The wisdom of Year 7 : thinking about groups

It's been nearly a year now since I changed my classroom configuration from rows to groups:

Overall I'm very pleased with the results - it's working for almost every class. The one class where I have wondered if I should revert to rows have begged me not to - challenging me to think more deeply about my classroom management for this class - I'm working on it! But there is no looking back now. These insightful comments from my Year 7 students, given as anonymous student feedback, reveal the benefits and challenges of setting up group tables.

Group Table Configuration : The Good

"Helps with learning because always someone u can ask 4 help"

"You can ask for help when the teacher is busy"

The group configuration helps deal with the challenge of answering questions from thirty students at once. Sometimes the group may come up with the wrong answer - but I rarely see this happen and am much more likely to detect any misconceptions if four students share them. What I do see on many occasions is students debating the answer, and they will ask for help if they aren't sure of their answer.

"Interesting learning from different perspectives"

Students discover how their peers view and understand the content - enriching their own understanding, and providing opportunities to develop metacognition : becoming aware how knowledge is obtained and processed.

"Let's me compare my answers and help people"

A powerful gift to offer to students : creating an environment for helping each other - developing generosity. One of my four pillars from the Circle of Courage.

"It helps cos if u don't understand something and 2 shy 2 ask u can ask ur friends" 
Wow! How many students are held back because of this? A powerful insight on how a group table structure can help overcome emotional, personal and social barriers to learning.

"No need to be a loner - there are people around to help and support"
"Being alone is lonely"
How can we know the emotional needs of all students - let alone be able to help thirty students? Sitting students together, supporting them during class time to be together may just turn out be very important to some students who might be alone at other times. I was moved to read these comments.

Group Table Configuration: The Bad
"I would like to sit with different people"
I'm still uncertain if it's best to organise students or let them self-select groups. I worry about bullying and social exclusion, allowing students to set up hierarchies "you are in my group, you aren't". For now my answer is I assign the groups for Year 7 and Year 8 - and consider any problems on a case by case basis. A part of me also thinks it's important I maintain control of the seating.  Any ideas welcome!

"I can never see the board properly"
Ouch. This is the biggest issue  - and I think it's serious - especially since perhaps 30% of my lesson time is whole class instruction. Research that argues for sitting in rows claims this is the major problem with the group configuration. There are four seats in my configuration where this is a problem. I wish my classroom was wider to optimise the layout, but some tables don't get a good view of the board. I'm now going to establish it as a norm that those four students to turn their chairs to face the board during whole class instruction.

"Sometimes people just give you the answer"
An insightful comment from one student! Group configuration discourages solitary work - which is essential at times - and allows for students to just give each other answers. I often use an A/B/C/D paper approach to ensure each student at the group table has a different set of problems to work on - getting help has to be real help, not answers. But time doesn't always permit this, and if we are using the textbook, they are working on the same questions. I think I will need to be more explicit with students about ways of helping to maximise the learning.

Something not mentioned in the feedback is groups can encourage off-task behaviour and conversation. Fortunately with this class, that's not a problem - when they do go off-task (they are students!) they respond quickly  to my request to get back to mathematics. This isn't the case with all my classes - more on that in another post.

The Verdict?
Unquestionably (for me) : Yes. The learning and social benefits are so high, it's worth persisting to deal with, or minimise the down sides.  I'm looking forward to seeing how the comments next week from the class where I am having some class management issues will compare to those quoted above.

Note: My student feedback forms have an Opt-In indicator "Tick if you are OK for these comments to be shared with others". The forms themselves are completely anonymous, allowing for students to give me frank feedback without concern for any consequences.

A visit to the Function Zoo

Do you remember your early encounters with the animal kingdom? So many wonderful different animals - it may even have been a bit overwhelming at first. But very quickly we learnt to group the animals into a scheme that made sense to us. In mathematics we have a similar extravaganza of different 'animals', which can be overwhelming for students to make sense of. Enter the idea of The Function Zoo - first introduced to me by Mary Barnes in her amazing Investigating Change books.

Here is how I worked the idea into a Year 11 class, several lessons into the Functions topic:

A look at the different species of animals ....

... and how we might organise them.

The challenge:

Students worked in groups of four, using large sheets of butcher paper to sketch their ideas. There were at least two laptops per group and the students had just enough GeoGebra skills to be able to turn algebraic expressions into graphs. 

The results were incredible: great conversations between students about functions. With GeoGebra on hand, I was able to encourage students to explore their questions, rather than give them answers, and even ask them more questions if they were ready for it.

Twenty minutes later I quietly threw this slide on the screen but otherwise said nothing:

The groups noticed it soon enough - and went wild. Seeing a few more functions they knew but had forgotten gave them new energy to keep going. Others asked each other questions, trying to work out the graphs they didn't recognise.  Most recognised the last graph from our "explore your calculator" game. We then debriefed as a class, and explored why the idea of the Function Zoo is helpful and interesting. Apart from the obvious benefit of being able to organise our thinking, the real benefit comes in being able to make connections - as I suggested in these slides:

As often happens in student exploration activities, the class produced something unexpected, a gift from them to extend the lesson idea.  One group drew the absolute value of a quadratic function - a blend of two of our function families. We decided this new function was like the cross-species breeding you sometimes see on display at the zoo : the lion bred with a tiger to make a liger.

Absolute value of a quadratic function : a "liger" in our function zoo.
Liger drawing: St Hilare (1772-188). Function by GeoGebra.

A fun and powerful idea - allowing students to see that even quite unusual functions can be seen as blend of function attributes they already know how to work with.

Download lesson slides & annotations: (Google Drive)  PDF  PowerPoint

Teaching Notes:

• A graphing tool makes a huge difference to the success of this lesson. Without it, students would spend a very long time plotting to explore their ideas. There is time for careful plotting later - this lesson is about seeing the bigger picture.
• I found the group structure allowed for a high degree of differentiation - I could customise leading questions for each group, depending where they were up to on the functions journey.
• I can't stress enough the value of developing students' GeoGebra skills (or other computer graphing application) when doing mathematics at this level. I sneak some GeoGebra learning into every lesson - even if it's just the class watching me do a quick check of an equation or a graph. Show them one small GeoGebra idea per lesson and by the end of term they will know the product well - especially if they are using GeoGebra at home as part of their study.
• Why am I such a GeoGebra fanboy? Most importantly because all my students can download a copy to use home. GeoGebra is free and runs on Windows and Macintosh and it doesn't need an internet connection to run.

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!

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.

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.