Monthly Archives: January 2013

Grouping Problems in 1st Grade

Grouping Problems in 1st Grade

My wife (Josie) was showing me the work she is doing with her first grade students in math. They are talking about grouping tens and ones, ultimately looking to explore place value. Her activity was to have students imagine situations involving collecting groups of items, and then looking at the mathematical structure behind those groups. One wrote about how a thief had a container that could only carry 10 ice cream cones at a time, which meant that he had to leave some of the ice cream cones he was stealing from a house behind. Another talked about the Grinch stealing twenty Christmas trees at a time from a forest that had 255.

There are two things that I really like about the approach. One is that it doesn't do the common backwards approach I have seen in elementary math programs where the math problem comes first. It seems off to asking students to add 3 + 4 = 7, and then 'make up a story problem' that matches this abstract idea. Here, the students are coming up with problems that matter to them, and creating organization (groups) that make sense to them. Going from abstract to concrete works marginally well at best at the high school level for developing understanding, let alone for six and seven year olds that are wrapping their heads around abstract ideas like place value.

I also really like that Josie didn't push the students to consider only even groupings. (255 trees into groups of 20? There's a remainder. THERE'S A REMAINDER!) Word problems are often contrived to have even numbers only to make them 'easier to understand' and consequently even less real world. I just thought it was neat to see that she is making her students manage that messiness from the beginning.

This is clearly different from the higher level courses that I usually concern myself with in high school, but the idea still transfers well, regardless of the level. It's always great to see things being done right by the younger students as well.

Angry Birds Project - Results and Post-Mortem

In my post last week, I detailed what I was having students do to get some experience modeling quadratic functions using Angry Birds. I was at the 21CL conference in Hong Kong, so the students did this with a substitute teacher. The student teams each submitted their five predictions for the ratio of hit distance to the distance from the slingshot to the edge of the picture. I brought them into Geogebra and created a set of pictures like this one:

Screen Shot 2013-01-29 at 7.57.47 AM

After learning some features of Camtasia I hadn't yet used, I put together this summary video of the activity:

I played the video, and the students were engaged watching the videos, but there was a general sense of dread (not suspense) on their faces as the team with the best predictions was revealed. This, of course, made me really nervous. They did clap for the winners when they were revealed, and we had some good discussion about modeling, which videos were more difficult and why, but there was a general sense of discomfort all through this activity. Given that I wasn't quite able to figure out exactly why they were being so awkward, I asked them what they thought of the activity on a scale of 1 - 10.

They hated it.

I should have guessed there might be something wrong when I received three separate emails from the three members one team with results that were completely different. Seeing three members of one team work independently (and inefficiently) is something I'm pretty tuned in to when I am in the room, but this was bigger. It didn't sound like there was much utilization of the fact that they were in teams. I need to ask about this, but I think they were all working in parallel rather than dividing up the labor, talking about their results, and comparing to each other.

Some things I want to remember about this:

  • I need to be a lot more aware of the level of my own excitement around activity in comparison to that of the students. I showed one of the shortened videos at the end of the previous class and asked what questions they really wanted to know. They all said they wanted to know where the bird would land, but in all honesty, I think they were being charitable. They didn't really care that much. In the game, you learn shortly after whether the bird you fling will hit where you want it to or not. Here, they had to go through a process of importing a picture, fitting a parabola, and finding a zero of a function using Geogebra, and then went a weekend without knowing.

    While it is true that using a computer made this task possible, and was more enjoyable than being forced to do this by hand, the relativity of this scale should be suspect. "Oh good, you're giving me pain meds after pulling my tooth. Let's do this again!"

  • A note about pseudocontext - throwing Angry Birds in to a project does not by itself does not necessarily engage students. It is a way in. I think the way I did this was less contrived than other similar projects I've seen, but that didn't make it a good one. Trying to make things 'relevant' by connecting math to something the students like can look desperate if done in the wrong way. I think this was the wrong way.
  • I would have gotten a lot more mileage out of the video if I had stopped it here:

    Screen Shot 2013-01-30 at 9.23.26 AM
    That would have been relevant to them, and probably would have resulted in turning this activity back around. I am kicking myself for not doing that. Seriously. That moment WAS when the students were all watching and interested, and I missed it.

Next time. You try and fail and reflect - I'm still glad I did it.

We went on to have a lovely conversation about complex numbers and the equation $latex x^{2}+4 = 0 $. One student immediately said that $ sqrt{-2} $ was just fine to substitute. Another stayed after class to explain why she thought it was a disturbing idea.

