Assessing Student Proficiency in Early Number Sense (ASPENS)
Mathematics
Summary
Assessing Student Proficiency in Early Number Sense (ASPENS) is a series of three curriculumbased measures administered for the purposes of universal screening of students’ mathematical proficiency. ASPENS assesses number sense for both kindergarten and firstgrade students using gradeappropriate 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 firstgraders 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
 Where to Obtain:
 Ben Clarke, Russell Gersten, Joseph Dimino, Eric Rolfhus
 ctran@inresg.org
 Contact Christopher Tran at Instructional Research Group
 (714) 8269600
 Instructional Research Group (www.inresg.org)
 Initial Cost:
 Free
 Replacement Cost:
 Contact vendor for pricing details.
 Included in Cost:
 This is a not a commercial screening tool and therefore does not have a formal pricing plan. Contact Christopher Tran at Instructional Research Group (ctran@inresg.org). 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. 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.
 • 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.
 Training Requirements:
 14 hrs of training
 Qualified Administrators:
 Educational professionals and other schoolapproved personnel, provided they have received sufficient training on the administration and scoring rules and how to interpret the data.
 Access to Technical Support:
 Assessment Format:

 Onetoone
 Scoring Time:

 2 minutes per student
 Scores Generated:

 Raw score
 Developmental benchmarks
 Developmental cut points
 Composite scores
 Administration Time:

 7 minutes per student
 Scoring Method:

 Manually (by hand)
 Technology Requirements:

 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.
Descriptive Information
 Please provide a description of your tool:
 Assessing Student Proficiency in Early Number Sense (ASPENS) is a series of three curriculumbased measures administered for the purposes of universal screening of students’ mathematical proficiency. ASPENS assesses number sense for both kindergarten and firstgrade students using gradeappropriate 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 firstgraders 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
ACADEMIC ONLY: What skills does the tool screen?
 Please describe specific domain, skills or subtests:
 BEHAVIOR ONLY: Which category of behaviors does your tool target?

 BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each subdomain or subconstruct.
Acquisition and Cost Information
Administration
 Are norms available?
 No
 Are benchmarks available?
 Yes
 If yes, how many benchmarks per year?
 3
 If yes, for which months are benchmarks available?
 Beginning, middle and end of the school year.
 BEHAVIOR ONLY: Can students be rated concurrently by one administrator?
 If yes, how many students can be rated concurrently?
Training & Scoring
Training
 Is training for the administrator required?
 Yes
 Describe the time required for administrator training, if applicable:
 14 hrs of training
 Please describe the minimum qualifications an administrator must possess.
 Educational professionals and other schoolapproved personnel, provided they have received sufficient training on the administration and scoring rules and how to interpret the data.
 No minimum qualifications
 Are training manuals and materials available?
 Yes
 Are training manuals/materials fieldtested?
 Yes
 Are training manuals/materials included in cost of tools?
 No
 If No, please describe training costs:
 Contact Christopher Tran at Instructional Research Group (ctran@inresg.org).
 Can users obtain ongoing professional and technical support?
 No
 If Yes, please describe how users can obtain support:
Scoring
 Do you provide basis for calculating performance level scores?

No
 Does your tool include decision rules?

Yes
 If yes, please describe.
 Testing for each measure is discontinued after a student misses 5 items consecutively
 Can you provide evidence in support of multiple decision rules?

