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Examining construct validity of the quantitative literacy VALUE rubric in college-level STEM assignments.

An individual's quantitative literacy and competence with data evaluation is helpful in all areas of life, including academia. Because data-driven decision making is increasingly viewed as essential in a globally competitive society, educational objectives often emphasize learning outcome elements such as data analysis and how to use the data to draw conclusions. Data analysis without an understanding of the implications limits appropriate actions that can be taken by individuals and businesses (Tufte, 1997). Further, hiring managers seek individuals with empirical and quantitative skills because they have the ability to see connections and systemic problems (National Association of Colleges and Employers, 2016). Indeed, findings from the Spellings Commission panel stated that, "better data about real performance and lifelong working and learning ability is absolutely essential if we are to meet national needs and improve institutional performance" (U.S. Department of Education, 2006, p. 30).

Over the past two decades educational policies in the United States were changed by congressional legislation (e.g., No Child Left Behind Act [NCLB], 2001; Every Student Succeeds Act [ESSA], 2015). McGuinn (2006) maintains that the NCLB was implemented in response to public sentiment to hold educators accountable for the instruction students receive. More recently, initiatives to augment standardized testing with performance-based assessment (PBA) have increased as educators progressively respond to mandates for authentic measurement of student attainment. This progression is particularly reflected in the recently legislated ESSA (Gewertz, 2015), which is anticipated to go into full effect during the 2017-2018 academic year. The next section briefly reviews some of the policy implications for assessment professionals.

Impact of Policy Changes on Assessment Professionals

NCLB in particular affected the responsibilities of educational assessment professionals in requiring that each state must measure student progress for an academic year using single summative tests (Gewertz, 2015). As a result, a reliance upon standardized tests quickly developed to assess student attainment and inform process improvements in educational service delivery (Supovitz, 2009). Such testing often took the form of high-stakes, multiple-choice examinations. However, in the last decade, initiatives to extend assessment methods to include performance-based student work have gained momentum at many institutions (State Higher Education Executive Officers Association [SHEEO], 2016). As ESSA implementation moves toward completion, assessment professionals and state officials anticipate that it will provide them with options that include multiple measures during an academic year, including merging results from both standardized tests and performance-based tests (Gewertz, 2015). While many call the assessment of performance-based work a more authentic method of rating student attainment (Montgomery, 2002; Peden, Reed, & Wolfe, 2017; Rhodes, 2010; Rhodes & Finley, 2014), efforts to validate the way it is rated or scored present challenges for educators (Montgomery, 2002).

PBA Challenges

PBA implies that in response to the assignment prompt, a student reveals the skills they have attained to date. That is, the student response contains authentic agreement between what the student knows and their ability to demonstrate that knowledge (Cobb, 2014). Unlike standardized tests, PBAs typically consist of written student work samples (e.g., essays, experimental or research lab summaries, and presentations). However, while PBA holds an advantage of authenticity it also presents a disadvantage. Montgomery (2002) lists concerns reported in the literature, including the difficulty of avoiding rater subjectivity when scoring authentic student work samples.

In contrast, normed scores for standardized tests for specific student populations typically guide comparisons based on equity and excellence. PBA often requires the introduction of a rubric to increase rater objectivity. Use of rubrics adds structure and consistency to the performance level assessment and comparisons (Montgomery, 2002).

VALUE Rubric Development as a Solution-Oriented Assessment Approach

Indeed, Montgomery (2002) recommended the use of rubrics for assessing authentic student work because they are tools that communicate to students the expected elements to include in the completed assignment. Rubrics for setting criteria and determining student attainment of the target objectives have been suggested to uphold equity and excellence for all students (Montgomery, 2002; Peden et al., 2017). That said, an evidence-based approach for evaluating PBAs using validated rubrics was needed.

A campus-based assessment initiative, led by the Association of American Colleges and Universities (AAC&U), published 16 Valid Assessment of Learning in Undergraduate Education (VALUE) Rubrics (AAC&U, 2017b). Faculty and other educational professionals gathered from over 100 different institutions of higher education, under the direction of the AAC&U, to develop the rubrics. The VALUE rubrics were designed to be scoring guides that can be used by universities to evaluate authentic student work samples. Further, the AAC&U outlined four families of Essential Learning Outcomes in order to advance VALUE rubrics as relevant assessment tools across a wide range of disciplines, courses, and objectives (National Leadership Council for Liberal Education & America's Promise, 2008).

