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 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.

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? 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.

This was started a week ago, but I was distracted. What grabbed my attention, by the throat, was a smackdown with the flu. I lost.

One of the exciting things about Algebra on Demand is that the students are taking charge of their own learning and this is spreading beyond the mathematics classroom. Some have asked for thatquiz.org in other subjects. My teaching partner in grade 8 mathematics is making quizzes for their other subjects, because they like using it as a quick check. They are aware of what they have mastered and what still needs work “Why are we having that test now, when all it’s going to show is that we don’t know it yet?”. I think the next step is to get the kids onto thatquiz to generate tests themselves, replacing the ones I found or made. I don’t think testing is the be all end all at all (enough alls?), but we use it as a check. I used the analogy of thinking you’re a great dancer, then you see yourself bust a particular move on film and rethink that jerky motion. Did you ever see Elaine dance on Seinfeld? Although it’s great to have thatquiz for students to check skills and understanding, I don’t think anyone should ever be told they can’t dance.

For the record I think that timed tests and exams are very stressful and unnatural settings to check for understanding. Kids need to be taught about stress management and that old fight or flight thing that happens in many of our brains, when confronted with a test, while in our educational systems as benchmarks for obtaining such things as places in tertiary institutions. The pleasing thing is that kids are showing more awareness of what is being taught and learnt and not just going along for the ride. They want time to explore and master concepts and skills before moving onto the next thing. School can feel like a race at times, for teachers and students alike. AoD is giving the students a chance to stop and smell the roses, all of them if they want to.

At play in kindergarten

Some of them are even playing maths games in their own time. A few teachers have said to me “Mangahigh, I know. But we can’t get them off it!”. They weren’t all impressed, but I was. Playing games that teach and foster mathematical thoughts and processes for FUN, in their own time! I am a fan of mangahigh, where is that like button?

Learning through play is so natural. How do we learn new things on this wonderful worldly wise web of ours, master new software, become a blogger, learn the world of twitter and see what it can give us? We play, we make mistakes, we work out the tricks and the way things work. We even learn how to get to the end without going through all the steps. Kids need to play to learn too, just as much as adults.

Ask yourself if you read the manual or jump right in to see if you can work it out yourself? I am the latter and will refer back to manual, if needed. Gaming is big with youths. I need to learn more about it all, so that I can tap into this.

Scratch has just recently caught my eye. What did I do? I jumped right in and played around. For those who like the manuals, there is so much on the internet that you could read for days before you got started. Technology does not change the need for play it just offers different avenues for adventure. Technology can sometimes make us race a little faster to some sort of ‘finish line’. Before I even develop the task for my students they will have Scratch downloaded and installed on their tablets. Some will muck around and explore before they were meant to. Perfect.

With any class or new thing, AoD BETA, as it were, “it aint all roses”. My concern that some students would rest on their laurels and not challenge themselves was warranted. At the same time, however, some just wouldn’t be aware that they were doing this and hang about too long on one particular skill. To help students to be more cognisant of their progress I made a simple chart. Each lesson we begin with some colouring in. Of course I play up the colouring in bit. Students begin the lesson, after a brain break, with a task that takes seconds. They colour in the column for the previous lesson. It is immediate feedback and we are getting lots of different looking learning graphs. Some are quite linear.

Example of the graph students use to track their progress

The graphs showed areas of concern immediately, highlighting skills that students had sat on for days (I just got another idea for gradients!). We spoke as a class about challenging ourselves and setting short and long term goals, but when you are having a fine old time in mathematics land you might not notice being on skill five for three to FOUR lessons. I wasn’t surprised as it was a concern when I was putting this all together. Some students do need extra time, especially at the basics. I have one student who has only just mastered the first five skills, while others have moved into the teens. This is where that student should be and I am so proud of him, and he is pretty pleased with himself too. It’s the other ones that I know should be further along, that concerned me.

Each column represents about 70 minutes of mathematics, including the odd film and brain break here and there. I asked students what it meant to be on one skill for three to four lessons. They “did the maths” in their heads and replied, at times tongue in cheek:

We’re lazy

We are playing mangahigh too much

Stupid

We might need some help

It was ‘needing more help’ that I was looking for. No-one is stupid in my classes, we all have strengths. I have met some stupid adults in my time that beg belief (blind lady riding a bicycle in Ha Noi is a particular favourite of mine), but not kids. They set about colouring in. Two lessons later walking around checking their progress graphs and chatting with them, you could see the pick up in pace.

