Access to HE
Mathematics
GCSE Equivalent Scheme
Handbook
2011-12
Contents:
Section / Title / Page1 / Context / 2
2 / GCSE Equivalent Status / 2
3 / LASER Endorsement of GCSE Equivalent Status / 2
4 / Summary of Units in the Scheme / 3
5 / Assessment Methodology / 3
6 / Retention of sample marked assignments and test scripts / 4
7 / Claiming the Access GCSE Equivalence Certificate for Students / 4
Appendix 1 / Units / 5
Appendix 2 / Extract from Key Stage 4 Mathematics Requirements / 9
Access to HE Mathematics Equivalent Scheme
1. Context
This scheme has now replaced the previous AVA Mathematics GCSE Equivalent schemes inherited by Laser Learning Awards (LASER) from the former AVAs of OCNHIS and OCNKM.
LASER will endorse the scheme as being equivalent in standard to a GCSE grade C pass for appropriate student matriculation into HE purposes.
From 2011-12 onwards, this scheme will be the only GCSE Maths equivalence scheme endorsed by LASER. Older schemes will no longer be awarded a GCSE Equivalent certificate. Where other qualifications are used to evidence GCSE equivalence, this should be registered using APCL.
2. GCSE Equivalent Status
2.1 This scheme is only for use by students on LASER Access to HE Diplomas. The GCSE equivalent scheme for Mathematics is intended to enable Access students to meet the matriculation requirements for entry to a range of HE degree courses where a GCSE pass A-C grade is required.
2.2 The scheme does NOT have any function beyond this and is not intended to be used as a substitute for any statutory requirements placed on an individual in order to be competent to practice, whether this is as a teacher, nurse, or midwife etc.
2.3 Access centres must make clear the status of any GCSE equivalent to student upon commencement of the Access Diploma. Students obtaining a place on an HE course using a LASER approved GCSE equivalent scheme, must be advised that they may have to undertake additional statutory requirements (such as obtaining an actual GCSE or taking another prescribed test) in order to be qualified to enter a specific career.
3. LASER Endorsement of GCSE Equivalent Status
The status of GCSE Equivalence is conferred on the achievement of the units outlined below only when achieved as part of an LASER AVA Access to HE Diploma.
The following conditions and rules apply:
a) All four units totalling 12 credits at Level Two must be achieved by a student.
b) The ‘Minimum Assessment Requirements’ (see below) have been met
c) The credit achievement may be included in, or be additional to, the Diploma rules of combination where it is required for progression to HE.
d) Achievement of credit in other LASER-validated Mathematics units will not confer GCSE equivalence, although centres may use the LASER APL process where appropriate.
4. Summary of Units in the Scheme
Unit Title / Level / Credits / National Code / Unit Code / StatusShape, Space and Measurement / Two / 3 / RB42SE901 / SER945 / M[1]
Collecting, Recording and Analysing Data / Two / 3 / RB72SE904 / SER946 / M
Development of Ideas in Algebra / Two / 3 / RB32SE903 / SER947 / M
Number and Algebra / Two / 3 / RB32SE904 / SER948 / M
Total Credits / 12
Click on links to go to the unit details
5. Assessment Methodology
All learners must compile a portfolio of evidence comprising marked assignments which are mapped to the relevant assessment criteria in the units for internal verification and LASER external moderation.
5.1 Across the units, learners should be given the opportunity, and encouraged to:
· use and apply Mathematics accurately in practical, real-life situations as well as within the classroom
· recognise the rich historical and cultural roots of mathematics
· select mathematical tools that are appropriate to the problem
· use methods that communicate mathematics effectively
· understand the creative process in mathematics, combining understanding, experiences, imagination and reasoning to construct new knowledge
· develop convincing arguments, and pose appropriate questions to challenge others’ arguments
· use the abstract concepts of mathematics to model, interpret or represent situations.
5.2 The AVA is committed to regional standardisation in assessing the Access to HE GCSE equivalence Mathematics units. Therefore, for GCSE equivalence, the AVA requires all centres to undertake a standard pattern of assessment outlined below.
a) Centre-devised marked assessments: There must be evidence of achievement of all assessment criteria in all units. Mandatory assessment information is provided below. Centres should devise their own assessments, within the permitted assessment rules for each unit.
