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The Stability Problem of Value-added Models in Teacher Effectiveness
Estimations: A Systematic Review Study
Ismail Aslantas
School of Education, Durham University, Durham, United Kingdom
ismail.aslantas@durham.ac.uk
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The Stability Problem of Value-added Models in Teacher Effectiveness
Estimations: A Systematic Review Study
This article provides evidence by undertaking a systematic review on the stability
problem of using value-added models in teacher effectiveness estimates from the
perspective of the impact of the number of previous test scores employed aimed at
answering a unique review question (This is a long sentence that lacks clarity – it
could be broken down for a clearer meaning): How stable is teacher effectiveness
estimates measured by VAMs? By using the terms: teacher performance, student
performance, value-added model, stability and their other related synonyms, a
comprehensive search was conducted in 17 databases along with employing hand
search in Google Scholar and contacting authorised persons by email. In total 1439
records were found as a result of the searches. After completing the screening
process, 50 studies remained for data extraction.
Out of 50 a total of studies in the review list, 13 focused on the stability of VAM
estimates regarding using the number of prior test scores. In summary, there is a
common view that the use of prior year data in on value-added estimates for teacher
effectiveness has a positive impact, however, with regard to the impact of multiple
previous year data, different voices arose from the researchers.
Keywords: teacher effectiveness, value-added model, stability, systematic review
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Introduction
Although the use of value-added models (VAMs) in the field of business and economics at
first, as researchers in the education sector began to be interested in these models to measure
teacher performance, it appears that there were research (studies) on VAMs in this field in
the late 1900s. (Sanders & Horn, 1994, 1998; Sanders, Saxton, & Horn, 1997; Webster &
Mendro, 1997; Kupermintz, 2003). With the effect of No Child Left Behind Act of 2001
(NCLB) based on the belief that the most important school-related factor affecting student
achievement is the quality of the teacher (Aaronson, Barrow, & Sander, 2007; Rivkin,
Hanushek, & Kain, 2005), the studies done in this field gained momentum (Ballou, Sanders,
& Wright, 2004; McCaffrey, Lockwood, Koretz, Louris, & Hamilton, 2004; Newton,
Darling-Hammond, Haertel, & Thomas, 2010). In order to measure the effectiveness of
teachers, several types of VAMs were developed and applied by states and school districts in
the US such as the Tennessee value-added assessment system (TVAAS) and the Dallas
value-added accountability system (DVAAS). The common assumption of these models that
the growth/decline of the students’ achievement in the standardised tests is attributed to their
teacher performance. In all VAMs concepts, it is assumed that the quality of students’
performance in the school reflects the quality of the teaching received (Darling-Hammond,
2015). A teacher’s value-added scores can be calculated by subtracting his/her students’
predicted scores from their actual scores in the standardised test(s) (Sanders, Saxton, &
Horn, 1997). The predicted score is subjected to the same students’ one or more previous
year test scores and their characteristic features in most VAMs (Ouma, 2014). These
prediction methods are likely to be beneficial to identify the most and least effective teachers
in a school, district and/or state (Colorado, 2007).
As a result of the increasing number of research studies in parallel with the interest of
researchers in this field, it was possible to discover the strengths and weaknesses of VAMs.
