Things I Learned about Marking, Students Collaborating, Diagnostic Questions, and Students’ Reasoning (Notes from the Maths TeachMeet in Kuala Lumpur)

The maths TeachMeet in I attended today at Alice Smith School in Kuala Lumpur was inspiring. I attended sessions about marking (by Denise Benson from Beacon House School), a collaborative KS3 scheme of work (Phil Welch from Alice Smith School), things learned from Craig Barton (John Cartwright from Garden International School), and ways to deepen students’ reasoning  talk (Simone Dixon from Tanglin Trust School).

I also led a workshop about career progression for teachers (materials here). One of the tips I give is about reflective journaling. I recommend starting a blog, for instance. Someone asked me about my own blog and I realise I should probably practice what I preach and write some posts. A good first goal would be once a month since I’m currently writing a lot less than that.

Smart Marking (by Denise Benson from Beacon House School)

My main takeaways were twofold, one of which is not even about marking. First, exit tickets are the way Denise marks because it provides her with feedback for the planning and teaching of the next lesson and because it’s immediately useful to the student as well to see if they understood the lesson. I was struck that it would make them easier to have a little pre-printed form that they use and then the next lesson they could stick it in their book (if I deem that it would be useful for them to keep them). The scribbles below are a mock-up from my notes; hope you can read them!

Secondly, teachers complain about marking because they don’t have time. But actually teachers give up lots of time for lots of things, for example, reading teaching blogs, writing worksheets, or going to a TeachMeet on a Saturday. The problem with marking is that it’s not always a good use of time. Denise was saying that we should find a way to make it quicker and worth the time it takes.

She left us with a brilliant question.

A collaborative KS3 scheme of work (Phil Welch from Alice Smith School)

We had some good background discussion first about what KS3 looks like in each of our schools (using a Padlet). But I shall skip forward to the thing that struck me: Phil has capitalised on a timetabling quirk in that the whole of year 7 has maths at the same time. Thus they can have one week a term in which the students do a collaborative project in mixed groups. Also, the school has pairs of big classrooms with sliding doors between so they can squish a whole year group in for introduction or closing sessions. They also have a lot of breakout/corridor space for groups to work on projects. Really, this is such a great idea that works thanks in part to the brilliant facilities they have at Alice Smith School. Collaborative projects would still work in my school but would be a bit messier.

Highlights of the things learned from Craig Barton (John Cartwright from Garden International School)

Craig Barton was already one of my maths heroes but this feeling was intensified. John attended some CPD with Barton recently and in this 45 minute workshop he shared some of the highlights. It’s clear that I have to spend more time getting to know and using the Diagnostic Questions and Mr Barton Maths websites. John even said that all the classroom examples he uses on the board are now taken (via screenshot) from Diagnostic Questions. They are so good because the four multiple choice answers each stem from a common misconception.

Ways to deepen students’ reasoning  talk (Simone Dixon from Tanglin Trust School)

I was intrigued by the idea of multiple representations today – something I thought that I had considered before, but maybe I had not! Ha. Why do the triangles I draw on the board always look the same? Why are my fraction drawings always of 2D shapes? She showed this lovely example (poor picture alert) of fractions of a cuboid.

I’ve been lucky enough to go to a similar session by Simone in the past (we work at the same school). She mentioned both times an idea that I think would work for me. Put up questions around the room and ask for ‘silly answers’ to be written on them. For my students, who are older than hers, I might rephrase this to be ‘answers which look plausible but are actually not right’. This connected in my mind with what John said earlier in the day about having his students create diagnostic questions – complete with three wrong answers that each stem from a single misconception. Students have to really think hard about a concept to understand the misconceptions that others might have about it.

 

Besides these four sessions, I also enjoyed good chats with lots of thoughtful maths teachers. I always feel more energised and encouraged after a day like this one. What has encouraged you lately?

Which is More Valuable: Getting or Giving Feedback?

