Research School Network: OFSTED Research Review Series: Mathematics Deb Friis picks out some of the key points from the recent maths research review from OFSTED

On 25^th May Ofsted released a new document in their Research Review series on Mathematics. It is a long document of 30 pages with a further 15 pages citing over 200 articles. What follows is a brief summary.

​“Ambition for all”

Although pupils in England achieve highly compared to other countries on average, there is a wider attainment gap between high and low achievers and also between advantaged and disadvantaged pupils. The report highlights the importance of the subject, but acknowledges that for some the subject remains ​“mysterious and difficult”.

Maths Curriculum Content

The report classifies mathematical content into three types of knowledge which can be prefaced by the sentence stems in the table below. The Type 2 sub-category represents the development of this knowledge over time.

Curriculum progression

The curriculum sequence should allow for systematic acquisition of knowledge of all types which can later be built upon to form consistent patterns of information. The initial focus should be on familiarity with facts and methods so that these can be reliably used when solving problems later on. The report emphasises the long-term impact of laying firm foundational knowledge and focusing on depth over breadth, covering fewer topics in more detail.

It is suggested that the risk of pupils falling behind is minimised by designing content and the sequence of content more centrally and using systematic teacher-led approaches early on in pupils’ school career. Positive attitudes towards maths and enjoyment of the subject come through success and teachers are advised to ​“put pupils on the causal pathway that leads from success to motivation”. Again it is emphasised that it is early proficiency and strong foundational knowledge that help avoid maths anxiety, and time is better spent closing gaps rather than removing tests or expecting students to learn through mistakes.

Curriculum sequencing

Declarative knowledge

The report discusses the start of the school journey and the importance of exposure to a ​“maths-rich” environment in the home to later progress in maths. It suggests that the playing field can be levelled by prioritising systematic provision of core declarative knowledge from an early age. Fundamental features such as pattern and structure should be made explicit, but care should be taken not to negatively impact pupils who are already proficient. Teachers should help pupils to develop automatic recall of key facts.

Procedural knowledge

The report suggests that manipulatives and representations should be non-distracting and used as a bridge to more formal methods later on. It warns against the use of a variety of informal procedures and self-generated methods and says that these may be self-limiting and encourage pupils to resort to guesswork. ​“Teachers can even teach methods of evaluation of algebraic expressions and ways to set these out as a series of steps for pupils to learn by heart”.

Conditional knowledge

Problem solving should come after pupils are fluent with the relevant facts and methods. They should be taught how to look for the deep structure beneath surface features and to make connections between topics. Although pupils who are already proficient may be able to use generic strategies to solve problems, this is not always the case, so strategies should be planned into particular topics.

Meeting pupils’ needs

Teachers should be cautious of allowing pupils to decide on their own pathway through mathematics as they may not know enough to make the right choices now. Problem solving should also be avoided as a differentiation strategy as this may mean that not all pupils are exposed to problem solving strategies. All core content and links should be an entitlement for all pupils. Content should also be revisited regularly so that learning can be consolidated.

The report suggests that pupils should stay together in classes ​“not because higher attainers are being held back, but because lower attainers can ​‘keep up’ “. It is advised that systematic instruction is particularly beneficial for pupils with SEND, and pupils who struggle should be given more time to complete tasks rather than different tasks.

Pedagogy

New learning

Again, the report makes the point that novices require explicit, systematic instruction and this will help to close the gap, and that in fact this method of instruction is beneficial to all pupils. Use of worked examples and intelligent variation is highlighted.

Consolidation of learning

Regular opportunities to rehearse and apply knowledge are important to transform initial moments of success to long term memories. Work should be supported by regular homework assignments and time should be given for practice and opportunities for overlearning. Choral response, timing and goal setting could be used. Teachers should create a balance between rehearsal of core facts, and explaining, justifying and proving. The report discusses good and bad features of textbooks and says that they are particularly important for low attainers. Comments are also made on computer technology, saying that core content should be followed by ​“mini-games”, but the report warns that not all pupils make the same progress when learning on computers. The ideal environment for periods of independent learning would be one with no background noise at all.

Assessment

Frequent low-stakes tests should be used but these should be formative rather than summative to avoid pupils who do not experience success becoming demotivated. The report suggests that competitive maths games could be used.

Systems at the school level

There should be an emphasis on high quality bookwork with systematic and orderly calculations which help pupils to spot connections and errors.

Teachers, particularly new teachers, will also benefit from regular opportunities to observe others, a chance to plan collaboratively and the provision of sequenced schemes of learning. There should be school-wide approaches to providing resources and time to develop knowledge of the subject and to learn from colleagues.

The full report can be found here.

There has already been much discussion of this report and its implications from all parts of the maths teaching community and this is sure to continue.

Deb Friis

Deb is a maths teacher at Durrington High School. She is also a Maths Research Associate for Durrington Research School and Sussex Maths Hub Secondary Co-Lead and is currently delivering our training on the EEF Guidelines for KS2 and 3 Maths.