Assessing Student Proficiency in Early Number Sense (ASPENS)

Mathematics

Cost

Technology, Human Resources, and Accommodations for Special Needs

Service and Support

Purpose and Other Implementation Information

Usage and Reporting

Initial Cost:

This is a not a commercial screening tool and therefore does not have a formal pricing plan. Contact Christopher Tran (ctran@inresg.org) for details. Costs include reproduction costs only or the minimal costs to prepare and send all the relevant electronic forms. ASPENS materials are available for benchmark and progress monitoring for students in kindergarten and first grade.

 

Replacement Cost:

Contact vendor for details.

 

Included in Cost:

A Benchmark Manual, Scoring Booklet for the Benchmark Assessments, Progress Monitoring Manual, and Scoring Booklet for the Progress Monitoring Assessments are provided for kindergarten and first grade.  Training opportunities are provided by the authors of ASPENS at Instructional Research Group (www.inresg.org). Materials not included but required for implementation include a clipboard, pencil, and a digital timer/stopwatch.

 

Technology Requirements:

  • No technology is required

 

Training Requirements:

  • 1-4 hours of training

 

Qualified Administrators:

Educational professionals and other school-approved personnel, provided they have received sufficient training on the administration and scoring rules and how to interpret the data.

 

Accommodations:

  • The use of a marker or ruler to focus student attention on each line of the assessment materials. First try to administer the assessment without a visual aid. If it is determined that the student needs this accommodation, retest the student with an alternate form of the Progress Monitoring Materials.
  • Student materials that have enlarged print to accommodate students with visual impairments.
  • The use of colored overlays, filters, or lighting adjustments for students with visual impairments.
  • The use of assistive technology, such as hearing aids and assistive listening devices, for students with hearing impairments.

 

Where to Obtain:

Website: www.inresg.org

Address: 4281 Katella Avenue Ste 205, Los Alamitos, CA 90720
Phone number: (714) 826-9600


Access to Technical Support:

Not applicable.*

 

*Training opportunities are provided by the authors of ASPENS at Instructional Research Group (www.inresg.org).

 

Assessing Student Proficiency in Early Number Sense (ASPENS) is a series of three curriculum-based measures administered for the purposes of universal screening of students’ mathematical proficiency. ASPENS assesses number sense for both kindergarten and first-grade students using grade-appropriate Magnitude Comparison and Missing Number measures, but also adds one additional aspect of mathematical proficiency at each grade level. The Numeral Identification measure is given in kindergarten only while the Basic Arithmetic Facts and Base 10 measure is given to first-graders to efficiently assess more sophisticated aspects of mathematical proficiency. 

The kindergarten ASPENS measure includes the Numerical Identification, Magnitude Comparison, and Missing Number subtests. Numbers for each subtest range from 0 to 20, and the score is the number of correct responses given in one minute. For the Numeral Identification measure, students are asked to name numbers as quickly as possible. The Magnitude Comparison measure requires students to name the greater of two visually presented numbers. The Missing Number measure is comprised of pages with boxes containing strings of three numbers with the first, middle, or last number of the string missing, and students name the missing number.

 

The first grade ASPENS measure also includes Magnitude Comparison and Missing Number subtests. The tests use the same procedures described above; however, the range of numbers is 0 to 99 for first graders. The Basic Arithmetic Facts and Base 10 measure is added in the middle of first grade to assess recall of basic arithmetic facts. Students are presented problems that contain elements that can be composed or decomposed in the Base 10 system (e.g., 5 + 9 becomes 4 + 10) to assess fact fluency. The score is the number of correct items (1 point for each problem) solved in two minutes.

