips to the market – figuring out how to say what I am looking for. This was my first visit to the market since my summer acquisition of an iPad, which together with Google Translate, tended to improve the quality of my communication with the dealers to an extent this time. It was, however, still a challenge.

After some wandering around and some awkward interactions with parts dealers that weren’t sure why we were there, my dad and I ended up in a booth with a pair of women intrigued by the site of us in their store. I get the impression on every visit that foreigners don’t enter the building with any regularity, so I’m used to it. I pulled out the iPad and entered ‘gas sensors’ , showing the translation to the women. They pointed to a column of plastic containers beneath a glass counter, gesturing and pointing while saying (in Mandarin) what each one was. Eventually with Translate’s help, they ended up identifying the various gases that they had sensors for, and I came to the conclusion that I needed to do more research before making any purchases. Bottom line – they had some great stuff, much of it exactly what I was looking for.

I went through a similar process in getting some platinum temperature sensors and aluminum blocks with strain gauges for measuring a cantilevered force.

Needless to say, the whole experience was a good one. We all left happy and having had a good time. Here’s just a start of what’s bouncing around in my head for how this experience connects to set up learning opportunities for my students:


I felt free to experiment and play in my learning environment.

I loosely defined goals for my time at the market, but there was no pressure for me to buy anything if I didn’t want to. If my attempts to communicate and find what I was looking for were unsuccessful, I would have other chances to figure it out later on. I wasn’t being evaluated on my time at the market – I was instead free to have fun and try my best to achieve the goals I set for myself.

How much time do we give our students to experiment and play with the material we want to teach them? How are we making the most of the tools we have available to let them do this?


I had the tools I needed to make up for my weaknesses.

The iPad translating capability really made it possible for me to communicate in the way I needed to communicate to achieve my goals. I do want to learn more Mandarin, but I don’t see it necessary that I learn Mandarin completely before I visit the market for my other learning goals. Since my goal had nothing to do with learning the language, but instead to use the tools I had (iPad, electronics market, seemingly amused dad looking on) to reach a desired outcome, I felt free to be creative in how I used the tools to have success.

I speak enough Spanish to be able to have been able to joke and shoot the breeze with cab drivers, store clerks, etc. in the Latin American countries that Josie and I have visited. I have really missed that ability here in China, though I am getting better. The technology lets me be comfortable and interact in a way that makes the entire process enjoyable rather than frustrating. Some frustration is to be expected when trying something new, but not so much to be uncomfortable throughout the process.

How much do the learning goals we set for our students require students have acquired previous skills? How do we address deficiencies in these skills when they arise? Do we give them the tools so they can reach the goals we set for them, or do we modify the goals themselves for these students?


I accepted that I was going to make mistakes, and felt comfortable changing my approach in response to these mistakes.

There were many times when even Google Translate failed to communicate exactly what I was saying (or what the parts dealers were saying) not to mention the challenges that arose in figuring out what I wanted to ask. There were times when I used the Mandarin I did have to confirm that I understood what they were saying, and many times they showed me that I did not. In either case, the dealers were incredibly patient and supportive in figuring out how to help me. It was clear that they were enjoying the process as much as I was, which made me appreciate the time they were willing to take to get me what I wanted. I knew instantly from their reactions to my translated questions whether I had communicated clearly to them, and we were both gesturing and checking that we understood each other as often as possible.

How do we encourage and acknowledge mistake-making as part of the learning process? How do our students feel about making mistakes? How do we develop an environment in which students feel comfortable experimenting and getting things wrong along the way to getting them right?

I love these trips to the market because the feeling of exhilaration and achievement I get when I succeed is worth every moment of frustration. The worst thing that can happen is I walk away empty handed. What usually happens is a scene like the one below:

Somewhere along the line in my classroom, however, students get the feeling that there’s a lot more at stake, that others (unfortunately including me) must be judging their abilities when they don’t get a question right the first time. Students get the feeling that they shouldn’t need to use the tools they have in front of them (graphing calculator, laptop, Geogebra, etc) to learn if they are smart enough. How do I show them that it isn’t about being smart, it is about working hard to get it right in the end? Is it enough to value the mistakes they make? Do I need to share my own mistakes in doing things? (This is part of my plan, at the moment, and is partly why I made the decision to commit time to blogging about what I do in the classroom.)

If I can turn my lessons into explorations and activities in which students feel safe experimenting with concepts, sharing their ideas and helping each other learn, it would make every other goal I have for what I want my students to achieve possible. I’m all ears if you have ideas on how to make this happen!

Lens Ray Tracing in Geogebra

One of my students came to me today to ask about ray tracing in preparation for his SAT II tomorrow in Physics. What happened is a good example of what tends to be my thought process in using technology to do something different.

Step 1 – I looked through some of my old worksheets, which I haven’t used in a while since I haven’t taught physics since 2009. The material I was happy with back then suddenly didn’t work for me. Given the fact he was standing there (and that time was of the essence) I wasn’t about to make a whole new worksheet.

Step 2 – I started drawing things on the board. This started working out fine, but I realized that every drawing I made would have to be erased or redone or saved in some other format. The student, after all, was most interested in learning how to do it and getting some practice. We did a couple sketches for mirrors, but when we got to lenses, I realized there had to be a better way. The sign for me for technology to step in is when I find myself doing the same thing over and over again, so the next step was pretty obvious.

Step 3 – Geogebra to the rescue. This is a particularly sharp student, so I was pretty happy with just talking him through what I was doing and asking him questions as I put together a quick demo of how to do this. He was pretty impressed with how logical the concept of ray tracing was, and had read the basic procedure in the textbook, but actually seeing it happen made a big difference. As he was standing there, his questions pushed me to make the applet (to steal Darren Kuropatwa‘s term) “a little more awesome.”

He asked what happens when the object is inside the focus of the lens. This led to throwing in some simple logic to selectively display the rays to show the location of the image when it is virtual and real. He asked what the difference is for a diverging lens. I told the student that I didn’t know what would happen if I switched the primary and secondary foci in Geogebra, but we talked about why that would relate to a diverging lens. Sure enough, the image appeared virtual and upright in the applet.

Step 4 – I then adjusted it a bit to show a diverging lens when the primary focus was on the left side of the lens, cleaned up some things, added colors, and now I have this cool applet to use when I get to working on lenses in the spring.


I like when I can think on my toes and use a tool like Geogebra to make something that will really make a difference. When I do this activity in the spring, it would be cool to put this side by side with an actual lens and an object and have students compare what is happening in both cases.

Check out the applet here: http://www.geogebra.org/en/upload/files/weinbergmath/Lens_Ray_Tracing.html

You can direct download the Geogebra file from here but be aware that I made the mistake of creating it in the beta version of 4.2. At some point, I’ll do it in the stable version.

You can drag the head of the arrow around, as well as move the primary focus F_p around to change it into a diverging lens. Clearly there are limitations to this – drag the object to the right side of the lens, for example, but I think it’s pretty cool that Geogebra can show something like this after an hour or so of playing around.

Have fun!

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