These VALUE rubrics serve as a scaffold to government policies that endeavor to guarantee the quality of education across the United States for all students (AAC&U, 2017b). Though policies vary by state, they broadly included six educational objectives: critical thinking, communication, empirical and quantitative skill (EQS), teamwork, social responsibility, and personal responsibility. In the southwestern United States, the Texas Higher Education Coordinating Board (THECB) adopted the six aforementioned objectives for implementation in the most recent revision of the Texas Core Curriculum (TCC; THECB, 2011). The THECB required that all two-year and four-year educational institutions submit regular reports detailing the assessment practices and results for student TCC objective attainment within general education courses that have been approved and designated for inclusion in the TCC (THECB, 2011). Decision making regarding methodologies for rating these performance-based student work samples was left to the discretion of each institution by the THECB.

Preliminary studies supported by SHEEO and AAC&U consisted of a collaborative effort by 60 institutions in nine states who agreed to test the utility of the VALUE Rubric to rate authentic student work (SHEEO, 2016). In 2014-2015, they examined faculty ratings of authentic student work to determine levels that indicate healthy thresholds for student mastery (Lederman, 2015). While the multi-state collaborative vetted two rubrics in the practice of evaluating student work during its initial phase and current studies expanded to include more institutions, to date, they have not explored rubric construct validity. Studies are needed to investigate the extent to which the measures within each VALUE Rubric accurately represent a single construct.

Importance of Studying the Quantitative Literacy VALUE Rubric

Case studies document the use of the VALUE Rubrics nationwide (AAC&U, 2017a; Peden et al., 2017). This study examines the construct validity of the AAC&U Quantitative Literacy VALUE Rubric for evaluating EQS, a TCC objective. EQS allows an individual to understand information or raw data that is presented in tables, charts, graphs, or figures and evaluate it to draw accurate conclusions. Identifying applications of EQS across academic disciplines is straightforward. The ability to take information, analyze it, and predict outcomes is a common theme in the hard sciences such as engineering, physics, chemistry, and biology. In addition, EQS is utilized across disciplines, for instance, in nursing, business, and psychology.

Individuals possessing skills such as EQS are in high demand because they can use this expertise to find evidence-based solutions. EQS is typically described using action verbs including identify, extract, validate, and report (Georgesen, 2015). Further, the process often follows an ordered set of action steps. For example, Georgesen (2015) extended the list as a set of four steps: 1) define, scope, identify, document; 2) extract, aggregate, transform, create; 3) develop, analyze, simulate, validate; and 4) report, recommend, implement, monitor. The extent to which these verbs can be translated into observable measures is essential to evaluating student attainment of the TCC objective EQS.

The current study focused on the measures within the Quantitative Literacy VALUE Rubric and its utility for measuring EQS. The six skill indicators measured by this rubric are Interpretation, Representation, Calculation, Application/Analysis, Assumptions, and Communication. Explanations for each are contained in the rubric (see Appendix). Our hypothesis is that there is a single underlying trait or "latent variable" of which the six different skills are indicators. In short, we wish to validate that the six different skills being assessed, taken together, are reliable measures of something more general.

Method

The skills within the Quantitative Literacy VALUE Rubric were assessed using written samples of undergraduate student work from approved Signature Assignments embedded in the existing undergraduate TCC courses at a four-year public institution in an urban setting. The institution met requirements to serve as a Hispanic Serving Institution by the U.S. Department of Education (2016) and, importantly, received the R-1 designation by the Carnegie Classification of Institutions of Higher Education (2015), the definitive list for top doctoral research. The measurement of student attainment of EQS is of extreme interest because of the institutional focus on research.

Signature Assignments were designed to be authentic performance-based work in which students responded to pedagogically relevant prompts. For example, some Signature Assignments consisted of written summaries of actual lab experiments conducted by students in life and physical sciences courses. These papers, illustrated by tables and figures, essentially included measurable elements of Interpretation, Representation, Calculation, Application/ Analysis, Assumptions, and Communication. All the Signature Assignments in this sample were collected from courses related to science, technology, engineering and math (STEM). Trained faculty and staff who participated in calibration and training exercises (described in more detail to follow) performed the ratings.

