## Thursday, January 26, 2012

### SBG - A view from a rookie, one year later

It's almost a year now since I started using Standards Based Grading ideas in my teaching. Actually it's almost a year since I started teaching! So how did SBG work out for this rookie teacher?

 Happy Birthday : 1 year using Standards Based Grading Photo: Theresa Thomas (Creative Commons) http://www.flickr.com/photos/theresasthompson/2311733808/

SBG in your first year of teaching
Hmm .. it's a bit ambitious. There are so many things to come to terms with as a new teacher, adding SBG to the mix might be pushing it - especially if you are the first teacher in your faculty to try it out. I took the plunge - probably a little foolishly - SBG seemed just so right for so many reasons. I did at least have the sense to try a full implementation with only one year group.

Preparing SBG resources (quizzes, grading sheets) and the extra marking will take more time, something in very short supply in your first year,  but it will help you develop some critical teaching skills. Creating and using a list of standards will ensure you know the content, help you focus on what is important to teach, and provide clear direction for your lesson planning. Using quizzes on a regular basis will give you continuous feedback how your teaching efforts are translating into actual, measured student learning.  It's your first year - and you most definitely need the feedback - the sooner the better to help develop good habits. As a new teacher, you are likely still learning the basics of providing and receiving student feedback, so SBG will provide you a scaffold for these essential teaching skills. If you aren't using SBG, you will likely not find out until end-of-topic tests - which is too late to find out you were teaching it the wrong way.

Would I recommend SBG for new teachers in their first year? Cautiously - and only with support from your head teacher. Try it with only one class, carefully choosing a class that will not be overly testing your still nascent classroom management skills or content knowledge. If you don't have head teacher support or a class you feel confident with, then perhaps consider what I'm calling SBG-Lite for the first year.

SBG-Lite
While faculty and legislative constraints prevented me using a full SBG implementation with all but two of my classes, I found that even in classes where I was not allowed to use SBG for end of semester grades, I used many SBG tools while teaching each topic. Even if you can't use SBG data to determine official school grades, the information gained about a student's learning aligned to your standards provides rich data to include in written comments in school reports and in conversations with students and their parents.

So what does SBG-Lite look like? You still have standards, you still have quizzes, you still receive and give regular feedback on student mastery of the standards. The only real difference is it doesn't directly translate into end of semester grades. It's up to you to convince students their efforts to achieve mastery of standards will ultimately translate into better grades and that tracking standards and repeat attempts on quizzes are worth the effort. It's a harder sell - but you believe it - don't you? While SBG-Lite most likely doesn't help improve motivation and engagement to the same degree as a full SBG implementation (because it lacks the element of direct student control over their marks), it remains a helpful addition to the learning environment.

Of course I would like to be able to use a full SBG implementation with more of my classes, but sometimes you just have to adapt with your current system - especially when you are the new kid on the block. Pushing too hard will just trigger a response to shut down SBG in those classes where you can use it.

SBG and the challenge of "Working Mathematically"
A serious problem in most mathematics assessment practices, and consequently in most mathematics teaching practices, is an overemphasis on procedural skills development, often at the cost of understanding, reasoning and problem solving. There is a risk that using SBG amplifies this focus on skills fluency - reducing learning mathematics to a list of skills to be evaluated. But it doesn't have to be that way - it depends on the standards you use. My solution was to label my standards with the "Working Mathematically" proficiencies (Understanding, Skills, Problem Solving and Reasoning). This helped me see the balance (or lack of it) in my learning outcomes as well as offering guidance as to the different types of  learning strategies which help students master the different types of standards.

SBG: What worked ...
Can I categorically say SBG improved the results of my class? No. But I can say the class did well in their final results - most students mastered most of the standards, as shown in end of year tests, and I do know we had a very positive class environment - so I stand by a 'did no harm' claim while suggesting SBG may have led to better outcomes.

Students responded well to SBG - in their feedback they indicated they appreciated having more control over their grades. Many students and even some parents remarked at the end of the year how student attitudes to mathematics had changed from one of fear and anxiety to one of feeling able to do the work - and even enjoy it! SBG definitely helped me develop my teaching skills, providing an anchor in the maelstrom that is the the first year of teaching.

