Interactive Jumping Puzzle

In this period where I’m not in the classroom, I’m trying to keep myself busy with a few little projects. One of those things is working on updating my coding skills by creating interactive activities using Javascript.

The first of these is a simple puzzle where the aim is to switch the positions of the two sets of counters by jumping them over each other. If it seems familiar, that may be because I posted about using this puzzle in class in 2014. (Or it may just be that this is a fairly well known puzzle). That post has more information about how I related the puzzle to a nice quadratic relationship, and used it to explore distributing and factoring*.

The puzzle is embedded below, but the full version of the puzzle will be more useful for using in class. It explains the rules of the puzzle more clearly, and includes options to change the counters into higher contrast (for those that find that useful) or into cute little frogs (which is far less useful).

I want to continue to find the time to keep working on little interactives that will (might) be useful to use in the classroom. My next project involves visualizing Riemann approximations. Hopefully I’ll be able to upload that one soon.

* That is, expanding and factorising if you’re in Australia. I figure that if I’m in the US now, I need to start using the appropriate terminology.

 

Life update!

Four. Months. That’s how long it’s been since my last blog post here.

Although, I think I’ve had a bit of an excuse. Things have been rather crazy for me lately. I’m as guilty as anyone of saying “things have been crazy” when I really mean “things have been the normal amount of excessively busy which comes with being a teacher”. But these are pretty exceptional circumstances I’ve been in lately.

So ever since Sarah and I announced our engagement, there’s been a little of this going around:

Well, the answer is…

pause for effect

I am moving to the US (Drumright, OK specifically) in a few short weeks. Sarah and I are getting married shortly after that. Moving to the other side of the world was never on the list of things I planned to do with my life, but it’s funny how quickly plans can change when you meet the most amazing person in the world.

After six years, I have left my job as a maths teacher at Kaniva College and moved out of my house in Kaniva. I still intend to teach (eventually, when all the paperwork’s done) once I move. I guess I have to get used to being a math teacher now.


Leaving my house for the last time.

I know this might sound nuts when I haven’t blogged at all in four months, but I’ve started a new blog. I’m still going to be using this one to write about lessons ideas, reflections and anything else math and teaching related. But I want to be able to share about my move as well.

Dropping the S is where you want to head to for that. I’m not entirely sure what it’ll involve. My main intention is to share my life with my family and friends in Australia, but even if that’s not you, feel free to follow along with this new step in my life.

 

Making a box

Problem I gave to Year 9 a few weeks back: Imagine taking an A4 sheet of paper, and cutting the corners out so it folds into a box. What is the maximum volume possible?

Or how I actually presented the problem:

I’m sure that any non-metric types could easily adapt this to letter size paper. 😉

This is the type of question I’d typically use with my Year 12 class, and expect them to use calculus to solve. But Year 9 had to use other strategies. (One student did manage to find a website that told him he would have to use differentiation, and wanted me to teach him what it is, there on the spot…)

So, trial-and-error was the game instead. Some students realised this immediately, while others needed a little bit more of a push. I remember being a student and hating trial-and-error as a strategy, because it always seemed to me that there should be a more efficient method to solving each problem. Of course, there usually was.

I’m realising more that giving students a task that’s relatively easy, but also slightly tedious, is a great way to provoke curiosity with the question Is there a better way to do this? Of course, I always prefer it if the kids are asking, and answering, that question themselves.

The reasoning that students went through went something like this:

  • I’ll just pick a size for the corner, and see what that is. (Some of them found it a little difficult to reach this by themselves, so I had to suggest it.)
  • Now I can find the dimensions of the box.
  • Now I can find the volume.
  • I should try this with another size corner.
  • Huh, that made it bigger/smaller.
  • This is taking a while, maybe there’s a pattern to calculating these.
  • Even with a pattern, this is still taking forever.

The next step, which I had to hint at a bit for them to get it, was that they could use their computers to do the repetitive work for them. Because of my well established obsession with Desmos, they quickly guessed that Desmos could be used. So they started doing something like this:

I think this type of frustration, where a problem is easy but tedious and crying out for a more elegant solution, is a powerful technique in engaging students and differentiating work for them. Some students found just calculating the volume of each box was challenging enough. Others found it simple, and it was their own desire to avoid doing the ‘boring’ calculations that drove them to using different mathematical techniques to find the solution faster. In this case, generalising the problem by describing it algebraically required deeper thinking.

The use of Desmos forces them to represent their with appropriate algebraic notation. Another solution students could have used would be using a spreadsheet. While that wouldn’t use mathematical notation, it’s still teaching them to represent abstract ideas with symbols.

Of course, they would have been really annoyed at me had they known the solution can be found just by doing this:

Though my students didn’t get to it, I also prepared the following extension question:

 

Managing different student learning

I’ve been left in an interesting situation with my Year 10 class. This is their last semester before moving into VCE or VCAL, where they get to choose their own subjects. This means that they’ll be studying a variety of maths subjects, at different levels of difficulty. Not to mention that under the Australian Curriculum, maths already has an extra level of content beyond Year 10 (“10A”).

Further complicating things is the fact that I only took over this class halfway through the year.

I want each student to have the best preparation possible for their plans for Year 11. How a student is planning to continue with their study has a lot of bearing on the content they need to be working on now.