Participants

Signature Assignments were obtained from 296 undergraduates enrolled in core curriculum courses in STEM areas at the university. The readability of a portion of the assignments (n = 51) was poor because they were scanned copies of handwritten summaries from lab books or "blue books." As such, these 51 Signature Assignments were dropped from the sample and not rated. Ratings were available for 245 of the student Signature Assignments. Over half of the participants were female (61%; n = 149), which closely matched the gender ratio at the university. The sample also reflected a rich diversity of students. About a third of the student participants identified as White (33%; n = 80), almost a third identified as Hispanic (27%; n = 67), and the balance was split between African American; Asian; foreign, nonresident alien; multiple ethnicity; and unknown, not specified. Students represented nine of ten colleges and schools at the university (see Table 1).

Procedure

Faculty currently teaching undergraduate courses in STEM areas agreed to submit the course set of authentic student work deemed as the Signature Assignment for this study. The syllabus for each core curriculum class at the university describes the Signature Assignment and the students enrolled in these courses complete it as they would any other assignment or required course work. The samples submitted for this assessment process were ungraded, de-identified copies. Steps to redact personal and academic information were followed for two reasons. The first was to prevent any bias among rater scores in response to the grade the paper received from the professor. The second was to protect the confidentiality of student, faculty, and course information.

Assessment Instrument

The Signature Assignments were assessed using the VALUE Rubric for Quantitative Literacy (AAG&U, 2009), which categorizes EQS into six measures: Interpretation, Representation, Calculation, Application/Analysis, Assumptions, and Communication . The rubric describes each measure and uses a four-point Likert scale for determining scores (see Appendix). Higher values indicate more evidence of EQS. Using the rubric, raters assigned a score to each of the six skill measures.

Typically, in student samples, the six measures are adequately represented in the narrative of the Signature Assignment. It is important to note that visual communication in the form of charts, graphs, and figures enhanced the identification of the Representation and Communication measures. This is not unexpected because communication (written and visual) is required for fleshing out and articulating ideas in STEM areas. Visual communication is particularly important, and in many cases essential, for depicting information in STEM areas.

Raters, Rater Calibration, and Scoring

For the purposes of this study, the unit of analysis was an individual rater's score for a particular Signature Assignment. Raters scored the student writing samples during a scheduled scoring day so each paper was read and then rated by at least two separate raters working independently in a group setting. The rater group included ten faculty members and professional staff with advanced degrees. Scoring day began with an orientation and description of the rating process. Then, the entire group read one anchor paper chosen by the facilitator. Next, the facilitator led a discussion focused on reaching a common understanding of the EQS measures and finding exemplar indicators within the anchor paper for the rubric's levels of mastery. Then the rating process began and raters individually read their assigned papers to score each measure with the rubric (four-point Likert scale). Two raters independently rated each paper. Measure scores were calculated as the average of both scores. The facilitator checked each paper, after the completion of the two ratings, to review whether disagreement between measure ratings exceeded acceptable metrics. If so, the facilitator assigned a third rater as a separate, impartial mediator. In those cases (n = 4) the outlier of the three ratings was replaced.

Inter-rater Agreement

To examine the agreement between raters, an estimate of inter-rater reliability was calculated to see how frequently the rater pairs agreed on the score when rating the same paper. Conclusions about the consistent measurement of the six measures depend on this estimate. A calculation of the intraclass correlation coefficient (ICG) was used to determine the level of inter-rater agreement. High IGG values indicate more agreement between raters. A one-way random model was used to measure consistency within the mean measure values. IGG values for Interpretation, Representation, Calculation, Application/Analysis, Assumptions, and Communication indicated good inter-rater agreement (see Table 2) even though rater pairs varied across ratings, which typically results in lower IGG values (Landers, 2015).

