How do I make sure I am challenging high attainers in mathematics in my secondary classroom?
Mathematical high attainers, pupils who are gifted and talented mathematically and pupils who are naturally curious about numbers and mathematical patterns may all need different approaches to extend their learning. You may find high attainers in the top set, or they could also be in lower sets if they have other particular learning needs.
For all teachers of high attaining pupils, the NCETM Portal has a variety of ideas for resources and teaching strategies. You will find just a few of them highlighted below.
They include answers to questions such as:
How do I find the right activity to extend all the pupils who are interested in mathematics in different ways?
How do I know who the mathematically gifted and talented pupils in my class are?
Practical ideas and resources for gifted and talented pupils in the classroom
How do I make sure the gifted and talented pupils are making good progress in their learning?
How do I find the right activity to extend all pupils who are interested in mathematics in different ways?
Firstly, as a department or on your own, you could examine the departmental workshop entitled ‘Effective day to day provision for able, gifted and talented pupils’.
Then you could think about how extending activities for pupils who have an aptitude for mathematics in some way is a challenge for all mathematics teachers. The best sort of tasks, are those that have straightforward starting points and then many different ideas that can be pursued at the next stage. A good source of these activities is in the secondary magazine. Sometimes ideas that stimulate high attainers come from higher level mathematics. For examples give students the opportunity to explore the Fractals as described in Issue 73 Focus on Introducing Fractal Ideas
Sometimes the ideas about mathematics come from an everyday situation or game. For example as in the article on Dominoes.
Another good way to extend thinking at all stages is to ask particular types of questions. For example, the ‘sometimes, always, never’ strategy is one that many teachers have found useful to challenge all students in their class.
Other helpful teaching strategies can be found in the What makes a good resource microsite.
And, in the Mathemapedia an article about questioning Volleyball not ping pong looks at how to develop discussion amongst pupils across the class.
When you are planning to play a game to consolidate understanding, more able pupils could be asked to create another similar game for use with another class. Issue 5 has the link to the Tarsia Jigsaw puzzle site.
You can find materials about gifted and talented pupils across all key stages.
This reading written for the Early Years is also useful for Secondary and Primary teachers. You may wish to discuss how teachers in your department find out about the mathematical talents that the students in your classes have. Finding and exploring young children’s fascinations gives some excellent background information about the key characteristics of higher attainers in mathematics.
Look at this thread on Comment only marking in the Assessment for Learning Community. Discuss with colleagues what type of feedback gets the best progress in learning for higher attainers in mathematics?
Explore a piece of mathematics
When teaching particularly high attaining students in mathematics they are often intrigued by problems that seem to be beyond the normal curriculum.
However, when doing these tasks they are developing a range of mathematical skills that can be used in any area of mathematics. The idea of using railway shunting problems to teach mathematics is explored in Issue 80 of the Secondary Magazine.
You could also examine, either on your own or preferably as part of a departmental activity, one of the many NCETM Departmental Workshops. For example, the workshop on Circle theorems would be great for examining how you using this subject, you could challenge high attainers in the classroom.
It has been said by some recently that ‘teachers learn best when they learn from each other’. If you know of another link to an activity or resource on the NCETM website that you think would be useful or appropriate for readers of this guidance, please use the comments box below to let us and them know of your idea.
We have many courses and networks available, search in our Professional Development Calendar
to find a suitable course or network.
“Activity by itself is not enough; it is the sense that is made of it that matters” (DRIVER, R. (1983) The Pupil as Scientist?, Milton Keynes, Open University Press.
For the things you have tried out for yourself in your own classroom to become useful pieces of professional learning, there is a need to capture them, reflect upon them and remark on them. The NCETM Personal Learning Space (PLS) allows you to do this.
Use My Learning Journal to collect your thoughts and reflections as well as to log actions; documents can be attached to your entries. You could do this now by visiting your own PLS.
Use My Favourites and Notes to take note of and organise interesting things you have found (like this page) and want to return to easily in future.
Use the Sharing and Contacts facility to share elements of your PLS with colleagues, selecting them from your own list of contacts
Use the “Request a reminder” function
Find out more details of these and other functions of the PLS.