Assessment Format:

  • One-to-one

 

Administration Time:

  • 5-9 minutes per student

 

Scoring Time:

  • 2 minutes per student

 

Scoring Method:

  • Calculated manually

 

Scores Generated:

  • raw
  • developmental benchmarks
  • composite scores
  • developmental cut points

 

Classification Accuracy

GradeK1
Criterion 1 FallHalf-filled bubbledHalf-filled bubbled
Criterion 1 WinterHalf-filled bubbledHalf-filled bubbled
Criterion 1 SpringHalf-filled bubbleHalf-filled bubble
Criterion 2 FallHalf-filled bubbleHalf-filled bubble
Criterion 2 WinterHalf-filled bubbleHalf-filled bubble
Criterion 2 SpringHalf-filled bubbleEmpty bubble

Primary Sample

 

Criterion 1, Fall

Grade

K

1

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

25

21

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.16

0.20

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.80

0.80

Specificity

0.75

0.67

Positive Predictive Power

0.37

0.37

Negative Predictive Power

0.95

0.93

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.82

0.80

AUC 95% Confidence Interval Lower Bound

0.75

0.74

AUC 95% Confidence Interval Upper Bound

0.88

0.86

 

Criterion 1, Winter

Grade

K

1

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

54

30

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.16

0.20

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.80

0.81

Specificity

0.73

0.78

Positive Predictive Power

0.36

0.48

Negative Predictive Power

0.95

0.94

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.83

0.85

AUC 95% Confidence Interval Lower Bound

0.77

0.79

AUC 95% Confidence Interval Upper Bound

0.89

0.91

 

Criterion 1, Spring

Grade

K

1

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

90

45

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.17

0.21

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.80

0.80

Specificity

0.74

0.76

Positive Predictive Power

0.38

0.47

Negative Predictive Power

0.95

0.93

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.85

0.84

AUC 95% Confidence Interval Lower Bound

0.80

0.79

AUC 95% Confidence Interval Upper Bound

0.90

0.90

 

Criterion 2, Fall

Grade

K to 1

1 to 2

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

25

19

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.18

0.16

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.83

0.79

Specificity

0.78

0.73

Positive Predictive Power

0.46

0.35

Negative Predictive Power

0.95

0.95

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.87

0.86

AUC 95% Confidence Interval Lower Bound

0.81

0.81

AUC 95% Confidence Interval Upper Bound

0.93

0.91

 

Criterion 2, Winter

Grade

K to 1

1 to 2

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

55

28

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.21

0.16

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.81

0.80

Specificity

0.77

0.79

Positive Predictive Power

0.48

0.41

Negative Predictive Power

0.94

0.96

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.88

0.88

AUC 95% Confidence Interval Lower Bound

0.83

0.84

AUC 95% Confidence Interval Upper Bound

0.93

0.93

 

Criterion 2, Spring

Grade

K to 1

1 to 2

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

92

Not Provided

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.22

Not Provided

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.81

0.79

Specificity

0.77

0.86

Positive Predictive Power

0.49

0.51

Negative Predictive Power

0.94

0.96

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.86

0.89

AUC 95% Confidence Interval Lower Bound

0.81

0.84

AUC 95% Confidence Interval Upper Bound

0.91

0.94

 

Additional Classification Accuracy

The following are provided for context and did not factor into the Classification Accuracy ratings.

 

Primary Sample

 

Criterion 1, Fall

Grade

K

1

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

35th percentile

35th percentile

Cut points: Performance score (numeric) on criterion measure

50

26

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.40

0.40

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.80

0.81

Specificity

0.61

0.65

Positive Predictive Power

0.58

0.60

Negative Predictive Power

0.82

0.84

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.77

0.79

AUC 95% Confidence Interval Lower Bound

0.72

0.74

AUC 95% Confidence Interval Upper Bound

0.83

0.84

 

Criterion 1, Winter

Grade

K

1

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

35th percentile

35th percentile

Cut points: Performance score (numeric) on criterion measure

82

37

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.41

0.42

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.80

0.81

Specificity

0.62

0.78

Positive Predictive Power

0.60

0.73

Negative Predictive Power

0.82

0.85

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.79

0.84

AUC 95% Confidence Interval Lower Bound

0.74

0.80

AUC 95% Confidence Interval Upper Bound

0.84

0.88

 

