Algebra on Demand is HERE – The Khan Academy

Many moons ago myself and Clint Hamada, @chamada, discussed how we could better prepare our middle school students for high school mathematics and other lucky disciplines that use it.  The Algebra unit was finished and we were moving on, as you do, to the next unit. However, you know deep inside as you move on that some had not mastered the skills or the understanding, that more time would have really helped. Pacing and the differentiation of mixed ability classrooms has many challenges. We wanted to reach all the kids and ensure that they felt they had the mathematical muscles for high school.

The key, I believe, is algebra, the language we use to solve problems. Not so much being able to do a ton of problems, but to understand how it works, why the notation is helpful and not actually awful. If kids can do some algebra and apply some correct notation, then problem solving becomes easier. The different strands of mathematics also become more approachable. Those wily letters confuse students and have for an eternity. The little letter x can cause early heart disease.

Salman Khan explains it best, in his TEDtalk, with his bicycle anedote. This is the problem we were trying to fix, the Swiss cheese gaps of maths:

Salman Khan talks about Algebra (and more) on Demand at TED

Salman: “… imagine learning to ride a bicycle, and maybe I give you a lecture ahead of time, and I give you that bicycle for two weeks. And then I come back after two weeks, and I say, “Well, let’s see. You’re having trouble taking left turns. You can’t quite stop. You’re an 80 percent bicyclist. “So I put a big C stamp on your forehead and then I say, “Here’s a unicycle.” But as ridiculous as that sounds, that’s exactly what’s happening in our classrooms right now. And the idea is you fast forward and good students start failing algebra all of a sudden and start failing calculus all of a sudden, despite being smart, despite having good teachers, and it’s usually because they have these Swiss cheese gaps that kept building throughout their foundation. So our model is learn math the way you’d learn anything, like the way you would learn a bicycle. Stay on that bicycle. Fall off that bicycle. Do it as long as necessary until you have mastery. The traditional model, it penalizes you for experimentation and failure, but it does not expect mastery. We encourage you to experiment. We encourage you to failure. But we do expect mastery.”

Watch the TEDtalk to see that The Khan Academy is  now so much more than video tutorials. It has interactive exercises including hints and teachers get detailed data on their students. It’s like the worksheets, tutorials and thatquiz.org that was used to create the Algebra on Demand wiki, that my blog is named after, but slicker, prettier, better. It’s really exciting to see it come to life. Salman Khan says that games are coming too, which is all that Algebra on Demand tried to deliver. Clint has set up Google accounts for all of our Grade 8 students and I am using it with my IB Diploma Mathematical Studies students too.

The kids log in with a Google or Facebook account and then nominate a coach. My Diploma kids were first, before our Christmas break, so they have nominated myself and Clint so we can both follow them.  They can nominate their parents and tutors as coaches too.  When our kids move on to the next grade and teacher, they nominate them and the data follows them. Can it move from one Google account to another? I don’t know. This is a question for Salman and Bill Gates and Googlers. When international kids move on, they lose their old school email, so how they keep their data? These emails are the user names we use for Khan Academy Google accounts.

Homework for Grade 8 this week: watch the TEDtalk with their parents.

At first when my Grade 8 kids went on I wanted them to do the exercises on linear equations, but most started at addition, right at the beginning and then followed the concept map routes. Now I am very happy they did that. The Swiss cheese gaps are being filled. An all too common problem in international schools. I went to a lot of schools as a kid across hemispheres and continents. Having a birthday right in the middle of the year meant that changing schools was rarely linear with grade level progression. Grade four was a lot of fun, but there was no maths, grade five didn’t really happen and I missed half of grade six. I still HATE my eight times tables and don’t mind telling my students that. Perhaps I can utilise the Khan Academy too. My boyfriend does. I’ve told other mates about it studying post-graduate courses facing what they believe is the horror of mathematics again. I’ve been a fan of The Khan Academy for some time, but now it’s supersonic with more on the way. Free self paced education for those with access to a computer. Hooray for Salman Khan.  And he used to do evil maths – hedge funds.

Will it replace what we do in the classroom? Impossible. Investigations and projects need a different structure, but I don’t see why we can’t provide a regular time slot to help prepare middle schoolers for high school and beyond.  My work is done and I didn’t even do it. Nice!

Here is the wiki that came about from the early days of Algebra on Demand: http://algebraondemand.wikispaces.com/ 

Now I need a new name for my blog.

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Cool Maths – Deadly Maths

Before I start to go on about what my kids are doing in my grade 8 class, a link…

Professor Marcus du Sautoy is behind this:

http://www.mathsinthecity.com/

It ticks so many boxes of what I am trying to get my kids to see.  Maths is everywhere, and in a pleasing way. My hope is that some of my kids run with this and even enter. I haven’t read the fine print, but maybe I can meet Marcus if I enter and get a symmetrical object named after me.  Maths in Hanoi, chaos theory, surely!

