It Wasn’t on Purpose, but I like it…

This post relates to the previous one on the Casino Task and Gamefication.

Levels Posters - collecting badge(r)s

When students believe that everyone in their group is ready to show they have completed a level, I interview them to check.

I choose who will speak, so all of the group members must be ready. They can send me away, if they realise some more work needs to be done.

The part that I did not deliberately plan for, but it should have been an obvious side benefit of the levels and gamification, is that students are practising for the assessment interview with little question and answer sessions as they work towards designing a successful casino game.

I comment on their notation, their mathematical language, clarity of communication, interesting ideas and more.
Students make a note of the feedback so that they can use it for the final interview.

Supersonic Badge(r)

Extra Supersonic Badge(r)s are handed out when students impress me with the following:

    • eloquent mathematics
    • great team work and support of each other
    • thinking outside the box

Casino Night and Gamification

Spending about 30 hours marking assignments to learn not very much at all was a Spring break holiday activity that I did not enjoy. Working with the kids during classes meant there weren’t too many surprises for me in the reports.

Something wasn’t right and I tried to think how to make the marking process just as valuable for the kids without the bonus  hours and hours for me after the task is done. I like to return work quickly to students, so 30 hours (outside of teaching,planning and meetings × 100) makes that a terribly difficult goal, unless you do have holidays to complete it all. Before you begin to think, or maybe it’s too late, that I am a very slow marker, I have over 60 students, in Grade 8, and they produce large reports, not just problems that are right or wrong. No tick, cross, tick, tick, cross… My kids are mathematicians, exploring, investigating and applying.

Another issue is electronic marking. It takes longer than old fashioned paper copies. I’ve been thinking about that too, but that’s another blog post.

For the final task of the year, for Grade 8, the final large task, I had to do a rethink or seriously consider running away. It’s the Casino Task and if Casino Night doesn’t happen, lots of people are disappointed. It’s a big school event and kids ask about it when they commence Grade 8.

A lot of time goes into Casino Night. Kids design their games before they build them, using the MYP Design Cycle. The idea in my head was if I know the work so well before I sit down to assess it, then I should be able to assess as they progress. Another challenge is to assess students individually even though it’s a group task. Individual reports only do so much for this.

Instead of taking you through all the ups, downs and swirls of my thoughts I will take you to the solution. If you want to see how students chose their groups, you can check out this Google Doc*.

*NBF = new best friend

THE SOLUTION: GAMIFICATION and INTERVIEWS

DESIGN STAGE:

Students will work through levels earning badges (the images at the top of this post) as they proceed (gamification) with extra points available.

Each level has a minimum number of points required.

When students accumulate enough points, they can then, and only then, begin to create  their game.

When creation begins, they will have:

    • design of the equipment: the parts of the games (spinners, dice, lucky dip…), betting board, sign and rules
    • plan of who needs to do what in the groups with expected times
    • the Mathematics behind the probabilities and the house odds

It is expected that they work as a group ensuring that everyone is comfortable with the Mathematics.

CREATE STAGE:

While they are being busy like the elves in Santa’s workshop, I will call them over one by one to interview them about their game.

The Task Question: HOW CAN WE MAKE OUR CASINO GAME SUCCESSFUL?

Each student will describe their game and why they believe it will be successful on Casino Night. I will assess them there and then applying two MYP criteria: Knowledge and Understanding and Communication.  The Reflection  criterion must wait until after the big night.

    • The Mathematics behind the events of their game will need to be explained.
    • How they made their games attractive to customers to keep them at their table – Mathematics and Design.

Students, as always, have the assessment criteria at the beginning of the project.

I decided it would be easier to show you, so I took what I made as a Onenote Notebook for the kids and put it into wikispaces, so I could share it with other Mathematics and MYP teachers.

Here is the G08WikiSpaces

I would like to say a HUGE thank you to Clint Hamada, @chamada, (our school tech faciliTATOR and all round great guy for bouncing ideas off) and EARCOS. I did not go to EARCOS, but Clint went and saw John Rinker‘s, @johnrinker, presentation on Gamification. Very timely!

Thanks to @zomoco for the ideas of internet memes for award badges – the kids LOVE them

Roaming Free in the Maths – Google’s 20% Time by Accident

rolling down a hill

rolling down a hill by woodleywonderworks licensed under CC by A

It isn’t actually 20% of allotted time for Grade 8 Mathematics, more like 17%. Close enough when not dealing with NASA type accuracy.