.. and what didn't work
Teaching for my first year was challenging - and that's an understatement. As the year progressed I found it harder to be consistent in my SBG implementation. In the rush to complete my teaching program, SBG sometimes fell by the wayside. I'm hoping with more experience this won't happen in 2012.

In the middle of the year, I tried using SBG with my youngest class, fresh from primary (elementary) school  but I couldn't get the class in a 'learning about learning' space and I had to give up. I'm not sure if this was because SBG is too demanding for students of this age group, or if I need more experience working with younger students - possibly the latter. I'll find out this year because I'm trying SBG again with the same year level.

One of the central ideas of SBG - being able to reassess individual standards - started to slip - most likely because I didn't promote the link between quizzes and the end of year mark sufficiently - so as the year progressed, students didn't retake quizzes. One solution would have been to use a web-based tool like ActiveGrade - unfortunately several factors conspired against this - not the least an inflexible attitude from my school district network administrators who deemed the application unsafe for schools (go figure).

Three ideas for 2012:
• SBG for the struggling, disengaged class: Like most mathematics faculties, we use so-called 'ability streaming' to allocate students to classes. As a consequence, we end up with entire classrooms of students with a well-established pattern of low mathematics achievement and high levels of disengagement, factors which typically get worse as the students progress through the school system.   Previously I was concerned SBG would be too hard to manage for this type of class, but now I realise we have nothing to lose by trying something different. I'm going to try SBG-Lite with one of these classes (unfortunately full SBG isn't an option due to faculty grading policy for this year level).
• Provide better visibility of student standards achievement: At the close of each topic, I will provide each student and their parents with a view of their grade book, making it clear to them which quizzes they might wish to retake in order to improve their topic result.
• Leverage SBG through student summary books. I have designed workbooks made of one or two standards per page with lots of blank space between each standards where students can write their own summaries of what the standard means to them.
The verdict after the first year? SBG was a valuable and helpful tool - it's a core part of my teaching practice. I'm ramping it up for Year Two!

## Tuesday, January 10, 2012

### Early morning maths will kill you - just ask Descartes!

Sorry - I couldn't resist. It's the hook I use to bring Descartes into my classroom. More below.

Do you remember the first time you encountered the idea that all those geometry concepts you had learnt for years could be expressed in algebra? How suddenly those two totally different topics in your maths classes could be viewed as one? I hope this was a special moment for you*.  At this special time, why not treat your class to a some time with  Descartes? There are many contemporary source materials on the internet just waiting to be woven together into a fascinating story of intrigue, intellectual curiosity and even the very question of our existence.

 Portrait of Rene Descartes (1596 - 1650) Louvre Museum - Richelieu - Level 2 - Room 27

Catch their attention with the story how Queen Christina killed Descartes.
I love telling the story how Queen Christina of Sweden killed Descartes by making him get up at six o'clock in the morning to teach her mathematics. Who can't relate to that story? Depending on your class and if you want to go there, they might also get a chuckle out of answering this question: which person in this picture is Queen Christina? You might like to explore the conspiracy theory Descartes was poisoned over religious turf wars. The Wikipedia pages on Descartes and Queen Christina offers some interesting starting points for further investigation.

 Queen Christina of Sweden (on the left!) and Descartes.  Pierre Louis Dumesnil (1698-1781); 1884 copy by Nils Forsberg  http://en.wikipedia.org/wiki/File:Ren%C3%A9_Descartes_i_samtal_med_Sveriges_drottning,_Kristina.jpg See also http://commons.wikimedia.org/wiki/File:Dispute_of_Queen_Cristina_Vasa_and_Rene_Descartes.png

And now we have the class interested ...

Show the big picture: Descartes was interested in much more than just maths
The amazing thing is Descartes' work on analytic geometry first appeared as an appendix in a much larger book: The Discourse on Reason. I like to show students some of the images from the Geometry appendix.