Criterion 2, Fall

Grade

K to 1

1 to 2

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

35th percentile

35th percentile

Cut points: Performance score (numeric) on criterion measure

44

23

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.42

0.27

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.81

0.80

Specificity

0.69

0.69

Positive Predictive Power

0.65

0.48

Negative Predictive Power

0.83

0.90

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.85

0.84

AUC 95% Confidence Interval Lower Bound

0.80

0.78

AUC 95% Confidence Interval Upper Bound

0.90

0.89

 

Criterion 2, Winter

Grade

K to 1

1 to 2

Criterion

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

35th percentile

35th percentile

Cut points: Performance score (numeric) on criterion measure

76

32

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.43

0.27

False Positive Rate

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Sensitivity

0.79

0.80

Specificity

0.70

0.78

Positive Predictive Power

0.67

0.57

Negative Predictive Power

0.82

0.91

Overall Classification Rate

Not Provided

Not Provided

Area Under the Curve (AUC)

0.84

0.86

AUC 95% Confidence Interval Lower Bound

0.79

0.81

AUC 95% Confidence Interval Upper Bound

0.89

0.91

 

Disaggregated Data

Fall

Subgroup: English Learners

Grade

K

1

K

1

Criterion

TerraNova3

TerraNova3

TerraNova3

TerraNova3

Cut points: Percentile rank on criterion measure

35th percentile

35th percentile

15th percentile

15th percentile

Cut points: Performance score (numeric) on criterion measure

83

25

11

25

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.38

0.46

0.09

0.19

False Positive Rate

Not Provided

Not Provided

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Not Provided

Not Provided

Sensitivity

0.82

0.80

0.83

0.83

Specificity

0.23

0.65

0.85

0.51

Positive Predictive Power

0.39

0.66

0.33

0.28

Negative Predictive Power

0.67

0.79

0.98

0.93

Overall Classification Rate

Not Provided

Not Provided

Not Provided

Not Provided

Area Under the Curve (AUC)

0.65

0.78

0.80

0.70

AUC 95% Confidence Interval Lower Bound

0.50

0.68

0.49

0.56

AUC 95% Confidence Interval Upper Bound

0.79

0.87

1.00

0.83

 

Winter

Subgroup: English Learners

Grade

TerraNova3

TerraNova3

TerraNova3

TerraNova3

Criterion

35th percentile

35th percentile

15th percentile

15th percentile

Cut points: Percentile rank on criterion measure

Not Provided

Not Provided

Not Provided

Not Provided

Cut points: Performance score (numeric) on criterion measure

82

36

40

30

Cut points: Corresponding performance score (numeric) on screener measure

Not Provided

Not Provided

Not Provided

Not Provided

Base rate in the sample for children requiring intensive intervention

0.39

0.53

0.09

0.22

False Positive Rate

Not Provided

Not Provided

Not Provided

Not Provided

False Negative Rate

Not Provided

Not Provided

Not Provided

Not Provided

Sensitivity

0.81

0.81

0.75

0.81

Specificity

0.47

0.78

0.78

0.70

Positive Predictive Power

0.49

0.81

0.24

0.44

Negative Predictive Power

0.79

0.78

0.97

0.93

Overall Classification Rate

Not Provided

Not Provided

Not Provided

Not Provided

Area Under the Curve (AUC)

0.71

0.84

0.81

0.84

AUC 95% Confidence Interval Lower Bound

0.60

0.77

0.63

0.74

AUC 95% Confidence Interval Upper Bound

0.83

0.92

1.00

0.93

 

Reliability

GradeK1
RatingEmpty bubbleEmpty bubble
  1. Justification for each type of reliability reported, given the type and purpose of the tool: Test-retest reliabilities of kindergarten and first-grade ASPENS measures are in the moderate to high range. Test-retest reliabilities provide an estimate of the stability of scores across time.