There has been a lot of discussion about The Khan Academy. It’s made some people very happy and some people sound quite vexed. I personally like it. Is it what is fascinating and wonderful about mathematics? No. Does it help some of our kids progress with skills? Yes, it does.

My grade 8s have the joy of Mathematics five times every fortnight, every Tuesday and Friday an alternating Wednesdays. The Wednesday lessons are slightly shorter than the others. After we finished our unit on Statistics and Linear Equations we then looked at the Mathematics they had been applying to their investigations in its simplest or purest (abstract) forms. They had been successfully applying it, but it then posed a challenge for some when it lacked a context. Quite interesting to go the other way. It is at this point where I like to give students a chance to fine tune their algebraic skills so that they are ready for high school Mathematics and Science. Not just a few lessons, but a regular time in classes to work on their skills, particularly algebra. This is where Algebra on Demand came from.

Every Wednesday my Grade 8s take a break from their unit, currently Probability, and do what they need to. The original plan was the Khan Academy, but this has changed in a very exciting way. It was the students who led me there.

Now my students choose what they do:

  • Khan Academy for skill mastery. Some of my students have their parents and tutors as coaches. Some parents have even joined in.
  • Work from other schools.  Our Korean and Japanese students often have extra Mathematics, needed for entry into schools back home.
  • Interesting Student Led Investigations. These students started using Khan for Mathematics beyond our Grade 8 curriculum. This led to them asking questions which lead to investigations purely out of interest. That’s a win! I don’t ask for written reports. Sitting with them, seeing what they have found and discussing the Mathematics is feedback enough that they are pushing themselves further. Why take the fun away?
Being able to move around the room and check on progress is key. I also really push the idea that I am a resource to be used, as are their fellow students. I did not mean for this to be the Google 20%, but it happened and I love it. The students really like that they get to choose to where to focus their mathematical attention.  I love this class.
Outside of this we are doing what we do in Mathematics in this exciting time of using technology. It is not chalk and talk. It is not just Khan. It is not just textbook. It is not just investigations. It is so many things.
Can The Khan Academy replace a Mathematics curriculum and teacher? I don’t think so. Is it useful? I do think so.

Patterns and Prediction

“This was really useful for our last lab in science”.

That was a win. In mathematics this year I wanted to address a problem I saw when proofing reports last year. In a nutshell I was proofing middle school reports and there was a glaring area requiring assistance. Processing data needed attention. I delved further as mathematical assistance would probably help.

IB DP Question: Obvious Pattern. Dubious Data. Getting kids to observe and analyse

Bivariate data analysis. Kids weren’t choosing scatter graphs and were asking technology to find trend lines without much work at how that happens.

I think teaching this is in a scientific context is the best way. Teaching in context just makes sense. In our curriculum the mathematics came at the end of the grade 8 year, so this year it is combined with algebra. We’ve called it Patterns and Prediction. Science likes it so much that we are planning to kick off next year with this unit.

One of my goals for my students is for them to be able to converse with anyone. I have a few things I do for this, but talking about the weather, it’s handy. To prepare students for their Interdisciplinary Unit (IDU – MYP term) we used data banks of Latitudes and Temperatures. Each class had to form a hypothesis and then we used Google docs to collaborate when collecting data.

Using the science departments guidelines we took grade 8 students on a journey that included:

  • Data collection – Google Docs
  • Data storage – Google Docs, Excel
  • Data Manipulation – Excel and Autograph
  • Scatter Graphs – Excel and Autograph
  • The Language of Analysis – using the wonderful 100 People website (see page 23 of PDF)
  • Trend Lines (Lines of best fit)
  • By eye using the shape of the data and the centroid. Find the y-intercept via extrapolation, then find the equation in slope intercept form
  • Using technology – Excel and Autograph.
  • Presentation of a report – fonts, layout, hard page, table headers, table formatting and labeling

They are now forming their own hypotheses and hunting for data (we have set up a Diigo group to get them started) so they run their own lab. Students will be using all of their mathematics and science classes this week and will be assessed in both classes.

Have a look at the graph above that I included for practice. Can you see the problem? It’s not with pattern spotting. It’s what the pattern predicts. Glad I am not  a bunny.