No
 If yes, please describe.
 Please describe the scoring structure. Provide relevant details such as the scoring format, the number of items overall, the number of items per subscale, what the cluster/composite score comprises, and how raw scores are calculated.
 Unitweighted composite scores were created using the procedure detailed in the ASPENS Administrator’s Handbook. Users multiply the raw subtest scores by a weight and then add the weighted subtests scores together. The unit weighting is accounted for by the multiplication weights assigned to each subtest. The weights for each subtest are based on the standard deviation (SD) of the raw scores for that subtest. The subtest with the largest SD is weighted a 1. The remaining subtests with smaller SDs (i.e., those with lower means and with inherently more difficult items) are given weights greater than 1, in proportion to the subtest with the SD of 1. Details of this approach are provided by Good, PowellSmith, and Kaminski (2011). We explain this to practitioners as indicating that “raw scores for the subtests are combined, but the subtests are weighted differently before they are combined, with more weight given to measures that are harder for students at a particular age range” (Clarke et al., 2018). Developing benchmark goals and cutpoints for risk: Odds of achieving subsequent reading goals. Presentation at preDIBELS Summit, Albuquerque, NM. Retrieved July 15, 2011 from http://hprec.org/DIBELS/Summitt2011Presentations/Keynote.pdf Clarke, B., Gersten, R., Smolkowski, K., Haymond, K., Dimino, J. & Sutherland, M. (2018). Exploring the validity and reliability of a screening measure that focuses solely on number knowledge for students in the primary grades. Manuscript submitted for publication.
 Describe the tool’s approach to screening, samples (if applicable), and/or test format, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.
 The tests are administered onetoone to help facilitate student performance. Additional approaches ensuring appropriate use of the measure for diverse populations are addressed via training.
Technical Standards
Classification Accuracy & CrossValidation Summary
Grade 
Kindergarten

Grade 1


Classification Accuracy Fall  
Classification Accuracy Winter  
Classification Accuracy Spring 
TerraNova, Third Edition: Math Form G (Same Year)
Classification Accuracy
 Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
 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 normreferenced 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.
 Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.
 Describe how the classification analyses were performed and cutpoints determined. Describe how the cut points align with students atrisk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).
 Diagnostic statistics were estimated for students at risk, defined by the 15th percentile on the TerraNova. We first generated receiver operating characteristic (ROC) curves for each of the screening measures administered in the fall, winter, and spring. ROC curves plot the proportion of true positives (sensitivity) against the proportion of false positives (1 – specificity) for all values of the screener. We next calculated the area under the curve, A. Based on a review of the literature on signal detection theory and academic outcomes, Smolkowski and Cummings (2015) considered values of A above .95 as excellent, values from .85 to .95 as very good, and values from .75 to .85 as reasonable. Estimates and confidence intervals for A were produced by SAS PROC LOGISTIC (SAS Institute, 2016). We chose decision thresholds based on the screener score with a sensitivity value closest to .90. For each measure, we reported A with confidence intervals, the selected decision threshold (i.e., recommended cut point), sensitivity and specificity with confidence bounds, negative and positive predictive values, the proportion of students who screened positive (τ), and the base rate or proportion determined to be at risk on the criterion measure. Confidence bounds around sensitivity and specificity were formed using a normalcurve approximation (Harper & Reeves, 1999), which are recommended only when cell sizes (e.g., number of false positives, number of true negatives) were greater than 10. We also defined confidence bounds around the cut scores, which represented the lowest and highest screener scores for which the sensitivity confidence intervals contained sensitivity of .90. Frequency statistics were produced with SAS PROC FREQ (SAS Institute, 2016).
 Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No
 If yes, please describe the intervention, what children received the intervention, and how they were chosen.
CrossValidation
 Has a crossvalidation study been conducted?

No
 If yes,
 Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
 Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.
 Describe how the crossvalidation analyses were performed and cutpoints determined. Describe how the cut points align with students atrisk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).
 Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?
 If yes, please describe the intervention, what children received the intervention, and how they were chosen.
TerraNova, Third Edition: Math Form G (Next School Year)
Classification Accuracy
 Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
 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 normreferenced 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.
 Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.
 Describe how the classification analyses were performed and cutpoints determined. Describe how the cut points align with students atrisk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).
 Diagnostic statistics were estimated for students at risk, defined by the 15th percentile on the TerraNova. We first generated receiver operating characteristic (ROC) curves for each of the screening measures administered in the fall, winter, and spring. ROC curves plot the proportion of true positives (sensitivity) against the proportion of false positives (1 – specificity) for all values of the screener. We next calculated the area under the curve, A. Based on a review of the literature on signal detection theory and academic outcomes, Smolkowski and Cummings (2015) considered values of A above .95 as excellent, values from .85 to .95 as very good, and values from .75 to .85 as reasonable. Estimates and confidence intervals for A were produced by SAS PROC LOGISTIC (SAS Institute, 2016). We chose decision thresholds based on the screener score with a sensitivity value closest to .90. For each measure, we reported A with confidence intervals, the selected decision threshold (i.e., recommended cut point), sensitivity and specificity with confidence bounds, negative and positive predictive values, the proportion of students who screened positive (τ), and the base rate or proportion determined to be at risk on the criterion measure. Confidence bounds around sensitivity and specificity were formed using a normalcurve approximation (Harper & Reeves, 1999), which are recommended only when cell sizes (e.g., number of false positives, number of true negatives) were greater than 10. We also defined confidence bounds around the cut scores, which represented the lowest and highest screener scores for which the sensitivity confidence intervals contained sensitivity of .80. Frequency statistics were produced with SAS PROC FREQ (SAS Institute, 2016).
 Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No
 If yes, please describe the intervention, what children received the intervention, and how they were chosen.
CrossValidation
 Has a crossvalidation study been conducted?

