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Inspired by a Charles Lovitt workshop introducing the idea of choice into student learning through the construct of a Menu Model, Aaron has developed and integrated the approach into his teaching with great success. In this article he tells us of his students' responses and details some of his organisation. Tribute is paid to Charles through several of his expressions borrowed for the article.
Kingsbury Primary School, Victoria
Find the Being a Mathematician chart here and add your own mathematician. Aaron has chosen Terence Tao, a young Australian mathematician, currently Professor of Mathematics at UCLA.
Okay kids, what did you enjoy about our class this term? I asked as a reflective activity on the last day of term 2.
I like this class because we do the Maths Menu.
It went around the circle and I was blown away by the positive responses from the students. Of course not everyone said 'Maths Menu'. There was the occasional 'I like the games,' or 'The students are friendly' but the mode was definitely 'Maths Menu.'
Me too, I like the Maths Menu.
I couldn't help but compare this with the start of the term. I had been away sick one day and the replacement teacher who had taken my class must have liked maths, because she did it with them all day. They did number sums from the board with her drilling them in how to conduct the written algorithm. All the while she made sure they understood the importance of maths.
If you can't do maths you won't get anywhere in life.
Well, did she make an impression on those kids! They didn't want to even hear the word 'maths' after that - even my clever little problem solvers who had a talent for it, let alone those who already lacked confidence. Implementing the Maths Menu wasn't directly related to this incident, but it sure went a long way to improving the students attitudes to maths, problem solving and learning in general.
The work requirements are always explicit and negotiated with the class. We collectively agreed that if students don't finish the required workload, then they complete tasks in their own time (recess, after school). We spend about four sessions a week working on our choices from the Maths Menu. It was three sessions, but because the class enjoyed it so much, they asked if we could bump it up to four. Each task must be conferenced with the teacher.
What Is It?
Amusing anecdotes aside, the Maths Menu has been a vehicle which helped me improve the way that I teach maths. And it looks a bit like this.
The maths menu is a collection of tasks. The students then approach the menu and choose which activity they would like to complete. In our classroom we decided that we should be able to complete one Hands-on Task, one Computer Task and one Worksheet task as well as the Compulsory Task in a week.
|So much pops up that can be addressed at the student's point of need.
A conference is a short discussion about the maths task. I will generally ask questions like:
I try to keep it short, but sometimes it's easy to get carried away. So much pops up that can be addressed at the student's point of need.
- What did you have to do?
- How did you work it out?
- Have you shown me how you worked it out in your book?
- What could you try next?
Why Try The Menu Model?
When you walk into a restaurant, what do they give you? That's right, a menu. Why do you get one? Good, so you have a choice. Why don't they say 'Sit down, shut up and eat what I tell you?' Well, because that's home. Or I guess, in an educational context, sometimes school too.
My point is ... choice. If students are to become the independent, autonomous learners we hope for them to be, we should start now. Students are capable of making their own choices about their learning. Moreover, they are enthusiastic about it.
Having a choice creates many additional benefits for a productive learning environment; it's non-threatening. I colour code the tasks so that the students have a guide when they go to choose. That way I can also check on students who should be challenging themselves. However, it has been a hugely positive experience to see students with very low levels of confidence in maths choosing a task with their mate saying 'Let's go for a red one this week. Let's try a hard one, hey.' Imagine how that student would react if I forced them to do a 'hard one.' He obviously feels safe from making a mistake now.
||My point is ... choice. If students are to become the independent, autonomous learners we hope for them to be, we should start now.
By providing a variety of tasks on the menu I can cater for mixed abilities. I teach a 4/5/6 composite class and have perhaps a 7 year gap in the knowledge of my students. However, this is the same predicament that teachers can be faced with in a straight grade class. It is a reality we have to deal with. The Maths Menu allows me to provide activities to support, encourage and challenge all my students.
Another bonus in using the Menu Model has been the way my students talk to each other during maths lessons. I believe that students construct their own knowledge of the world through experience. The social experience of working on a task together with a peer and the discussion that arises from that has helped create a positive learning environment in my classroom.
