Category Archives: studentwork

Students #flipping class presentations through making videos

Those of you that know the way I usually teach probably also know that projects are not in my comfort zone. I always feel they need to be well defined in such a way to make it so that the mathematical content is the focus, and NOT necessarily about how good it looks, the "flashy factor", or whether it is appropriately stapled. As a result, I often avoid them like the plague. The activities we do in class are usually student centered and involve  a lot of student interaction, and occasionally (much to my dismay) are open ended problems to be solved.

Done well, a good project (and rubric) also involves a good amount of focused interaction between students about the mathematical content. I don't like asking students to make presentations either - what often results is a Powerpoint and students awkwardly gesturing at projected images of text that they then read to the group in front of them. In class, I openly mock adults who do this to my students - I keep the promise that I will never ask them to read to me and their peers standing at the front of the room. Presentation skills are important, don't get me wrong, but I don't see educational gold in the process, or get all tingly about 'real-world skill development' from assigning in-class presentations. They instill fear in the hearts of many students (especially those that are students of ESOL) and require  tolerance from the rest of the class and involved adults to sit through watching them, and require class time in order to 'make' students watch them.

I'm also not convinced they actually learn content by creating them. Take a bunch of information found on Wikipedia or from Google, put it on a number of slides, and read it slowly until your time is up. Where is the synthesis? Where is the real world application of an idea that the student did? What new information is the student generating? If there's very little substantive answer to those questions, it's not worth it. It's no wonder why they go the Powerpoint slide route either - it's generally what they see adults doing when they present something.

In short, I don't like asking students to do something that even adults don't typically do well, and even then without the self-esteem and image issues that teenagers have.

All of that said, I really liked seeing a presentation (a good one, mind you) from Kelly Grogan (@KellyEd121) at the Learning 2.011 conference in Shanghai this past September. She has her students combine written work, digital media, audio, and video into digital documents that can be easily shared with each other and with her as their teacher. The additional dimension of hearing the student talking about his/her work and understanding is a really powerful one. It is but one distilled aspect of what we want students to get out of the projects we assign.

The fact that it isn't live also takes away a lot of the pressure to get it all right in one take. It also takes advantage of the asynchronous capability that technology affords us - I can watch a student's product at home or on my iPad at night, as can the other students. I like how it uses the idea of the flipped classroom to change the idea of student presentations. Students present their understanding or work through video that can be watched at home,  and then the content can be discussed or used in class the next day.

It was with all of this in mind that I decided to assign the project described here:

The proofs were listed on a handout given in class, and students in groups of two chose which proof they wanted to do. Most students submitted their videos today. I'm pretty pleased with how they ran with the idea and made it their own. Some quick notes:

  • The mathematical content is the focus, and the students understood that from the beginning. While the math isn't perfect in every video, the enthusiasm the students had for putting these together was pretty awesome to watch. There's no denying that enthusiasm as a tool for helping students learn - this is a major plus for project based assignments.
  • Some students that rarely volunteer to speak in class have their personalities and voices all over these. I love this.

My plan to hold students accountable for watching these is to have variations of them on the unit test in a couple weeks. I don't have to force the students to watch them though - they had almost all shared them before they were due.

Yes, you heard that right. They had almost all shared their work with each other and talked about it before getting to class. I sometimes have to force this to happen during class, but this assignment encouraged them to do it on their own. Now that's cool.

I have ideas for tweaking it for next time, but I really liked what came out of this. I've been hurt(stung?)  by projects before - giving grades that meet the rubric for the project, but don't actually result in a grade that indicates student learning.

I can see how this concept could really change things though. There's no denying that the work these students produced is authentic to them, and requires engagement with the content. Isn't that what we ultimately want students to know how to do when they leave our classroom?

Giving badges that matter.

The social aspect of being in a classroom is what makes it such a unique learning environment. It isn't just a place where students can practice and develop their skills, because they can do that outside of the classroom using a variety of resources. In the classroom, a student can struggle with a problem and then ask a neighbor. A student can get nudged in the right direction by a peer or an adult that cares about their progress and learning.

If students can learn everything we expect them to learn during class time by staring at a screen, then our expectations probably aren't what they should be. Our classrooms should be places in which ideas are generated, evaluated, compared, and applied. I'm not saying that this environment shouldn't be used to develop skills. I just mean that doing so all the time doesn't make the most of the fact that our students are social most of the time they are not in our classrooms. Denying the power of that tendency is missing an opportunity to engage students where they are.

I am always looking for ways to justify why my class is better than a screen. Based on a lot of discussion out there about the pros and cons of Khan academy, I tried an experiment today with my geometry class to call upon the social nature of my students for the purposes of improving the learning and conversations going on in class. As I have mentioned before, it can be a struggle sometimes to get my geometry students  to interact with each other as a group during class, so I am doing some new things with them and am evaluating what works and what doesn't.

The concept of badges as a meaningless token is often cited as a criticism of the Khan academy system. It may show progress in reaching a certain skill level, it might be meaningless. How might this concept be used in the context of a classroom filled with living, breathing students? Given that I want to place value on interactions between students that are focused on learning content, how might the concept be applied to a class?