Students can get feedback from me, their teacher, when I mark their work or talk to them in class.

Students can give feedback to me when I ask them about their learning.

Which is more valuable for student learning? According to an article I was reading today, getting feedback from students is more powerful than giving students feedback. Cris Tovani argues that when teachers obtain feedback from students they can make changes easily to subsequent lessons, and this leads readily to improvement in the students’ performance. Tovani is a reading teacher, so here are a few ideas from me to help get feedback from students.

Three Minute Feedback

I do love this strategy and it’s the only thing I’ve continued doing since the very first teaching I did at university. (Sometimes I forget to use it, though, for months at a time. Does anyone else have this problem, even with great ideas?!) See here for an example when my IB SL students were preparing for a test; see here for an example when students were learning to expand brackets. Here’s one I prepared for my year 9s for tomorrow; they are revising for a test. Tovani says that after she spots the patterns in her exit tickets, she throws them out – it was freeing to read that.

3 minute feedback revision

Looking for Themes in Book Marking

When I take in a set of books (or tests), I jot notes to myself about commonalities among the students’ work to see on which topics they need help. If it’s just a small group of students who need help with factorising, for example, I might invite them all around one table when the class are working on something.

Quick Quizzes

Short quizzes with only a few questions that can be done at the end of class let me know if a concept from earlier is still secure. For example, I gave a four question trigonometry quiz to my year 10s a few weeks ago (and discovered that I need to refresh their memories about the difference between trigonometry and Pythagoras). I would like to get into the habit of using more mini quizzes.

 

Giving and Getting Feedback

Each of these examples allow students to give me feedback about their learning but they are also a means of the students getting feedback from me. In the case of the Three Minute Feedback, they have the chance to reflect on their learning and identify what they need to do next. With book marking, I have been challenging myself to only write questions to prompt thinking that will help students improve. In the case of quick quizzes, I provide detailed exemplar solutions afterwards for them to see and analyse. Thus students know where they are now and how to improve.

Which do you find easier in the classroom: giving students feedback or getting it? Tweet me (@mathsfeedback) or comment below.

Fingers, Maths, and Music

To return to Trninic’s idea about body movement in maths, I was reading an article by Jo Boaler which mentioned students who count on their fingers. Boaler quoted a study which said that students see a representation of their fingers in their minds when calculating. Another study looked at finger perception – whether students know what finger is being touched when they can’t see. Amazingly, young students who get training on how to perceive and represent their own fingers go on to do better in maths. In fact, in six-year-old students, finger perception was a better indicator of maths performance than tests of cognitive processing. Boaler posits that this is also why some people are who are good at music are also good at maths.

[Sidebar: I’ve certainly known a lot of people who are great at both maths and music. I have quite a few in my department now. I had a friend who did joint Honours at university in maths and music and wrote a thesis that connected both. Recently I’ve seen some good IB Internal Assessments about harmonics and chord structure. Does this ring true with you also? (Punny!)]

Boaler has developed some activities for young children (pre-kindergarten/nursery) to increase finger perception. I would love to hear from anyone who works with younger children and tries them.

finger perception Boaler

Exploratory Practice

Recently I have been reading and learning about exploratory practice, thanks to a very interesting talk and a few articles.

Movement in Maths and Exploratory Practice

Last week I went to a talk at the Singapore National Institute of Education. Dragan Trninic was talking about how maths can be learned through bodily movements. He has done some work on proportional reasoning in which students raise their two arms to different heights above the desk while looking at a coloured screen. The screen turns green if the students raise their hands in a certain proportion, for example, if the right is double the height above the table as the left. (Read more here [pdf].)

exploratory practice notes_opt

Trninic was explaining that he designed his study to see if the physical experience would help students understand proportions better. (It’s such a hard thing to teach and understand.) He wondered if practicing in this way – he called it exploratory practice – would prove valuable. And it did.

By responding to questioning from the researchers, the students were able to voice their findings. This helped them develop an understanding about proportions.

