1. An introduction to Progressive Achievement Tests in Mathematics (PATMaths) Fourth Edition

2. About the tests PATMaths Fourth Edition:
Consists of ten mathematics tests suitable for Years 1 to 10
Can be used to track development of mathematics skills over time
Includes multiple-choice items covering number, algebra, geometry, measurement, statistics and probability
Provides group reports and individual reports showing performance by item and strand
Provides norm reference data based on an Australian student sample
Provides detailed information on students’ strengths and weaknesses to inform teaching and learning.

3. The Results What does all this mean?
All tests provide the following information:
Test score (total of correct responses)
Scale score
Percentile rank
Stanine
Mean and standard deviation of scale and test scores
Diagnostic information to inform teaching.
What does all this mean?

4. Test Interpretation Scale Scores
Scale scores enable results on tests of different levels of difficulty to be compared. Scale scores take into consideration both the level of difficulty of the test items and the level of ability of students and are used to measure progress.
For example, a test score of 18 on PATMaths Test 1 is equal to a scale score of 102.5, whereas the same test score on PATMaths Test 2 is equal to a scale score of In both cases the standard error of measurement is 3.9.

5. Test Interpretation Percentile Ranks
Percentile ranks provide a simple means of indicating the rank order and position of the student’s result in relation to the reference sample.
For example, a student with a percentile rank of 45 has a score that is higher than the score obtained by 45 per cent of the reference group students. A student with a percentile rank of 96 has a score that is higher than the score obtained by 96 per cent of the reference group.

6. Test Interpretation Stanines
Stanines are derived from percentile ranks. Percentile ranks are divided into 9 categories – called stanines (short for ‘standard nine’), and the categories 1 to 9 are used.
Stanines are particularly useful for grouping students. It is recommended that only differences of two or more stanines should be regarded as indicating a real difference in performance.

7. Relationship between Percentile Ranks and Stanines
Descriptor 9
Very high 8
High 7
Above average
4, 5, 6
Average 3
Below average 2
Low 1
Very low

8. The normal distribution curve

9. Corresponding percentile ranks Number of students in a class of 25
Relationship between percentile ranks and stanines
Description of Performance
Stanine
Corresponding percentile ranks
Percentage of cases
Number of students in a class of 25
Very high 9
96 and above 4
High 8
89-96 7
Above average
77-89 12
Average 6
60-77 17 5
40-60 20
23-40
Below average 3
11-23
Low 2
4-11
Very low 1
0-4

10. Interpretation of Scores
Score Ranges
Results as scale scores. It is also important to pay attention to the error margin, so that small differences in scale scores are not given more importance than they deserve. Error margins tend to be larger for very high and very low scores.
For example, a student with a test score of 30 on PATMaths Test 5 would have a corresponding scale score of The error margin for this score is 4.9. We can be confident that the student’s true score would be within the range and That is, plus or minus 4.9.

11. What to do with the data?

12. Key pages in the PATMaths Fourth Edition Teacher Manual
Information
Page Number
Administration instructions
Pages 9–18
Describing test content
Pages 1– 6
Sample reports
Page 23–28
Test items by level of difficulty by test
Page 48
Test items by strand
Page 52
Description of scale scores
Pages 29–32
Item descriptors and curriculum links
Pages 88–108
Definitions for percentiles and stanines
Page 68–70
Mean scale scores by year level
Page 62
Score conversion tables
Pages 77–87
Score key
Page 76
Scoring and reporting masters (also on USB or as a download)
Pages 75–108

13. Some suggestions
Make analysing the results of the testing a priority – allocating time for teachers to do this process is essential
Provide professional development for staff in how to interpret the data
Use the manual information to get the most out of the results.

14. Further suggestions
Use stanines to identify students who would benefit from further diagnostic testing
Use group diagnostic reports to identify the types of questions students have had difficulty with to inform teaching
Use levels of achievement figures to identify the types of skills students should be working towards
Use direct instruction approaches to help students develop skills
Monitor progress during the year – informally and consider use of easier tests and/or an alternative assessment
Re-test on an annual basis to measure progress and the effectiveness of interventions.

15. Results used to