Hanoi Traffic
Hanoi Traffic by mr clearview licensed under CC by A NC SA

Marcus du Sautoy is someone you should follow, @marcusdusautoy, if you teach or even like mathematics. Google him and you’ll find amazing things you can use from television to websites and he’s involved in Manga High.

My grade 8s are almost ready to submit their latest assessment task. I rejigged the old Pythagoras investigation as I do each year. This time, however, it was more of an overhaul. The biggest change was to drop the very popular approach of getting students to ‘find’ the relationship all by themselves (with some guidance *ahem*).

Instead they were shown the theorem and how it worked. Part of their job, this time, was to prove it geometrically and with data. Some students also looked into algebraic proofs. Still, that isn’t anything new. What was truly cool about Pythagoras and his precious right angled triangles were the blasphemous irrational numbers he found in his calculations. Rumours surround how he died, how he was murdered. These numbers upset all of the Greek Gods and that’s a lot of anger.

Day 85/365: We Love Diversity

Day 85/365: We Love Diversity by Kugel licensed under CC by A NC SA

Pythagoras and his apostles were burnt inside their school is one legend. There are so many more too. Students were fond of the one where he was chased to a field of beans and couldn’t go any further, so they cornered him and the rest is history. Pythagoras and his followers did not eat beans, they represented testicles. Student: “I don’t think I would have run into the field of beans either.”

Students enjoyed looking up the stories of his death and about Pythagorean beliefs. They were told very little and I learnt some new things too.

To introduce this part of the task I asked students to name some mathematicians. As ever lots of dead ones were mentioned. Then I asked for some that were still alive and expected silence…

Silence was not what I got. I was so impressed with my class of budding mathematicians. You may not agree with all of these, but I don’t want to edit out what the kids contibuted.

Ngo Bao Chau

Bill Gates and Steve Jobs

TED Talk peopleRobert Lang and Kashima and Margaret Wertheim

Professor Rose – teacher of Stephen Hawking

Stephen Hawking

Mr. Khan

Professor Du Sautoy (“Manga Maths guy”)

Dr. Dan (he visited us not so long ago and led some cool probability activities)

8BD and Ms. Griffin (I supplied 8BD, they threw me back to me)

Grigori Perelman 

Andrew Wiles

The last two were mine because they proved theorems too, just like Pythagoras did so many years ago.  When they succeeded in their task they were offered a reward of $1,000,000. Perelman said no thank you. He was in it for the mathematics. Not that Wiles wasn’t. He loves mathematics, really loves it. Pythagoras wasn’t offered any riches, they killed him. There are of course some million dollar prizes still for grabs

We very briefly discussed Fermat’s Last Theorem. They understood the concept, particularly as we have just been immersed in the Pythagorean Theorem. Andrew Wiles was a similar age when he read about in a library and was inspired to prove it, because he understood it.

So my students set out to show that perhaps a death sentence for being right was a little harsh. Poor clever Pythagoras, a band of barefooted dedicated apostles and a whole new number system to explore, but it only led to his death.

Athenian Temple by Jonathan Burr licensed under CC by A SA NC

Interested in why irrational numbers angered Zeus and all of his buddies? You are already online. Telling you everything ruins the thrill of deadly mathematics.  

And on a final note for this incredibly enjoyable task (there will be a little MYP speak at the end) at parent-teacher-student conferences tonight I had a parent say that they were enjoying the mathematics and learning something new too. They even had a question. Excellent, they are discussing maths at home.

For the MYPers out there: This is assessed using criteria C Communication and D Reflection.

The famous mathematicians lead in was from Charles Lovitt, a great sharer of resources, lessons and ideas from a workshop last week.

http://www.maths300.esa.edu.au/

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?

Trees for the wood…

Today I had a different kind of “I want to do better” meeting with a student after school. Yesterday a student emailed me asking if she could take a test again. This stems from the handful of students who decided to go back and review work they decided needed some more practice. When a feeling of mastery takes over their mathematical souls, they would take another version of the first test. To me, this is fair and the MYP is about progress, not averaging scores.

Head in Hands

Head in Hands by Alex E. Proimos licenced under CC by A

This however was a request to go from a 7 to an 8, out of 8.

She had scored in the highest band of the criterion.

She had displayed a thorough understanding.

She took her test home.

She showed her parents.

Not good enough. You are so careless.

Look at these mistakes.

These mistakes you shouldn’t make.

So she (they) asked for a retest, because her fantastic test was a disappointment to her parents.