Trninic linked this kind of exploratory practice to the way people learn dance or martial arts. In those disciplines, students learn through a collection of sequenced movements, making improvements as they go. Trninic was careful to distinguish this from the kind of repetitive practice of a single skill that we sometimes use in maths classrooms; that kind of practice doesn’t include any variation and hence students learn efficiency and speed for the atomic skill. Exploratory practice, on the other hand, is set up by the teacher in a way that students are asked to learn as they go by trying to generalise.

Shanghai Maths and Procedural Variation

This reminded me of some reading I have been doing about procedural variation. In the UK, there has recently been a two-year-long teacher exchange with Shanghai. Sue Pope and Mike Ollerton wrote in Mathematics Teaching 250 (ATM members’ access required) about their experiences with secondary maths teachers from Shanghai in the UK. They recount that they were asked to read an article in advance: “Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics” by Lai and Murray (pdf, free).

The article by Lai and Murray quotes international maths comparisons that show that Chinese learners have a very secure understanding of the mathematics they have learned, and that they can apply it. Yet some Western onlookers say that mathematics education in China is characterised by rote learning or passive transmission. Without an explicit focus on conceptual understanding, why can Chinese students understand and apply maths so well? Lai and Murray aim to illuminate the “paradox of the Chinese learner” by describing the teaching as procedural variation.

Carefully Constructed Exercises

When teachers in China use procedural variation, they set up a carefully constructed set of examples or experiences for students, who are then expected to attend to essential features and notice connections. The tasks are chosen help learners to create generalisations, and are sequenced to help this occur.

The article includes an example about the teaching of division involving decimal numbers. This series addresses the misconception that “division makes smaller” and invites students to form a new conclusion about division.

Problem 1: There are 9L of apple juice and every 3L is put in a jar. How many jars are needed?
Problem 2: There are 9L of apple juice and every 1L is put in a jar. How many jars are needed?
Problem 3: There are 9L of apple juice and every 0.3L is put in a jar. How many jars are needed?
Problem 4: There are 9L of apple juice and every 0.1L is put in a jar. How many jars are needed?
Problem 5: There are 9L of apple juice and every 0.05L is put in a jar. How many jars are needed?

In this series of tasks, the total amount of apple juice was kept constant while the amount in a jar was varied from a whole litre to less than a litre. This exercise might be considered rote drilling if computing for a correct answer is the focus. However, an experienced mathematics teacher will organise this series of tasks hierarchically and provide scaffolding to illustrate and generalize… mathematical ideas.

This type of procedural variation involves varying the problem. The variation is created by changing a constraint or feature of the the problem while other parts remain the same. (This reminds me of the what-if-not technique that I first read about in the book Adapting and Extending Secondary Mathematics Activities by Pat Perks and Stephanie Prestage. It’s also something Watson and Mason talk about in an article called “Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making“.) There are two other types of procedural variation: examining multiple methods of solving problems and using a single mathematical method in varied applications. Lai and Murray use examples to describe these also: first, simultaneous equations can be solved using multiple methods, which are then compared and contrasted; secondly, a combinatorial method can be applied to various problems including handshaking, crossroads, and diagonals.

This type of practice is what what I would describe as exploratory practice: the questions are designed to lead students to a greater understanding of an underlying idea or structure.

How Does This Apply in My Classroom?

A good question, and one which I have not fully answered yet. I am still reading about exploratory practice, thanks to the Watson & Mason article linked two paragraphs above.

First, teaching through movement. I have been encouraged by a recent Jo Boaler article to use movement and gestures more. For example, when talking about transformations of shapes, we can use our hands to show reflection from palms up to palms down. (I wonder if this also extends to use of manipulatives?)

conditional probability

Boaler’s article also encouraged me to talk to students about how they see their fingers or bodies moving in their mind’s eye. But Trninic’s research is more about using movement to expose mathematical structure directly. He mentioned that he wants to work on conditional probability next. I am looking forward to hearing about it.

