Grading By Objectives: A Matrix Method for Course Assessment

Abstract

This article describes a method for linking course assessments to learning objectives. This method allows instructors to see the relative weight and performance of each learning objective, as reflected by course assignments and exams. While designing the course, instructors can use this information to ensure the relative weights are aligned with the relative importance of the learning objectives. When the course is completed, instructors can see, at a glance, which objectives students mastered and which ones they did not. This information can be used to modify the course prior to the next offering. Furthermore, this information may be utilized for learning outcomes assessment efforts. At our business school, this method was implemented via a spreadsheet and used for several years by a faculty member. We propose integrating the methodology into learning management systems.

Full text

13 Quality Approaches in Higher Education Vol. 6, No. 2
asq.org/edu
Linking course
objectives to
learning outcome
assessment efforts
in course design.
Grading By Objectives: A Matrix
Method for Course Assessment
Ido Millet and Suzanne Weinstein
Abstract
This article describes a method for linking course assessments to learning objectives. This
method allows instructors to see the relative weight and performance of each learning
objective, as ref lected by course assignments and exams. While designing the course,
instructors can use this information to ensure the relative weights are aligned with the
relative importance of the learning objectives. When the course is completed, instructors
can see, at a glance, which objectives students mastered and which ones they did not. This
information can be used to modify the course prior to the next offering. Furthermore,
this information may be utilized for learning outcomes assessment efforts. At our business
school, this method was implemented via a spreadsheet and used for several years by a fac-
ulty member. We propose integrating the methodology into learning management systems.
Keywords
Assessment, Learning Objectives, Grades
Introduction
According to Frazer (1992), the basis for quality in higher education is self-evaluation,
and a “mirror” is required for teachers and universities to become "self-critical and ref lective"
(p. 18). In this article we describe a method that allows instructors to see the extent to which
assessments are aligned with learning objectives, as well as how students have performed on
specific learning objectives. This allows instructors to adjust assignments and tests to better
reflect the desired balance across learning objectives. Because learning objectives with poor
student performance become visible, this reporting system can also lead to beneficial adjust-
ments to teaching strategies. For course objectives that reflect program-level objectives, the
information generated by this system may also contribute to program-level assessment.
Graded assignments and exams are one of the most important features of any course
because they provide the opportunity for both students and instructors to assess how well
students have learned the course content. The educational assessment process begins with
the development of learning objectives, which define what we expect students to know
or be able to do following the course or program (Biggs, 1999; Fink, 2003; Suskie, 2009;
Walvoord, 2004; Walvoord & Anderson, 1998; Wiggins & McTighe, 2005). According
to Wiggins and McTighe (2005), after learning objectives are developed, assessments are
designed to inform the instructor and the student about the extent to which the student
has met those objectives. When done effectively, this process results in course assignments,
projects, and tests that are closely aligned with each learning objective. Research has shown
that such alignment results in powerful effects on student learning (Cohen, 1987).
After the assessments are designed, the instructor plans the teaching strategies that
will prepare students to perform well on these tasks. However, even if faculty members
design their courses in this way, they may not take the time to evaluate the extent to which
their assessments match their objectives or how well students performed on each objective.
Instructors are typically more concerned with how well students performed on the com-
bination of assessments, which is how course grades are determined (Weinstein, Ching,
Shapiro, & Martin, 2010). Furthermore, a single assignment, project, or exam frequently