It’s a bold claim, but I think it’s a fair call, when I say that there isn’t a single student in grade 8, out of 66, that dislike mathematics. Usually there are quite a few that HATE it, an expected challenge. The spectrum of enjoyment is all positive. Every single one of them is achieving, at different rates, but that was the idea. The initial chaos has settled into a nice groove. Kids who have struggled with mathematics are telling me they are proud of themselves.

Being where I am makes me incredibly lucky. I don’t feel resistance anywhere. My teaching partner is excited to try this new approach and is now using parts of it in other grade levels, admin is behind me, parents seem to like it, we have a wonderful technology facilitator (my partner in crime when AoD was created in its early form) and the kids are willing to get stuck in and they appear to be enjoying it.

I think if I didn’t have this supportive group, I may have gone rogue.

I was so pleased with the lesson on how to use tutorials for learning. It feels like the message got through. I adapted my original lesson plan a little bit too. This blog post isn’t about mathematics. It’s about Learning to Learn, working independently and also getting students to work together and of course introducing the blended learning environment.

My concern was that students would watch a tutorial and think “Oh, that looks easy”, do a problem and think they had mastered the skill. Not because they are lazy, but because it would feel like they had.

Solution a three part lesson involving video tutorials. These became longer and more complicated. Instead of doing this as one lesson, I split it over three.

Lesson One:

In the last fifteen minutes of my lesson I told students to close their tablets (laptops) and to get ready to watch a video on a nifty way to do long multiplication. Some students recognised it as Napier’s Bones. The video comes from the crew at mathtrain.tv. When it was done I put a long multiplication problem on the board and said “Do it, and you must use the method you just watched”.

A variety of things happened. Some got right down to it. Some had a minor panic and then asked others for help. Some asked to see the video again. They all achieved. The video didn’t discuss how to carry when the sum of the diagonal is greater than nine, so they worked that out and some remembered from years before.

Then I showed the how to make an origami fox using a video from Youtube,

and said “Oh dear, we’ve run out of time. We’ll do this tomorrow”. I didnt’ say, we wouldn’t watch the video again. Lesson Two:

Students come in and sit down. I have bright fluoro paper at the front. Students take some time choosing a colour. They are excited by paper. I haven’t cut them into squares, which are meant to be 15cm by 15cm. Then, once they are seated with paper, rulers and scissors, I announce “Okay, make the foxes”.

Brilliant variety of responses.

WHAT?

But I don’t remember.

Miss!

Ooh I can do it, I practiced last night.

Show us the video again…. please….

That’s not fair.

Show me show me (to other students)

I calmed them down, and we discussed how they could have been better prepared, how they could have mastered making the fox puppet making. Then I showed the video again:

Wait! Wait! It’s too fast.

All my students have tutorials on a stick, so I pointed out that they all had the tutorial. So they waved me away. It was lovely walking around the class. They were helping each other and everyone was making a fox at a pace they were comfortable with.

Once we had our pack of foxes, we broke into small groups of four or five to make our origami fireworks. I did the same thing by telling them to close their tablets and just watch. Each student would need to make two to three of the same thing, then piece them together working as a group. I came up with this task. because I really want my students to support each other and help each other learn. Blended learning has the risk of being quite isolated.

The tutorial for the fireworks is quite fast in parts and it’s not as easy as the fox. Once the video was done I said “Go to it”. General panic again. After calming them down I asked what they needed. Of course, they all had it in their tutorials on a stick. It was a challenging task and they worked together brilliantly. Some of our origami masters became the walking talking real life tutorials and were therefore modelling helping and teaching each other.

We discussed everything that happened and how it will relate to the new way we are learning algebra this year. It was one of those lessons that went better than planned. Of course, some will forget but I have something concrete I can remind them of when they slip or begin lazy viewing. And it was just plain fun in the mathematics classroom and all of my students know there is some very cool mathematics in origami.
Their homework was to prepare to make a fox in class next time – only notes could be used.

Lesson Three:

Fox making time. Those who didn’t practice or make notes, couldn’t do it again, even though they could the lesson before. “Too many steps”. Students with notes or who had practiced or both had great success and helped those around them. Some could do it from memory, but very few. A great way to show different learners. I told them that randomly next week, they will have to make a fox in five minutes. I’ll cut squares for them.

So today they all begin their self paced learning. My wiki isn’t as pretty as I’d like it, but I am not a web developer person. We all have to start somewhere. It’s very exciting. I’m expecting a little chaos.

Now it’s time to ready the major pieces of assessment so that they can use their skills.

It’s time to blog and to unveil the first look of Algebra on Demandor #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