Regarding exploratory practice, creating or sourcing the exercises will be an interesting task. For number-sense exercises, I have used Pamela Weber Harris’ book Building Powerful Numeracy for Middle and High School Students. She presents problem strings which are sets of questions that lead a learner to see patterns and make generalisations about number.

Do you use exploratory practice in the classroom and have some resources to share? Tweet me (@mathsfeedback) or comment below.

Five Superb Maths Lesson Ideas #2

1. Pythagoras and Trigonometry Revision Activity

I love activities that get students out of their seats. This task (designed by Steel1989) asks students to distinguish between Pythagoras and trig questions. Yet instead of a worksheet, the questions are designed to be printed out and stuck around the room on sheets of paper. Students get one to work on, answer it (in their book or on a mini whiteboard) and then write the answer on the back of the sheet. Then they put the sheet back up on the wall. When another student answers the same question, they check their answer with the one already written there. If the answers differ, they students need to talk to each other to discover which is correct.

pythagoras or trig

2. Polygraph Desmos Activity

Oh, wow, I’ve discovered a great one here and maybe you’ve heard the hype already. Desmos has introduced a teacher section that allows you to run class-side activities. I tired out the Polygraph: Lines activity with one of my classes. Have a look at the teacher guidance to learn more. Only you as the teacher needs to create an account; you give students a code to join the game. One student chooses a linear graph and their assigned partner has to ask yes/no questions to guess which graph it is. Meanwhile, as a teacher you can see all the questions and answer being given, who has been successful with the task (or not). I called one of my students over when I saw that she had typed “Does your graph go through the point y = 2x?”. I was able to clear up a misconception I didn’t even know she had until then.

The student’s view is shown in the screenshot below. Desmos is adding to the collection of class activities and I’m sure I’ll use them all in time!

polygraph lines.PNG

3. Tree Diagrams Challenge

A few of my year 11 students are ready to take on the challenge of those nasty tree diagrams questions that lead to quadratics. Fortunately, tonycarter45 has created this lovely sheet with probability extension questions. The sheet includes the answers.

Tony (who works at my school) has produced quite a few nice worksheets and you can see them on TES Resources. He specialises in thought-provoking questions. I like that his investigative worksheets often remove scaffolding parts as the questions progress.

tree diagrams

 

4. Two is the Magic Number worksheets

Three activities called “Two is the Magic Number” from Just Maths. Each one is a collection of cards solving a short problem, only two of which are done correctly. The rest show common errors and misconceptions. The cards generally cover number and algebra skills such as simplifying terms, using indices, and calculating with fractions. Depending on what you have taught your students, there may be a few topics that they haven’t learned, so check first. (My bottom set year 8 need to practice like terms, but they can’t do a conversion between meters squared and millimeters squared.) These sheets are great for checking students’ misconceptions.

two-is-the-magic-number-1

5. IB DP Maths Resource Collection

I have a former colleague, Andrew Clarke, who is a brilliant resource collector. He has now started three curated collections of maths teaching ideas for IB teachers. The one that is most relevant to me is Teaching Diploma Program Mathematics. He has collected all kinds of teaching ideas for Maths HL, SL, and Studies SL. One item that caught my eye is an investigation about using calculus to describe concavity, which is one topic I have never found a good way of introducing.

Andrew’s other two sites may interest you: Teaching MYP Maths and Teaching PYP Mathematics.


What superb lesson resources have you seen or used recently? Comment below or tweet me @mathsfeedback.

Reading Notes: The One Minute Manager

When I read I usually take some reading notes (in Evernote) to help me retain the main points and some learnings. I thought it might be a good idea to start publishing these in an occasional series, in case they may be helpful to anyone. They are unedited; just notes that I take while reading about what struck me. There won’t be any commentary, just lots of bullet pointed ideas. Let me know if they are useful, interesting, or both.