 A search on Google images for "Descartes La Geometrie" will turn up many photographs of early editions. Personally I think students find this more interesting than just seeing reproductions of the diagrams.

and then take a look at the actual physical form of the original book. Here's a first edition auctioned at Christie's in 2010 for US$76,000.  2010 auction at Christie's http://www.christies.com/LotFinder/lot_details.aspx?intObjectID=5371784 After we finish gasping at the price, I show the students how they can get a free copy of the book in digital form at Project Guttenberg. A student in my class who was studying French helped us read the title and explained it to us (much to the cheering of her peers). Discours de la méthode pour bien conduire sa raison, & chercher la vérité dans les sciences. Plus la Dioptrique. Les Meteores. Et la Geometrie. Qui sont des essais de cete Methode. I love the intonation and literal sequence of words French - pour bien conduire - to well conduct reason, and to search for the truth in the sciences. It's a lofty aim. Descartes the scientist. Other appendices in the Discourse are on optics and astronomy. My students were fascinated how Descartes extended his observation how boats moved in a river to an explanation for the movement of astronomical bodies in a 'sea' of vortices. His ideas on vision and how the brain interprets the senses provides a rich opportunity to engage with students on questions of knowledge**.  The mind-body interface in the pineal gland watches the image formed on the retina (just like watching TV), and then orders the hand to move. Descartes the philosopher : Je pense donc je suis. Descartes said it in French first (1637) - unusually for the period - the Latin Cogito Ergo Sum came later (1644). "I think therefore I am" is the usual English translation. Can you explain the idea in your own words for your maths class? Check out the Wikipedia page on Mind-Body dualism and Cogito Ergo Sum for starters. For me the most interesting aspect is that it's not actually an argument that we exist, but that something we call our mind exists - the rest of our body and the world around us might not be real. I was pleasantly surprised how much my mathematics class took to even a surface discussion on the question of how do we know that 'we', or 'the mind' exists. I'm not a philosophy teacher and we did need to move on to the mathematics, so it was only a brief exploration, but I could see it was an important and possibly rare opportunity for students to go there. I suspect we seriously underestimate the need and interest young people have for engaging with deeper philosophical questions. And mathematics offers a window, or at least one introductory path, to this place. Is Descartes responsible for vivisection? This little twist is interesting and engaging: the Wikipedia article on Descartes suggests his view that animals don't have have a mind, and thus no feelings, was responsible for centuries of believing it was fine to do live animal dissections. I guess he never had a cat or a dog? Do pay a visit to Descartes next time you are in Paris. It turns out the famous portrait of Descartes (see above) is in the Louvre Museum (Richelieu 2nd floor, Room 27). I told the class I was very disappointed to discover this only this year, because in all my trips to the Louvre I had never seen the picture. I asked the students that when they went to the Louvre (and I assured them they would all eventually visit Paris!), could they please go and have a look at the picture for me and send a postcard. So what's the point of this Descartes' distraction? I spread this material over several lessons as a short element in each lesson during our first week of coordinate geometry. I have absolutely no evidence or make any claim it helped the class learn the content better - but I do hope it helped them see some of the people and worlds that produced the mathematics they are studying - and maybe encouraged them to explore further. Mathematics is not just concepts and skills - it's part of our culture - our never ending exploration of the intellectual and natural world, which that rightly belongs in our classroom. More resources: "Frogs and Birds" - the great Freeman Dyson muses on the differences and synergies of Francis Bacon and Rene Descartes. * There is a down side to this algebraic seduction - something I'll explore in a later post when I look at the ideas of another amazing mathematician, Michael Atiyah. ** Can't help it - just love that 'e' word (epistemology) ## Saturday, January 7, 2012 ### From rows to groups : meeting the challenges In this final part of the series on changing the classroom desk configuration from rows to groups (see Part1 and Part 2), I consider some of the challenges resulting from the changeover. Learning together about working in groups I’m still in the early days of learning to be an effective mathematics teacher, and arguably learning how to manage group activities introduces another level of complexity. One thing I did realise early on was the need to be explicit with students about the reasons why I rearranged the desks and we regularly discussed how to make the group configuration work better. I also asked students through my anonymous class surveys for their feedback. They told me they appreciated the group configuration, but did highlight areas I need to work on. Their main concerns were: that the group seating encourages them to be less focused; that sometimes it was hard to work alone without being distracted; and that during whole class instruction, the layout sometimes made it hard to see the teacher. All of which begs the question - what about when we aren't doing group