Music was fun

The kids seemed to enjoy the music and mathematics lesson.  No comments on the blog, but it was our last day of classes before UN Day and our Spring break and we are new to blogging. Must try to keep it moving even though I fear I will struggle to catch my breath as we head towards one of our four reporting sessions of the school year.

The feedback received though was from parents the next day at our UN celebrations. One very excited parent told me about her son asking if she’d like to hear some music he’d composed. Then he showed her the sheet music and played some more. It was then he revealed that it had happened in mathematics. My schools arts department is fantastic and so we were supported by a range of them. For me I saw three different ways to compose and all of them had mathematics in them whether that was obvious to the composer or not. The first lesson was a little shakey as I was forgotten and stumbled through. We did compose, so it was a success, but I was a little dizzy due to fighting the flu and medicated. Youtube didn’t want to cooperate, but then students know all sorts of tricks and everything clicked if not in the predetermined order. Mathematics isn’t linear. Life isn’t linear and I am more than prepared to take risks and make some mistakes, some, mistakes in front of my students if it’s what I ask them to be prepared to do.

Before I began each lesson I told them I had never read a note of music before putting the lesson together but wanted to show them order of operations in the real world and music just made sense. My hunch was right so off we went. Our 85 minute long lessons were perfect for the one off lesson.

More than anything it was fun. I still have a handful of kids who dread mathematics, but I am going to win them over. Might be time for another TEDtalk.

They all just sat their first unit test. Questions were written by them in small groups in an attempt to prepare them for mathematics in unfamiliar contexts and also helping them think about how to prepare for a test. It’s not a trick, they should be able to predict content. After about three hours of marking 60+ tests I am pleased to say there was a lot of very good mathematics and thinking on the paper. Poor little things looked stressed leaving, so I emailed them to tell them well done.

Our next unit is data, patterns, averages and predictions. Weather will feature. Perhaps they won’t be so cross when the weather forecast isn’t all that accurate afterwards.

Can you match the graphs to the cities. Wonderful activity from Maths300.

A New School Year, New Ideas and a Promise

At our information night when parents get to put a face to a name of their children’s teachers many of the grade 8 parents were assembled, so I asked them to make me a promise. As Dan Meyer says we have one of the toughest sales jobs in the world. We sell mathematics. The negative responses to the word math/maths/mathematics is a daily grind. I told the parents that they add to the battle, and asked them to promise me to stop making it more difficult:

Can you help me with my maths homework?

Oh I hated maths.

I can’t do maths.

Ask your mother/father.

I pleaded with them to at least look interested, even excited when their child spoke about their mathematics or asked them questions. Their children could explain it and they would be able to follow and might learn too. We shall see…

When Sea Levels Attack!

When Sea Levels Attack! by David McCandless licensed under CC by A NC

Infographics is an area that tickles me and it’s how more and more people are deciding to share information. Data Visualisation, or Visualization depending on where you are from, is the other buzz phrase.

Part of the problem with how mathematics has been traditionally taught is that it has little reflection on what real mathematicians do. They certainly don’t grind out twenty problems, check them and call it a day. Skill building is important, but kids need to see why. The only application of mathematics that I ever saw in class, before university, was buying a car (as if that was going to happen when I was in school, two years younger than the legal age to drive). Now I love mathematics.

Distracted Driving by  Christensen & Hymas licensed under CC by NC

Distracted Driving by Christensen & Hymas licensed under CC by NC

When you come from that kind of mathematical education, it can be hard to change. I’ve been at this teaching game for a long time and I shudder at some of my early attempts, though they felt quite good at the time.

Back to infographics. My grade 8s, all three classes, are going to create an infographic about themselves. My colleague, from the Design Technology department, lent me a limited edition copy of Feltron’s 2010 Annual Report to show the kids a personal infographic. Very nice of him. Very trusting. I think we’ll borrow some gloves from the science department or the nurse before 80+ kids touch it.

The goals are simple:

Include data about themselves clearly and in an eye catching way. Eye catching as in wow that’s cool, not dear god what is that?

Show a range of number and operation skills. How do you show an operation or order of operations? That’s pretty open ended, isn’t it? How do you show different types of numbers? Think of percentages, fractions, negatives, scientific numbers.

This year got off to a crazily busy start, which doesn’t look like slowing in pace any time soon, so this blog post sat in draft for a week. When the kids saw all the infographics online and some in print to hold in their hands and discuss with other they were buzzed. Some students need to work on multiplying fractions and some other number skills so the 85 minute lessons will be broken up with targeted workshops instead of making all of them sit through it again. I created a Google survey to see where the needs are and will use http://thatquiz.org so kids can self assess when they feel they have mastered a problem.

