Nice work when you can get it....

I graded my first set of physics tests today. With the group deciding not to take the class at the Advanced Placement level, we've been able to slow down and spend time experimenting and really engaging with kinematics and projectile motion. I assigned them problems and helped them learn, but I was more impressed with the experiments they worked on and their engagement level during those activities. I was concerned about what would happen when we returned to solving problems, but I was very pleasantly surprised.

I'm interested in sharing student work, so this is the first time I will be doing it. When I asked the student if it would be OK to share, the student agreed and was really excited that I would want to show the work to other teachers.

This student started out solving problems in a very scattered way: calculations here, sketches there, units nowhere to be found. When I showed the structure I wanted students to use to solve problems, it was initially a burden. The student didn't like doing it. Upon grading, I was very happy to see this:

The degrees vs. radians issue is one that I always battle, made especially difficult this year because students have me for physics (when I insist on degree mode almost exclusively) and then calculus (when I change my insistence to radian mode) right in a row. Yes, the student should have noticed that multiplying by the ratio should not have resulted in a negative sign for initial y-velocity. Yes, it should have again become obvious that something was up when he found he needed to 'add' a negative sign in the answer at the end to make the sign of the answer make sense according to his own sign convention.

The fact that the student can notice these things (and that I can see where the errors are) would not even be something I could discuss if it wasn't for the structure I put in place. By learning to use the structure to organize thoughts, this student became able to solve problems in a logical manner rather than with calculations all over the page. I don't like teaching procedures, but this is an example of where it pays off.

We like students exploring and experimenting and constructing their own knowledge. These are really good ways for them to spend time in our classroom. I include using correct mathematical notation, showing steps, labeling axes, learning terminology, and other things of that nature as part of my class expectations - at times a battle that seems unimportant in the context of what I really want students to know how to do in five or ten years. There is room for procedural knowledge, however, and this student's success is evidence of why we do it.

The main point (and the thing I've been working to change compared with how I did things for a while) is that these procedures should not be the meat of a lesson or the main focus of instruction all the time. These things CAN be taught by computers or videos and don't necessarily need a human in the room. It is important for students to have skills and have access to resources that help them develop those skills.

But getting answers is not the point - this is the tricky part that we have to do a better job of selling to students, at least I do. Clear communication of reasoning and sharing the logic of our ideas are some of those "21st century skills" that students should have when they leave our classrooms. If a student needs to learn a structure to help them with this process, it is worth the time needed to help them learn it.

"What can you do with this?" (WCYDWT) - Flood Gates Open

I've been making an effort to look for as much WCYDWT material as possible on a regular basis. This is not so much because I've had students asking 'when are we going to use this' though that is always brewing under the surface. Instead, I've been making an effort this year to spend less time in class plodding through curriculum, and more time getting students to get their hands dirty with real data, real numbers, and using their brains to actually figure things out. By recording screencasts, doing demos, and using Geogebrs, I've made some progress in getting the students to see the benefit of learning the routine skills-based stuff on their own for HW so we can use class time to do more interesting things. I've quizzed and am feeling pretty good about this thus far, but we'll see.

During my trip with the ninth graders to Shandong and my week off due to the national holiday when my parents visited, I've kept my eyes open on reasonable, non-contrived problems that might serve as applications of linear functions. I've wanted some problems with non-trivial answers along with some low-hanging fruit that might give all of the students in the class a way in.

I'm pretty happy with how things have ended up with the top three contenders. There are some other things in the works, but I'm hoping to keep those under wraps for the moment. Click on the links to read the details.

Climbing Mount Tai

This one I already started talking about in a previous post, but I spiced it up just a bit by putting images together and throwing the head image I've now used in a few places to be cute.

Ms. Josie and the 180 Days

I like this one especially since it has a good story behind it. My students know my wife, and I defer to her awesomeness quite a bit in class. Students certainly love it when their teacher is willing to knock him/herself down a few pegs, especially when it's for their entertainment and for comedic effect in class. I think this challenge is a good combination of mathematical reasoning and drama - I don't think I can lose!

Moving on up at the Intercontinental Hotel

I was looking for a third one that really jumped out as kinda cool and visually stunning since the others, though cool, weren't particularly impressive visually. On the last day my parents were in town, we went to the Intercontinental hotel in Hangzhou and the problem smacked me in the face.

The videos aren't all up yet - in addition to the two outside videos, the more enlightening videos (which I will post tomorrow before class) have a view of the elevator doors and the digital floor display as the elevator moves up and down. In addition, there is a nice reflection of the view out the glass wall of the elevator, beautiful in its own right, but perhaps a wee bit distracting from the really useful stuff in this problem. If I wanted to go the full-eye-candy route, I suppose I could have gotten a reflection of the elevator doors and floor display in the glass wall of the elevator. Maybe next time.


My plan is to let students choose which of the three projects they want to work on, and then give them tomorrow's class (and finishing up for HW) to put something together. I plan to grade according to this rubric:

I think it gives them enough detail on what I want them to do, without being overly difficult to grade. I am even thinking of giving them a chance to grade each other since they will all be posting their work (from groups) on the wiki page.