 

  1. Description of the sample(s), including size and characteristics, for each reliability analysis conducted: Kindergarten and first-grade students in six elementary schools from fours districts in California and Ohio. Data were collected from schools in Los Angeles, CA, Pasadena, CA, Springfield, OH, and Conneaut, OH. A total of 715 students (341 kindergarteners and 374 first graders) were tested during the 2009–2010 school year. The following school year sample (2010–2011) included 567 of these students (264 first graders and 303 second graders) to examine predictive validity across two years.

 

  1. Description of the analysis procedures for each reported type of reliability: Correlational data between two points in time.

 

  1. Reliability of performance level score (e.g., model-based, internal consistency, inter-rater reliability).

Type of Reliability

Age or Grade

n

Coefficient

95% Confidence Interval: Lower Bound

95% Confidence Interval: Upper Bound

Test-retest: Fall to Winter

K

341

0.84

Not Provided

Not Provided

Test-retest: Winter to Spring

K

341

0.85

Not Provided

Not Provided

Test-retest: Fall to Spring

K

341

0.76

Not Provided

Not Provided

Test-retest: Fall to Winter

1

374

0.84

Not Provided

Not Provided

Test-retest: Winter to Spring

1

374

0.87

Not Provided

Not Provided

Test-retest: Fall to Winter

1

374

0.77

Not Provided

Not Provided

 

Disaggregated Reliability

The following disaggregated reliability data are provided for context and did not factor into the Reliability rating.

Type of Reliability

Subgroup

Age or Grade

n

Coefficient

95% Confidence Interval: Lower Bound

95% Confidence Interval: Upper Bound

None

 

 

 

 

 

 

 

Validity

GradeK1
RatingEmpty bubbleEmpty bubble

1.Description of each criterion measure used and explanation as to why each measure is appropriate, given the type and purpose of the tool: The criterion outcome was mathematics achievement assessed via the TerraNova, Third Edition (CTB/McGraw Hill, 2008) in May of 2010 and May of 2011. The TerraNova is a nationally norm referenced and standardized achievement test used in the U.S. to assess K–12 achievement in reading, language, mathematics, science and social studies. Form G of the Mathematics subtest was used as the criterion. The criterion measure is independent and external to the screening measure.  

 

2.Description of the sample(s), including size and characteristics, for each validity analysis conducted: Kindergarten and first-grade students in six elementary schools from fours districts in California and Ohio. Data were collected from schools in Los Angeles, CA, Pasadena, CA, Springfield, OH, and Conneaut, OH. A total of 715 students (341 kindergarteners and 374 first graders) were tested during the 2009–2010 school year. The following school year sample (2010–2011) included 567 of these students (264 first graders and 303 second graders) to examine predictive validity across two years. 

 

3.Description of the analysis procedures for each reported type of validity: To obtain predictive validity, the fall and winter scores on the kindergarten and first grade ASPENS subtest measures were correlated with the spring scores on the TerraNova 3. To obtain concurrent validity, spring scores on the kindergarten and first grade ASPENS subtest measures were correlated with the spring scores on the TerraNova 3.

 

4.Validity for the performance level score (e.g., concurrent, predictive, evidence based on response processes, evidence based on internal structure, evidence based on relations to other variables, and/or evidence based on consequences of testing), and the criterion measures.

Type of Validity

Age or Grade

Test or Criterion

n

Coefficient

95% Confidence Interval: Lower Bound

95% Confidence Interval: Upper Bound

Predictive validity – Fall to Spring

K

TerraNova3

289

0.53

0.44

0.61

Predictive validity – Winter to Spring

K

TerraNova3

289

0.54

0.45

0.62

Predictive validity – Fall to Spring

1

TerraNova3

329

0.57

0.49

0.64

Predictive validity – Winter to Spring

1

TerraNova3

329

0.63

0.56

0.69

Concurrent validity

K

TerraNova3

341

0.58

0.50

0.65

Concurrent validity

1

TerraNova3

374

0.63

0.57

0.69

 

5.Results for other forms of validity (e.g. factor analysis) not conducive to the table format: Not Provided  

 

6.Describe the degree to which the provided data support the validity of the tool: The measure shows moderate correlations to a broad measure of the construct of interest (general mathematics performance). The correlations across multiple years remain at moderate levels, indicating long-term predictive value.