Continue reading

YAY!

aquarell

aquarell by Rafakoy licenced under CC by A

 So, the tests were ready, we needed a few different ones. Some students had mastered the first lot of skills long before, but that didn’t matter I told them. There were so many other things happening in #AoD, that the tests were put on the long finger for a little while. I told them if you can do it now, you can still do it later, just review – wake up and use those brain cells.  There are different versions of the test, as some students weren’t ready and so they will sit their first test later.

Nervous? Yes, myself and my teaching partner were. #AoD, it’s felt really good. They look like they are learning. They sound like they are learning. It’s a wonderful working atmosphere in the classroom, but when push comes to shove would they be able to pull that mathematics out under test conditions. First time reading this blog? Thinking what is this #AoD? What has worked? Read the first post, not too far down, or click here.

Boy oh boy oh boy did they learn! I am so proud of them I could burst. There were a couple of kids that I feared were moving too quickly, to keep up with their friends. The results showed some gaps, but that enabled me to have a chat with them about appropriate pace and not worrying about everyone else. Do what you do really well and then move up the ladder.

Algebra say what?
Algebra say what? by demandaj licenced under CC by A SA NC

We are an MYP school, so we assess with criteria and most students scored in the top band. The mistakes that were being made were what we refer to as “whoopses” not a lack of understanding of the content or skills.Things that NASA worries about. I don’t think tests are the be all end all, and I’ve said this before. When universities and others at the top change their approach to the selection of students, then they won’t be as pervasive in our schooling systems. We have cut down on them, and students let us know when they feel ready to take them.

Delighted faces arrived at my room to pick up their tests to take them home for their parents to sign. Seeing smiles in mathsland is such a reward.

Last week we broke up the #AoD with a visiting professor of mathematics from The USA, Dan Canada. He was interested to see what was happening at UNIS, he has a relative at UNIS, and dropped in on some of the UNIS classes to have a looksee. I want as many people to know about #AoD as possible for input. I know it is not a perfect system and can be improved, so that’s why I blog and have it on a public wiki. Now we might get even more feedback or even get other schools using it.

Dan also ran some probability sessions with my classes to think about theory versus reality. Incredibly interesting, fun and I let him at my 8s, 11s and 12s. More in another post.

So far so good..

The last few lessons have been #AoD doing its thing or more to the point my students doing their thing at their own pace.

As I walked around two classes, of grade 8, in a row every student was engaged and working well. The last two lessons of the day. They did their own brain break and two kids made a new one to kick off the lesson and then they all got down to it. All of them were ready to try new problems having watched some tutorials for homework

It’s early days and keeping this momentum going will be one of the challenges ahead. Watching students helping each other has also been delightful as well as a huge relief. One of my fears was that they’d be too independent. So far so good.

Day Off, Part 2
Day Off, Part 2 by NCM3 on Flickr

Part of my strategy to keep them motivated is to help them to see the mathematics all around them.

I have just  finished polishing off their first summative assessment task. The task was inspired by  Darren Kuropatwa. These two share all they do.

Gone are the autonomous days in our classrooms, which is a grand thing.

Meeting Darren Kuropatwa at the Learning 2.0 in Shanghai during a mathematics and tech unconference was fantastic. Presenting an Unconference  on Using Technology in the Mathematics Classroom was the highlight. I saw my little baby tech ideas, I had brought to Shanghai, on steroids and was so inspired to go back and design #AoD. It’s a work in progress, and it always will be.

One of the things Darren did with his students was to get them to take photos of parabolic objects. “De-constructing” the world around them, as a friend put it when I was gibbering about using tech to teach mathematics. Seeing the mathematics all around them is key I believe.  I have trialled this with my teeny grade 11 (juniors) class with parabolas and gradients. Now after my middle school students learn about gradients, I want them doing the same kind of thing.

I’ll get them to take photos of all sorts of gradients/slopes/steepness and annotate them. We can then build a class slideshow. Every student will do the task when they are ready, but will have to check all of the previous images, so that they don’t repeat any. This has the extra benefit of scaffolding students trying to move ahead. They can see the work and what is expected.

 

 

But how to store these images so they continually update? Flickr, and I manage  the folder, or can anyone add to a group we make? Slideshare maybe? Not familiar with it really, but not afraid to try? Wiki for #AoD? It won’t have enough storage… I think I need to be a web guru, or just tweet for help. I think it’s time I taught myself Slideshare. It’ s been on my to-do list and I hear it’s nice and easy.

The second assessment will be done together, so that we work as a class at some points and can discuss what we have learnt face to face. Preview http://veloroutes.org/ and maybe http://www.mapmyrun.com/. Students can map out a walk, run, bike ride, scavenger hunt anywhere in the world, and analyse the easy and difficult parts. It can be a place they know well or have been to once or somewhere they’d love to visit.  I did try this with my grade 11s and one of them said “But I only ever went to the hotel or the mall”. We were using their summer holidays. Funny as that was, I think I’ll open up the scope – oooh maybe MARS.

