An Action Research project by Rory McMahon (Mathematics)
Aims of the Project
The aim of this project was to research ‘Mastery in Mathematics’ and the implications its’ introduction would have on our Faculty in terms of:
- The new AQA Curriculum
- Adjustments to the Scheme of Work
- Alterations to lessons to promote ‘Mastery’
Background and context
This project started in response to the recent changes to the Maths curriculum which take effect from the 2017 GCSE’s. As a Faculty we looked to change our practice in light of the recent changes. The curriculum changes are as follows:
- There is more content to teach with harder topics being introduced.
- There is a greater emphasis on problem-solving and mathematical reasoning, with more marks in the GCSE exams being allocated to these higher-order skills.
- The total examination time is increasing with all exams taken at the end of the course.
- Students will also have to memorise formulae.
- There is a new grade structure from 9 to 1, with fewer marks at the lower grades and more marks at the higher grades.
Peer observations to gauge the level of Mastery evident in lessons in September/October
As a Faculty all teachers took part in peer observations during Term 1 in an attempt to see good practice in action as well as gauge the level of ‘Mastery’ evident in existing lessons. Positive and constructive feedback was given and a discussion on how ‘Mastery’ could become more visible in lessons was held during Faculty meetings.
Scheme of Work changed from Kangaroo to AQA
The decision was made in January to make the switch from the Kangaroo scheme of work to the new AQA scheme to attempt to get pupils used to the new format in time for the start of the 2016-2017 academic year. Although it was thought to be a better move in the long run, there were some challenges to this approach. Firstly, a comparison of the schemes had to be made and topics which were covered already had to be crossed off. However with the level of many topics increased, we needed to pick out sections of topics which students had not been previously been exposed to and teach those separately. Secondly, the increased difficulty of concepts and the change in focus to ‘Mastery’ proved to be difficult for students to adjust to. We were hoping they would adapt quickly to the problem solving nature of lessons as this was a style which they had not been previously used to.
Adaption of End of unit tests to support Mastery
End of Unit Tests now include Mastery style questions to build up resilience and retests are available and encouraged, so that students now have the key skills needed to succeed at this form of questioning. This is a work in progress which has been embraced by the pupils as they can see progression from the first sitting of the test to the second. It also gives them more opportunity to sample the type of examination questions they will be expected to answer in the coming years.
Further peer observations planned to see how Mastery is developing and lesson adjustments
Again in Term 3/4 the Maths Faculty undertook peer observations to observe the increase in focus towards ‘Mastery’ in lessons as standard practice. The Faculty was unanimous in the conclusion that Mastery questions were most easily integrated into the bell-work phase of the lesson or alternatively and possibly most effectively, during the Plenary phase. Personally, I found giving the students a ‘Mastery’ question as their plenary always challenged the pupils to think about the skills they had learnt in that lesson in a different way. Once the students spotted this they began to widen their horizons in terms of spotting links between different concepts learned. Some examples of Lesson alterations can be seen below.
Our pupils in this case would have spent the majority of the lesson learning about the sum of the interior angles of polygons. In this question, they have to apply that knowledge but also represent their answers as fractions in their simplest form.
A standard lesson on Factorising Expressions would concentrate on embedding the relevant skills needed as above. However, the Plenary to this lesson looks like the following slide below.
The students are encouraged to use a skill learned in the lesson to solve a different style of problem, thus establishing links between different concepts.
Adoption of Eastern Asian styles of teaching (learning information)
It is widely recognised that the countries of Eastern Asia out-perform their UK counterparts in relation to attainment of Mathematics in primary and secondary schools. International tests show that in these countries the percentage of 15-year-olds who are functionally innumerate – unable to perform basic calculations – was more than 10 percentage points lower than in England. As recently as 12/07/2016, news broke of a £41m support for 8,000 primary schools in England to adopt the approach which is used by the leading performers in Shanghai, Singapore and Hong Kong.
The Eastern Asian method has the following features:
- Emphasis on problem solving and comprehension, allowing students to relate what they learn and to connect knowledge
- Careful scaffolding of core competencies of :
- visualisation, as a platform for comprehension
- mental strategies, to develop decision making abilities
- pattern recognition, to support the ability to make connections and generalise
- Emphasis on the foundations for learning and not on the content itself so students learn to think mathematically as opposed to merely reciting formulas or procedures.
As a Faculty we have tried to integrate the techniques of embedding skills in the minds of our students and then getting them to apply these skills to problems. Previous lessons would consist of teaching skills and then getting pupils to practice these skills for the remainder of the lesson. Now, our attention has changed to using and applying these skills to problem solving for real-life situations.