The teacher performance results estimated by VAMs are highly affected by students’
characteristics and other conceptual predictors which teacher cannot control (Wei, Hembry,
Murphy, & McBride, 2012). These models should not be used for the high-stake decision
about the teachers unless the pros and cons of VAMs are fully revealed. Therefore, their use
should be limited to improve the educational institutions, provide teachers with the
opportunity to address their own shortcomings and provide justification for students’
academic progress. More accurate information is needed about value-added models to
expand the intended use of them. One of the robust methods to collect accurate information
from the literature is conducting a systematic review. Primarily the research has the aim to
determine whether the teacher performance results estimated by applying value-added
models under different conditions are stable or not. Specifically, observable teacher
characteristics, school characteristics, the students' test scores obtained over time and the
preferred data analysis methods are the different conditions that are referred to in this current
research. As one of the purposes of this study is to provide guidance and appraise to
policymakers and practitioners on the use of value-added models in the teacher performance
appraisal for high-stake purposes such as decisions on dismissal and monetary reward,
gathering evidence-based findings from a wide body of research systematically are needed
instead of from narrative literature. Therefore, this systematic review is utilised in order to
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synthesise the results of previous relevant studies that analysed the impact of conceptual
predictors and data analysis methods used on teacher performance evaluation. In line with
the purpose of this systematic review declared, a unique review question formulated to assist
in exhaustively examining the available evidence is;
How stable is teacher effectiveness estimates measured by VAMs?
where teacher effectiveness operationally defined by VAM as the estimation of the
differences between expected and observed student test scores (Kersting, Chen and Stigler,
2013). Moreover, in this systematic review study, the operational definitions of the term
stability refer to the stableness of the estimates due to (a) the number of test scores used, (b)
the predictors used in the estimations, and (c) the analysis methods applied. The existing
literature on the stability of VAMs estimates will be retrieved from these three perspectives.
Methods Databases and Searching Strategy
In order to conduct a comprehensive search in the impact of conceptual predictors and data
analysis methods preferred on teacher performance evaluation estimates, both published and
unpublished studies that met the inclusion criteria as explained below, are obtained until the
1st of May 2019. In order to identify the studies met the inclusion criteria, a total of 17
electronic databases and six their providers were employed (shown in Table 1). For reaching
other relevant sources, research centres, foundations, and researchers who have worked on
teacher performance evaluation based on VAMs were contacted personally.
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Table 1. Databases and their providers
Provider
Database
1
ProQuest
ProQuest Dissertations & Theses Global:
Social Sciences
Education Database
ERIC
International Bibliography of the Social
Sciences (IBSS)
Social Science Database
Applied Social Sciences Index & Abstracts
(ASSIA)
2
EBSCOhost
OpenDissertations
British Education Index
Business Source Premier
Education Abstracts
Educational Administration abstracts
PsycINFO
3
Web of Science
Web of Science Core Collection
Current Contents Connect
4
Elsevier
SCOPUS
5
SAGE Research Methods Core
SAGE Journals
6
Taylor & Francis Online
Educational Research Abstracts Online
To formulate the searching strings, first of all, the keywords which are “teacher
performance”,
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“student performance”, “value-added model” and “stability” were identified in parallel with
the review question. Then the related terms of the keywords were determined by identifying
which alternative terms were used to substitute the search terms in the related sample studies
found (shown in Table 2).
Table 2. Search keywords
Search Terms
Related Terms
Teacher
performance
Teacher effect* Teacher proficiency-rank
Teacher evaluation Teacher judgment
Teacher performance evaluation Educational effectiveness
Teacher appraisal Educator performance appraisal
Teacher performance appraisal Educator performance
Teacher quality
Educator evaluation
Teacher assessment
Educator quality
Teacher performance assessment
Teaching effect*
Teacher accountability
Measuring teach*
Teacher proficiency
Evaluating teach*
Student
performance
Academic achievement
Academic gains
Student test score
Student test score
Achievement
Achievement measures
Outcomes
Outcome measures
Student test-score
Student test performance
Value Added
Model
Value added modelling
Value-added model*
VAM*
Value added estimate*
Teacher value-added
Value-added estimat*
Stability
Concord*
Robust
Sensitivity
Imprecision
Variat*
Fluctua*
Instability
Persistence
Precision
Shrink*
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Inclusion and Exclusion Criteria
The research included in this systematic review met all criteria located in Table 3.
Table 3. Inclusion criteria
Inclusion Criteria
Criteria
Description
The population of this study is
teachers evaluated by their students'
outcomes
Only studies focused on teacher performance
evaluation based on student test scores will be
included in this systematic review.