No harm done.

P.S. - Anyone who uses this post as a reason not to try these ideas out with their class and to instead slog on with standard lectures has missed the point. I didn't do this completely right. That doesn't mean it couldn't be a home run in the right hands.

Why computational thinking matters - Part I

My presentation at 21CLHK yesterday was an attempt to summarize much of the exploration I've done over the past year in my classroom into the connection between learning mathematical concepts and programming. I see a lot of potential there, but the details about how to integrate it effectively and naturally still need to be fleshed out.

After the presentation, I felt there needed to be some way to keep the content active other than just posting the slides. I've decided to take some of the main pieces of the presentation and package them as videos describing my thinking. I'm seeing this as an iterative process - in all likelihood, these videos will change as I refine my understanding of what I understand about the situation. Here is the start of what will hopefully be a developing collection:

I want to express my appreciation to Dan Meyer for his time chatting with during the conference about my ideas on making computation a part of the classroom experience. He pushed back against some my assertions and was honest about which arguments made sense and which needed more definition. I think this is a big deal, but the message on the power of computational thinking has to be spot on so it isn't misunderstood or misused.

With the help of the edu-blogging community, I think we can nail this thing down together. Let's talk.

Four (not so) easy pieces - 21CLHK Debrief

I have had an amazing time over the last couple of days at the 21st Century Learning conference in Hong Kong. It's easy for a technology conference to dip into the red zone of using technology for its own sake. The presenters and attendees here though remained really focused on creating meaningful experiences for students through the tools as a fundamental principle, not an afterthought.

I'm tired, but I think it's important to note down a few important points that I want to remember to put into action when I return to school. These points, likely by design by the organizers, are framed nicely by the keynote speakers and their messages.

Teach students how to manage device anxiety. (Dr. Larry Rosen)

This needs to be done explicitly and modeled by teachers. This will not get better by accident - instead, we must make an effort to show students how to avoid losing focus through deliberate practice.

Help students form identities as producers of media. (Dr. Nichole Pinkard)

Hoping that students will produce excellent work in a context that does not extend beyond the classroom doors is a sure way to expect less from them. We must expect students to define their place in the digital media world through work that they find meaningful.

Connect students to the rest of the world. (Dr. Jennifer Lane)

With all of the expertise available through the internet, there is no excuse for limiting students to finding out information in isolation from people that use that information to do their jobs. I want to find feasible ways to put my students in contact with people that are solving interesting problems and doing real world work.

Share what I find perplexing with students, and help them do the same. (Dan Meyer)

Though it might feel good to say that I want my students to find things that interesting, I need to model this process if I want students to adopt it for themselves. Curating my own list of perplexing ideas and helping students maintain their own list is a perfect way to make this more than a pipe dream.

Here's to meeting you all again soon. Safe travels!

How Good is Your Model (Angry Birds) Part 2 - Refining my process

A year ago, I wrote about my attempt to integrate Angry Birds as part of my quadratic modeling unit. I was certainly not the first, and there have been many others that have taken this idea and run with it. This is definitely a great way of using the concept of fitting parabolas to a realistic task that the students can have fun completing.

As I said a year ago, however, the bigger picture skill that is really powerful with modeling is making do with less information. I incentivized my students last year to come up with a model that predicts the final location of the collision of a bird earlier than everyone else. In other words, if Thomas is able to predict the correct final location with ten seconds of data, while Nick is able to do so with only seven, Nick has done the better job of modeling. I did this by asking the students to try to do this with the earliest possible frame in the video.

This time, I have found a better way to do this. Five videos, all of them cut short.
I'm asking the students to complete this table:
Screen Shot 2013-01-22 at 6.03.12 PM

The impact ratio is defined as the ratio of the orange line to the yellow line, as shown in this image:
Screen Shot 2013-01-22 at 6.04.44 PM

Each group of students will calculate the ratio for each video using Geogebra. Some videos reveal more about the path than others. I'll sum the errors, rank the student groups based on cumulative error, and then we'll have a great discussion about what made this difficult.

The sensitivity of a quadratic (or any fit) fit to data points that are close together is what I'm targeting here. I've tried other techniques to flesh this out in students before - I still get students 'fitting' a table of data by choosing the first two or three points. I'm hoping this will be a bit more interesting and successful than my previous attempts.

Trimmed Angry Bird Videos: