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This post was going to be part of the Virtual Conference of Mathematical Flavours, which you can see all the keynote speakers and presentations here: https://samjshah.com/mathematical-flavors-convention-center/. The prompt for all the blog posts that are part of this conference is this: “How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?” In the end, it didn’t end up being there, because my computer started dying painfully at the critical time, but I still want to highlight the Virtual Conference anyway because it was a great idea.

There are many things I could have written about this, but I think I will choose one thing that is about my approach in the MLC to student questions. In the MLC everyone is worthy to ask both stupid and smart questions.

My Maths Learning Centre is a place where any student doing coursework at the Uni of Adelaide can visit to talk about their maths learning with a tutor (often me). People come to talk about all aspects of their maths learning in all sorts of places where maths appears, from dividing whole numbers by hand to understanding proofs about continuity of functions between abstract metric spaces. My point here today is that people from both ends of that spectrum and everywhere in between are allowed to ask questions that are about basics and questions that are about deep connections.

Imagine a student who has always been good at maths, who finds things easy and quickly grasps abstract definitions. It is natural for such a student to fold their goodness at maths into their identity, which often means they become extremely embarrassed to show any sign of struggling. They’re supposed to be the smart student and this simple stuff is supposed to be obvious for them. So if they have a question about the basics, they hide it and hope it will come clear eventually.

The thing is, having a question about something simple doesn’t make you stupid, and it doesn’t even make you not smart. Having a question about how to get from line 3 to line 4 is at the very least a sign that you’re paying close enough attention to wonder about that step; having a question about the definition is a sign that you know definitions are important; and having a question about some random bit of algebra or notation you happen to have never seen just shows you want to learn. In my Maths Learning Centre, I try to make it a place where everyone can ask a “stupid” question. Where stupid questions are treated with respect and answered clearly, with encouragement to make sense of what is happening.

Now imagine a student who has always struggled with maths, who just never seems to understand the explanation the teacher is giving the first time, and who struggles to get through the first few of the exercises. It is natural for such a student to fold their badness at maths into their identity, which often means they don’t even try to understand things and just look for some step-by-step instructions they can follow so it will be over with as quickly as possible.

The irony is, they never finish their exercises, so they never get to be part of that part of a maths class where the early finishers ask the deep and involved questions about theory and beyond-curriculum interesting stuff — the very stuff that can make maths a lot more fun. I know for a fact that students who feel they are bad at maths are intelligent people capable of logical and creative thought, and they deserve to ask their deep questions. So in my Maths Learning Centre, I try to make it a place where everyone can ask a “smart” question. If a student who is struggling asks about infinity or quaternions or what my PhD was about, I will damn well discuss it with them. If they look at the work they’re doing and ask how it is connected to some other bit of maths, we’ll explore that together. That curiosity is a treasure to be prized and I will not squash it by saying we have to get on with the assignment now.

And you know what, it turns out that many a basic question is actually a deep and clever question after all. Recently a student who was struggling asked why it was ok to add two equations together. Not one student in my ten years of working at the MLC has ever asked that question! There must be something really special about the person who asks this question, right? And it’s a really deep question about the nature of equality. I want my Maths Learning Centre to be a place were it is okay for everyone to ask a question that is simultaneously stupid and clever.

That’s all I have to say. I believe everyone deserves the chance to ask stupid questions and to ask clever questions and to ask questions that are simultaneously both. They are worthy to have their questions taken seriously and the answers discussed with respect for the humanity and intelligence of the asker. I have to always remind myself to give students the chance to ask these questions when I’m with them, especially students who are struggling to articulate the questions for whatever reason. And maybe if they’re not asking, I’ll sometimes ask the questions for them and we’ll answer them together.

How will you welcome all people in your learning spaces to ask all kinds of questions?

Posted in Being a good teacher, Thoughts about maths thinking | Tagged ,
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Since 2013, the MLC and Writing Centre have been doing a game called Letters and Numbers at Orientation Weeks and Open Days to create interaction with people. I tweeted a photo of one of our sessions during Open Day yesterday and it has attracted a lot of attention, so I thought I might record some details of the game for people to read if they’re interested.

The inspiration

In the early 20-teens, we had a show on Australian TV called “Letters and Numbers”. In it, contestants played two games: one where they got a random collection of letters and had to create the longest word they can, and one where they got a random collection of numbers and a random target and had to create a calculation that produced the target. They did this in a 30 second timeframe, counted down by a giant clock on the wall. The Australian show was based on a show which in the UK is called “Countdown” in reference to the clock, which in turn is inspired by a French show called “Des chiffres et des lettres”.

I was thinking of a way to have a combined MLC and Writing Centre activity to engage new students with us so we could talk to them about our services, and of course this TV show popped into my head — it was the perfect combination of low-stakes maths and language. All I needed was a way to do it live in a public place.

The setup

In the TV show games, the letters and numbers used are chosen randomly, and I needed a way to do this in a public place.  I could possibly have done a computer thing or had a pre-written list, but I really did want them to be random, and I liked the idea of the participants choosing the numbers/letters themselves, so I wanted to choose them from a bag or bucket. The letters use the same distribution as the tiles in a Scrabble set, so I could have just used a Scrabble set for those. But the numbers I would need to make myself somehow. I decided to use pop sticks with the numbers/letters drawn on them, which could be drawn randomly from buckets.

Here are the distributions of letters and numbers I put on the pop sticks:

Vowels 4A, 6E, 4I, 4O, 2U (half the vowels in a Scrabbble set)
Consonants 2B, 2C, 4D, 2F, 3G, 2H, 1J, 1K, 4L, 2M, 6N, 2P, 1Q, 6R, 4S, 6T, 2V, 2W, 1X, 2Y, 1Z (all the consonants in a Scabble set)
Target Three of each digit from 1 to 9, and two 0’s.
Small numbers Two of each number from 1 to 10
Big numbers One each of: 25, 40, 50, 60, 75, 100, 120, 125 (I added some extra on top of what is in the TV show)

 

The basic setup is to have a whiteboard with the instructions on it, a space marked out for the letters and numbers puzzles and plenty of space to write solutions.

Getting started

For the letters game, randomly choose four vowels from the vowels bucket, and five consonants from the consonant bucket and write them on the board.

For the numbers game, choose three digits from the target bucket, one after the other without replacement. Together these are the three digit target number, which you write on the board. (If the first digit is a 0, then you can treat the rest as a two-digit number if you like, or just rearrange so it doesn’t start with 0.)

Also for the numbers game, choose four small numbers and two big numbers and write them on the board too.

The rules

The rules of the Letters game that I put on the whiteboard are as follows:

Help to make as many and as long words as we can from these randomly chosen four vowels and five consonants. (Letters may only be used as many times as they are in the list.)

The rules of the Numbers game that I put on the whiteboard are as follows:

Help to make a calculation to produce the target, using some or all of these two big and four small numbers, and any combination of +, -, ×, ÷, and brackets. (Numbers can only be used as many times as they are in the list.)

It’s worth noting that in the original TV show, contestants can choose how many vowels and consonants they want, or how many big or small numbers they want. I dictated a specific number of everything so that we could quickly play the game with anyone who came up, or they could play by themselves if we were momentarily distracted!

Unwritten rules

There are some unwritten rules about how we go about doing the Numbers and Letters games that it’s worth making explicit.

For the letters game, small words and proper names are ok. Most word puzzles don’t allow those, but this game is designed specially for public interaction. If someone notices that they can spell Bernita or Spain, who am I to diminish their glory? Plus finding a host of small words like “to”, “of”, “for”, etc is a great start to get some words on the board, and you can often modify them to get them a bit longer words too.

For the numbers game, partial answers are ok. People do stare at the board trying to come up with the answer all in one go, and they need to realise that it’s ok to scribble some working, or have something that is close in order to maybe get closer upon modifying it. In fact, I have written about this before.

It’s also worth pointing out that the numbers game isn’t always solvable. Sometimes when it’s really tricky, what we usually do is try to get as close as we can. On the fly, it’s hard to prove it’s actually impossible, so at some point you need to call it close enough and do a new one.

On the other hand, sometimes the Numbers game is solved in the first few seconds. In that case, we usually try to find many different solutions, encouraging people to try to use different operations or more of the numbers.

Final notes

While it would probably work fine to choose the letters and numbers with a computer or app, the buckets have a sort of playful and tactile element that I really like. They also allow us to engage people passing, by going up to them with a bucket and asking them to pull out some popsticks for us. Yesterday every person I asked to choose some sticks for us came over to have a closer look at what we were doing.

I have written about my thoughts to do with the Numbers game three times in the past. I wrote about how the fact it is a game can help people participate when they otherwise wouldn’t, about how I encourage people to put partial solutions, and how I alleviated the fear caused by the numbers themselves and did something else instead.

These games have been part of the MLC and Writing Centre’s identity for five years. We do it at Open Day and also at Orientation every semester and I really look forward to it each time. For new students this sets up a  continuity between when students were just visiting university and when they arrive. For existing students, they’ll often seek us out at these times to tell us how they’re doing and engage in something that is a pivotal memory of their early time at university. Also it has become something that all the other service areas expect we do, and they come to join in as well during these events. I’m so glad people of Twitter have become interested, because it really is a fun thing to do.

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On the 23rd of July 2008, I started my first day as coordinator of the Maths Learning Centre at the University of Adelaide. Today is the 23rd of July 2018 — the ten year anniversary of that first day. (Well, it was the 23rd of July when I started writing this post!)

So much has happened in that time. I have given hundreds of hours of revision seminars, I have written/drawn on tonnes of paper, and used miles of sticky tape and chalk in mathematical artwork, and I have talked individually to over ten thousand students. I can’t possibly distill it all into one blog post, but I can talk about why I believe I am meant to be in this job and still meant to be in this job.

When I went to the interview for the MLC coordinator position, I thought it would be a pretty cool job to have. At the interview, I had the epiphany that it was not just a cool job but it was in fact the perfect job for me, the job I really needed to have. Travelling home from the interview, the thought that I might possibly not get the job made me cry almost the whole train journey. I remember praying to God that I would find out soon. They called me that very night to say I had won the position!

I still believe that this is the job I was destined to have. In no other job could I have been able to indulge my dual interest in both university pure maths concepts and fundamental maths concepts you meet in primary school. In no other job could I simultaneously help students overcome their crippling fear of mathematics and (sometimes the same students) become research mathematicians. In no other job could I make mathematical art and play an actual legitimate part of my work. Admittedly, I may have made some of those things part of my job when they weren’t part of it before, but it was being here in this role at this university that has allowed me to do so.

There are parts of the job that are annoying — interminable meetings, lecturers who take my offer of support as an affront, constant requirements to convince the establishment that what I do is important, semesterly reminders that we just don’t have enough funding to provide the level of support I think is necessary — but overall it is a most wonderful and amazing job.

When I started ten years ago, I already knew the pleasure in helping students learn, but since then I have learned the even greater pleasure of letting students help me learn. I have barely scraped the surface of learning first hand about how people think about maths and how they learn maths, and I don’t think I never get to the end of the wonder of it.

Thank you to the other MLC lecturer Nicholas and all my casual tutors for coming along for this ride of teaching at the MLC, for listening to me as I talk through my crazy ideas and plans, and for pushing me to be a better teacher and leader. Thank you to all the other staff of the university that have worked so graciously with me, especially those nearest in the other student development and support roles. Thank you to my new colleagues I have met through Twitter, who make me better as a teacher and a mathematician in so many ways. Most of all thank you to my wonderful wife and daughters for always believing in me, and tolerating my mind ticking over on work things most of the time – I could never do this without your love and encouragement.

It’s been a wonderful ten years at the MLC. I hope the next decade is just as wonderful.

Posted in Being a good teacher, How people learn (or don't), Isn't maths cool?, Other MLC stuff | Tagged , ,
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I think this will be my last post about Twitter Math Camp (TMC), getting in just before the TMC18 officially starts (though a lot of people are already there tweeting their TMC-eve adventures even as I write).
TMC is a truly remarkable conference, as I have described before, both in 2016 when I wasn’t there, and […]

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Here is another blog post in my series of only-a-year-late posts about Twitter Math Camp 2017 (TMC17). In this one I want to talk about the Crochet Coral workshops Megan and I did, but I don’t want to actually talk about the crochet coral. Instead I want to talk about the quietness.
TMC was a wild wild […]

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A year ago, I went to Twitter Math Camp (TMC) and it was a wonderful experience. TMC is a great conference full of all sorts of opportunities for maths teachers to learn from each other in many ways. The one way I like the best out of all the possibilities is “My Favourite”.
My Favourite is […]

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Fairy bread, in case you don’t know, is an Australian children’s party food.

Here’s how to make fairy bread: take white bread, spread it with margarine, and sprinkle with hundreds and thousands. Now cut into triangles and serve.
Notes:

It has to be white bread. If you try to make fairy bread with wholemeal bread, or multigrain bread, […]

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Last week we were booked in to do Human Markov Chains with several groups of school students, but it turned out there would be a lot fewer of them than we expected, and I didn’t think Human Markov Chains would work very well with under 20 students. I still dearly wanted to do a moving […]

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This blog post is about a moving maths activity that I have wanted to do for years and finally got an opportunity to do this year in 2018. It’s a model of a concept called a “Markov Chain” using human movement.
In a Markov chain, there is a thing that can be in any number of […]

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Something is bothering me about teaching at university: we are leaving the most important teaching to chance.
In most tutorials, there is an opportunity to try out things with a tutor there to talk to about it, or deep discussion of course content, or at the very least worked examples of using the ideas in practice […]

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