Among the studies that are interested in the
performance evaluation on more than one subject
such as teacher and school performance estimated
together in a single study, only the studies whose one
of the areas of interest is teachers will be given a
place in this systematic review.
The issue of the study is the stability
of the estimates
The operational definitions of the term of stability in
this systematic review refer to the stability of the
estimates;
(a) based on students’ test scores Studies that
use this measure for stability must have at least two
previous years test scores for the same or different
cohorts of students over time) (b) based on
predictors used
(c) based on the analysis methods applied
Studies are included if they use any one of the above
measures of stability.
Only empirical studies are reviewed
for this study
Empirical studies refer to primary research as
opposed to secondary research such as reviews,
government reports.
Studies analyzing secondary data such as panel,
administrative data are considered as primary
research.
The study setting of the research
interest is K-12.
(K) refers to kindergarten grade (age 5-6, equivalent
to Year 1 in the UK) and (12) refers to the 12th grade
(age 17-18, equivalent Y13 or 6th form in the UK. All
studies conducted from kindergarten to the 12thgrade
setting are included in this systematic review.
Published in English
Studies reported in English
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The studies were screened with regard to the below criteria as the exclusion criteria of this
research;
Not reported or published in English
Not primary research
Not about education
Not within K-12 (e.g. higher education, reception year or nursery)
Not about the evaluation of teacher effectiveness
About the use of value-added measures of teachers to predict teacher attrition
The outcome is not student test scores or gains (e.g. children’s behavior or attendance)
Using measures of teacher effectiveness to predict outcomes
Just about school effectiveness or school improvement (the studies focused on both school
(principal) and teacher effectiveness, they have potential to be included in the review)
About teacher effectiveness in non-mainstream school
Just about pupils with special educational needs (SEN)
About theories and policies, opinion pieces, discussion pieces
Instructional manual or promotional literature about how to measure teacher effectiveness
Literature about the characteristics of effective teachers
Findings
The research findings from this systematic review are presented mainly in the two sections:
description results and thematic analysis results. In the first section, overall explanatory
results for the searching process were exhibited. On the basis of the conceptual definition of
the stability of VAMs estimates, three themes have been determined for this study; a) the
number of previous test scores employed, b) the predictors used, and c) the data analysis
methods applied. As this article is a part of the uncompleted doctorate thesis, the key findings
of the included studies were only placed under the first theme; the number of previous test
scores employed.
Descriptive Results
For a more efficient and well-organized search process, the Preferred Reporting Items for
Systematic Reviews and Meta-Analyses (PRISMA) flow diagram is mainly guided. PRISMA
is a diagram that published in 2009 by the PRISMA group (Moher, Liberati, Tetzlaff, &
Altman, 2009) to help researchers to map out the number of studies identified, included and
excluded based on the criteria established. The number of studies included and excluded in
the review list was illustrated in the flowchart in Figure 1.
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Figure 1. The Modified PRISMA Flow Diagram
As a result of typing a combination of the searching strings into the providers’ search
engines, a total number of 1439 articles were found initially. In the process of merging, 667
cases were deleted from the review list as being duplicated cases of unique studies. Through
the phase I screening checklist form, all remaining 772 studies’ titles and abstracts were
screened, and 309 of them were excluded from this systematic review study in this screening
stage. The further 423 cases out of the remaining 473 studies, which were added 10 studies
came from the alerted results on the providers, were removed by employing the phase II full-
text screening checklist form. To ensure that the screening processes were undertaken away
from the prejudice of the researcher and to minimise the lack of potentially relevant articles
among the discarded papers, the randomly selected 70 papers were also screened by a second
independent reviewer. Although over 95 percent exact agreement reached between the
reviewers, the inter-rater reliability agreement was .86.
