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.

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.

Been Busy Elsewhere

Our class blog for grade 8 mathematics
It’s been quite a while since I blogged and I feel guilty about the work I am not doing right now. The pace of the year has not lessened, feels busier than ever before. I may not have blogged here, but I’ve been setting up the class blog. Yesterday it was unveiled to the students with three posts and some pages ready for them to read and comment on. Most commented on MangaHigh because they love it.

For them to enjoy I posted their poems on wallwisher and there is a page on TEDtalks. TED is new to most of the students and many of their parents. Homework from time to time will be to watch these and do so with their parents.

Tomorrow I will attempt the music lesson. I’ve never read a note let alone written or played any music properly. Banged on a few drums, was passed the triangle. My voice is nothing to write home about either. Mathematics is a key player in composition and making it all sound so pleasing. I figured it would make sense to look at it when we are covering fractions and order of operations. The latest blog for the class blog (for grade eight) has some extra music links for students. Hopefully they will comment on that post. We need to discuss writing comments and replies a little bit more. Most said they don’t ever read blogs.

Little bit nervous about the lesson due to my lack of musical knowledge, but all in all it should be fun and the kids should see how mathematics isn’t just in a textbook. This being one of my main goals of the year, oh, and making the mathematics class fun and inviting. Is this an assessment? No, just a one off lesson with links for kids to pursue the theme if they so wish. The blog being the perfect medium for such things.

Hopefully by the end of the year the kids will be posting and myself and my teaching partner will be only commenting.

And maybe just maybe things will settle down somewhat. I’d like to get back to my blog a bit more often so I can reflect on things.

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

Don’t Eat the Beans!

Rearrangement proof for Pythagoras' theorem. P...
Image via Wikipedia

If you read this blog from time to time and don’t like too much maths in your eyes, read on, it will be okay. I won’t go into proofs, this is more about how the kids would be introduced to the revolutionary blasphemous mathematics that got Pythagoras in all sorts of bother. For the record there are many stories about how he may have died. For the class I have ignored the less interesting ones.  But was it his theorem?

One of the things that didn’t work so well in #AoD, mostly with pacing, was letting kids do a summative MYP assessment task when they were ready. They were all working on different things, so were ready at different times. Not that I’m saying they should when they aren’t ready, but it would have been better to get my classes to do the Gradient Task at the same time, perhaps even take them to the water park to photograph more interesting surrounds.

They still got some enjoyable and valid mathematical experiences out of it, but as with all new things tried it won’t necessarily be right first off. I am already looking forward to fine tuning the program next year. Three weeks after the winter break we had a week off for Tet (Vietnamese New Year – chuc mung nam moi!). We also churned out set two of the four sets of reports for the year, so my tippy tapping blogging fingers were a bit distracted. It didn’t mean I wasn’t thinking about mathematics and blogging. I found time to read some blogs and comment on blogs. Must try harder. I’ve also been very distracted by Africa.

Puzzling over the not so perfect fit

Our latest adventure is all about Pythagoras and his famous theorem. I looked at what worked and what didn’t last year. This included how much and what students had learnt, but also what was ineffective or dull or both. Pythagoras’ Theorem features in mathematics curriculum all over the world, but I never did anything interesting with it when I was kid and I never take the time to apply it to see just how much distance or time I could save by cutting through rather than follow a path. Amazingly I can see it is shorter and that is enough. What I think is so cool about the theorem are the stories around it, the history and the impact it had on mathematics and the beliefs of the people at the time. And the murders. 

It was time to throw out the construction of squares on the sides of right angle triangles to help kids ‘discover’ the relationship all by themselves, using calculations and analysing data. We, maths type folk, are very into nutting out patterns, it’s in our nature, but that has been done to death with Pythagoras. It’s rumoured that he was killed, along with his apostles, for unearthing irrational numbers. Why beat him to death again?

The angle taken (you see what I did there?) is with Criterion D: Reflection and C: Communication and getting the students to show that his theorem does work, rather than find it. Not all students are ready for algebraic proofs so we are using geometry and data. If a student feels the urge to present an algebraic proof, they will be most welcome to do so.

Today, The Geometric Proof It was so much fun.

Kids like “make and do” (so do I) and even though I LOVE teaching with 1:1 tablets, it’s nice to touch things again – blocks, scissors, tape measures, paper. Finding the right balance is so important.

Each pair had some coloured paper and some white paper. They had to make squares. Two coloured with sides of 15cm and 20cm and the white one with sides of 25cm. Fluoro paper everywhere, short stubby ruler owners were challenged  moreso than those who had remembered their 30cm rulers. I gave them 5 minutes to get their squares ready, then asked them to clear their tables of everything except for their beautiful squares, and to sit back and just admire them.