Analysis Plan

We used confirmatory factor analysis to assess whether the six measured skills are reliable indicators of an underlying more general construct (Brown 2006). One key advantage of this approach is the ability to isolate the underlying construct from random error variance in the indicator measures. Further, correlations across the error components of each survey item can also be modeled to account for method effects that detract from the underlying construct, such as any tendency to rate two of the skills more similarly than the others. Figure 1 depicts the conceptual model ([H.sub.0]).

Because the measure ratings are in the form of a Likert scale, and therefore categorical, we used a mean-and variance-adjusted weighted least squares (WLSMV) estimator to estimate the loadings of each measure on the underlying EQS trait (Muthen & Muthen, 1998-2012).

The same estimator also yields fits tatistics that provide information on the overall reliability of the model in terms of its ability to reproduce the variances and covariances of the indicator measures. Ideally, the model reports a nonsignificant chi square value indicating that imposing the hypothesized structure on the data does not amount to a substantial loss of information. However, since chi-square statistics are proportional to sample size other statistics are commonly used to assess model fit. I n particular, a Root Mean Square Error of Approximation (RMSEA) statistic that is below 0.05 and a Comparative Fit Index (CFI) greater than 0.95 indicates a model that is a good fit to the data (Byrne, 2012).

Results

All the analyses were conducted in Mplus v.7.31 (Muthen & Muthen, 2012), which also reports ways of improving the model via modification indices. Analysis of the set of ratings from rater 1 and then the set from rater 2 (from the rater parings) indicated that significant model improvement would be obtained by allowing the random error variances in the Representation and Calculation measures to correlate. The fit statistics of the two models, i.e., the model with the specified error correlation (the [H.sub.1] model) and the model with no error correlations (the [H.sub.0] model), are summarized in Table 3. The [H.sub.1] model met all the criteria of a well-fitting model in terms of the key fit statistics: chi square, RMSEA, and GFI. The table also showed a significant loss of fit for the [H.sub.0] model in terms of a chi-square difference test.

The unstandardized loadings of each of the six skill measures on the underlying EQS latent variable are summarized in Table 4. The standardized estimates, along with associated standard errors, are shown in Figure 2. Also included in Figure 2 is the estimate for the error correlation between Representation and Calculation .

The estimates in Table 4 are akin to regression estimates of the effect of the underlying EQS trait on the skill in question--all of which were statistically significant at the 0.01 alpha level. The three strongest indicators were Communication, Application/Analysis, and Interpretation, and the amount of variance in these indicators explained by EQS is 77%, 73%, and 71%, respectively. Weaker effects were found in the case of Calculation (53%), Assumptions (47%), and Representation (42%).

Discussion

Current efforts toward the use of PBA to augment standardized testing with students present a challenge for educators because of the possible rater bias and other differences in scoring authentic student work; thus, there is a need to validate the rubrics that raters use. The goal of the current study was to examine the construct validity of the Quantitative Literacy VALUE Rubric, one of 16 rubrics developed by the AAC&U. Overall, the findings show that the six underlying skill measures tapped into a common underlying EQS trait. These results extend previous research that has primarily focused on the use of the rubrics to study trends in student attainment (SHEEO, 2016).

Summary of Findings

Our hypothesis-testing results suggested that the six measures each reflect EQS as an underlying trait and that raters using the rubric produced valid EQS scores. Significant consistency was confirmed by analyzing rubric ratings of authentic student work from STEM courses at a four-year public university. Each of the six measured skills loaded on the same construct and the model accounted for a large proportion of variance in each of the indicators. This validates that the six different skills assessed by the Quantitative Literacy VALUE Rubric are reliable measures of the general trait, EQS. Though the importance of nonsubjective measures of PBA has been well established, to our knowledge this is the first study that confirmed how well the measured skills in the Quantitative Literacy VALUE Rubric fit together as a model of EQS.

In addition, the pattern of results indicated three measures with very strong contributions to the model, Interpretation, Application/Analysis, and Communication . These three skill measures are widely used in statistical texts to describe the analytical process researchers use after research questions are posed, studies are designed, and data are collected. Without them, the research process is just a collection of numbers, and does not contribute answers to research questions that often have real consequence in many fields. Indeed, national surveys of employers repeatedly list skills involving Interpretation, Application, and Communication as essential qualities in job applicants (National Association of Colleges and Employers, 2016). The model confirmed the strength of the rubric in representing these highly marketable skills--those that are involved in quantitative literacy.