Finally, the remaining studies were also subjected to the quality appraisal in order to include
the findings from only the credible studies in this systematic review. Unfortunately, the
trustworthiness of all research done is not the same, so the credibility of their findings should
not be the same either. Therefore, to avoid an invalid and misleading conclusion, as of being
a practical way for evaluation of the quality of individual studies instead of complex technical
checklists in the literature, the modified “sieve” quality appraisal framework designed by
Gorard (2014) was employed in this systematic review. As the qualifications of the studies
were satisfactory for inclusion in this study, none of them was excluded from the review list.
Therefore, by the end of this searching and elimination strategies, 50 research that focused on
the stability of teacher effectiveness measurement estimates by VAMs were included in this
current study.
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Thematic Analysis Results
The final 50 studies retrieved in this systematic review by three main themes; the number of
previous year test scores employed, the prediction used, and the data analysis methods
applied in estimating teacher effectiveness. Although it was planned to present the results
under three themes, as the analysis process in other themes is not yet complete, only the key
findings related to the fist theme, the number of previous test scores employed, were placed.
The Number of Previous Test Scores Employed
In this section, the stability of teacher performance evaluation estimations with regard to the
number of students’ previous test scores used in VAMs was investigated. Although out of 50
studies, a total of 15 research studies are located in this theme.
The first study (Rothstein, 2009) claimed that the limited positive effect of using additional
scores was longitudinal research involved 49.456 students from grade 3 to 5 linked to 2844
teachers. The researcher discussed a bias problem in value-added estimates related to student-
teacher allocation issues. Although the study covers other aspects of VAM estimates, in this
systematic review, only findings related to the impact of a number of test scores from prior
years were included. To investigate the impact of using additional year test scores on teacher
effectiveness in grade 5, first, the authors added the nearest prior year score (test score in 4th
grade) and estimated the increase in R², which was .55. The 4th-grade test score contributed to
55 percent to the explanation of variance on test scores in grade 5. Moreover, the authors also
included two prior year test scores (pre- and post-tests in grade 3) in the previous model;
however, their contribution was very limited, R² only increased by .039 (3.9%).
The limited effect reported by the other study (Cunningham, 20014) was a thesis defended
for the Doctor of Philosophy degree. In order to provide sufficient information to
policymakers and practitioners in making the high-stakes decision regarding with teacher
accountability system, this study evaluated the impact of growth model preference, of how
many years of data used, and of student-level variable employed in the teacher performance
estimates. With using up to three successive years of student data, teacher effects were
estimated from five value-added models. Teacher rank orderings obtained in the five value-
added models by using either one or three years of test scores were highly correlated with
each other. The correlation exceeded .90 when using single-year data, and .80 when
conducting multiple years of data. The use of a single year of test scores instead of three
years resulted in a slight increase in correlation between the models and a slight decrease in
teacher movement between quarters.
The next study, Shafer et al. (2012), compared six growth models used for teacher
effectiveness estimates in the literature; quantile regression (QReg), ordinary least square
(OLS), growth score difference (year two minus year one), and three different transition
models (value-tables). Although the study compares the six growth models, it also covers the
impact of using additional previous year data in estimates of the growth models. With related
to this theme’s concept, the findings on the correlations between scores estimated in reading
and maths across four student cohorts allocated were presented. Mainly, the study claimed
that the inclusion of data from more previous years (at least two years) in the QReg and OLS
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models had a limited positive effect. For instance, the correlation between maths and reading
scores for cohort 1 students was found as .19 in QReg1 (used one prior year only) and .18 in
QReg2 (used two prior years); similarly the greatest change in correlation coefficients with
regard to use additional prior year data in OLS models was found as .01.
Oppositely, eight research in the review list claimed the advantages of using additional prior
years data in the teacher effectiveness estimates. One of them done by Lash et al. (2016) in
order to investigate how stable the teacher growth percentile scores over the years, so that the
authors compared the reliability of coefficients of the estimations. They claimed that stability
of performance scores increased from .5 to .67 when the results are obtained by averaging
over two years, and to .75 by averaging three years in maths, similarly in reading the increase
obtained from .41 to .58 by averaging two years, and .68 by averaging three years.
