What works in maths?

Written by: Suzanne O'Connell | Published:
Image: Adobe Stock

Maths is one of the subjects reported on in Ofsted’s series of research reviews. Suzanne O’Connell looks at the main themes and messages in the report and the implications for practice in our primary schools


Since Ofsted announced its renewed interest in the curriculum, it has begun publishing a series of research reviews and subject reports.

The reviews are designed to collate the research evidence that is available for a particular subject. Following the research review, subject reports are published. These are based more upon what inspectors find in schools when they visit. Both types of report are designed to help schools improve and develop their curriculum.

So far, there have been research reviews into history, music, geography, languages, science and RE. The maths review was published at the end of May (Ofsted, 2021) and explores the literature available as a preface to the publication of a subject report later this academic year.

The review classifies maths according to three categories of knowledge:

  • Declarative knowledge: Facts, formulae, concepts, principles and rules. This is conceptual understanding or the “I know that...”
  • Procedural knowledge: Methods, algorithms and procedures. This focuses on principles and mechanisms or the “I know how...”
  • Conditional knowledge: The ability to reason and solve problems. This focuses on reasoning or the “I know when...”

A major concern of the review is the gap between low and high achievers and the attainment gap between disadvantaged and advantaged pupils. This is an on-going issue that is not solely restricted to maths education, as we know.


Early mastering of the basics

According to the research presented, it is important for children to build their core knowledge at an early stage. The teaching of maths in the early years when children are “novice learners” needs to be daily and dedicated. Some of the basics they refer to include:

  • Automatic recall of number facts.
  • Familiarity with the main concepts such as the associative, distributive and commutative properties.
  • Fundamental features such as pattern and structure.
  • Conceptual building blocks for algebra.

However, this is not without its complications. Schools must also be wary that while they are trying to ensure that the basics are firmly embedded for less able students, those who already came to school with facts established should not become bored or disengaged. This is a conundrum for schools that is not easily solved.


Structured curriculum

The review clearly endorses the use of a systematic approach and the use of textbooks: “Systematic teacher-led approaches, particularly in the primary key stages, lead to better attainment. These then give pupils more opportunity to succeed in secondary school.”

The review acknowledges the importance of having a positive attitude but indicates that this is achieved through being successful at the subject rather than the use of games and other methods in an attempt to make maths more “enjoyable”.

They warn against removing tests for pupils who have experienced failure but instead advocate ensuring that they are more successful in them.

Teaching should follow a “pre-planned pathway” with the clear identification of what teachers want pupils to know. It warns against giving pupils ownership of their own path of progression.


The use of resources

The review is hesitant about the value of using everyday objects or “semi-concrete representations” when it comes to developing calculation methods. They suggest that the use of manipulatives does not always guarantee understanding and that it can become a distraction.

However, the use of a counting frame, such as a soroban, has been found among the approaches used in those countries where pupils experience early success. Pen and paper methods are in favour and readers are referred to the appendices of the national curriculum for examples of the format to use.

Informal methods are blamed for possibly inhibiting understanding later on. Informal and diagrammatic methods should only be used for a short amount of time and as a bridge to formal written methods. Scaffolds, frames, physical apparatus and alternative information sources are to be used sparingly and not relied upon as an “outsourced memory”.

The review appears to support independent work conducted in a quiet, if not silent, environment with group work being beneficial if it is “tightly managed”. Presentation is important in books so that pupils can spot errors, although there is also room for rough calculations.


Problem-solving

The review makes it very clear that pupils must be equipped with the correct knowledge to apply to their problem-solving endeavours. Problem-solving requires that pupils are taught:

  • The useful combinations of facts and methods.
  • How to recognise the problem types.
  • The deep structures that these strategies link to.

Fluency in facts and methods comes first. Again, it is recommended that teachers encourage their pupils to apply systematic strategies rather than relying on guesswork or unstructured trial and error.


The issue of differentiation

This is referred to in the report under “equity”. It is acknowledged that there seems to be little differentiation in East Asian classrooms but in spite of this all groups of pupils appear to do well.

For pupils with SEND the rehearsal of declarative and procedural knowledge is recommended along with teaching them the facts in a planned and systematic way. Research evidence suggests that pupils with SEND should be given more time to complete tasks rather than different tasks in order to commit core facts and methods to long-term memory. Textbooks are promoted as being particularly important for low attainers.


Consolidation

There have been times in the past when teachers were afraid to refer to “consolidation”. The review accepts that there should be opportunities for pupils to rehearse what they have learnt and that practice is a key component of any maths curriculum.

They describe this as the transfer of initial moments of success, realisation and understanding into long-term memories.
It is suggested that homework assignments can be a useful tool in ensuring that there is sufficient practice of key concepts learnt and that teachers should be encouraged to set pupils tasks that enable them to rehearse facts, methods and strategies.

Rehearsal for younger pupils can include games, songs, dominoes, counting sequences and be assisted through the use of computers.


Assessment

The review suggests that a mixture of approaches is ideal with regular tests of recently taught content alongside a final summative assessment. It is important that pupils are able to achieve a degree of proficiency so that they experience success in testing and are motivated to continue.

They refer to the importance of “low-stakes” testing which is more closely aligned with recently taught content. This might be timed to encourage the automatic recall of facts. Consideration should be given to the setting of stories and problems so that language is not a barrier.


Teacher training

There is an emphasis on teachers working together sharing ways of teaching within a framework of a school-wide approach. Young maths teachers should:

  • Have opportunities to observe and be mentored by experienced and successful teachers of maths.
  • Be provided with sequenced schemes and systematic plans supported by textbooks and teacher notes.
  • Have opportunity to engage in collaborative planning with more experienced and successful maths teachers.


Drawing comparisons

Research referred to in the review looks to the success of Asian countries and their level of maths fluency. The link is made to the methods they use. However, no strategy is directly transferable from one country to another. The impact of culture, history and expectations are important and must be given full recognition for the role that they play. Using this research review as their benchmark, it will be interesting to see how Ofsted reports on maths education during its school inspections in the coming months.

  • Suzanne O’Connell is a freelance education writer and a former primary school headteacher.


Further information & resources


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