Aligning curriculum and assessment reform with secondary school mathematics instruction

Mathematics is essential both for solving everyday problems in life and work and for helping shape the world around us, from industry and commerce to technological and scientific breakthroughs. In order for young people to receive an effective, high-quality mathematics education, a rigorous and consistent curriculum is required that gives students the knowledge and confidence to succeed.

In this two-part series, Carol Knights, NCETM Director of Secondary Mathematics, and I suggest ways to improve the secondary mathematics curriculum and assessment. This first post looks at the content of the curriculum. The second concerns assessment, which has a powerful influence on the teaching and learning of secondary mathematics.

Part 1: Curriculum

Improving transition from key stage 2 to 3 in mathematics

In a previous NCETM Director’s blog post, Debbie Morgan, NCETM Director of Primary Mathematics, and I discussed the mathematics curriculum for Key Stages 1 and 2. We argued that:

“…an overloaded curriculum remains a barrier to realizing the full potential of the Teaching Mathematics for Mastery program.” School leaders and teachers feel the tension between mastery and coverage, often unable to give all students enough time to fully grasp key concepts. Reducing curriculum content will give experienced teachers enough time to ensure that all students can build a deep and strong foundation of core content. This will lead to better results at Key Stage 2 – well above the current 50% ‘pass rate’ – and a cohort of pupils ready to study mathematics and related subjects in secondary school and beyond.”

Overloading the primary school mathematics curriculum causes problems in key stage 3 in two ways:

Many students enter Key Stage 3 without a clear understanding of key core content. This means that 7th grade teachers often have to reteach basic concepts rather than just review them so that students can master the middle school curriculum.
7th grade students often feel like they have “done it before” – regardless of whether they actually mastered the concept at a deeper level the first time. This can result in students becoming demotivated, distracted, and frustrated when repeating what they think they have already been taught.

An important aspect of NCETM’s Essentials of Teaching Mathematics for Mastery is that:

“Significant time is spent developing a deep understanding of the key ideas that are needed to support future learning.”

Maths Key Guide for Stage 3created by NCETM and published by the DfE in 2021, recognizes that the curriculum is overburdened at Key Stage 2 and provides detailed advice on how to alleviate the problems it causes. This guide helps secondary school mathematics teachers address students’ lack of understanding of core primary school mathematics content, but it cannot address the negative impact on student motivation that results from having to repeat “primary school” work.

We know that pupils’ progress in mathematics often stalls at key stage 3, particularly for disadvantaged pupils. ^I. The right curriculum, so that pupils’ knowledge of the primary mathematics curriculum is robust and secondary teachers do not have to re-teach key concepts, will help pupils have a more positive experience of the transition to mathematics at Key Stage 3, supporting better engagement in Key Stage 3 and stronger results by the end of Key Stage 4.

One aspect of the KS2 curriculum that carries over to KS3 is the formal calculation of fractions for two main reasons:

To give KS2 students enough time to gain a clear understanding of fractions before moving on.
Teach formal calculations when students are ready, consistent with high-performing international jurisdictions. ⁱⁱ.

Key Stage 2 will focus on developing a strong understanding of fractions through comparison in different contexts. A strong emphasis on reasoning, including equivalence, will lay the foundation for future use of common denominators and mental strategies for comparing and ordering fractions, as well as for calculations with fractions.

Teachers’ experience shows that students in grades 5 and 6 often have difficulty formally calculating fractions. Although students in Key Stage 2 can perform these calculations procedurally, their understanding is often too superficial to apply effectively to later problem solving.

Updating the high school math curriculum to improve learning for all

Mathematics education at Key Stages 3 and 4 should ensure that:

All pupils master Foundation Mathematics, enabling them to apply mathematics throughout the secondary curriculum, in work and in life, and enabling them to progress to further education, including Foundation Mathematics, which requires the application of Foundation Mathematics after age 16.
Many students also develop their mathematical knowledge, giving them the opportunity to study after 16 years of age, which may enable them to access higher education and/or careers in disciplines that require a high level of knowledge in mathematics and data analysis.
All students develop a positive attitude towards mathematics, appreciating its beauty and usefulness.