work? How does the group configuration work with Direct Instruction? As summarised by Hattie (2009), Direct Instruction occurs when “the teacher decides learning intentions and success criteria, makes them transparent to students, demonstrates them by modelling, evaluates if they understand what they have been told by checking for understanding, and retelling what they have been told by tying it all together with closure” (p. 206). Two other key elements are guided practice (in class) and independent practice (outside class). Hattie reports that Direct Instruction has one of the highest effect sizes (d=0.59) of all teaching strategies, so it remains an important tool in our kit - especially when understood as something other than just lecturing at students. A learning program designed exclusively on group activities has the potential to miss out on teacher modelling and guided practice, demonstrated to be particularly important when developing procedural knowledge (Marzano 2007, p.80) as well as opportunities for review*. Hattie is clear however that we do not need to choose between teacher-centred teaching or student-centred learning – we can and should achieve a blend of the two approaches. So in this mixed-mode teaching environment, the classroom configuration needs to support Direct Instruction. When it's time for guided practice, the group configuration does seem to be at a disadvantage to the row configuration, it seems to require more effective classroom management skills to ensure students can work without distractions. To help with the classroom management, I have two standalone desks on the side and move students who can’t focus to those desks temporarily. When it comes to teacher modelling – usually most efficiently done as whole-class instruction – the group configuration can make it harder for students who are ‘side on’ to see and hear clearly. I’m still working on optimising the sight lines for some desk and will experiment this year with students turning out their desks as needed. So is rearranging the furniture worth it? Moving from rows to groups is certainly not without challenges, and the mere act of physically moving desks doesn’t magically transform teaching and learning. However it seems provide strong support for the outcomes I seek: learners working together, solving problems, sharing their learning and hopefully enjoying their time in math class. Looking at the bigger picture, I’m aiming to create an environment where students manage their own learning and develop the skills and inclinations to work effectively and creatively with others. These are the critical skills that will help my students in their future lives, more than their ability to factorise non-monic quadratic expressions (as much as I think that’s important!). References Hattie, J. (2009). Visible Learning : A synthesis of over 800 meta-analyses relating to achievement. Oxon : Routledge. Marzano, R. (2007). The Art and Science of Teaching. Alexandria, VA: ASCD. Update and a warning.... There is some research that strongly advises against arranging desks in group cluster. Here is an article from the Guardian that points at the work. Need to do some more thinking ... Here is post by Pak Liam with a different take Classroom desk arrangements; Rows, Clusters or U Shape? * This year I’m planning for students to take turns to perform the role of conducting reviews for the class – Reciprocal Teaching (d=0.74 !) More than one way to bake this cake! ## Friday, January 6, 2012 ### Rearranging the desks (Part 2) Why you might consider rearranging the desks in your high school mathematics classroom from rows to groups? In Part 1, I suggested that by doing so we emphasise to students that a central theme for the class is that "they are their own teacher", at least as much as the adult standing at the front of the classroom. Let's consider two other ideas: how changing the configuration might help reduce maths anxiety, and how it might affect the teacher.  The funny thing is our primary (elementary) school teachers have known this for more than fifty years. What makes middle and high school so different it doesn't apply? Reason 2: To create a positive environment that reduces "maths anxiety". Most mathematics teachers will have one or maybe two "high achiever" classes per year. The remaining classes have students ranging from those who dislike and struggle with mathematics to those who tolerate it and just want to get through the next fifty minutes without too much being demanded of them. In addition, for some students, mathematics creates high levels of anxiety, and, as I’ve come to discover, this anxiety is also present in high achieving classes, arguably in even more harmful forms because these students may define their self-worth by their current success at mathematics. Before I can even begin to hope for high quality learning outcomes, I need to face this challenge. I am inspired by the words of Lindsay Grimison: "We must change the mathematical experiences of so many school students who regard the subject with a mixture of fear and loathing tinged with perceptions of failure and irrelevance". It seems to me that unless our students can be made to feel welcome in the mathematics classroom, that it is a place where they can enjoy learning, we won’t get off the starting block. Collaborative group work is far less threatening than whole class discussion - no-one is put "on the spot" in front of the whole class. Students are more likely to take risks and ask questions of their peers. Now I’m not saying a classroom with rows is unwelcoming – but I do feel the group configuration helps develop and sustain a positive environment. I want everything in my kit that