# Assessment Objective AO3

Having just completed (apart from the tidying up, query and edit process) the authoring of a collection of materials to accompany the new Collins 4^{th} edition Mathematics GCSE Foundation student book, it is apparent that AO3 has really become a focus of the new changes.

The brief required, for each chapter of the student book, a context based problem that “**will help to build students skills and confidence for tackling (AO3) problem-solving questions.”** When these are made-up into a video there will be a worked solution with audio commentary that talks the students through a suitable strategy for tackling the question and the skills needed to solve it.

There was a need to offer an evaluation opportunity, so that students could be prompted to evaluate the method used and the answer obtained. There also needed to be an opportunity to consider whether alternative methods could have been used.

The difficult task was not in creating contexts in which to locate problems, but thinking of ways in which to incorporate the syllabus requirements embedded in AO3, that students should be able to:

- interpret results in the context of the given problem
- evaluate methods used and results obtained
- evaluate solutions to identify how they may have been affected by assumptions made.

These will, within questions at Foundation Tier, make life difficult for students.

In the past, a question looking at different methods for purchasing something – a deposit of varying percentages followed by differing monthly payments – would require an evaluation of the results, but not the method used. Previously students have encountered questions that ask them to *explain*, *show*, *prove* but not to also incorporate comments about assumptions that they have made, or indeed a comment about the method they have used.

On top of this, more questions are going to be set in a context from which students will be required to extract information rather than be presented with a rather stark equation to solve or diagram asking them to workout *x*. So not only is there a requirement to interpret results, they have to interpret the question accurately as well.

This is going to present huge challenges if, like me, you work with students whose first language is not English, or students who maybe have poor literacy skills.

So what kind of questions can be expected, and how are they to be answered.

For example, when looking at properties of number I had a scenario involving three looping tracks in a model railway, circuit times were 18, 20 and 28 seconds. Part of the question involved finding the highest common factors of these numbers (1260 seconds or 21 minutes). The most efficient method is to use prime factor form (arrived at by different methods) but students could have started producing strings of multiples – an agonisingly long process, 18 would have a list of 70 multiples before arriving at 1260. For this part of the question an evaluation of method is possible, comparing the use of prime factors with the use of lists of multiples.

When examining direct proportion we are all used to questions such as,* 3 men take 6 days to build a wall. How many days would it take 4 men to build the same wall?* We would expect most of our students to come up with an answer of 4½ days, but would we also expect them to add that they assumed that the length of the working day was the same in each case, or that the 4 men worked at the same rate as the 3 men?

Questions may contain phrases such as, *Show how this is possible.* This is the clue to an *evaluative* solution being required. Not only do students need to produce a numerical answer, they then have to comment on that result, such as making a comparison of the result against an alternative. The question could also be one of comparing a method, for example, simple percentage change against repeated percentage change.

Because of context setting it is clear that students will have fewer clues as to the solution *from* the question itself – simple percentage change and repeated percentage change solutions might be triggered in a student’s mind by key words such as bank account, percentage interest, number of years invested. For example, I used the declining numbers in a wildlife population to cover this topic and, after calculating a population in a given year, ask students to evaluate models that two bird watchers had used to arrive at a forecast of population numbers. Students need to carefully consider the nature of the problem, devise a strategy, communicate the developing solution, and provide an evaluation with summary conclusion. The wording of questions will not immediately signal the method of solution.

We might conclude that from now on there is a good deal more *narration* expected.

Communicating method, describing the steps taken, clearly explaining the significance of a solution; these are the skills being extended under the new syllabus and embedded in assessment objective AO3.