I gave the students an assignment for homework at the end of the last class to choose five problems that tested a range of the ideas that we have explored during the unit. Most students (though not all) came to class with this assignment completed. Here was the idea:

  • Share your five problems with another student. Have that student complete your five problems. If that student completes the problems correctly  and to your satisfaction, give them your personal 'badge' on their paper. This badge can be your initials, a symbol, anything that is unique to you.
  • Collect as many people's badges as you can. Try to have a meaningful conversation with each person whose problems you complete that is focused on the math content.
  • If someone gives a really good explanation for something you previously didn't understand, you can give them your badge this way too.

It was really interesting to see how they responded. The most obvious change was the sudden increase in conversations in the room. No, they were not all on topic, but most of them were about the math. There were a lot of audible 'aha' moments. Some of the more shy students reached out to other students more than they normally do. Some students put themselves in the position of teaching others how to solve problems.

In chatting with a couple of the students after class, they seemed in agreement that it was a good way to spend a review day. It certainly was a lot less work for me than they usually are. Some did admit that there were some instances of just having a conversation and doing problems quickly to get a badge, but again, the vast majority were not this way. At least in the context of trying to increase the social interactions between students, it was a success. For the purpose of helping students learn math from each other, it was at least better than having everyone work in parallel and hope that students would help each other when they needed it.

It is clear that if you want to use social interactions to help drive learning in the classroom, the room, the lesson, and the activities must be deliberately designed to encourage this learning. It can happen by accident, and we can force students to do it, but to truly have it happen organically, the activity must have a social component that is not contrived and makes sense being there.

The Khan academy videos may work for helping students that aren't learning content skills in the classroom. They may help dabblers that want to pick up a new skill or learn about a topic for the first time. Our students do have social time outside of class, and if learning from a screen is the way that a particular student can focus on learning content they are expected to learn, maybe that makes sense for learning that particular content. In a class of twenty to thirty other people, being social may be a more compelling choice to a student than learning to solve systems of equations is.

If we want to teach students to learn to work together, evaluate opinions and ideas, clearly communicate their thinking, then this needs to be how we spend our time in the classroom. There must be time given for students to apply and develop these skills. Using Khan Academy may raise test scores, but with social interaction not emphasized or integrated into its operation, it ultimately may result in student growth that is as valuable and fleeting as the test scores themselves. I think in the context of those that may call KA a revolution in education, we need to ask ourselves whether that resulting growth is worth the missed opportunity for real, meaningful learning.

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.


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.


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.

Having conversations about and through homework

I've been collecting homework and checking individual problems this year. I grade it on completion, though if students tell me directly that they had trouble with a question before class (and it is obvious it isn't a case of not being able to do ANY of it because they waited until the last minute to try) I don't mind if they leave some things blank. I did this in the beginning since I had heard there were students that tried to skip out on doing homework if it wasn't checked. We do occasionally go over assigned problems during class, but I tend not to unless students are really perplexed by something.

I have lots of opinions on homework and its value. Some can use the extra practice and review of ideas developed in class. Some need to use homework time to make the material their own. In some cases, it gives students a chance to develop a skill, but in those cases I insist that students have a reliable resource nearby that they know how to use (textbook, Wolfram Alpha, Geogebra) to check their work. I don't think it is necessary to assign it just to "build character" or discipline. I read Alfie Kohn's The Homework Myth, and while I did find myself disagreeing with some aspects of his arguments, it did make me think about why I assign it and what it is really good for. I do not assign busy work, nor do I assign 1 - 89 - each problem I assign is deliberately chosen.
Among the many ways I try to assess my students, I admit that homework doesn't actually tell me that much about the skill level of a student. Why do I do it then?

My reason for assessing homework is for one selfish reason, and I make no secret of it with my students:

The more work I see from students relating to a concept, the better I get at developing that concept with students.

I would love to say that I know every mistake students are going to make. I know many of them. If I can proactively create activities that catch these misconceptions before they even start (and even better, get students talking about them) then the richness of our work together increases astronomically. You might ask why I can't get this during conversation or circulation with students during the class period. I always do get some insight this way. The difference is that I can have a conversation with the student at that point about their thinking because he or she is in the room with me. I can push them in the right direction in that situation if the understanding is off. The key is that most of my students are alone when they do their work, or at least, have only online contact with their classmates. In that situation, I can really see what students do when they are faced with a written challenge. The more I see this work, the better I get.

I am not worried about students copying - if they do it, it always sticks out like a sore thumb. Maybe they just aren't good at copying. Either way, I don't have any cases of students that say 'I could do it in the homework, but can't do it when it comes to quizzes or tests.' Since I can see clearly when the students can/can't do it in the homework, I can immediately address the issue during the next class.

