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Raising achievement in GCSE mathematics - NRICH - Which Quadratic, Parabolic Patterns


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 22 July 2011 by ncetm_administrator
Updated on 04 October 2011 by ncetm_administrator

Raising achievement in GCSE mathematics

Resource: NRICH
School: Swavesey Village College
Teacher: Tabitha George

Resource

NRICH, Which QuadraticParabolic PatternsMore Parabolic Patterns

What we did – the use of the resource and the impact on learning

As a classroom teacher I have the following aims:

  • I want my students to enjoy maths and be curious about the world in a mathematical way
  • I want to enjoy teaching their lessons
  • I want students to succeed in whatever assessments or exams they need to take

To achieve my aims, I use the following techniques:

  • Making links – both between traditionally ‘isolated’ topics in maths and between other curriculum areas.
    Why? – Students encounter, use and apply topics lots of times in lots of contexts. If made aware of this, then their understanding can be reinforced and the learning becomes embedded more deeply.
  • Using rich tasks that require these links to be made – Nrich can provide these tasks.
  • Making it clear to the students what they have learnt and how this is relevant to the GCSE (or equivalent) assessment objectives

I go to the Nrich website for ideas, starting points to inspire a more interesting lesson to engage me as well as my students. I do this for the majority of the lessons I teach and I go with an agenda – to find resources to cover specific content on the scheme of work or calendar.

As an example, at GCSE, in particular, links can be made very easily between maths and coursework in science. Students are expected to use mathematical processes in this coursework but the focus is on using the process rather than understanding why the process works.

I covered the topic of transformations of graphs in this way. Using a combination of three Nrich ideas,  Which Quadratic, Parabolic Patterns, More Parabolic Patterns, I developed a lesson in which students were analysing images created using quadratic functions. They were applying prior knowledge to further understand how graphs can be transformed and which components of their equations influence this.

They went on to create their own designs, manipulating equations on Geogebra and developing their understanding of different forms such as x = y2. Some discovered the equation of a circle and continued to explore how to manipulate this to move a circle away from the origin.

Which Quadratic was used as a starter. This was used as a collaborative task in which a student was issued with one card displaying a quadratic graph and the rest of the class were allowed just eight questions to ‘discover’ the hidden quadratic and suggest its equation. This encouraged them to think about the questions they were asking and arguments arose over which were useful questions. Evaluation of the most successful questions led to students identifying the key features of a graph. Those features identified included: the axis of symmetry, the location of the maximum / minimum point and the coefficient of x2.

A combination of  Parabolic Patterns and More Parabolic Patterns was then used as the main activity. Two images were provided on a sheet that students worked on in pairs. Key questions were highlighted on this sheet, with the aim of students identifying the equations of each component of the image with minimal information. An emphasis on convincing each other (and me) of their solutions was key, as this consolidated ideas and discoveries into concepts that could be applied in other situations.

The cross-curricular inspiration for this was from discussions with a science teacher who sought confirmation from me as to the equation of the curve of best fit for a selection of experimental results. The curve was a quadratic symmetrical about the x-axis. At this point I realised how essential it was that students actually understand how to identify and recognise the equation of such lines as this is not something that all science teachers are able to explain.

Next steps

The following lesson was spent in a PC room. Students used Geogebra to create their own designs. The brief given was that completed designs should be symmetrical in some way and that the more interesting they were, the better!

Communication with science teachers needs to be established to ensure that these links are being reinforced from both sides.

Top tips

NRICH is a massive bank of resources. Going into it can be daunting and unproductive without a starting point or idea to focus your search. ‘Search by topic,’ is the first tip. Curriculum mapping documents are also a good pointer. Remember that these should be used as ideas and inspiration, not always as stand-alone tasks to present to a class.

Potential barriers and possible solutions

Time.! A common theme would be: 'At GCSE in particular we have a lot of content to cover before exams; we don’t have time to do extended tasks and investigations on top of the normal teaching.'

Solutions… Teach concepts and content through the rich tasks rather than using them as an end of topic investigation. If you consider your objectives carefully and ensure that these are communicated clearly to learners throughout the activity or task then traditional consolidation is not necessary.

Personal Learning

Reflective thoughts

Nrich activities are an excellent tool to equip curious learners with deep mathematical understanding. However, this doesn’t just happen! You need to adapt and refine activities, personalising them to your teaching style, your class and your objectives. The potential for students to explore and investigate is wonderful, but as a teacher you must be prepared to devote time to working through the problem, finding the different routes through and the possible destinations. The questions that you ask will guide learners in a particular direction and the way in which you introduce a task will enable you to emphasize particular objectives and therefore make these clear to students. 

 
  
 


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