We are also hoping to use www.mangahigh.com to help kids improve their mathematics. Lots and lots of ideas. Linear equations, the coordinate plane and statistics will hopefully use data collected in their science classes. MYP science has an entire criterion on these skills. Perhaps together in context, we can teach this a little better – context and reason. A new year, new ideas and a promise.

Here are some wonderful sites with infographics. Be careful they’re addictive:

http://www.informationisbeautiful.net/

http://www.guardian.co.uk/news/datablog

http://flowingdata.com/

http://www.nytimes.com/interactive/2011/01/29/us/20110130mixedrace.html

NBFs: “What’s The Chance Of That?”

The end of the school year is hurtling towards us at an astonishing pace. My grade 12s/seniors/final year students will sit their IB Diploma exams in the first week of May, and I’m excited for them, but that’s another blog post.

Although my head swims with my grade 12s who I refer to as “my babies”, this post is about my grade 8s and their probability unit. We are pressed for time so how to get it all in was a challenge. Every year we have a casino night and to not do it would upset students and parents. The solution was not to teach the content prior to tasks, just start investigating (with some scaffolding). We started with an investigation called “What kind of gambler are you?”. NCTM has a great activity called SKUNK and we MYPed it.

Before I begin I will digress a little, again, and say stick with this post until the end. The collaboration in this investigation has been incredible and the method can be used in any subject. The great game of NBF will be explained further down.

From NCTM:

Before the students knew it was related to assessment we just played it and discussed it. Kids love it. Some of my students decided that the dice would decide if they remained standing or sat down. If that made no sense, go back and read the rules, it won’t take long. Some used odd versus even, low or high.

From NCTM - Fabulous site for mathematics teachers

We used the SKUNK dice simulator from NCTM, real dice which I rolled. then a student wanted ‘control’ so I happily passed it over to who has now become “Mr. Snake Eyes”.

Their task is to make a SKUNK user guide. How to be a successful skunk player both as a high roller and a play safe type gambler. They need to produce strategies for both types of players and back up them up with evidence. The assignment will be submitted on Tuesday.

When I teach probability I introduce the great game NBF. NBF stands for New Best Friend. Every lesson students get an NBF. I have the tables numbered from one to twenty-four. As the kids come into class they reach into the NBF lucky dip and pull out a number. This is where they sit. For the first couple of minutes they must chat with their NBF. I told my kids that being able to talk to anyone is such a great skill to have. While they might be out of their comfort zone, it’s worth it. They now look forward to it. Two kids actually sat next to each other three classes in a row. “What’s the chance of that?”, when you get a genuine question like that, you stop, grab the student directed moment and run with it.  

What I hadn’t anticipated was how wonderful the great game of NBF was going to be for an investigation. Students worked together in the first lesson to collect data, make predictions, record results. Their homework was just to review what they had recorded so that when they met their NBF the next lesson they could explain it to them. NBFs share ideas and results and the investigation took shape in a way that wouldn’t have happened if they had continued to work with their same friend each lesson.

I told them that long ago mathematicians would travel for weeks, even months to meet someone working in the same field, to find an NBF in the mathematical world, that they were fortunate to pick so many wonderful mathematical minds and to share ideas.  This is how each lesson began.

3d people partner.

3d people partner by 姒儿喵喵 licensed under CC by A SA

Were they taught tree diagrams and outcome tables? No. Did they appear? Yes, everywhere. All year we have focussed on the MYP criterion of Communication and you could see this paying off for this investigation. When this investigation finishes we will spend a lesson on a few more games, then they can just start their design of the casino game with their teacher in the background nudging them forward, showing them the mathematics they need when it is needed, in context.

If you have an investigation over a week or more and students can work together but need to produce individual reports, I can’t recommend this enough. Totally by chance this came my way, and that’s quite fitting. Oh yes, and it is fun. And learning should be fun.

 

An interesting thing to do if you are teaching probability, is for you to grab a random number for NBF and give to the students and then discuss how they felt and if it actually made any difference.

An extra resource I found is from www.100people.org that I used for a statistics unit for grade six. On page 24 of this document is the language of observation and analysis. Great for any subject that studies results. Remember we are all EAL teachers. It’s important to support our students in their writing.