can help me with this challenge. Reaons 3: To encourage me to change my teaching practice. What message did I receive when I walked into my classroom with its rows of desks? The whole class is looking at me – I’m the centre of attention. As much as I wanted to include more student-centred activities, I found myself talking more and more – becoming the lecturer that my decades of schooling tell me that’s what teaching is. In contrast, facing a classroom organised in a group configuration forces me on a daily basis to evaluate what I am (or am not) getting students to do. You just can’t keep up the lecturing for long stretches when the desks configuration is just screaming out to be used for collaborative student work. On a very practical level, with the row configuration I found it difficult to spend quality time with each student. There were fourteen or fifteen pairs of desks to stop at. Even allowing just two minutes per stop (hardly quality time), that’s more than half the period gone. Meanwhile there are students on the other side of the classroom, desperately waiting for me to visit them. The students sometimes seemed so dependent on me it was like they were helpless unless I was at their desk, answering their questions. And yet – sitting right next to them, or behind or in front of them, was a student who could help them. What I discovered when I moved to a group configuration, was I only needed to visit seven desk groups – making it easier to spend time with more students, to listen to them talk about and engage with mathematics. And because I could encourage students with unresolved questions to work with their peers, I could move to another group without leaving those students unsatisfied. If it sounds like a cop out to expect other students to do my teaching for me, I take heart there is very strong evidence that peer tutoring helps the tutor as much as the tutee – it pushes their learning further when they have to deal with misconceptions held by other students. So arguably, the group configuration encourages me engage more with students, to help students to help each other and helps me find out more about what is actually happening in my classroom. If I’m at the front talking all the time – or spending one to two minutes with each student (if that) – how can I find out what they are doing, beyond just assessing their final products of the lesson? In the final part of this series I consider some of the challenges posed by the group configuration, ask where Direct Instruction fits into this arrangement and look at the bigger picture beyond learning mathematics. References L. Grimison & J. Pegg (Eds.) (1995) Teaching secondary school mathematics: Theory into practice. Sydney: Harcourt Brace. ## Thursday, January 5, 2012 ### Rearranging the desks: from rows to groups At the beginning of Term 4 in 2011, I took the plunge and did this to my classroom: When I first reconfigured the desks in my classroom from rows to groups, it was a leap into the unknown. Two factors pushed me to make the change: feedback from students that I was talking too much; and participating in some group activity sessions at the MANSW 2011 conference run by the incredible Charles Lovitt, which so clearly demonstrated to me the power of doing something different from lecturing in the mathematics classroom. The change has not been without challenges, and I’ve been doing some hard thinking if I should continue using the group configuration during 2012. In the next few posts, I’m going to discuss why I’ve decided to stay with my group configuration, and then consider some of the challenges raised by the change, ask where Direct Instruction fits into the picture and finally think about the bigger picture beyond mathematics (yes - surprisingly there is one!). Thanks to the many colleagues on Google+, Twitter and the AAMT mailing list who helped me reflect on this and consolidate my thinking. Reason 1:To make the idea that the "student is their own teacher" central to my classroom What message do high school mathematics students receive when they walk into a classroom with the desks arranged in groups? My hope is the message they receive is that in this classroom, an important part of learning mathematics will be working together. It’s possible they may also think the teacher is a bit odd, or that this reminds them of primary school, or that this is going to be a great opportunity to have a chat for the next fifty minutes. Hopefully these less helpful messages are dispelled once students receive a clear message I'm serious about using class time for learning and working on mathematics. The benefits of peer learning are clear and measurable. John Hattie (2009) reports highly ranked effect sizes for Peer Tutoring (d=0.56) and Cooperative versus Individualist learning (d = 0.59). In Hattie’s description of his synthesis of best practice, he writes: "The remarkable feature of the evidence is the biggest effects on student learning occur when teachers become learners of their own teaching, and when students become their own teachers. When students become their own teachers they exhibit the self-regulatory attributes that seem most desirable for learners (self-monitoring, self-evaluation, self-assessment, self-teaching)" (p.22). In contrast, what message do students receive when they walk into a classroom of rows of desks, all lined up to face the front? The predominant message is mathematics is a solitary activity, you will learn it from your teacher, you will practice and internalise it on your own. Don’t get me wrong - in no way am I saying I want to totally abandon teacher led instruction. As Hattie points out there is an important place of Direct Instruction, however