No
 If yes,
 Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
 Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.
 Describe how the crossvalidation analyses were performed and cutpoints determined. Describe how the cut points align with students atrisk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).
 Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?
 If yes, please describe the intervention, what children received the intervention, and how they were chosen.
Classification Accuracy  Fall
Evidence  Kindergarten  Grade 1 

Criterion measure  TerraNova, Third Edition: Math Form G (Same Year)  TerraNova, Third Edition: Math Form G (Same Year) 
Cut Points  Percentile rank on criterion measure  15  15 
Cut Points  Performance score on criterion measure  25  21 
Cut Points  Corresponding performance score (numeric) on screener measure  
Classification Data  True Positive (a)  
Classification Data  False Positive (b)  
Classification Data  False Negative (c)  
Classification Data  True Negative (d)  
Area Under the Curve (AUC)  0.82  0.80 
AUC Estimate’s 95% Confidence Interval: Lower Bound  0.75  0.74 
AUC Estimate’s 95% Confidence Interval: Upper Bound  0.88  0.86 
Statistics  Kindergarten  Grade 1 

Base Rate  
Overall Classification Rate  
Sensitivity  
Specificity  
False Positive Rate  
False Negative Rate  
Positive Predictive Power  
Negative Predictive Power 
Sample  Kindergarten  Grade 1 

Date  20092010; 20102011  20092010; 20102011 
Sample Size  
Geographic Representation  
Male  
Female  
Other  
Gender Unknown  
White, NonHispanic  
Black, NonHispanic  
Hispanic  
American Indian/Alaska Native  
Other  
Race / Ethnicity Unknown  
Low SES  
IEP or diagnosed disability  
English Language Learner 
Classification Accuracy  Winter
Evidence  Kindergarten  Grade 1 

Criterion measure  TerraNova, Third Edition: Math Form G (Same Year)  TerraNova, Third Edition: Math Form G (Same Year) 
Cut Points  Percentile rank on criterion measure  15  15 
Cut Points  Performance score on criterion measure  54  30 
Cut Points  Corresponding performance score (numeric) on screener measure  
Classification Data  True Positive (a)  
Classification Data  False Positive (b)  
Classification Data  False Negative (c)  
Classification Data  True Negative (d)  
Area Under the Curve (AUC)  0.83  0.85 
AUC Estimate’s 95% Confidence Interval: Lower Bound  0.77  0.79 
AUC Estimate’s 95% Confidence Interval: Upper Bound  0.89  0.91 
Statistics  Kindergarten  Grade 1 

Base Rate  
Overall Classification Rate  
Sensitivity  
Specificity  
False Positive Rate  
False Negative Rate  
Positive Predictive Power  
Negative Predictive Power 
Sample  Kindergarten  Grade 1 

Date  20092010; 20102011  20092010; 20102011 
Sample Size  
Geographic Representation  
Male  
Female  
Other  
Gender Unknown  
White, NonHispanic  
Black, NonHispanic  
Hispanic  
American Indian/Alaska Native  
Other  
Race / Ethnicity Unknown  
Low SES  
IEP or diagnosed disability  
English Language Learner 
Classification Accuracy  Spring
Evidence  Kindergarten  Grade 1 

