This page looks more closesly at the process involved in matching each PIM question to the appropriate APP assessment criteria and explains some of the more complex examples.
Each question in the written and digital versions of the PIM tests has been matched as closely as possible to the sub-point at the appropriate level taken from the four Maths assessment focuses in the APP Assessment criteria for levels 2 to 8, these being:
- using and applying mathematics
- number
- shape, space and measures
- handling data
The mappings have been informed by the Curriculum content categories given in Table 3 of the Teacher’s Guide for each test.
Some of sub-points in the APP Assessment criteria are quite detailed, but the overall coverage is narrower than the National Curriculum Programme of Study. So, for example, ‘place value’ is mentioned under ‘numbers and the number system’ at all of levels 2, 3, 4 and 5, but only very specific aspects are mentioned at each level, as illustrated below.
| Level | Sub-point |
|---|---|
| 2 | Begin to understand the place value of each digit; use this to order numbers up to 100 |
| 3 | Understand place value in numbers to 1000 use place value to make approximations |
| 4 | Use place value to multiply and divide whole numbers by 10 or 100 |
| 5 | Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000 and explain the effect |
So understanding place value in numbers over 1000, for example, does not appear.
Let's take this a step further and look at some mapping examples in detail:
1) Place value is an essential aspect of a wide range of mathematical problems, including, for example, Question 22a in PIM 14. This requires pupils to use the number fact:
325 × 648 = 210600
to fill the gap in:
32.5 × _________ = 2106
This problem, which is pitched at level 5, requires pupils to reason about place value, but it does not really involve multiplying and dividing whole numbers and decimals by 10, 100 and 1000. In the original Curriculum content categories in Table 3 of the Teacher’s Guide, this particular questions was attributed to Calculations. It was therefore decided to attribute the question to a level 5 Calculating sub-point (Use known facts, place value (and) knowledge of operations … to calculate). However, this is clearly only one of a range of possibilities, none of which fit exactly but all of which are defensible.
2) Where a question clearly assesses sub-points that have been specified at a different level in the APP criteria, and does not seem to fit comfortably with anything at the level of the question, it has sometimes been mapped to the adjacent level sub-point with an indication in the table that this has been extrapolated up or down to the level of the question.
So, for example, Question 4 in PIM 11 asks pupils to calculate the number of vans carrying 192 boxes that can be filled with 62400 boxes.
This question is pitched at level 4, but it does not really fit any of the ‘Calculating’ sub-points at that level. However, it does match the level 3 sub-point -`solve whole number problems`including those involving multiplication or division – but with numbers that go beyond the range expected at this level. This question has therefore been mapped to this level 3 sub-point, but with an indication that this has been extrapolated up to level 4.
3) On the other hand, Question 5 in the same test requires pupils to match angles of 10°, 60°, 120° and 170°, drawn in various orientations, to their measures. This question is again pitched at level 4, but Angle is not mentioned at all at this level, or, indeed, at level 3. At level 5, however, pupils are expected to measure and draw angles to the nearest degree, when constructing models and drawing or using shapes. This goes beyond the demand of the level 4 question, but the ability to identify an angle of a given measure is a necessary precursor to the level 5 skills. This being so, the level 4 question has been mapped to the level 5 bullet point, but with an indication that this has been extrapolated down to level 4.
Other examples of extrapolations up or down can be found in the mapping grids.
Go to PIE/PIM Mapping Grids.
Go to Assessing Pupils' Progress.
Go to Assessment Focuses.
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