I think the message of students taking control of their own learning is so important I want a desk configuration that reinforces it. What do you think of this reasoning? Part 2 considers two other reasons for staying with the group configuration: because it creates a positive environment that reduces "maths anxiety", and because of the effect it has on my teaching. References Hattie, J. (2009). Visible Learning : A synthesis of over 800 meta-analyses relating to achievement. Oxon: Routledge. ## Tuesday, January 3, 2012 ### Bringing Marcus du Sautoy into your classroom I've had a wonderful helper in my classroom during 2011 - although he's totally unaware of it. Whenever I needed a high quality video to explain or demonstrate concepts, or just wanted an entertaining break that was still directly relevant to the mathematics curriculum, it was time to bring Marcus du Sautoy's BBC program "The Code" into my class. My students absolutely love the program. Without fail, even if I had a class that wasn't in the mood for a maths video, if I could get to them to watch just a few minutes (see teacher tips below), they were hooked. So why would you want to bring Marcus into your classroom? Apart from his incredible enthusiasm (which students respond to well), he shows mathematical ideas in action, in the real world, in surprising and engaging ways.  Original image from The Code Episode 3 (c) BBC with annotations. No copyright infringment intended. Some of the segments show things we should already be aware of as mathematics teachers, but with his (and the BBC's resources) we can actually see them. Other things are so different and quirky you marvel at de Sautoy's ingenuity and inspiration to present the material this way. For teachers interested in making links between mathematics and science, as well as mathematics and critical thinking, The Code has an underlying message of rich and deep significance which at least some of your students will respond to. Here are some of my favorite sequences: • Marcus goes to the fish market, asks a very solid fisherman about his day's catch, then pulls out his iPhone to do some calculations and predicts the size of the biggest catch the fisherman ever made. "We call them doormats!" the fisherman beams back. And all with the purpose of showing the number π appears in places not necessarily related to circles! • The amazing expert bubble blower (my students were thrilled there was such a profession!) who makes a dodecahedron out of bubbles - no kidding! • An explanation of how Jackson Pollock's art links to fractals. It turns out my students were already making Pollock style pictures in art class, so I'm planning a joint lesson with our art teachers next year to combine the art and the maths. • Marcus puts his life at risk sitting in the path of a 30kg metal ball. Now there is faith in the accuracy of your mathematics! • Marcus debunks the myth of the suicidal lemmings. Someone at Disney Studios has some explaining to do! and there are many more wonders to enjoy. One challenge with using a program like The Code in a classroom is that it's three hours long - and I'm really not comfortable with students sitting in class passively watching even one full episode at a stretch (in normal circumstances). It's not very good pedagogy and we really don't have the time - the curriculum and teaching program waits for no-one (sadly). So my approach was to show ten or fifteen minutes segments at appropriate times in the teaching sequence. The next challenge is to remember which sequences and topics are covered by The Code, and where they appear in the three episodes. During the holiday break I've finally kept a promise to myself: to catalogue, by syllabus topic (loosely) every segment in The Code, with time sequences so I can quickly get the pieces that I want. If like me you're a fan of The Code, you might like to download this analysis and fit it into your planning documents. The Code - Content Analysis Teaching Tips • Some classes (especially those who don't like mathematics) will really resist watching a maths video. Probably because they've been forced to watch some hideous videos in the past. For these classes, I make a promise at the start : "Let's watch the first five minutes - if you hate it after that, I'll turn it off". I've never had students turn down watching more of The Code. On the contrary - I have a hard time stoppping the video before the next segment starts - they are hungry for more. Usually I relent for at least one more segment (if I see it's a genuine interest and not a way to avoid work!). • Does "end of the year" silliness happen at your school after reports are done and the official program is over? Where students end up watching "The Lion King" and "Kung Fu Panda"? No need to put up with that in your class - time to watch a whole episode of The Code. If they have only seen segments, they will enjoy seeing the whole picture. If not, go for it! Getting The Code • A Region 2 (UK) DVD is available from the BBC and Amazon UK. Excellent news : Region 4 DVD coming to Australia Feb 2012 (thank you SBS!) • Some extracts are available on BBC You Tube site. • BBC Online appears to allow UK based browsers access to the program online. When I visit, I get a "Not available in your area" message . Hear the sound of my teeth gnashing. If you like using maths documentarys in class, consider also Bronowski's Ascent of Man. I've written a content analysis of his Episode 5: Music of the Sphere in an earlier post. ### Building confidence in maths class with SET! A few months ago, a friend asked me to look after her 9 year old daughter for an afternoon. I was scrambling for things to do - and rummaging through my cupboards found a deck of cards for the pattern matching game SET! At the time the young girl was struggling with mathematics, so I wasn't sure how she would take to it, but to my surprise, we ended up playing the game for hours. I knew I was on a winner - I rushed out to the games store and bought three more decks with the intention of seeing what would happen if I tried SET! with a class of teenagers who really disliked being in math class.  