Criterion measure  TerraNova, Third Edition: Math Form G (Same Year)  TerraNova, Third Edition: Math Form G (Same Year) 
Cut Points  Percentile rank on criterion measure  15  15 
Cut Points  Performance score on criterion measure  90  45 
Cut Points  Corresponding performance score (numeric) on screener measure  
Classification Data  True Positive (a)  
Classification Data  False Positive (b)  
Classification Data  False Negative (c)  
Classification Data  True Negative (d)  
Area Under the Curve (AUC)  0.85  0.84 
AUC Estimate’s 95% Confidence Interval: Lower Bound  0.80  0.79 
AUC Estimate’s 95% Confidence Interval: Upper Bound  0.90  0.90 
Statistics  Kindergarten  Grade 1 

Base Rate  
Overall Classification Rate  
Sensitivity  
Specificity  
False Positive Rate  
False Negative Rate  
Positive Predictive Power  
Negative Predictive Power 
Sample  Kindergarten  Grade 1 

Date  20092010; 20102011  20092010; 20102011 
Sample Size  
Geographic Representation  
Male  
Female  
Other  
Gender Unknown  
White, NonHispanic  
Black, NonHispanic  
Hispanic  
American Indian/Alaska Native  
Other  
Race / Ethnicity Unknown  
Low SES  
IEP or diagnosed disability  
English Language Learner 
Reliability
Grade 
Kindergarten

Grade 1


Rating 
 *Offer a justification for each type of reliability reported, given the type and purpose of the tool.
 Testretest reliabilities of kindergarten and firstgrade ASPENS measures are in the moderate to high range. Testretest reliabilities provide an estimate of the stability of scores across time.
 *Describe the sample(s), including size and characteristics, for each reliability analysis conducted.
 Kindergarten and firstgrade 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.
 *Describe the analysis procedures for each reported type of reliability.
 Correlational data between two points in time.
*In the table(s) below, report the results of the reliability analyses described above (e.g., internal consistency or interrater reliability coefficients).
Type of  Subgroup  Informant  Age / Grade  Test or Criterion  n  Median Coefficient  95% Confidence Interval Lower Bound 
95% Confidence Interval Upper Bound 

 Results from other forms of reliability analysis not compatible with above table format:
 N/a
 Manual cites other published reliability studies:
 No
 Provide citations for additional published studies.
 Do you have reliability data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?
 No
If yes, fill in data for each subgroup with disaggregated reliability data.
Type of  Subgroup  Informant  Age / Grade  Test or Criterion  n  Median Coefficient  95% Confidence Interval Lower Bound 
95% Confidence Interval Upper Bound 

 Results from other forms of reliability analysis not compatible with above table format:
 Manual cites other published reliability studies:
 No
 Provide citations for additional published studies.
Validity
Grade 
Kindergarten

Grade 1


Rating 
 *Describe each criterion measure used and explain 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.
 *Describe the sample(s), including size and characteristics, for each validity analysis conducted.
 Kindergarten and firstgrade 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.
 *Describe 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.
*In the table below, report the results of the validity analyses described above (e.g., concurrent or predictive validity, 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  Subgroup  Informant  Age / Grade  Test or Criterion  n  Median Coefficient  95% Confidence Interval Lower Bound 
95% Confidence Interval Upper Bound 

 Results from other forms of validity analysis not compatible with above table format:
 N/a
 Manual cites other published reliability studies:
 No
 Provide citations for additional published studies.
 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 longterm predictive value.
 Do you have validity data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?
 No
If yes, fill in data for each subgroup with disaggregated validity data.
Type of  Subgroup  Informant  Age / Grade  Test or Criterion  n  Median Coefficient  95% Confidence Interval Lower Bound 
95% Confidence Interval Upper Bound 

 Results from other forms of validity analysis not compatible with above table format:
 Manual cites other published reliability studies:
 No
 Provide citations for additional published studies.
Bias Analysis
Grade 
Kindergarten

Grade 1


Rating  No  No 
 Have you conducted additional analyses related to the extent to which your tool is or is not biased against subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)? Examples might include Differential Item Functioning (DIF) or invariance testing in multiplegroup confirmatory factor models.
 No
 If yes,
 a. Describe the method used to determine the presence or absence of bias:
 b. Describe the subgroups for which bias analyses were conducted:
 c. Describe the results of the bias analyses conducted, including data and interpretative statements. Include magnitude of effect (if available) if bias has been identified.
Data Collection Practices
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