Units: Collecting, Recording And Analysing Data, and Shape, Space and Measurement
The assessment criteria for these units may be evidenced entirely or in part by work produced for the other units on an Access Diploma course. Alternatively centres may generate specific assignments or use a combination of specific assignments and other work produced on the Access Diploma.
b) Evidence from other parts of an Access Diploma: Where centres choose to draw evidence for achievement from other elements of an Access to HE Diploma, there must be a clear explanation of how the chosen evidence meets the assessment criteria in the relevant GCSE equivalence unit. This is best demonstrated by using a cover sheet for such pieces of evidence which clearly identifies how the evidence meets the individual criteria.
c) Written tests: At least two tests, of at least 40 minutes duration, must be set and marked internally and taken under examination conditions.
The centre must relate the contents of the tests to learning outcomes in the units listed below. At least one learning outcome from each of the units must be tested across the two tests.
· Development of Ideas in Algebra
· Number and Algebra
Centres could test all of the unit contents via appropriately set tests or supplement the test evidence with additional course work as required.
Unit Title / Level / Credits / Mandatory Test? / Course Work Option?Shape, Space and Measurement / Two / 3 / Y
Collecting, Recording and Analysing Data / Two / 3 / Y
Development of Ideas in Algebra / Two / 3 / Y / Y
Number and Algebra / Two / 3 / Y / Y
Total Credits / 12
6. Retention of sample marked assignments and test scripts
Centres should retain representative samples of marked student assignments relating to each unit in the scheme. Further guidelines can be found in the current version of the Access Quality & Moderation Guidelines but as a minimum centres should retain the equivalent of one full student portfolio of evidence for the scheme per year. These should be retained for a minimum of three years. An LASER Access external moderator will sample the evidence produced by students and will produce an annual report on each centre using the scheme.
7. Claiming the Access GCSE Equivalence Certificate for Students
The GCSE Mathematics Equivalence units must be included within the units available for the Access Diplomas at the centre. Where a student has achieved the required units, this should be recorded on the RAC in the usual way. The box claiming the GCSE equivalent for Mathematics for each learner on the RAC must also be ticked. At the point of certification the student will receive a certificate stating that s/he has achieved an equivalent to GCSE Mathematics grade C and above and the units will be listed on his/her credit transcript. LASER levies a charge to centres for each GCSE equivalent certificate produced per student. Please see current Access charges for further details.
Appendix 1 - Units
UNIT TITLE: Shape, Space and Measurement
LEVEL: Two
CREDIT VALUE: 3
UNIT CODE: SER945
NATIONAL CODE: RB42SE901
(Access/A2)
This unit has 3 learning outcomes.
LEARNING OUTCOMES / ASSESSMENT CRITERIA /The learner will: / The learner can: /
1. Understand and use properties of shape. / 1.1 Distinguish between specific triangles, quadrilaterals and polygons by their properties.
1.2 Distinguish 3D shapes by their properties and recognise their nets.
1.3 Measure angles in 2D shapes and deduce their size using the following:
- angles in a straight line,
- angles around a point, and
- opposite, alternate and corresponding angles.
2. Understand the basic trigonometry of a right-angled triangle.
/ 2.1 Calculate measurements using similar right-angled triangles.
2.2 Use Pythagoras' theorem to calculate the length of a side in a right-angled triangle.
3. Solve problems using measurements in two and three dimensions. / 3.1 Calculate, where appropriate, perimeters, areas, surface areas and volumes of simple regular shapes.
3.2 Interpret scale drawings.
3.3 Estimate measurements of everyday items.
3.4 Convert measurements between units (e.g. cm2 and m2) and make rough conversions between imperial and metric units.
3.5 Make calculations using compound measure (e.g. speed, density) and use appropriate units.
UNIT TITLE: Collecting, Recording and Analysing Data
LEVEL: Two
CREDIT VALUE: 3
UNIT CODE: SER946
NATIONAL CODE: RB72SE904
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES / ASSESSMENT CRITERIA /The learner will: / The learner can: /
1. Collect data for a purpose. / 1.1 Design and use a questionnaire to collect data comprised of open and closed questions.
