Supporting Highly Able Mathematicians - Teachers

Whatever the size or phase of your school you are likely to meet some highly able mathematicians at some point in your career. If you are a highly competent and confident mathematician yourself, these students will be a challenge and often a delight. If you teach maths but are not particularly confident then meeting the needs of highly able pupils can be quite a challenge. Below are some ideas to prompt your thinking, and links to helpful information and resources.

There are different ways in which teachers can meet the needs of their most able mathematicians. The most prevalent in UK schools is through acceleration - pupils move through the school curriculum faster than others, often taking assessments or examinations early. For some highly able students this is fine, so long as these three conditions can be satisfied:

• the pupil should have absolute mastery of the content so far - i.e. they would be expected to get a really high score on any assessment
• they should be emotionally and socially secure enough to be working at a higher content level (this is less important in maths than, say, in English, but does matter if students are to be working with older pupils)
• there should be a clear pathway through to the next stage of mathematical education - ensuring continuity and progression and not a 'stop-start' or repetitive experience.

However here at NRICH we believe that acceleration sends a message that maths is about speed of working through content, and that there are other preferable, (or additional) ways of working with highly able students which are more enriching, enjoyable, challenging and prepare them much more effectively for their future in mathematics.

Mathematics involves both mathematical content and mathematical thinking

At NRICH we strongly believe that the very best way to nurture and grow mathematical talent and interest is to pose challenging, stimulating problems which encourage deep mathematical thinking. This can easily be done with age-appropriate mathematical content within the right problems.
 
Did you know:

• It is possible to ask mathematically challenging questions on easy content or to ask mathematically easy questions on advanced content.
• Accelerated young mathematicians will typically take examinations or work from textbooks containing relatively easy questions on advanced topics.
• Accelerated students who don't engage in any challenging problem-solving activities whilst at school often encounter difficulties in mathematics when they start university.
• Mathematics as viewed by mathematicians is a highly creative and collaborative discipline - if you only ever work on mathematics individually you are missing out on a great part of what makes mathematics so seductive and fascinating.
• Mathematics does not always have a 'right answer'. Often one question leads into another and mathematicians often say 'I wonder what happens if ...?' rather than stopping at the end of a question.
• There are lots of different styles of mathematics -- there is no single type of mathematics, style of learning or intervention which will appeal to all highly able mathematics students. And there is no 'best' or 'hardest' piece of mathematics which must be learned!
• There are often lots of different ways in which a challenging or rich mathematical problem can be solved. All clearly-expained solutions are valid mathematics!
• Some good mathematics problems take days or weeks to solve or consider in detail; most mathematicians love to have a few ongoing problems that they are 'thinking about'.
• Whether you teach primary, secondary, or post-16 aged pupils, the same principles apply.

What should highly able mathematicians do in school?

These students come equipped with a wide range of interests, skills and motivations. Such students need, ideally, to do three things:

1. Think in detail about lots of stimulating mathematical challenges - they should be offered a mixture of questions which yield a definite answer or conclusion along with more open investigative problems.
2. Read more about what mathematics is likely to come next and about many of the applications and uses of mathematics.
3. Find somebody with whom mathematics can be discussed in detail.

NRICH can help with all three of these.

1. Mathematical problems:

The activities on NRICH are tagged with one, two, or three stars. For highly able mathematicians, the three star problems will typically be difficult and challenging problems. (You can read more about the types of NRICH problems here.)  There are hundreds of three-star problems which are archived and you can search for them according to topic using the search bar at the top right of the page. Your students may be interested in the different ways other pupils have solved the tasks, and they can find examples of these under the 'solutions' tab.

Usually at least one new three-star problem is published each month for each key stage, and we encourage children of all ages to submit their own solutions to our problems. Bear in mind that the extensions to some of these problems might challenge and intrigue many adult mathematicians!

Not used NRICH before?

2. Mathematical reading:
Many of the activities at KS3 and above have linked readings, some of them on NRICH but others on our sister site, PLUS.  We have also put together a list and description of recommended books here.
 
3. Mathematical networks:
There are several of these that meet at different locations around the country. Tap into the UKMT network (for secondary), or the Royal Institution Masterclass series (primary and secondary). New on the scene is Mathsjam, a new adult network that meets (usually in pubs) around the country.

Web 2.0 means that communication is easier than ever. For pupils who want to discuss NRICH activities, we have set up three blogs. The Infinities blog is for primary-aged pupils, Irrationals is for secondary students and Fractals is for post-16.

Ask NRICH has become the place to share problems and discoveries about any mathematics - a team of postgrads here at Cambridge will respond within a very short time and support pupils who want to understand and share their work.

Other linked NRICH pages:

Supporting highly able mathematicians - who are they?

Supporting highly able mathematicians - for parents and carers

Supporting highly able mathematicians - resources for teachers

Supporting highly able mathematicians - resources for parents and carers

Supporting highly able mathematicians - academic research links

The Templeton Projects

Extension, enrichment and/or acceleration?

Working with highly able mathematicians