An introduction to
Progressive Achievement Tests in
Mathematics (PATMaths) Fourth Edition
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.
The Results
All tests provide the following information:
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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?
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 110.3. In both cases the standard
error of measurement is 3.9.
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.
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.
Relationship between Percentile Ranks and Stanines
Stanine
Descriptor
9
Very high
8
High
7
Above average
4, 5, 6
Average
3
Below average
2
Low
1
Very low
The normal distribution curve
Relationship between percentile ranks and stanines
Description of
Performance
Stanine
Corresponding
percentile ranks
Percentage
of cases
Very high
9
96 and above
4
High
8
89-96
7
Above average
7
77-89
12
6
60-77
17
5
40-60
20
4
23-40
17
Below average
3
11-23
12
Low
2
4-11
7
Very low
1
0-4
4
Average
Number of
students in a
class of 25
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 142.2.
The error margin for this score is 4.9. We can be confident
that the student’s true score would be within the range
137.3 and 147.10. That is, 142.2 plus or minus 4.9.
What to do with the data?
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
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.
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.
Results used to