The truth about calculators for Maths A Levels - Will Hornby

This blog was originally published on 07 June 2017.

Important update:

We continue to receive lots of questions about which calculators are allowable and/or required for the new AS/A Levels in Maths and Further Maths, so in this updated blog we’ll answer these questions and clarify the requirements.

First, we must say that we do not, and cannot, endorse specific calculators. Second, this guidance is specifically about the assessment of the qualifications; what you use in the classroom is entirely up to you.

The rules about what you can and cannot have are covered by two documents: the JCQ Instructions for Conducting Examinations and the specification document for the particular qualification. There is a wide range of calculators that satisfy the requirements in these documents.

GCSE students may be interested to know that any calculator that meets the A level Maths criteria will be permitted for the calculator papers on GCSE (9-1) Mathematics (and OCR 6993 FSMQ: Additional Mathematics). 

Teachers may also be interested to know that most of the newer calculator models also have computer based emulators. These are useful for whole class teaching demonstrations, and can be used by candidates as part of special access arrangements (Mathematics assessment - the use of computer technology as part of special access arrangements).

The latest version of the JCQ Instructions for Conducting Examinations (Instructions for conducting examinations 2019 – 2020) details the general guidance on calculators in Section 10. Using Calculators (page 16)

In practical terms this bans symbolic functions or Computer Algebra Software (CAS), along with the ability to communicate. This precludes some of the more expensive graphical calculators, but not most.

Calculators must be:

* of a size suitable for use on the desk;
* either battery or solar powered;
* free of lids, cases and covers which have printed instructions or formulas.

The candidate is responsible for the following:

* the calculator’s power supply;
* the calculator’s working condition;
* clearing anything stored in the calculator.

Calculators must not:

* be designed or adapted to offer any of these facilities: -

    * language translators;
    * symbolic algebra manipulation;
    * symbolic differentiation or integration;
    * communication with other machines or the internet;

* be borrowed from another candidate during an examination for any reason;

* have retrievable information stored in them - this includes:

    * databanks;
    * dictionaries;
    * mathematical formulas;
    * text.

JCQ – Instructions for Conducting Examinations 2016 -2017

The requirements from the specification document depend on the qualification. I’ll deal with Mathematics first, then Further Mathematics. Note that this guidance is correct for both OCR A and OCR B (MEI). The only paper with special rules is the OCR B (MEI) Further Mathematics option Further Pure with Technology, for which see the specification.

GCSE students may be interested to know that any calculator that meets the A level Maths criteria will be permitted for the calculator papers on GCSE (9-1) Mathematics (and OCR 6993 FSMQ: Additional Mathematics).

Teachers may also be interested to know that most of the newer calculator models also have computer based emulators. These are useful for whole class teaching demonstrations, and can be used by candidates as part of special access arrangements (Mathematics assessment - the use of computer technology as part of special access arrangements).

Mathematics

The DfE Subject Criteria for Mathematics says the following:

Use of technology

8.    The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A Level mathematics.

Calculators used must include the following features:

    * an iterative function
    * the ability to compute summary statistics and access probabilities from standard statistical distributions.

Department for Education Mathematics AS and A Level Content, April 2016

The first sentence is about the teaching and learning of the course. We are interested in the two bullets about what calculators must have.

• An iterative function: this refers simply to the use of the “Ans” button in order to perform iterations efficiently. Almost all calculators now have this capability and students may well be used to using it from GCSE Maths. For more sophisticated calculators it might involve the use of a table or spreadsheet function, but there is no need for these.
  
• "The ability to compute … and access ....” This requirement is the more complex one. 

In the specification we are more specific about it and state that it is the binomial and normal distributions that they need. Note that it doesn’t say that calculators must have specific statistical functions that find the probabilities. I think that there are three (or four) categories of calculator to think about:

1. Those scientific calculators that include Binomial and normal distribution functions, such as the Casio fx-991EX ClassWiz or Texas Instruments TI-30X Pro. These calculators are the balance point between ease of access to the probabilities and cost/complexity.
2. Graphical calculators, so long as they have the relevant functions (but do check with older models) and don’t have computer algebra software, ways to communicate etc., are absolutely fine, but they are not necessary. The scientific calculators mentioned above, plus computer or mobile phone software such as Geogebra, Desmos or Autograph form a complete tech solution for the classroom.
3. Simpler scientific calculators, which may have a normal distribution function, but don’t have a binomial function. These calculators are fine, up to a point, so long as they have a sigma function to sum cumulative binomial probabilities. The issue is that when n gets large, the calculator will not cope with the factorials.
   
   Calculators with binomial distribution functions will rely on the normal approximation to the binomial, but your AS Level students won’t be able to use that get around unless you teach it to them.
   
   If you need to find inverse probabilities, then you will need to do some trial and improvement, or in some cases use an inbuilt table function. This class of calculator is not ideal; they will do in most cases, but there may sometimes be assessment items that students cannot access.
4. Even simpler scientifics without either of these functions, but with a definite integral function and a sigma function. If you are willing to memorise the normal distribution function, then you can find those probabilities. Again, the inverse function requires trial and improvement, and binomial with large n requires the normal approximation to the binomial. This is really not ideal, and we wouldn’t recommend this approach.

Further Mathematics

For Further Mathematics there is an additional requirement from the DfE’s Subject Criteria, which is that calculators used must have the ability to perform calculations with matrices up to at least order 3 x 3. For both OCR A and OCR B (MEI) the only additional clarification is that the standard statistical distributions they should be able to access includes the Poisson distribution if they are taking the Statistics option. Since the two calculators mentioned above include both matrices and the Poisson, they are suitable for these Further Maths qualifications as well or students may use graphical calculators (without CAS, etc.) if you/they prefer.

General approach to calculator use in assessment

For the two OCR suites we have taken a joint approach to calculator use in the assessments that both allows the technology to permeate the teaching and learning, and also gets rid of the awkward grey areas that exist in the legacy specifications about what one can, or cannot, offload onto the calculator.

The rule is that “Allowable calculators may be used for any function they can perform.”

The new qualifications allow students to use functions such as polynomial solvers, definite integrals, gradient at a point and simultaneous equation solvers as standard.

Knowledge of performing these functions is still required by the content and can be assessed in specific questions that indicate students should provide a response featuring ‘detailed reasoning’ (for more information on such questions, please see below), without also using marks in other questions on these basic skills.

It also serves to increase access for weaker learners to questions that they might otherwise not be able to access because they cannot perform the basic techniques, allowing them to demonstrate their ability to interpret the outcomes of modelling or problem solving processes in a way that would otherwise be much harder, and more synthetic, to engineer.

It is frequently the case that a well-prepared and fluent student can perform these functions without a calculator just as quickly, or even more quickly. It is not a requirement to use a calculator all the time, rather it is about developing appropriate use of technology, which will depend to some extent on the student.

When a question includes the instruction “In this question you must show detailed reasoning” students must give a solution that leads to a conclusion showing a detailed and complete analytical method.

Their solution should contain sufficient detail to allow the line of their argument to be followed. This is not a restriction on a learner’s use of a calculator when tackling the question (e.g. for checking an answer or evaluating a function at a given point), but it is a restriction on what will be accepted as evidence of a complete method.

For more details, please see the specifications and sample assessment materials available via ocr.org.uk/alevelmaths.

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