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Assessing the numeracy
skills of adult learners

Chris Lane
Ministry of Education


October 12
Presentation outline

Literacy and Numeracy for Adults Assessment Tool:

• Results from 2011 for three numeracy skills assessed

• Issues in measuring skills and gain

• General Numeracy profiles and gains according to
gender and qualification level
Assessment Tool 2011: Percentage of
assessments for each numeracy skill
               5.7

         8.8




                             General Numeracy

                             Number Knowledge

                             Number Strategies and
                             Measurement




                     85.5
Learning Progression Steps on first
                          assessment in 2011 for numeracy skills
                                          35
Percentage of first assessments in 2011




                                          30

                                          25

                                          20

                                          15

                                          10

                                          5

                                          0
                                               General Numeracy             Number Knowledge                Number Strategies and
                                                                                                               Measurement
                                                                              Numeracy skill

                                                          Step 1   Step 2   Step 3   Step 4    Step 5   Step 6
Correlations between first assessment
scores for the three numeracy skills

                       Number Number Strategies
                      Knowledge and Measurement
                             0.81           0.75
  General Numeracy
  Number Strategies         0.83
  and Measurement
Percentage of learners reassessed for
                  numeracy skills, by initial Step
                                            50
Percentage of learners reassessed in 2011




                                            45
                                            40
                                            35
                                            30
                                            25
                                            20
                                            15
                                            10
                                            5
                                            0
                                                 General Numeracy            Number Knowledge              Number Strategies and
                                                                                                              Measurement
                                                                                Skill assessed

                                                         Step 1     Step 2   Step 3   Step 4     Step 5   Step 6
Statistically significant gain for numeracy
                                  skills in 2011, by first assessment step
                                           70
Percentage with significant gain in 2011




                                           60


                                           50


                                           40


                                           30


                                           20


                                           10


                                           0
                                                General Numeracy                Number Knowledge            Number Strategies and Measurement
                                                                       Numeracy skill assessed and reassessed

                                                              Step 1   Step 2   Step 3   Step 4   Step 5   Step 6
Issues in measuring skills and gain

• Coverage: percentage of learners assessed, reassessed
• Composition: different learner mixes in different programs
• Random variation, measurement error
• Assessment type: adaptive (full, snapshot), non-adaptive
• Preparation, engagement and motivation
• Greater gains for those who initially score low: more scope
for improvement, more educational attention, support from
peers?
• Practice effect: learning the assessment vs learning the
skill
Learning Progression Steps at first assessment for
General Numeracy, by gender
                                           35
 Percentage of first assessments in 2011




                                           30

                                           25

                                           20

                                           15

                                           10

                                           5

                                           0
                                                 Female                                            Male
                                                                            Gender

                                                Step 1    Step 2   Step 3     Step 4   Step 5   Step 6
Percentage of learners with significant gain for
                           General Numeracy, by initial Step and gender
                                           70
Percentage with significant gain in 2011




                                           60

                                           50

                                           40

                                           30

                                           20

                                           10

                                           0
                                                Female                                              Male
                                                                           Gender

                                                Step 1   Step 2   Step 3     Step 4   Step 5   Step 6
First assessment Steps for General Numeracy
                              in 2011, by qualification level
                                          45
Percentage of first assessments in 2011




                                          40

                                          35

                                          30

                                          25

                                          20

                                          15

                                          10

                                          5

                                          0
                                               Level 1   Level 2            Level 3           Level 4        Levels 5-7   Bachelors+
                                                                             Level of qualification

                                                         Step 1    Step 2    Step 3    Step 4    Step 5   Step 6
Percentage of learners reassessed for General
                      Numeracy, by initial Step and qualification level
                                           50
Percentge of learners reassessed in 2011




                                           45

                                           40

                                           35

                                           30

                                           25

                                           20

                                           15

                                           10

                                           5

                                           0
                                                Level 1   Level 2     Level 3       Level 4     Levels 5-7   Bachelors+
                                                                    NZQF level of qualification
Percentage of learners with significant gain for
                                     General Numeracy, by initial Step and
                                     qualification level
                                           60
Percentage with significant gain in 2011




                                           50


                                           40


                                           30


                                           20


                                           10


                                           0
                                                Level 1                         Level 2                        Level 3
                                                                       NZQF level of qualification

                                                     Step 1   Step 2     Step 3    Step 4    Step 5   Step 6

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NTLT 2012 - Assessing the numeracy skills of tertiary learners