In further support for the model, analyses revealed inter-rater reliability estimates in the moderate to good range for the six measures. This suggests that rater calibration activities conducted on scoring day may have held a degree of utility in terms of promoting agreement among raters. The literature about VALUE rubrics contains many case studies of the use of calibration as a best practice (AAC&U, 2017a; Finley, 2011; Peden et al., 2017) yet, to our knowledge, it does not contain findings related to calibration activity effectiveness that directly compared a trained group of raters with a group that did not undergo any sort of training.

In addition, while inter-rater agreement may have differed with the introduction of more than two raters for all Signature Assignments, the study design accounted for the importance of good inter-rater agreement by planning the facilitator-led calibration activities and using a third rater to mediate unacceptable differences. Indeed, Stanny, Gonzalez, and McGowan (2015) mention improvement in rater agreement through the use of similar activities that operationalize rubric guidelines with "notes [added to the rubric] about difficult decisions, to build and maintain consensus for future decisions" (p. 905). Further, Finley (2011) recommends that rating sessions include the type of facilitator-led discussions that were used in this study before the application of the rubric to ensure adequate agreement. Though not a primary focus of the current study, findings suggested that the level of agreement for the ratings in the sample provided adequate justification for proceeding with the analysis of the rubric's construct validity.

In addition to strengths already mentioned, the model improved when the association between Calculation and Representation was allowed to covary. This makes sense because a single-minded focus on Calculation makes drawing conclusions hard to visualize and a skill such as Representation strengthens its meaning. In that way, Calculation and Representation dovetail together. In practice, calculation turns to representation to derive meaning and understanding as two parts of the same whole. In the process of problem solving, making a visual representation is a natural process for deriving meaning from computational problems (Van Garderen & Montague, 2003) and for enhancing the decision-making value of quantitative information (Tufte, 1997).

Limitations

The findings of the current study are promising but a few limitations should be noted. For instance, student samples only represented STEM courses in the life and physical sciences. This limited the ability to examine the independent effects of other types of courses and potential confounds. In future studies, course types should be extended to include all three of the foundational component areas required by the THECB (life and physical science, mathematics, and social and behavioral science). Though all students at the university were also required to take courses across eight foundational component areas as part of the TCC, conclusions would be strengthened through the incorporation of a wider range of courses. Additionally, performance-based work was gathered only from TCC-approved courses and the naturalistic design of the study did not allow for randomized assignment of papers from across all the STEM courses on campus regardless of level. Nonetheless, the student demographics suggest that the sample was consistent with the campus population as a whole.

Conclusion

Continued efforts are needed to promote the use of authentic student work in educational assessment. This study examined a widely utilized rubric using a relatively large sample of STEM assignments to capitalize on the strength of the AAC&U initiatives that measure student attainment of broadly accepted educational learning objectives. Results suggest that the six skill measures contained in the Quantitative Literacy VALUE Rubric fit together well to explain EQS. Consequently, efforts to promote VALUE rubrics have the potential to accurately measure student attainment of EQS. Further research is needed to confirm the construct validity of the full array of AAC&U VALUE Rubrics. Continuation of this line of inquiry is essential for maximizing the effectiveness of PBA.

Keywords: quantitative literacy, empirical and quantitative skill, VALUE rubric, STEM, EQS, performance-based assessment, Texas Core Curriculum, AAC&U

Appendix
Quantitative Literacy VALUE Rubric

for more information, please contact value@aacu.org

Definition

Quantitative Literacy (QL)--also known as Numeracy or
Quantitative Reasoning (QR)--is a "habit of mind,"
competency, and comfort in working with numerical data.
Individuals with strong QL skills possess the ability to
reason and solve quantitative problems from a wide array
of authentic contexts and everyday life situations.
They understand and can create sophisticated arguments
supported by quantitative evidence and they can clearly
communicate those arguments in a variety of formats
(using words, tables, graphs, mathematical equations,
etc., as appropriate).