The One Minute Manger by Ken Blanchard and Spencer Johnson

“The best minute I spend is the one I invest in people” (63)

“People who feel good about themselves produce good results” (19)

One Minute Goals
1. Agree on your goals.
2. See what good behavior looks like.
3. Write out each of your goals on a single sheet of paper using less than 250 words.
4. Read and re-read each goal, which requires only a minute or so each time you do it
5. Take a minute every once in a while out of your day to look at your performance, and
6. See whether or not your behavior matches your goal.

One Minute Praisings
1. Tell people up front that you are going to let them know how they are doing.
2. Praise people immediately.
3. Tell people what they did right – be specific.
4. Tell people how good you feel about what they did right, and how it helps the organization and the other people who work there.
5. Stop for a moment of silence to let them “feel” how good you feel.
6. Encourage them to do more of the same.
7. Shake hands or touch people in a way that makes it clear that you support their success in the organization.

At first, praise things that are approximately right, and help people move towards desired behaviour.
If, instead, we leave people alone and then punish them when they don’t do exactly the right thing, then they start to do as little as possible.

One Minute Reprimands
1. Tell people beforehand that you are going to let them know how they are doing and in no uncertain terms.
the first half of the reprimand:
2. Reprimand them immediately. [reprimand the behavior only, not the person or their worth]
3. Tell people what they did wrong – be specific.
4. Tell people how you feel about what they did wrong – and in no uncertain terms.
5. Stop for a few seconds of uncomfortable silence to let them feel how you feel.
the second half of the reprimand:
6. Shake hands, or touch them in a way that lets them know you are honestly on their side.
7. Remind them how much you value them.
8. Reaffirm that you think well of them but not of their performance in this situation.
9. Realize that when the reprimand is over, it’s over.

Never save up negative feedback, always give it immediately and in very small doses.
Definitely don’t have surprises at performance management time.
“When you ____, I feel ___.” Then reaffirm their worth.

“We are not just our behaviour, we are the person managing our behaviour.” (93)

why does it work?
“the number one motivator of people is feedback on results” (67)

“feedback is the breakfast of champions” (67)
there would be no point playing golf in the dark; people need to know how successful they are being

“most companies spend 50-70% of their money on people’s salaries. And yet they spend less than 1% of their budget to train their people” (64)

Mathematics Homework: 26 Good Ideas

This week I have been reading, thinking, and chatting about homework. On Monday I posted some doubts about homework and mentioned that I set homework in accordance with the school policy, which at the moment means I assign it after every class and it is mostly routine practice. Today I participated in a Twitter chat about mathematics homework as part of the #eduread group. The idea of the group is that we read an article each week and then discuss it on Twitter and our blogs. This week’s article was “Homework: A Math Dilemma and What to Do About It” by Patricia Deubel. You can read our Twitter chat on the Storify summary.

Meaningful and Purposeful Homework

The main point that hit home for me was there is no use setting homework unless it is both meaningful and purposeful. I sometimes set homework mindlessly and don’t value it much. I am coming to think that homework should only be assigned if there is a clear academic purpose and the task is not just rote practice.

Differentiation of Homework

Also, homework should be differentiated, says our reading. This is a struggle and I would love to hear from teachers who have managed this. I think my main barrier is the time to do it, but I realised that one way would be a homework task with differentiated products. Students would choose their own method of demonstrating their understanding. This is still an idea in its infancy for me and needs more thought.

26 Good Ideas for Mathematics Homework

During my reading and thinking, I made a list of possible homework tasks.