  • 1. Assessing the numeracy skills of adult learners Chris Lane Ministry of Education October 12
  • 2. Presentation outline Literacy and Numeracy for Adults Assessment Tool: • Results from 2011 for three numeracy skills assessed • Issues in measuring skills and gain • General Numeracy profiles and gains according to gender and qualification level
  • 3. Assessment Tool 2011: Percentage of assessments for each numeracy skill 5.7 8.8 General Numeracy Number Knowledge Number Strategies and Measurement 85.5
  • 4. Learning Progression Steps on first assessment in 2011 for numeracy skills 35 Percentage of first assessments in 2011 30 25 20 15 10 5 0 General Numeracy Number Knowledge Number Strategies and Measurement Numeracy skill Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 5. Correlations between first assessment scores for the three numeracy skills Number Number Strategies Knowledge and Measurement 0.81 0.75 General Numeracy Number Strategies 0.83 and Measurement
  • 6. Percentage of learners reassessed for numeracy skills, by initial Step 50 Percentage of learners reassessed in 2011 45 40 35 30 25 20 15 10 5 0 General Numeracy Number Knowledge Number Strategies and Measurement Skill assessed Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 7. Statistically significant gain for numeracy skills in 2011, by first assessment step 70 Percentage with significant gain in 2011 60 50 40 30 20 10 0 General Numeracy Number Knowledge Number Strategies and Measurement Numeracy skill assessed and reassessed Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 8. Issues in measuring skills and gain • Coverage: percentage of learners assessed, reassessed • Composition: different learner mixes in different programs • Random variation, measurement error • Assessment type: adaptive (full, snapshot), non-adaptive • Preparation, engagement and motivation • Greater gains for those who initially score low: more scope for improvement, more educational attention, support from peers? • Practice effect: learning the assessment vs learning the skill
  • 9. Learning Progression Steps at first assessment for General Numeracy, by gender 35 Percentage of first assessments in 2011 30 25 20 15 10 5 0 Female Male Gender Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 10. Percentage of learners with significant gain for General Numeracy, by initial Step and gender 70 Percentage with significant gain in 2011 60 50 40 30 20 10 0 Female Male Gender Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 11. First assessment Steps for General Numeracy in 2011, by qualification level 45 Percentage of first assessments in 2011 40 35 30 25 20 15 10 5 0 Level 1 Level 2 Level 3 Level 4 Levels 5-7 Bachelors+ Level of qualification Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
  • 12. Percentage of learners reassessed for General Numeracy, by initial Step and qualification level 50 Percentge of learners reassessed in 2011 45 40 35 30 25 20 15 10 5 0 Level 1 Level 2 Level 3 Level 4 Levels 5-7 Bachelors+ NZQF level of qualification
  • 13. Percentage of learners with significant gain for General Numeracy, by initial Step and qualification level 60 Percentage with significant gain in 2011 50 40 30 20 10 0 Level 1 Level 2 Level 3 NZQF level of qualification Step 1 Step 2 Step 3 Step 4 Step 5 Step 6

Editor's Notes

  1. Based on records of 81,000 numeracy assessments in 2011.
  2. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 50,000 learners assessed at least once in 2011 for General Numeracy; approximately 5,900 learners assessed at least once for Number Knowledge; and approximately 3,800 assessed at least once for Number Strategies and Measurement.
  3. Based on approximately 2,700 learners assessed for both General Numeracy and Number Knowledge; approximately 1,700 assessed for both General Numeracy and Number Strategies and Measurement; and approximately 1,000 assessed for both Number Knowledge and Number Strategies and Measurement.
  4. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 50,000 learners assessed at least once in 2011 for General Numeracy; approximately 5,900 learners assessed at least once for Number Knowledge; and approximately 3,800 assessed at least once for Number Strategies and Measurement.
  5. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 16,000 learners assessed more than once in 2011 for General Numeracy; approximately 1,100 learners assessed more than once in 2011 for Number Knowledge, and approximately 600 learners assessed more than once in 2011 for Number Strategies and Measurement.For General Numeracy, the number of reassessed learners at each first assessment step was: Step 1: 700Step 2: 1,000Step 3: 3,300Step 4: 4,300Step 5: 4,600Step 6: 2,100
  6. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 21,000 female and approximately 30,000 male learners assessed at least once in 2011 for General Numeracy.
  7. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 8,000 female and 8,000 male learners assessed more than once in 2011 for General Numeracy;
  8. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 29,000learners whose qualification level could be identified and who were assessed at least once in 2011 for General Numeracy.
  9. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 29,000learners whose qualification level could be identified and who were assessed at least once in 2011 for General Numeracy.
  10. Steps 1-6 in the legend refer to the Learning Progressions steps corresponding to learners’ first assessment scores in 2011.Based on records of approximately 8,900learners whose qualification level could be identified as Level 1, 2 or 3, and who were assessed more than once in 2011 for General Numeracy.