The current secondary school mathematics curriculum and assessment structure means that many pupils do not perform these functions well.

Mastering fundamental mathematics for life and work meets the goal of the current Foundation level GCSE mathematics, but the current Foundation level curriculum is too long and contains topics such as solving quadratic equations and using trigonometric functions that do not overlap. to this end. The consequence of this curriculum overload is that teaching and learning are often rushed and superficial, preventing many students from mastering fundamental mathematics. Students may perceive mathematics as an ever-expanding set of rules and instructions to memorize rather than as a coherent and coherent discipline.

We recommend some reduction in the mathematical content that all students should learn. In addition to the general reduction of the curriculum for these students, we would add the use of spreadsheets, which are ubiquitous in work and daily life and promote a practical understanding of algebra. We would also like to add a basic understanding of risk and the application of mathematics to personal finance. Such a curriculum can still be demanding, rigorous and entirely mathematical, as MEI’s work on potential GCSE resit reform shows. ^III.

To prepare for courses that require high levels of mathematics and data analysis, many students must also master the broader high school mathematics curriculum, which should be revised to ensure that its content develops the mathematics and data skills needed for support for learning after 16 years of age. in disciplines requiring a high level of quantitative knowledge and skills.

As part of the overall curriculum review, the mathematics curriculum and other quantitative subjects should be aligned to ensure coherence and consistency and to highlight the transferable nature of mathematics skills. Examples include rearranging equations and interpreting data and graphs. The Royal Society’s Mathematical Futures report highlights the importance of consistent mathematics and data education across the curriculum. ^iv. The curriculum and the way it is taught should emphasize the usefulness of mathematical knowledge and skills so that students see the value of learning mathematics beyond just passing an exam.

Developing a deep mathematical understanding is inspiring and engaging, expanding students’ thinking and helping them appreciate the beauty of mathematics as well as its usefulness. Examples include the relationships between fractions, decimals, and percentages, connections between equations and their graphs, and how trigonometric functions relate to the unit circle.

Providing more space in the curriculum for pupils to develop a robust and coherent understanding of mathematics and emphasizing its usefulness in other subjects and for work and life will help pupils develop positive attitudes towards mathematics. This will improve achievement and speed up progression to Foundation Mathematics, AS/A Level Mathematics and Further Mathematics after 16 years.

Conclusion

Moving formal calculations with fractions from the KS2 curriculum to the KS3 curriculum will encourage deeper learning in mathematics, allowing more time in primary school to explore other aspects of the KS2 curriculum. This will improve students’ math transition from primary to secondary school.
Reducing curriculum content at foundation level GCSE maths will give more time for all pupils to master the fundamental maths everyone needs, helping to boost young people’s maths confidence.
The usefulness and application of mathematical knowledge and skills should be emphasized, ensuring that the curriculum is relevant to work, life and further learning in an increasingly mathematics and data driven world.
A curriculum that emphasizes developing a deep and coherent understanding of mathematics, as well as an appreciation of its beauty and usefulness, will help students develop a positive attitude toward learning mathematics.

We know that assessment often drives teaching in the secondary classroom. ^V. Reform of the secondary school mathematics curriculum should be considered alongside assessment. To help young people achieve a deep and coherent understanding of mathematics, assessment must enable pupils to demonstrate their mathematical knowledge and skills, and their ability to use mathematics to solve problems in context. In part two, we look at how secondary mathematics assessment can be redesigned to support the development of robust, transferable knowledge and skills.

^I XTX Markets – Ways to develop mathematics

ⁱⁱ Learning fractions doesn’t have to be hard (NCETM)

^III New GCSE mathematics syllabus for post-16 students (MEI)

^iv Royal Society Mathematical Futures Program

^V Coordinating mathematics success: mathematics subject report (Ofsted).