The other thing I have started doing is changing the type of feedback I give students on homework. I still fall into the habit of marking things that are wrong with an 'x' when I am not careful. I now try to make all feedback a question or statement, as if I am starting a conversation with a student about their work through my comments, whether positive or negative:

  • Great explanation using definition here.
  • Does x = 7 check in the original equation? (This rather than marking an x when a solution is clearly wrong.)
  • (pointing out two correct steps and then third with an error) - mistake is in here somewhere.
  • You can call "angle CPK"  "angle P" here.
  • Good use of quotient rule - can you use power rule and get the same answer?

The students that get papers back with ink on them don't necessarily have wrong answers - they just have more I can chat with them about on paper. The more I can get the students to understand that the homework is NOT about being right or wrong, but about the quality of their mathematical thinking, I think we are all better off.

This does take time, but it is so valuable to me, and I think the students not only benefit from the feedback, but appreciate the effort on my part. I don't check every problem, just key ones that I know might cause trouble. If a student has everything right on the questions I am checking, it's a chance to give feedback on one of the others. If there's nothing to say because the paper is perfect (which is rare), I can praise the student for both their clear written solutions, hard work, and attention to detail.

I decided at the beginning of this year to look at more student work, and checking homework in this way is letting me do this. I am lucky to have prep time in the morning, and I have committed to using morning time for looking at student work almost exclusively. I have had to force myself to do this on many mornings because it's so easy to use the time for other things. Some of my best ideas and modifications to lessons come after seeing ten students make the same mistake - it feels good to custom fit my lessons to the group of students I have in front of me.

In the end, it's just one more way the students benefit from having a real teacher working with them instead of a computer. Every mark I make on the paper is another chance to connect with my students and conversation that can help make them better thinkers and learners. I don't think I really need to justify my presence in the classroom, but it feels good to say that this is one of the reasons it's good I'm there.

Dare to be silent.

I made a promise to myself today - I was going to force the physics class to speak. It isn't that they don't answer questions and participate, it's that usually they seem to do that to please me. Sometimes they will explain ideas to each other and compare answers, but it never works as beautifully as I want it to.

So today I told them I wasn't going to talk about a problem I gave them. They were. And then I sat on an empty table and waited. It was really difficult for me. Eventually someone asked someone else for an answer. I stayed quiet. Then another person nodded and agreed and then said nothing. I stayed quiet. Then someone disagreed.

Full disclosure - at this point I gestured wildly, but still stayed quiet.

After about five minutes of awkward silence punctuated with half explanations that trailed off, something happened - I don't know what the trigger was because if I did I would bottle it and sell it at educational conferences - a full discussion was suddenly underway. I was so amazed that I almost didn't think to capture it - thankfully I did get the following part:

Especially cool to see this knowing that English is not the first language of the students speaking.

I'm going to try to do this more often, though I again must point out that it was incredibly difficult working through the silence. The students in the end decided they had something to say, so they shared their thoughts with each other. I did nothing but wait for it to happen.

Build the robot the way you want...No, you're doing it wrong!

I teach an exploratory class for middle school students in robotics. The students rotate between robotics and some other electives during each quarter of the year, and there are no grades - just an opportunity to learn something interesting while doing. I like the no grades part, particularly because assessing progress in robotics is quite hard to do. My usual model is saying you get x points for doing the bare minimum (a D) and then incremental increases in the grade for doing progressively more challenging tasks.

It works, but I really like getting the opportunity to not have to do it. There are so many things you could measure to assess the students in their building and programming skills, but in my experience, the students don't tend to explore or tinker as much in that situation.

Today while working on the day's challenge on using sensors and loops, a student was fixated on building the following:

There weren't any instructions to do this - he just started putting things together, liked what he had created, and continued building it today.

I had to stop myself for a moment because teacher Evan started to come out and remind him to stay on task and contribute toward his team's solution to the challenge. Thankfully robotics Evan intervened and let it happen.

This is an exploratory class. It's supposed to expose the students to new situations that might interest them later on. Why in the world would I stop the exact sort of thinking and exploring the class was designed to provoke? It also turned out that this student, along with the other two in the group, were all taking turns in the programming and building so that each would have a chance to play in this way. In spite of their taking time to free build, this group actually solved the three challenges before the rest in the class.

It connects to a great TED talk on doodling by Sunni Brown. One idea from her talk was that doodling contributes to "creative problem solving and deep information processing." I think that these students (and all of us that 'play' with building toys like LEGO) are engaging in a similar process by free building. The connections students are making in figuring out how the tools work through play are not easy to measure. This is a horrible reason not to provide them time to do so. I do think there is an interesting connection between the tendency of these students to play and their ability to figure out the subtler parts of the class challenges.

After all, as David Wees pointed out, giving explicit step-by-step instructions on how to use creative tools like LEGO takes the creativity (and much of the fun) out of it. There has to be time to experiment and learn by doing how the tools work together, and that's exactly what this student was doing.

My final reaction during the class today was that I told them all that I wanted to take a picture of every off-topic LEGO design they create. Document it all. If it's cool enough to engage you for the time it takes to create it, I want a gallery of those designs to celebrate them.

The sad part? This made some of them stop. I can't win!

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.