The next study claimed a substantial improvement obtained in the reliability of VAM
estimates by employing additional years of observations is belonging to Goldhaber and
Hansen (2013). In order to examine the long-term stability of teacher effectiveness, the
authors used up to ten years of longitudinal data in maths and reading across 3rd to 5th grade.
After running a series of value-added estimates, the authors reached that there is a substantial
improvement in the reliability of the estimates by using multiple prior year test scores. The
reliability coefficient increased from 0.29 with a one-year VAM to 0.52 with a six-year
VAM.
Another longitudinal study (Hu, 2015) involved 1210 maths, and 1239 reading teachers were
conducted to explore the impact of adding student prior achievement into the estimates of
teacher effectiveness by using the longitudinal students’ data (one to three previous year test
scores depend on grade and year) into hierarchical linear models. As a result of this study,
students’ up to three prior years test scores explained more than half of variance in their
current scores was found. Besides, the researcher claimed that not surprisingly, the nearest
previous year test score had an important role in this explanation. The average of 57% and
59% of the variance in students’ current achievements in maths and reading, respectively,
were explained by the nearest prior test scores. Similarly, the additional previous year test
scores also contributed to the explanation of the variance in students’ current achievement,
but not as large as the nearest prior year’s. For instance, 67% of total variance in students’
mathematics achievement in Grade 7 in 2009-10 were explained by their achievement in
grade 6 and 5 (the impact of the achievement score in grade 5 was 12%), and 69% of
variance in grade7 in 201011 was explained by the achievement scores in grade 6, 5 and 4
(the impact of achievement score in grade 4 was 2%).
Discussion and Initial Conclusion
This systematic review study is utilised as a part of the researcher’s own doctorate thesis in
order to synthesise the results of previous relevant studies that analysed the impact of
conceptual predictors and data analysis methods used on teacher performance evaluation In
line with the purpose of this systematic review, a unique question was formulated in order to
retrieve the available evidence. Namely, how stable is teacher effectiveness measured by
VAMs? In this systematic review study, the operational definitions of the term stability refer
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to the stableness of the estimates due to (a) the number of test scores used, (b) the predictors
used in the estimations, and (c) the analysis methods applied. The existing literature on the
stability of VAMs estimates will be retrieved from these three perspectives.
Since the researcher's doctoral process is ongoing and the analysis chapter is not completely
finished, yet, only the key findings related to the first theme, the number of previous test
scores employed, were placed in this conference proceedings paper. The stability of teacher
performance evaluation estimations with regard to the number of students’ previous test
scores used in VAMs was investigated. Out of 50 studies, a total of 15 research studies are
retrieved in this theme. In general, although there is a consortium on the impact of prior year
data on value-added estimates for teacher effectiveness, unfortunately, this consortium is
disintegrated about the impact of using additional previous year(s) data on the estimates.
Keep in mind that the evidence in this theme is not very robust because of preferring not
strong design for their research questions and involving a considerable amount of missing
data. Eight studies in this theme, seven of them were rated 2 * from middle bound, and one
with 1 * from the lower bound, claimed to be advantageous with adding additional year test
scores to the estimates. Although the other seven studies, one of these was rated 2 * from
upper bound, and the rest were rated with 2 * from middle bound reported that using
additional prior year test scores have a positive impact, but the research also found that the
impact is limited, or even little if any. Therefore, the findings are mixed with almost an equal
number of medium quality studies suggesting that there are advantages in including
additional year test scores as well as those advocating having little benefit. However, the
stronger study (rated 2a) suggests that there is little benefit of using additional test scores
from previous years. More robust studies may be needed to confirm the results, but at the
moment, there is no evidence that using additional prior test scores is useful.
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