Evaluators are encouraged to assign a zero to
any work sample or collection of work, that does
not meet benchmark (cell one) level performance,

                             Capstone 4              Milestones 3

Interpretation         Provides accurate        Provides accurate
Ability to explain       explanations of          explanations of
  information            information              information
  presented in           presented in             presented in
  mathematical           mathematical forms.      mathematical forms.
  forms (e.g.,           Makes appropriate        For instance,
  equations,             inferences based on      accurately explains
  graphs, diagrams,      that information.        the trend data
  tables, words)         For example,             shown in a graph.
                         accurately explains
                         the trend data
                         shown in a graph
                         and makes reasonable
                         predictions
                         regarding what the
                         data suggest about
                         future events.
Representation         Skillfully converts      Competently converts
Ability to convert       relevant information     relevant information
  relevant               into an insightful       into an appropriate
  information into       mathematical             and desired
  various                portrayal in a way       mathematical
  mathematical           that contributes to      portrayal.
  forms (e.g.,           a further or deeper
  equations,             understanding.
  graphs,
  diagrams,
  tables, words)
Calculation            Calculations attempted   Calculations attempted
                         are essentially all      are essentially all
                         successful and           successful and
                         sufficiently             sufficiently
                         comprehensive to         comprehensive to
                         solve the problem.       solve the problem.
                         Calculations are
                         also presented
                         elegantly (clearly,
                         concisely, etc.)
Application /          Uses the quantitative    Uses the quantitative
Analysis                 analysis of data as      analysis of data as
  Ability to make        the basis for deep       the basis for
  judgments and          and thoughtful           competent judgments,
  draw appropriate       judgments, drawing       drawing reasonable
  conclusions based      insightful,              and appropriately
  on the                 carefully qualified      qualified
  quantitative           conclusions from         conclusions from
  analysis of data,      this work.               this work.
  while recognising
  the limits of
  this analysis
Assumptions            Explicitly describes     Explicitly describes
  Ability to make        assumptions and          assumptions and
  and evaluate           provides compelling      provides compelling
  important              rationale for why        rationale for why
  assumptions in         each assumption is       assumptions are
  estimation,            appropriate. Shows       appropriate.
  modeling, and          awareness that
  data analysis          confidence in final
                         conclusions is
                         limited by the
                         accuracy of the
                         assumptions.
Communication          Uses quantitative        Uses quantitative
  Expressing             information in           information in
  quantitative           connection with the      connection with the
  evidence in            argument or purpose      argument or purpose
  support of the         of the work,             of the work, though
  argument or            presents it in an        data may be
  purpose of the         effective format,        presented in a less
  work (in terms         and explicates it        than completely
  of what evidence       with consistently        effective format or
  is used and how        high quality.            some parts of the
  it is formatted,                                explication
  presented, and                                  may be uneven.
  contextualixed)

                            Milestones 2                  1

Interpretation         Provides somewhat        Attempts to explain
Ability to explain       accurate                 information
  information            explanations of          presented in
  presented in           information              mathematical forms,
  mathematical           presented in             but draws incorrect
  forms (e.g.,           mathematical forms,      conclusions about
  equations,             but occasionally         what the
  graphs, diagrams,      makes minor errors       information means.
  tables, words)         related to               For example,
                         computations or          attempts to
                         units. For               explain the trend
                         instance, accurately     data shown in a
                         explains trend data      graph, but will
                         shown in a graph,        frequently
                         but may                  misinterpret the
                         miscalculate the         nature of that
                         slope of the             trend, perhaps by
                         trend line.              confusing
                                                  positive and
                                                  negative trends.

