What Changes To Secondary Maths Would You Like To Happen?
Mathematics is a discipline that blends creativity with rigor and curiosity with logic, providing the foundations for both scientific discoveries and technological enhancements. But, to what extent is the utility, beauty and power of mathematics evidenced in secondary mathematics education? Based on many pupils’ approaches to mathematics combined with exclamations of “But WHY do I need to learn about [insert any topic within the mathematics National Curriculum] I’ll never use it once I leave school!”, currently very little.
There has yet to be a cohort of GCSE students to ‘benefit’ from learning under the more challenging National Curriculum (introduced in 2014). In this interim time, pupils and in turn teachers are expected to ‘make-up’ the difference between pupil’s actual knowledge and the knowledge that they are expected to have mastered. Thus, I intend to discuss possible immediate changes within the classroom that may be implemented to reduce the associated problems or whether another major reform is necessary.
The principal aim of the current National Curriculum is for all students to ‘become fluent in the fundamentals of mathematics’ such branches of mathematics explored is limited to Number, Algebra, Probability, Statistics, Geometry (including measures) and proportion (including ratio and rates of change). According to the National Centre for Excellence in the Teaching of Mathematics, achieving fluency in a topic requires efficiency, accuracy, and flexibility in the application of knowledge.
Indeed, pupils should have the confidence to apply knowledge in different contexts and reason appropriately to choose effective representations and methods to solve problems. But are these skills assessed effectively within the trio of terminal assessments taken by students? How are different contexts represented in examinations? Craig Barton categorises the contexts seen in GCSE maths questions as either pointless, confusing, or dangerous. Such contexts either mask the simple calculations, tested within KS2 SATs, acting as a literacy barrier for many students, or result in oversimplification or contrived relationships with real mathematics involved in real life problems.
The supporting aims of the 2014 National Curriculum is for all pupils to ‘reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language’ and ensuring that all pupils ‘can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions’.
I, and many of the teachers I have spoken to, find the current assessment of such skills are formulaic, and do not provide students with the freedom to trial an unclear line of inquiry whilst having multiple successful methods of approach. Indeed, questions are often constructed so that students must follow a single correct line of inquiry to reach the intended correct answer. If students are asked to engage in multi-step problems, they naturally focus on the end goal of the question causing significant anxiety when they do not immediately know how to solve the problem. These questions culminate in the development of ‘mathematical anxiety’, leading to the avoidance of mathematics in all forms, providing the foundation for the public’s general negative attitude to mathematics.
What is the solution to this? So-called ‘Goal-free’ problems. According to AQA, the best Goal-free problems provide a relatively limited amount of information that students can generate from the given information. Indeed, providing support for students to adapt throughout completing the question. Such ‘Goal-free’ question prompts still require the application and retrieval of content taught, thus providing a suitable form of assessment.
Whilst there are undoubtedly pitfalls with the secondary mathematics curriculum, these barriers to students' learning can still be overcome whilst fostering a love of mathematics. Through passionate and knowledgeable mathematics teachers who can share their love of mathematics and expose pupils to the various branches of mathematics, pupils may succeed. Indeed, it is gratifying to see change in the student's maths confidence and attitude through teaching.
By Maths Scholar 2022/23
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