1.2 Use data collection sheets to record data from a practical exercise (e.g. measuring temperature change over time).
1.3 Identify strengths and weaknesses of different methods of data collection.
2. Categorise and record data. / 2.1 Using information from tables, lists, or computer databases construct frequency and grouped frequency tables.
2.2 Using suitable examples distinguish between discrete and continuous data.
3. Represent and interpret data.
/ 3.1 Using suitable data construct bar charts, pictograms, pie charts and line graphs.
3.2 Interpret critically statistical diagrams and graphs, explaining the main features of the data represented.
3.3 Construct and use histograms with equal intervals from frequency distributions.
3.4 By drawing a scatter diagram and a line of best fit by inspection, comment on the correlation of the data.
4. Analyse data. / 4.1 Calculate mean, median and mode from lists, ungrouped and grouped frequency tables.
4.2 Calculate range and interquartile range.
4.3 Calculate the probability of a single event within the context of the data collection.
6
UNIT TITLE: Development of Ideas in Algebra
LEVEL: Two
CREDIT VALUE: 3
UNIT CODE: SER947
NATIONAL CODE: RB32SE903
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES / ASSESSMENT CRITERIA /The learner will: / The learner can: /
1. Manipulate algebraic expressions in order to solve problems. / 1.1 Change the subject of a formula where the subject appears in one term only.
1.2 Simplify expressions using the rules of indices.
1.3 Expand expressions involving brackets and factorise simple expressions.
1.4 Solve simple linear equations up to those including brackets, and where the unknown appears on both sides.
2. Use graphical methods to represent algebraic relationships. / 2.1 Construct a table of values from linear algebraic equations.
2.2 Plot the graph of a linear function from a table of values.
2.3 Use the formula y = mx + c to calculate the values of m and c from a graph or table of data.
2.4 Recognise and sketch graphs of y = x2, y = x3 and y = a/x.
3. Use graphical and non-graphical methods to solve algebraic problems.
/ 3.1 Solve simultaneous equations containing two variables graphically.
3.2 Plot the graph of a quadratic function.
3.3 Solve quadratic equations of the form x2 + ax + b = 0 using a graphical method.
3.4 Solve simple algebraic equations using a 'trial and improvement' method.
4. Perform an investigation, which leads to an understanding of sequences. / 4.1 Recognise and continue a pattern of numbers to a specified term.
4.2 Recognise patterns of triangular numbers.
4.3 Find an algebraic expression for the nth term of a linear sequence.
UNIT TITLE: Number and Algebra
LEVEL: Two
CREDIT VALUE: 3
UNIT CODE: SER948
NATIONAL CODE: RB32SE904
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES / ASSESSMENT CRITERIA /The learner will: / The learner can: /
1. Demonstrate an understanding of mathematical language with respect to number. / 1.1 Use the following terms appropriately: whole numbers, natural numbers, integers (both positive and negative values), digits, factors, prime numbers, fractions, decimals, reciprocals, percentages, indices, standard form.
1.2 Identify place value.
1.3 Convert percentages to decimals and fractions and vice versa.
1.4 Recognise square numbers up to 15 x 15 and the cubes of 2,3,4,5 and 10.
2. Undertake and solve mathematical problems. / 2.1 Perform calculations using addition, subtraction, multiplication, division and simple applications of ratio using the types of number and terms stated in 1.1.
2.2 Perform calculations involving brackets and apply operators in the correct order.
2.3 Round numbers to a stated number of significant figures or decimal places.
2.4 Estimate the results of calculations.
2.5 Choose and use appropriate levels of accuracy to express an answer.
3. Demonstrate an understanding of the need for and use of symbolic notation, and use correctly. / 3.1 Substitute numerical values into given formulae.
3.2 Perform addition, subtraction, multiplication and division using algebraic terms.
4. Use a Cartesian graph to represent information. / 4.1 Draw axes with appropriate scales.
4.2 Plot points using Cartesian co-ordinates.
4.3 Interpret and sketch graphs from practical situations (e.g. Hookes Law).
4.4 Extract information from graphs (e.g. conversion or distance/time graphs).
4.5 Extrapolate and interpolate graphical data and draw a line of best fit.
Appendix 2: Extract from Key Stage 4 Mathematics Requirements