SET! is a pattern matching game which initially really hurts your head. Find sets of three cards where for each attribute (shape, colour, quantity and fill), that attribute is either all the same or all different. Try it online at the New York Times SET! puzzle page. At first they didn't want to try the game. I didn't force it, but eventually one group of students decided it might be more fun than regular class work and were willing to give it a go. Working out how to play SET! does take a little time and I wondered how patient they would be with it. For a while it looked like it might not work, and then suddenly one of my least engaged students - who repeatedly told me she can't do maths - started finding all the patterns. Suddenly the competitive nature of the students kicked in. Other students started asking to be taught the game. Over the next few weeks, most of the class was lured into the game. For higher achieving mathematics classes, you won't need any subtlety to introduce SET! - they will take to it like ducks to water - marvelling at the elegant simplicity of the game that manages to hide so much variation and complexity. A key feature that makes SET! so engaging is there are many different types of sets (patterns) to find in the deck. Some are fairly easy to spot, others are quite complicated. This means that students at different skills levels of the game can play together - there is something for everyone. Once the weaker students start having success finding the easier patterns, they get more involved and before long most are finding the harder patterns. Bringing SET! into the classroom gave some students for the first time (I think) a tangible demonstration they could succeed at challenging mathematical tasks. They knew it was a game that required skill, patience and some strategy to master, and some of them were absolutely fantastic at playing the game. As a teacher, I was amazed to see students who usually had an almost non-existant attention span, starting intently and silently at a set of cards for minutes at time. Highly recommended - give it a try! Teaching Ideas • Start off by reducing the deck to cards of only one colour. This reduces the complexity of the game by one dimension. Warn the students it will get "much much" harder when you put in the rest of the deck (and it will) - but they will soon be begging for the harder version. When they do get the full deck it will hit them hard - but by now they are hooked :-). And when they do master the full game - the pay off is sweet. • Ask the students to describe and name the card attributes. Let them tell you. Ask the students to choose names for the shapes. Once they name the shapes with their names, it becomes their game - use their terminology as you play the game. I like to share the names my 9-year old friend gave them: diamonds, peanuts and airplane windows. And I find using slightly childish names for the counts ("onesies, twosies, threesies") adds to the fun and reduces any stress students may feel about a maths game. • Have a 15 second time out rule : If one student in the group is finding all the sets, put them on a 15 second timeout to give others a chance to learn the game. • Go gently. Don't over-emphasise the logic elements - allow students to develop the idea over time that logic and strategy will help them locate patterns more efficiently. Some lower achieving mathematics students will be intimidated by the game - I found a gentle approach, and allowing them to watch others play worked well. Their friends will encourage them to play - you don't need to. It's wonderful to hear students who initially told you the game looked stupid now encouraging other students to learn it with them. • Choose your time wisely to discuss pattern finding strategies. Don't rush it - wait until they are really hooked. It doesn't matter it they don't find all the patterns - deal out some more cards. When students are ready for it, I like to rearrange the face up cards into number groups while discuss pattern finding strategies. • SET! makes a great activity to use a 'group rotation' style activity session where you have different activities at each table and students move around the classroom. You may find SET! takes longer than your other activity and counts for 2 time slots in the rotation (so make two tables). • Put an interactive SET! game up on your Interactive Whiteboard. Once students have mastered the (physical) card game, try the online version. The New York Times offers 4 SET! puzzles each day, 2 basic and 2 advanced. Invite groups of students to come up to the board and solve them. Could also make a good reward for students who complete work early. • The SET! website has some interesting mathematics teacher resources about SET! There are many high quality investigations students of all levels could be encouraged to try out. Purchasing SET! • Amazon sells SET! at good prices - around US$12. Unfortunately they will not deliver this product to Australia. In Sydney, Games Paradise (Pitt St) sells them for around AUD\$20 - and good to support this friendly and helpful specialist shop.
• One pack will keep around four students occupied. 3-4 packs for a classroom is enough as not all your students will be playing SET! at once.