Mathematics

 

Aims and Purpose of the Mathematics Curriculum

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Department View

‘You don’t have to be a mathematician to have a feel for numbers’

John Forbes Nash

 

Mathematics is an essential part of our students’ education.  The skills mastered will be used throughout the whole life of our students from telling the time, managing their finances, cooking for their families, completing a DIY project or problem solving, as well as in their future careers.

 

Throughout their five year journey of studying mathematics at Sewell Park Academy our students are encouraged to explore how different elements of mathematics are integrated into the world around them; both in terms of practical problem solving, as well as the application of skills to a wide variety of contexts.  Emphasis is also placed on making cross curriculum links to showcase how mathematical fluency can facilitate learning, understanding and success in other disciplines and settings.  

 

Alongside the core curriculum of mathematical knowledge, we believe that it is essential for students to gain a 360 degree exposure to the history, developments, discoveries and emerging ideas within mathematics.  In addition, we also feel it is integral for students to see, and appreciate, the beauty of mathematics from symmetry in architecture to how it can be seen in the world of nature.  These elements are introduced and explored with our students through our wide ranging ‘big ideas’ programme. 

 

Our overarching purpose is to inspire and enthuse the next generation as well as introduce ideas of careers and options which students may not necessarily have previously.  We believe this will open the minds of our students to the diverse range of opportunities that success in mathematics provides.

 

National Curriculum

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Purpose of study 

Mathematics underpins everything we do on a daily basis.  By studying mathematics our learners will be able to perform calculations, analyse information and make informed and reasoned decisions across a wide range of situations and settings.  A confident Sewell Park Academy learner will:

• have a solid and balanced understanding of the concepts from the six core branches of mathematics (algebra, number, ratio and proportion, geometry and measure, probability and statistics);

• be able to investigate and patterns; they should be able to apply problem solving techniques, recognise and describe patterns as relationships with generalised rules as well as drawing conclusions consistent with findings;

• be able to communicate effectively in mathematics; they will be able to use appropriate mathematical language (notation, symbols and terminology) appropriately and accurately in both oral and written explanations.  In addition, learners will also be able to use different forms of mathematical representation such as formulae, diagrams, tables and charts;

• learn to critically reflect on their findings; specifically, students are encouraged to consider whether their results make sense in the context of a problem and interpret the meaning of their results.

 

Aims 

The overarching aim for mathematics in the national curriculum is to promote high standards of numeracy, reasoning and problem solving by equipping pupils with a strong command of the fundamentals of mathematics.  The national curriculum for Mathematics aims to ensure that all pupils: 

 

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;

• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;

• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

 

Habitus Curriculum

 

Big Ideas

 

Across the five years of study of mathematics at Sewell Park Academy students are exposed to 40 different ‘big ideas’ which reflect some of the most interesting, thought provoking and practical ideas within mathematics.  None of the big ideas are part of the National Curriculum or examination syllabus but, instead, are designed to enrich and inspire students about the history, applications and broader ideas linked to our subject.  The big ideas are grouped into five distinct themes with a particular theme linked to each of the five years of study.

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Future You

 

A programme of ‘Future You’ careers is being developed with roles being linked as closely to units where possible.  The roles are linked to the year group and unit so, by the end of Year 11, every unit student will have been introduced to 106 different careers.

Academic Literacy

 

Academic literacy is an integral component of the mathematics curriculum and is delivered on a formal and informal basis throughout each topic as part of everyday lessons.  Students are encouraged to use, in correct context, mathematical language and terminology to describe concepts and ideas as well as to reason, justify and communicate their decisions and ideas.

 

The three formal components of our academic literacy built into teaching routines and practice are outlined below:

 

1 - Use and understanding of keywords and mathematical terminology

Alongside each unit there is a list of identified keywords and mathematical terminology that students need to recognise, understand the meaning of and be able to use in context to assist their fluency in that unit of work.  This list is differentiated in accordance to the three stages in years 7 to 9 and the four stages in years 10 to 11.  Furthermore the list is split into ‘red’ and ‘black’ components; the red being keywords and terminology that is deemed to be essential and therefore must be defined with students during the unit at the first opportunity presented and those in black which teaching staff may feel beneficial to also explicitly define during the teaching of that unit.

 

Alongside the teaching of this component specific care needs to be given with some of the polysemy terms in maths such as the term ‘parallel’, where its meaning in different units varies (eg properties of a 2D shape versus parallel lines in the context of equations of straight lines).

 

In addition staff are encouraged to discuss the etymology of words (such as the word ‘polygon’ being made up of the components of ‘poly’ (many) and ‘gon’ (angles).  Through this approach we believe that we can assist in extending the vocabulary of students both within mathematics and across a wider content (eg ‘polymer’ being a chemical of many repeating units’).

 

The keywords (along with agreed definitions over time) will be shared with the Raising Achievement team for integration and development within the catch up and nurture programmes that are delivered.

 

A list of keywords, terms or phrases linked to each unit (broken down into the different stages of learning) can be found here.

 

 

2 - Key processes and instructions focused on common misconceptions within a unit of study

Within each unit of study (differentiated for each unit of study where appropriate, consideration has been given to identifying three common misconceptions which, if mastered, will significantly assist understanding, accuracy and progress within the unit.  For each of these misconceptions students will write a set of instructions as to how to complete a specific process or task (for example how change the subject of an equation).  These instructions can be delivered via a range of written methods including:

 

• Step by step instructions;

• A worked example that explains each step of the process being performed;

• A flow chart (which may be useful where there are different outcomes to consider);

• Looking at a worked example where a mistake has been made and explaining the error and then writing out instructions to correctly perform the process (with the extension option of explaining what checks could be carried out to identify the error where applicable).

 

3 - Exploring and discussing mathematical misconceptions

Linked to work in section 2, students will be set three starter tasks per unit which focus on a question (or questions) linked to misconceptions previously explored.  These questions will be differentiated by stage of study.  The questions will take the form of:

 

• A statement which is either true or false (or maybe both true and false depending on the circumstances);

• A question asking “how would you approach this problem”;

• A question asking to “explain the steps” to solve a mathematical process;

• A question asking to explain the difference between a polysemy term (eg “what is the difference between ‘finding one half’ and ‘raising to the power of one half?’;

• A question asking for the link between two ideas (eg the link between x12 and x-12).

In each case students will be required to justify their answers (using appropriate mathematical language and terminology) with attention being given to accurate reading of the question posed and ensuring that the answer given actually covers the requirements of the question.  

 

A google sheet for the delivery of section 2 and 3 of the academic literacy strategy can be found in the academic literacy resources folder.  Each sheet contains the link to each specific starter activity as well as notes to assist non subject specialists understand the specific issues with each of the misconceptions defined.