For instance, the students who want to study Mathematical Methods (the second hardest maths in VCE behind Specialist Maths), or are considering it, would be best served by strengthening their algebra skills, and covering some of the material in 10A. That includes indices, logarithms and polynomials. The first topic I cover in Year 12 Maths Methods is the Remainder Theorem. I would love if these kids could be exposed to that in Year 10.

At the other end of the spectrum, we have the students who want to do VCAL Numeracy, which focuses on basic numeracy and skills needed for employment in trades or similar. These kids really would not be thrilled with me if I tried to teach them about logarithms.

And in the middle, we have the students planning on General Maths, and eventually Further Maths in Year 12. Even within this group there’s a wide range, from those who aren’t particularly fond of maths but who know it’s important, to those who could possibly do Methods if they really wanted to, but have decided not to. I still want to extend these students where I can, and not rule out the possibility of changing their minds during the subject selection process.

In a large school, students could be divided into classes that would allow them to focus on the areas most relevant to their future. But in a small school like mine, we only have the one Year 10 maths class. Instead, I need to find a way to manage the possibility of students all doing different work.

The Plan

I want to have students decide their own plan for what they would study. I gave each student this template:

The first two sections, I had students complete themselves:

  • Maths and Science subjects I am planning to study next year.
  • My Maths learning goals for this semester.

The next section was filled in by the student and myself together. Over a few lessons, I sat down with each student and discussed what their plans are, and we negotiated the skills I’m expecting them to complete this semester.

The codes that are listed match my SBG skills. I identify each unit with two letters, then each skill with a number. This is the same class I first tried SBG with last year, so they’re used to the system. At the very start of this term, they were given this complete list of the skills for the semester:

Reflections

This has worked well for the most part, but is not without some issues. Students know what is expected of them at all times, and have been able to work at their own pace. This class are usually very good at taking responsibility for their own learning, so it hasn’t been too hard to motivate them. For instance, I had one student work on one unit while in class and work on another one in her free lessons, because she knew she was going to be absent for an extended period of time.

But there are still many things that need to be improved with this strategy:

  • While I usually try my hardest to get away from using the textbook, it is a lot easier to assign a list of textbook questions to work on than to find different tasks for each student.
  • Collaboration becomes that much more difficult, because students are in different places.
  • A few students feel like they can just cruise, rather than keep pushing themselves.
  • I can get many students seeking help from me for a variety of different topics all at the same time. And sometimes my students get very impatient with me.

Though as it turns out, some of that has a way of sorting itself out. As students are waiting for me for help, they start helping each other. This has a tendency of pulling the pace of the faster students back to the rest of the group, while they gain the benefits from explaining the work to others.

I’m trying to reset everyone’s pace a little bit for the start of next term. Most kids are working on Probability, or Surds, Logs and Indices, so I’ve asked them to complete PR2 or SL2 over the September break. Hopefully from then on, it’ll be easier to set deadlines for groups of kids and keep them working on the same skills together. This will mean that I can give them collaborative activities to introduce topics, and save the textbook for practice questions.

Another issue I’ve found is with my own organisation, and making sure I have quizzes written before students get to those skills. But hopefully the break will help there again, and allow me to get out ahead with my quiz writing a bit more.

I would love some comments about all of this, whether this seems like a great or terrible idea, and where there is anything else I should be improving. I’m still not completely convinced this system works, but I’m optimistic that it is allowing students to work to their own needs and strengths in my class.

I’m definitely not advocating this as a good idea in most general. I would almost always prefer having students work on the same activities, and differentiate within those activities. But for this specific situation, allowing students to tailor their own learning path seemed like something I should at least try.

 

Student Feedback – The Less Serious Ones

I’ve been doing student feedback reflections recently. As much as I stressed to students to take this seriously, I was always going to get a bunch of silly suggestions. So, without comment, here are some of them.

Give us stuff. Mostly food.

  • Mr carter should start bringing us food so we are more motivated.
  • Give rewards to people who finish all of there work.
  • Give us prizes.
  • Give us pizza.
  • Give us all the answers.
  • More food involved lessons.

Change your style.

  • Start growing a beard.
  • Stop shaving.
  • Change the lack of beard.
  • Change your serious lack of facial hair!
  • Grow a moustache.
  • Start wearing better clothes.
  • Stop wearing bad clothes.
  • Change your hair style.
  • You should strut into the classroom with your shades on with The real slim shady playing from your massive speaker as you get to the front of the class you whip your shades off and start spitting mad rhymes and start krumping like a boss.

Keep your style.

  • Keep the swag.
  • Stop nothing.
  • Being a legend.
  • Keep keeping on.
  • You should keep on being swag, and keep everything that’s in your class.

I don’t know what to say.

  • Start teaching maths. Stop teaching maths. Keep teaching maths. Change teaching maths.
  • SORRY CAPS LOCK ISN’T TURNING OFF!
  • Stop teaching algebra! (Multiple ones of this, with some variation of “maths shouldn’t have letters” thrown in for good measure.)
  • Keep the carpet clean.
  • Let us throw things around the room.
  • Stop, drop and roll when there’s a fire.
  • Needs more death metal blaring out of the Smartboard when we are doing bookwork.
  • You should change nothing because you’re a lad of a teacher and your teaching skills are maaaaaaadddd, keep up the good work.
  • Change tomatoes into potatoes.