Then I asked them to imagine they represented something wonderful, like gold or chocolate or…

My favourite commodity were the “squares of love”. That student had been one the singing telegrams for Valentine’s Day not so long before.

Once chosen I then said they had to choose between them. One member got the two coloured squares and the other member of the group got the white square. It was important not to use any adjectives meaning big or small. There was some friendly banter and in under a minute happy and resigned faces placed their squares in front of them.

“Who got the white square?” lots of whooping and shouting of victory about scoring the big square.

I praised those who decided to forego the big white square for the smaller colourful ones, then told them they were equal. The confusion about the lack of victory was amusing.

The task of showing me they were equal was then assigned. Confused faces. “Show me, any way you’d like to, that the area of the white square is the same as the coloured squares”. One voice pipes up: “Can we use scissors?”. And they were off. No mention of the right angle triangle at this point, though, some students were talking about it.

The girls prove it. Step one in getting closer to the deadly numbers

 One pair found it didn’t work, but their 25cm sides were actually 30cm. Problem fixed, mostly.

Time to reveal the right angled triangle and where the squares fit. Story telling time begins too.

We then discussed the famous rule, which many had seen before. We looked at the diagram of the squares  sitting on their right triangle and then in their pairs they discussed the accuracy of their geometric proofs

It was a fun hands on, no tablet lesson. My next post will show the groovy technology we use to show this theorem at work.

Here is a preview

Mathsnet has a great section on Pythagoras and his theorem. Proofs 2 and 11 are accessible to any student, and proof 11 is pretty groovy in its simplicity. One of my kids then found this online version of number 11..

Braining Camp is new to me, so it has been added to this task too, for practice.

I haven’t told the kids why Pythagoras and his followers did not eat beans and I won’t tell you yet. We have one lesson for the history and the numbers that led to his death. Would you die for mathematics?

Africa in MY EYES

BIG KITTIES in AFRICA – Mating pair, Day 7

 
So, it’s been quite a while since my last post, but it was the festive season. It’s the annual UNIS Talent Show tonight and I’m involved up to my eyeballs, so I’m keeping myself busy (anything but marking!) until 6pm kick off.  Should be done and dusted by half seven.

My first classes were charged with my alarmed body clock and a yearning to be back in Africa.  Better to use this to my advantage than to sulk. Sulking didn’t really happen, and I am still buzzing on my Africa experience.

My grade 8s all sported happy little faces back in mathsland. No major mathematical hurdles jumped on day one, more of a scooping up and refreshing of their mathematical minds. A few quick reminders and where are you ats so that students would be ready to get down to it, in a mathematical way, the following lesson.

We enjoyed a lesson I called MATHS IN MY EYES! I asked them to take about five minutes and write down all the maths they experienced on their holidays alone. I want kids to use all of their senses to experience maths. After the five minutes I let them chat to each other, which led to more entries on their individual list. I didn’t just throw them into the activity, I shared some maths from my holiday with them. Luckily for me there was some splendid nerd/geek/quality company on this holiday, so I didn’t have to keep my maths to myself. One of the group covered her ears when we talked of things like charts, but she’ll come around.  It’s so nice not to have the normal reaction to my job “Oh, you teach maths“.  Poor maths, such a bad reputation, and it’s so cool and EVERYWHERE!

This is just a sample of things I put down. The lion stats and rates are quite staggering:

Quick Notes in Class

During our unconferences on Wednesday, run by Clint Hamada our tech facilitaTOR, someone ran a discussion board session. Perfect. Now we are adding our observations to the discussion board on the school portal. Too bad it’s locked down or I’d post a link. I don’t have the fear of public web spaces others do. I quite like them. But I was wondering how to set it up – blog? wiki? confused! problem solved.

And I ask YOU: What maths did you encounter over your festive season? From the mundane exchange rates and does my money go further here , or just how long will this toaster in my holiday digs take to make perfect toast – here’s a cool chart:

via ilovecharts (who doesn’t?)

Were you lucky enough to check out the Statue of David? So much maths!

And the burning mathematical question just how much does one hippo on average poo into rivers each day? They stink! Poo to water ratio would be interesting too.

Hippos doing their “aren’t I just so cool” thing.

Last but certainly not least is the Twiga flow chart. Twiga is Swahili for Giraffe. The lives of some African animals are quite simple. This started with crocs, but giraffes have such an appeal. Below is the simple flow chart scribbled in the back of a landrover by my now chart hero.

Simplistic life of African Animals
Twigas – are they hungry? no, not moving

and then upon his return home made this – click on the link – it’s great!