Let the blogging begin

It’s time to blog and to unveil the first look of Algebra on Demand or #AoD to its friends. #AoD doesn’t have many friends yet, but I hope that will soon change. #AoD needs friends to help it grow and become what it wants to be. It also wants to be a friend to educators and students of all ages. This blog and the wiki isn’t just for mathematics. Well, it is in its current form, but I believe the model can be used in other disciplines too.

If you are not a mathematics teacher, please keep reading as I think #AoD has something more than just mathematics to offer.  ‘Just mathematics’ isn’t  an appropriate pairing of words anyway. It is also most certainly about using technology in education. I also want feedback, advice, guidance. I am excited about the opportunities technology provides, but I am, as some of my tweeps in twitter put it, in my #rookiehour. By the way, if you don’t tweet, you should. It’s the most amazing professional development at your fingertips. Twitter’s #mathchat daily online newspaper grabs some of the best tweets in the #mathchat world. I’m @lissgriffin, see you there.

#AoD was made in wikispaces so that it sits in a public space for any teacher or student of algebra to access. It is also a wiki so that others, including my first guinea pigs the grade 8 algebra classes at UNIS Hanoi 2010-11, can add to it. It is still undergoing some construction.

#AoD began a few years ago when myself and my teaching partner, Clint Hamada, were discussing the frustration of the mathematical leak over the summer breaks.  I think most educators have experienced the “But I KNOW you know this. I saw you using it, doing it, applying it last year or the year before…” or the review unit that becomes a normal unit of work. The thing is, and I tell my students this, it isn’t a leak. The knowledge and skills aren’t gone, they are hibernating in cave somewhere in our grey matter. I know that ten years without calculus or the cosine rule meant that when it came time to teach it, I didn’t actually remember all of it. Shocking, I know. What I had to do was review the content and practice a little and I had it again, ready to teach.

So do we need the mathematics we learn in school? I coped very well without calculus and more during the wilderness years. That’s a whole other blog post, but it gives me food for thought when I am in the mathematics classroom. It is also something that helped me develop this unit of middle school algebra. I want the students to learn and apply the skills, but I also want them to enjoy learning this wonderful language and to see the mathematics in the world all around them. 

Back to how it began… A few years ago Clint and I decided to keep algebra running once a week after the unit had ‘finished’.  Making the mathematics classroom a positive experience can be a tall order. We get bad press from all sorts of sources, so it’s a challenge from the get go. If students can master some solid algebraic skills, those feelings of dread and nausea can be left at the door. Problems, patterns and applications become possible.  Me, I love the challenge of making mathematics accessible to all that come into my classroom.

Once a week we would interupt the unit we were working on and every student consolidated or added to their algebraic skill set. The huge range of skills meant that every student could be working on something different. My school, UNIS Hanoi, is now a one to one tablet school and so we have the technology to maybe, hopefully, successfully try this approach from the very beginning. Students will be learning middle school algebra at their own pace from the start.

The process used is sometimes referred to as reverse learning and some are referring to it as the Fisch Flip. Karl Fisch pays respect to these two pioneers Jonathan Bergmann and Aaron Sams. I have just found a link to a workshop they are running in June 23-25, 2010 – oooh… I am such a newbie to this, so I might get some of the jargon wrong, don’t hate me.

My model is based on what they have been doing, but not nearly as organised. I expect some initial chaos, okay quite a bit, as we settle into the groove of working on things all over the place. Chaos is okay, there is mathematics in chaos too. And this blog is where I will scream for help or just scream for the sake of screaming. Maybe I’ll be screaming and noone will be there, in my own private blog. I can scream at the little red dot highlighting Viet Nam on my widget map thingie showing me who reads by blog (I want one), then realise I am screaming at myself. It’s like that if scream in a forest and noone can hear you question. Hopefully I will also jump and down excitedly, and virtually, when things feel fine and groovy.

To keep this learning groove grooving #AoD has different facets to keep students engaged, I hope. There are video tutorials from a variety of sources on the internet, games (you should check out www.mangahigh.com), interactive online activities, movies and fun videos, brain breaks and even online quizzes that send the results straight to me as well as the students from www.thatquiz.org.

The goals of #AoD are:

  • students in my classes learn algebra at their own pace
  • students ENJOY learning mathematics
  • students see, hear, smell, touch and taste the mathematics all around them
  • students becomes better at being independent learners
  • students help to teach the world mathematics

Big dreams, I know, and kind of bold, but definitely exciting too in  mathsy techy geeky kind of way. We want our students to be risk takers and think outside the box, so here I go…

Am I nervous? A little, yes. Am I ready? I hope so…

“I am always doing that which I cannot do, in order that I may learn how to do it.”  Pablo Picasso