I've had these things in my mind for a little while - I admit, after how this particular class made an impressive effort I am really excited to see what happens next.

Modeling anyone? Fans on carts edition.

After reading a lot about the success that others have had with teaching physics using the modeling method, I'm giving it a shot as I start Newton's laws with my physics class. When I taught this with my AP physics previously, I did a traditional development of Newton's laws describing (I admit it - lecturing) about Newton's understanding of what caused acceleration. We talked about acceleration being proportional to net force and inversely proportional to mass, and then went from there exploring what it meant for net force to be zero through a series of problems involving net forces, components, etc.

What I did seemed to work in so far as students were able to solve the problems I gave them. The undying assumption of course is that what I did was efficient and made me feel that I had got across the material to students, but along the way I wasted an opportunity for students to SEE the principles in action and try to figure things out on their own. Since my students this year are not taking the course at the AP level, I see no reason not to try this and see how it compares in the long run to student understanding and enjoyment of the exploration of physics concepts. It is the sort of thing that I can see doing even in the Physics B curriculum, as dense as it is, given the fact that students really need a chance to play to connect the mathematics of the equations to the fact that physics describes the real world, not just idealized situations.

Here's where I'd love to get some input though - I am giving my students a test in the first half of the 85 minute period tomorrow, and then my plan is to let them spend the rest of the time watching some videos that I took this afternoon of toy fans attached to cars on an air track. The students will get to play with the actual air track, but I want to introduce to the way I want them to play by seeing these videos that I created.

I have posted the series of videos here at my wiki site. The general instructions for what I want them to do are there, but I might as well run through them here as well.

First, I want them just to watch all the videos. No physics, just observation. After they have done this, I've posted a number of questions I want them to use to classify, analyze, and predict based on constant velocity and non-uniform velocity cases. I plan to have them sketch what effect a single fan would have on the motion of the cart. My plan in the end is to have them construct a situation with the fans that results in a given scenario. For example: arrange the fans on the cart so that The cart has zero initial velocity and an acceleration to the left. Draw position, velocity, and acceleration graphs, and then use Tracker to confirm/refute what their models suggest will happen.

Let me know your thoughts either here or through Twitter (@emwdx) - I am excited to try this, and excited to give the students a chance to get some first hand experience testing their own ideas. I had a blast playing with it this afternoon, and while I do have a different standard for what is 'fun' at times, I don't think this is one of those times.

Wiki site: http://wiki.hischina.org/groups/gealgerobophysiculus/wiki/52698/Unit_2__Carts_with_Fans.html

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!

Climbing Mount Tai - #wcydwt edition

I am spending an amazing few days with students on this year's class trip to Shandong province in China. We spent a couple days wandering around Qufu, the home of Confucius, and the location of the temple and mansion constructed for his relatives. There were some cool opportunities to think about mathematical thinking in Chinese architecture (more on that later) but nothing ready for prime time.

Today's trek led us to the foot of Mount Tai, China's #1 mountain for it's cultural significance (not due to it's height.) we decided as a group to trek up the mountain from the Heaven's Gate which reduced the climb somewhat, but will descend the full height of the mountain in the morning after watching the sunrise.

From Wikipedia (to be replaced by my own pics when I get home, I promise.)

20110927-191557.jpg

The realization that I might be able to do something really cool with this came after regretting that I had decided to leave two of my favorite data collection devices (heart rate monitor and hiker's GPS) at home being unsure during packing if they would really be worth bringing. I had done this hike in March and had several conflicting reports of the exact height we climbed up and down. The students were asking me how many steps there were, and I vaguely recalled something around 7,000, but I wasn't sure. This question actually popped out from a few different students as we passed the first set of steps. It got me thinking. Is it possible to take either one of these numbers (height or number of steps) and try to calculate or estimate the other? If the students were asking it standing at the bottom looking up, there might be a possibility they would be interested in answering it on their own if posed the right way.

I grabbed my camera and grabbed the best standard length measure I had on me: my iPhone.

20110927-194659.jpg

(It probably isn't necessary to say this, but this is just an example I took in the hotel.)

I took a number of pictures like the one above on way up the steps, trying to come up with a fairly random sampling of the size of stairs compared to the phone along the entire height. Through some combination of Geogebra, pencil & paper calculations, and some group discussion, I can see some height calculations for the climb coming out of this.

On the way up, there was also a perfect "answer" to this challenge posted in the form of a placard fixed to the wall that says both the vertical height and the number of steps - again, I will include a picture of this when I can transfer photos from the camera I used to take the good photos. I could see cropping this photo in a way that hides the answer, though I'm sure there is a more dramatic Act 3 to this challenge out there.

I think there is some potential here for some fun, as well as for good student discussion and writing about how close the number actually gets to the right answer. This is the second time in a week that I've been able to find something good that could work for a class activity, and I wanted to get the details out while still buzzed about its prospects.

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