  1. read or outline a chapter (pre-learning)
  2. complete an organizer of a chapter (pre-learning)
  3. write down questions they have about a reading/activity
  4. write/diagram all you know about [upcoming topic]
  5. do a few sample questions and explain the steps
  6. do practice questions (time-based)
  7. answer journal questions about something done in class (ask students what was done and why)
  8. two parts: 1. three problems to check understanding of a concept taught today; 2. ten problems to practice a concept previously learned
  9. draw pictures/diagrams to illustrate a key word
  10. create a concept map
  11. write two problems for others to solve
  12. list the four most important ideas about ….
  13. read and write sticky notes for things you have questions about
  14. design your own learning strategy for a topic covered in class (cards, song, poem, etc)
  15. create a Q&A game
  16. write directions that teach someone else
  17. test corrections: must write why they missed that question, then answer the question correctly
  18. find examples of … at home, in the news, etc; take pictures of … ; then use these in the next class
  19. respond to a thread on Edmodo/other VLE asking a question or sharing an idea
  20. “sandwich” homework: give students the problem and answer and they must fill in the middle
  21. write a summary of today’s class
  22. write a reflection of your work in today’s class
  23. in class, do a notice/wonder activity and generate questions, then students pick one/two to investigate for homework
  24. a project that shows your understanding
  25. adaptive online software such as Khan Academy or MathXL
  26. teacher chooses 3-5 problems, then student chooses another 3-5 from a set
Students’ questions (posted on Edmodo) after reading an article giving English Premier League football standings if only English players’ goals counted

Using Homework in the Next Lesson

Another thing that really struck me started with this quotation: “Homework in the best classrooms is not checked–it is shared.” I was inspired to try to use homework that would generate discussion in the next class. Or it would contribute to the next class’s learning experiences. (Also, I hate checking homework. If the assignment needs to be used for something in the next class then it is kind of “self-checking”.)

Students' sticky notes with a question they had based on their homework reading (pre-learning for an upcoming topic)
Students’ sticky notes with a question they had based on their homework reading (pre-learning for an upcoming topic)

Things to do with homework in class instead of collecting or checking it:

  1. self-assess your homework in terms of effort, understanding, completeness, or accuracy
  2. reflect on which questions were the easiest/hardest and why
  3. find a peer who approached the problem differently than you and discuss our strategies
  4. quiz with 2 randomly selected questions from the homework assignment
  5. get your peer’s feedback on some aspect of your homework
  6. work with a friend to get a best answer to one hard question
  7. give a new problem and ask how it compares to the homework problem(s)
  8. choose the two homework questions that were most alike or most different and explain why you picked them
  9. gallery walk of the results of investigates into notice/wonder questions (see idea 23 above)

More Homework Ideas and Links

I am still learning and thinking over these things. (Sidebar: I love being a teacher because I am always learning. Ten years in and I am excited to be learning about good practice in my profession.) Please share your homework thoughts in the comments or tweet me @mathsfeedback.

Here is a list of the things I read this week while thinking about homework:

 

Please share one good homework idea!

Mathematics Homework: My Dilemma

A few months ago I started compiling my viewpoints about mathematics education. What I mean is that I have been using sticky notes to record my beliefs about mathematics education and collecting them on a piece of flipchart paper on my back classroom wall. (Strangely, no students have asked about this. I wonder if they read the stuff on the walls at all??) The viewpoints poster has been a personal exercise to help me clarify my thoughts and see which issues I have strong feelings about.

viewpoints on maths ed 1

I used yellow sticky notes for beliefs I can justify and for which I can provide examples. I used pink sticky notes for issues about which I don’t yet know what I believe. One of these is homework. It seems to me that some people feel quite strongly that homework is bad and should be abolished. Others hold that homework is essential; for some it is even sacred. I have no idea where I sit on this issue, hence the pink sticky note.

viewpoints on maths ed 2

Most of the time, I feel as though my thoughts don’t matter too much because homework policy is determined by the school I work in. If my school says to assign homework, I do so. I usually follow the lead of my head of department in what types of homework I set and how much.

But I think it is time to do some reading around this subject of homework and come to some conclusions of my own. After all, I have strong views about all manner of other things (for example, setting students into classes by ability and acceleration of more able students), and my views have to submit to the policy of the school and my department. So why not form some views about homework?