Representation         Completes conversion     Completes conversion
Ability to convert       of information but       of information but
  relevant               resulting                resulting
  information into       mathematical             mathematical
  various                portrayal is only        portrayal is
  mathematical           partially                inappropriate
  forms (e.g.,           appropriate or           or inaccurate.
  equations,             accurate.
  graphs,
  diagrams,
  tables, words)
Calculation            Calculations attempted   Calculations are
                         are either               attempted but are
                         unsuccessful or          both unsuccessful
                         represent only a         and are not
                         portion of the           comprehensive.
                         calculations
                         required to
                         comprehensively
                         solve the problem.
Application /          Uses the quantitative    Uses the quantitative
Analysis                 analysis of data as      analysis of data as
  Ability to make        the basis for            the basis for
  judgments and          workmanlike (without     tentative, basic
  draw appropriate       inspiration or           judgments, although
  conclusions based      nuance, ordinary)        is hesitant or
  on the                 judgments, drawing       uncertain about
  quantitative           plausible                drawing conclusions
  analysis of data,      conclusions from         from this work.
  while recognising      this work.
  the limits of
  this analysis
Assumptions            Explicitly describes     Attempts to describe
  Ability to make        assumptions.             assumptions.
  and evaluate
  important
  assumptions in
  estimation,
  modeling, and
  data analysis
Communication          Uses quantitative        Presents an argument
  Expressing             information, but         for which
  quantitative           does not effectively     quantitative
  evidence in            connect it to the        evidence is
  support of the         argument or purpose      pertinent, but
  argument or            of the work.             does not provide
  purpose of the                                  adequate explicit
  work (in terms                                  numerical support.
  of what evidence                                (May use
  is used and how                                 quasi-quantitative
  it is formatted,                                words such as
  presented, and                                  "many," "few,"
  contextualixed)                                 "increasing,"
                                                  "small," and the
                                                  like in place of
                                                  actual quantities.)


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Julie S. Gray, Ph.D.

The University of Texas at Arlington

Melissa A. Brown, M.Ed.

The University of Texas at Arlington

John P. Connolly, Ph.D.

The University of Texas at Arlington

CORRESPONDENCE

Email julie.gray@uta.edu

Caption: Figure 1. Conceptual Model of Underlying EQS Traits

Caption: Figure 2. Standardized estimates for final solution ([H.sub.1])
Table 1. Student Characteristics for the Rated Sample of
Signature Assignments

Categorical Variables                           N     %

Gender
  Female                                       149   60.8
  Male                                         96    39.2
Ethnicity
  African American                             33    13.5
  Asian                                        49    20.0
  Caucasian                                    80    32.7
  Foreign, nonresident alien                    6     2.4
  Hispanic                                     67    27.3
  Multiple                                      5     2.0
  Unknown, not specified                        5     2.0
College/School
  College of Architecture                       2     0.8
  College of Business                          24     9.8
  College of Education                         13     5.3
  College of Engineering                       15     6.1
  College of Liberal Arts                      26    10.6
  College of Nursing                           61    24.9
  College of Science                           61    24.9
  School of Social Work                        15     6.1
  Undeclared                                   26    10.6
  (a) Missing college or school information     2     0.8
Level
  Freshman                                     67    27.3
  Sophomore                                    85    34.7
  Junior                                       49    20.0
  Senior and above                             42    17.1
  (a) Missing level information                 2     0.8

Note: N = 245 for each of the categorical variable.
(a) Information was missing

Table 2. ICC Values by Measure

Measure                 ICC Value

Interpretation             .52
Representation             .51
Calculation                .47
Application/ Analysis      .56
Assumptions                .51
Communication              .60

Note: N = 245 for each measure.

Table 3. Model fit statistics for the [H.sub.1]
and [H.sub.0] models with [chi square] difference test

                   N     [chi     df   P-Value   RMSEA   CFI
                        square]

[H.sub.1] Model   245    9.31     8     0.317    0.03    0.99
[H.sub.0] Model   245    47.31    9     0.000    0.13    0.98
Difference Test          19.40    1     0.000

Table 4. Weighted Least Squares estimates for the six skill measures

                       Estimate   S.E.   Est./   Two-Tailed
                                         S.E.     P-Value
Interpretation (a)       1.00     0.00
Representation           0.77     0.07   11.20     0.000
Calculation              0.87     0.07   12.72     0.000
Application/Analysis     1.02     0.06   17.62     0.000
Assumptions              0.81     0.06   12.91     0.000
Communication            1.04     0.06   18.98     0.000

Note: (a) For the purpose of scaling the latent
variable, Interpretation is treated as the marker
indicator. As such, the associated loading of this
indicator on EQS is set at a value of one
(Brown, 2006, p.71).
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Title Annotation:science, technology, engineering and mathematics
Author:Gray, Julie S.; Brown, Melissa A.; Connolly, John P.
Publication:Research & Practice in Assessment
Article Type:Report
Date:Jun 22, 2017
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