In addition to these benefits, the Menu Model provided me with the flexibility to juggle the features of the maths classroom I wanted. I could include ICT, hands-on problem solving and independent investigations. I could have tasks with co-operative group problem solving, kinaesthetic or visual features. It helped me to juggle some of the many features we have recognised which help engage and enthuse kids in learning.
Choosing The Tasks
As the manager of the restaurant, I have a responsibility to provide high quality fare. Thus, each task placed on the menu ideally undergoes my strict scrutiny. However, time being at a premium for teachers, this isn't always easy. These resources are extremely useful:
- Task Centres: These problem solving tasks are fantastic for engaging the students in maths. They work so well with the Menu Model. Each task has 3 lives. It can function as a problem solving task for a pair of students, a whole class investigation, or an independent extended investigation by providing a few guiding questions which students respond to in their books.
- Maths 300: An extensive library of lesson plans based around whole class investigations. Many have grown from the Tasks. All offer me ideas for Menu Maths.
- Maths 300 Software: About one third of the Maths300 lessons are supported and extended by software. An Investigation Guide can easily be prepared to partner the use of specific parts of the software in Menu Maths. The lessons Chart Strategies and Number Charts are examples.
- Real Materials: such as junk mail, recipes, photographs, maps and many more provide good starting points for tasks.
- School Grounds: A walk around the school can contain a lot of maths. Tessellations, area and perimeter, distance, mapping, numbers and many other concepts can be explored.
- Internet: There are many great web sites out there with software that is perfect for the class. These can be turned into tasks with a couple of guiding questions which could be as simple as:
- What maths were you using?
- What did you find difficult?
- What did you learn?
A Typical Session
Unit Focus: Number - fractions
Lesson objective: For students to understand the concept of fractions (whole and equal parts) and to be able to recognise the correct notation.
- 10 - 15 minutes ... Fraction Estimation
Using a length of rope with the labels 'home' on one end and 'school' on the other end ask three different students to demonstrate estimating where 3 fifths would be. Ask students to vote on which person is the closest. Students can change their estimation if they like. Ask the class 'How do we check?' Check by folding. Ask the class 'How do we write 3 fifths?' Students can demonstrate and explain notation.
- 40 minutes ... Maths Menu
Explaining the tasks on the menu was the focus of another lesson. Students now choose an activity from the Menu which contains extensions to Fraction Estimation (Maths300 Lesson 33 & Task Centre 205) as well as other fraction tasks. Most activities are targeting an understanding of the concept of fractions as parts of a whole, fractions as divisor, fractions as a number etc.
- While students are working independently on Maths Menu the teacher conducts small group work with some students with shared misconceptions as shown in pre-assessment (fraction interview) - 10 minutes.
- After completing small group work Teacher opens themselves up for 'conferencing.' Students may write their name on the board to arrange a conference. Teacher listens, questions and takes anecdotal notes
- 10 minutes ... Share Time
Students are invited to share something they have learnt with the class. Alternatively, the teacher has asked someone who has reached an understanding witnessed through a conference to share their work. Students respond to what has been shared. Class summarises what they have learnt.
The options are endless. There is no 'one size fits all' solution. That way of thinking goes against one of the main reasons to use the menu - to cater for the range of students in your classroom. The Menu Model may look completely different compared to the teacher next door. It does at my school.
Having A Go
Perhaps the best advice I could give you if you are interested in trying a Menu Model approach to maths is to keep at it. Chances are you won't get it perfect first go, I didn't. It took about a year of modifying and playing around until I got it to where I wanted, but I'm glad I did. Besides, if the students gave up first go, what would you say to them?
Secondly, this approach is flexible, so start small. Try it a day a week and include activities that are familiar to you.
- Nothing on the menu is mandatory.
- What is on there is there because I wanted it there.
- You don't need the different headings.
- You can have more than one compulsory task.
- You could suggest the students work in small groups for some activities.
And choice. That's the first criteria of a mathematician's work. First give me an interesting problem.