As a first step, I will be participating in the #eduread discussion about mathematics homework. The plan is to read the assigned article by Patricia Deubel and write about it. Then there is a twitter chat about it on Thursday morning (June 4). (Or Wednesday night if you live in a North American time zone. Or the wee hours of Thursday morning for Europeans…. Maybe Europeans are better off reading the summary afterwards.) Update: The second post in this series about homework is: 26 Good Ideas.

Do you believe in homework?

Giving More Useful Feedback to Students: an #eduread post

How to give better feedback is always a goal of mine. I sometimes (maybe frequently) find it hard to keep up with the pace of teaching, assessing, giving feedback, and reflecting on it. What about you?

Today I was reading a short article titled “How Am I Doing?” with some pointers for effective feedback. Five very useful ideas were presented; have a look at the article to see them all.

2014-04-24 13.56.23

The item that struck me the most was that students need a clear view of where they are heading with their learning and what their learning target is. Phrased in this way, it is a very simple idea and one I have been familiar with for years. However, I have found that at times students think their job in my classroom is to complete the activities I give them. They think that completion of activities is the success criteria. Instead I need to get across to them that their job in my class is to reach desired learning outcomes.

This relates to feedback in that there is no use giving feedback when students think they have successfully completed the task of “learning”. Feedback may seem like giving them more work to do, rather than helping them learn. But if students know their job is to achieve a learning goal. Feedback about progress towards learning goals helps students know how their efforts are leading to success.

In my classroom I am not the best (yet! growth mindset!) at giving indicators of where learning is heading and how we will get there. I was marking student work today and saw this comment (pictured above): “This is confusing because you have not explained what you are trying to do.” As it turns out, that is exactly what I need to hear myself! I appreciated this article as a reminder to expose the learning goals more frequently. And to provide personalised, specific feedback to students about how they are going towards meeting those goals.

#eduread is a group of mathematics teachers that read an article each week and discuss it on Twitter. Here is the blog that organises it. The chat is on Wednesday evenings in the US, which is Thursday morning for me. I can’t always participate in the Twitter chats but I can usually follow along later thanks to the hashtag. Would you like to join us?

Do you find it easy to give useful feedback to students?

Better Group Work

I just finished reading an article called “When Smart Groups Fail” (Barron, 2003). It’s a study of groups of three sixth graders solving maths problems. Barron divides the groups into less successful and more successful at solving the problems and then analyses what features of their group work were significant.

Surprisingly to me, the success of a group of students was not influenced by:

  • the amount of talk
  • the average achievement level of the students
  • whether anyone in the group had a correct idea

Instead, Barron found that group success was marked by:

  • accepting or discussing correct ideas rather than dismissing them
  • correct ideas were brought up when they related to ideas that were being discussed at the moment
  • group members paid attention to each other and if the others were paying attention to them
  • group members physically showed their togetherness by eye contact and standing around or pointing to a common workbook

This article’s findings indicate to me that my classroom culture can lead to better group work. I can help students learn to discuss a mathematical idea by building on each other’s thoughts. A well-managed whole group discussion can lead to more cooperative group work sessions. I want my students to learn to listen carefully to what is said and then agree or disagree or ask questions. I can request these responses in whole class time. Then students will see they are the norms that also should guide their group work.

Furthermore, the groups in Barron’s study were of mixed ability and their previous achievement levels did not correlate with their success as a group. This adds to my feelings about the benefits of mixed ability teaching. If students of differing abilities can be helped to communicate well, they can all achieve well.

The study also found that students in successful group went on to be more successful in individual tasks. Interestingly, students in less successful groups did as well as if they had worked on their own. Thus poor group work neither helped nor hindered their achievement. However, good group work improved the success of individual students in to a significant degree.

The school year is just about to start and I am looking forward to inculcating a culture of social, mathematically focused talk.

Barron, Brigid. “When Smart Groups Fail.” The Journal of Learning Sciences 12.3 (2003): 307-359.