 

 

Disaggregated Validity

The following disaggregated validity data are provided for context and did not factor into the Validity rating.

Type of Validity

Subgroup

Age or Grade

Test or Criterion

n

Coefficient

95% Confidence Interval: Lower Bound

95% Confidence Interval: Upper Bound

None

 

 

 

 

 

 

 

 

Results for other forms of disaggregated validity (e.g. factor analysis) not conducive to the table format: Not Provided 

Sample Representativeness

GradeK1
Data
  • Regional without Cross-Validation
  • Regional without Cross-Validation
  • Primary Classification Accuracy Sample

    Criterion 1, Fall

    Grade

    K

    1

    Criterion

    TerraNova 3

    TerraNova 3

    National/Local Representation

    Western & Midwestern Region

    Western & Midwestern Region

    Date

    2009-2010

    2010-2011

    2009-2010

    2010-2011

    Sample Size

    289

    329

    Male

    Not Provided

    Not Provided

    Female

    50.2%

    50.2%

    Gender Unknown

    Not Provided

    Not Provided

    Free or Reduced-price Lunch Eligible

    Not Provided

    Not Provided

    White, Non-Hispanic

    8%

    24%

    Black, Non-Hispanic

    23%

    11%

    Hispanic

    42%

    47%

    American Indian/Alaska Native

    9%

    7%

    Other

    Not Provided

    Not Provided

    Race/Ethnicity Unknown

    18%

    11%

    Disability Classification

    Not Provided

    Not Provided

    First Language

    Not Provided

    Not Provided

    Language Proficiency Status

    English learner – 25%

    English learner – 29%

     

    Criterion 1, Winter

    Grade

    K

    1

    Criterion

    TerraNova 3

    TerraNova 3

    National/Local Representation

    Western & Midwestern Region

    Western & Midwestern Region

    Date

    2009-2010

    2010-2011

    2009-2010

    2010-2011

    Sample Size

    322

    357

    Male

    Not Provided

    Not Provided

    Female

    52%

    50%

    Gender Unknown

    Not Provided

    Not Provided

    Free or Reduced-price Lunch Eligible

    Not Provided

    Not Provided

    White, Non-Hispanic

    8%

    23%

    Black, Non-Hispanic

    22%

    11%

    Hispanic

    44%

    50%

    American Indian/Alaska Native

    9%

    6%

    Other

    Not Provided

    Not Provided

    Race/Ethnicity Unknown

    17%

    10%

    Disability Classification

    Not Provided

    Not Provided

    First Language

    Not Provided

    Not Provided

    Language Proficiency Status

    English learner – 29%

    English learner – 33%

     

    Bias Analysis Conducted

    GradeK1
    RatingNoNo
    1. Description of the method used to determine the presence or absence of bias: Not Provided  

     

    1. Description of the subgroups for which bias analyses were conducted: Not Provided

     

    1. Description of the results of the bias analyses conducted, including data and interpretative statements: Not Provided

    Administration Format

    GradeK1
    Data
  • Individual
  • Individual
  • Administration & Scoring Time

    GradeK1
    Data
  • 7-11 minutes
  • 7-11 minutes
  • Scoring Format

    GradeK1
    Data
  • Manual
  • Manual
  • Types of Decision Rules

    GradeK1
    Data
  • Discontinue Rule
  • Discontinue Rule
  • Evidence Available for Multiple Decision Rules

    GradeK1
    Data
  • No
  • No