On-going adaption of the Scheme of Work to include NRICH activities to further develop Mastery
Before the focus on ‘Mastery’, the Maths Faculty always felt that problem solving was a crucial attribute for students to develop. This was enhanced by our used of ‘The Nrich Project’ from the University of Cambridge.
“NRICH is a team of qualified teachers who are also practitioners in RICH mathematical thinking. This unique blend means that NRICH is ideally placed to offer advice and support to both learners and teachers of mathematics.”
NRICH aims to:
- Enrich the experience of the mathematics curriculum for all learners
- Offer challenging and engaging activities
- Develop mathematical thinking and problem-solving skills
- Show rich mathematics in meaningful contexts
- Work in partnership with teachers, schools and other educational settings
For teachers of mathematics, NRICH:
- Offer free enrichment material (Problems, Articles and Games) for all ages that really can help to inspire and engage learners and embed RICH tasks into everyday practice.
- Help to promote RICH thinking in classrooms by offering on-line and face-to-face support at Primary and Secondary level.
- Deliver professional development courses and workshops in rich mathematics.
- Help teachers to think strategically about ‘next steps’ and progression in problem solving.
In 2014-2015 ‘NRICH lessons’ were held once per term to help enhance the problem solving skills of students. In 2015-2016 it was felt that the Faculty should conduct NRICH lessons once per fortnight as the shift in focus was becoming apparent at that stage. Moving forward, the Maths Faculty has created a bank of NRICH lessons to be used in conjunction with the new Scheme of Work for the academic year 2016-2017. Some snapshots of how these were integrated can be seen below.
As a Faculty, we have discussed the possible impact of our endeavours to adjust our teaching and learning to the new and challenging ‘Mastery’ curriculum. As this style of teaching and type of examination questions have been rolled out, students have become more familiar with the concept. Therefore, we can say there has been definite progress in the students’ familiarity with the style of future exam questions.
Secondly, we can state that the confidence of our pupils has increased with regard to structuring an answer for these questions. At the beginning of the year, receiving answers from students for bellwork and plenary ‘Mastery’ questions was a difficult ordeal! Gradually through practice and knowing they should be able to use some of the content they had covered in lessons, many were then able to attempt a reasonable answer. This developed over time so now we not only have our highest attaining students putting answers together but our bottom sets are also successful.
Finally, the AQA practice papers were an invaluable resource. As with the previous strategies, students found the change in structure and expectations very difficult to deal with. Therefore, we gave students the practice paper to attempt and gave them a grade. Once the papers were handed back, students could then go through the mark scheme with green pens to see where they could have picked up more marks. Also, answers that had four, five or even six steps were often broken down by the teachers for the class. Students then had the opportunity to re-sit the examination as a confidence building exercise. Slowly but surely the results for the first sitting of the tests began to improve but as a Faculty we realise this is a work in progress.
- The new AQA Curriculum has been rolled out and used for six months this academic year (2015-16) allowing teachers the opportunity to familiarise themselves with the format and tests.
- The new Scheme of Work has been adjusted to accommodate ‘NRICH’ lessons which we see as crucial to embedding a culture of problem solving across the department.
- New lessons have been created and existing lessons have been amended to include ‘Mastery’ questions in the bellwork or plenary phases.
- There is a confidence in the Faculty that we are ready to begin the 2016/2017 secure in our knowledge of the new requirements to ensure the continued progress of pupils in the Mathematics Faculty.
Department for Education (DfE). (2013a). National Curriculum in England: Framework Document. London: Department for Education.
Kilpatrick, J. Swafford, J. & Findell, B.(eds.)(2001). Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee: National Research Council.
NCETM (2014a). Developing Mastery in Mathematics. [Online] Available from: https://www.ncetm.org.uk/resources/45776 [Accessed: 28th September 2015]
NCETM (2014b). Video material to support the implementation of the National Curriculum. Available from: https://www.ncetm.org.uk/resources/40529 [Accessed 28th September 2015]
NCETM (2015). National Curriculum Assessment Materials. [Online] Available from: https://www.ncetm.org.uk/resources/46689 [Accessed 28th September 2015]
Ofsted (2015) Better Mathematics Conference Keynote Spring 2015. Paper presented at the Better Mathematics Conference, Norwich, Norfolk.
Featured image: original image ‘Map of Mathematics Poster’ by Dominic Wallman, licensed under CC BY-NC-ND 4.0 https://www.flickr.com/photos/95869671@N08/32264483720