12/11/18
Sue Pine, Accredited Facilitator, shares information, resources, and advice about mixed ability grouping in mathematics.
Traditional approaches to teaching mathematics often rely on ability grouping, and a focus on procedures, memorisation, and the ability to do maths, in particular computation, quickly.
There are many consequences of ability grouping and procedural teaching, particularly on students’ self-efficacy. Ability grouping often leads to a fixed mindset for students (and adults) about their mathematics ability – that they are either a maths person, or they are not. No matter what you call your ability groups students still know which group they are in, often predetermining what they think they can achieve in mathematics.
Ability grouping is least effective for students in the lower groups. Often teachers who teach the lower groups have lower expectations, despite their best intentions. When working with lower ability groups, teachers usually give students less challenging tasks below their curriculum level, including problems which are less complex or with smaller numbers. This becomes inequitable for these students as they are denied the opportunity to access the curriculum at a higher level.
In recent years many teachers have moved away from the use of ability groups in mathematics towards a more flexible approach using mixed ability groups.
When students are given the opportunity to work in mixed ability groups on carefully designed tasks they begin to see themselves as being able to do mathematics, which builds a positive mathematical mindset and identity. Often teachers notice that students are able to solve maths problems they didn’t think they were capable of. They gain more confidence in their ability and contribute more. In addition, students report that they enjoy maths a lot more.
Careful selection of students in small mixed ability groups to work on rich tasks that involve reasoning, argumentation, and a variety of perspectives proves to be a much more equitable approach. However, it is more than just mixing students up and continuing to teach the same way.
There are other shifts in practice that teachers need to make in order to make this approach successful. Students need to be taught how to work collaboratively on maths problems, be supported so that they can explain their thinking, ask questions, and justify their solutions. Teachers have to be comfortable with the locus of control moving to the students and be able to facilitate discussions through effective questioning. Promoting productive struggle is an important part of learning and the ability to design tasks which develop a conceptual understanding as well as being accessible to all students, often referred to as low floor – high ceiling, are all important components.
As I mentioned, mixed ability grouping is more than just mixing students up and expecting them to be able to work collaboratively on problems. Groups of 3–4 students must be carefully selected and it is essential that the tasks that students engage with are designed to be low threshold, high ceiling and develop a clear mathematical understanding.
Students need to be taught how to work collaboratively, to explain their thinking, ask questions, and justify their solutions. They also need to know how to record their thinking including using tools and representations. Developing positive mindsets and providing a safe environment focused on learning rather than performing is paramount, and this all takes time.
A great place to start is to explore Jo Boaler’s website youcubed. This is full of resources including ideas to teach basic facts and problems that support a mixed ability approach. Jo has developed four series of lessons called Week of Inspirational Math in which the intention is to convey to students (and teachers) positive mindsets and to engage them in low floor, high ceiling tasks around rich mathematical concepts. Jo’s book, Mathematical Mindsets offers some good explanations and links to various research as well as practical ways to get started.
Another great resource I was introduced to this year which is designed to encourage students to reflect on what good group work looks like can be found on Sara Van Der Werf’s blog 100 numbers to get students talking. It is easy to implement and a great way to get started on setting up effective group work.
As this teaching approach relies heavily on developing mathematical discourse, the implementation of Talk Moves by Anderson, Chapin, and O’Connor is vital. These are easy to implement not only in mathematics but across the curriculum.
Other structures and pedagogical practices to explore are Complex Instruction and the Five Practices.
Finally the NZMaths website provides a wealth of rich problematic tasks directly related to our curriculum that can be adapted to support this pedagogical approach. NZMaths is continually being updated and not only provides tasks and units of work, it has several PLD modules, curriculum elaborations, and links to research.
Further readings …
Ability and mathematics: The mindset revolution that is reshaping education
This article by Jo Boaler cites a range of research into the effect of ability groupings as well as mixed ability groupings on mindset and achievement.
Teaching strategies that work – Mathematics
This 2018 report by the Education Review Office highlights the use of mixed ability groups as an effective approach to raise student achievement.
Yes I can! Paying attention to well-being in the mathematics classroom
This article published by the Ontario Ministry of Education emphasises the importance of developing positive experiences for students in mathematics.
Also on our website …
Raising the bar with flexible grouping
In this 2017 blog, Professor Christine Rubie-Davies challenges the practice of grouping students by ability, arguing that it constrains learning. Instead Christine recommends that teachers use flexible forms of grouping to ensure that all students are challenged and engaged.