14 Quality Approaches in Higher Education Vol. 6, No. 2asq.org/edu
assesses multiple course objectives, making it difficult to map
students’ performance back to individual course objectives.
How Course Design Strategy Enhances Assessment
In this article we will describe a matrix method for assess-
ment that is easy to implement and can help instructors improve
the design of their courses while also contributing to program-
level assessment.
Courses are commonly designed around topics. For example,
an introductory psychology course may cover topics such as the
biological underpinnings of behavior, memory, and abnormal
behavior. In contrast, instructional design experts advocate that
courses be designed around learning objectives, which are state-
ments that delineate what students will know or be able to do after
taking the course (Wiggins & McTighe, 2005). In this process,
called constructive alignment (Biggs, 1999) or backward design
(Wigg ins & McTighe, 2005), the instruc tor begins with the desi red
results before developing assessments and teachingstrategies.
Using the introductory psychology course as an example, the
faculty member may state that he/she wants students to be able
to compare and contrast the different theories of learning. He/
She would then design an assessment, perhaps an essay question
on a test, which aligns with that objective. The next step involves
determining what activities students should engage in so that
they are prepared to answer the essay question. For example,
they may first read about the theories and then engage in a class
discussion. When course objectives drive course design, both
students and instructors are clear about what students will be
able to know and do after completing the course.
Many instructors include instructional objectives in their syl-
labi and course design process, but how can we provide evidence
that the course actually achieves its stated objectives? Aligning
learning objectives with as signments and tests ca n help answer t his
basic learning assessment question (Diamond, 1989; Fink, 2003;
Huba & Freed, 2000; Nitko, 1996; Suskie, 2009; Walvoord &
Anderson, 1998; Walvoord, 2004; Wiggins & McTighe, 2005).
Explicit links between course objectives and assessments offer
benefits beyond the course design process. Such links can ensure
that an appropriate percentage of course assessments address each
learning objective. Such links can also help measure students’ per-
formance on each learning objective. The instructor can then use
this information to improve the course in appropriate ways. For
example, the information may prompt the instructor to add assign-
ments and test questions linked to a relatively neglected course
objective. Similarly, a course objective with relatively poor perfor-
mance may prompt the instructor to change the course design to
address the deficiency. Likely causes of low performance on a par-
ticular learning objective include problems with the objective itself,
the assessments used to evaluate the objective, or the teaching strat-
egies used to prepare students for the assessment (Suskie, 2012).
Beyond the contribution to course design and evaluation,
linking assessments to course objectives may also benefit pro-
gram-level assessment. If some course-level objectives address
program-level objectives, the evidence of student performance
on these objectives can be incorporated into the program assess-
ment materials. This “embedded assessment” strategy can save
time for instructors (Weinstein et al., 2010).
What follows is a method for linking course objectives to
assessments using computer software. Once these links are estab-
lished, no extra effort (beyond the usual grading of assignments
and tests) is needed to generate the information described above.
A Matrix Method for Grading By Objectives
The core idea behind the proposed grading by objectives
(GBO) method is that each graded task (assignment, exam ques-
tion, quiz, or project) should be linked back to course objectives
via a matrix. Figure 1 shows a simple case where a matrix links
two graded tasks with two course learning objectives (LO).
Derived weight
Objective Matrix Max points Weight
LO one 100% 70 70%
LO two 100% 30 30%
Task one Task two
Max points: 70 30
Figure 1: A Simplified Matrix That Associates Tasks With
Learning Objectives
Although this scenario, in which each task is linked to only
one objective, is overly simplified, it serves to demonstrate how
useful information can be generated with minimal input from the
instructor. For each graded task, the instructor simply needs to
specify the relative extent to which it evaluates each of the course
learning objectives. Given the relative weights (or points) assigned
to each task, this allows us to compute the relative grading weight
assigned to each learning objective. For example, the maximum
points derived for objective one are 100% x 70 (from task one) and
0% x 30 (from task two) for a total of 70 points, or 70% of the
grading in this course. If the instructor believes the intended rela-
tive importance of a learning objective does not match its actual
derived grading weight, an obvious next step would call for chang-
ing the composition or relative weights of the tasks to close the gap.

15 Quality Approaches in Higher Education Vol. 6, No. 2asq.org/edu
When Tasks Are Not Specific to Learning Objectives
The case above was extreme in the sense that each task was
tied specifically to only one learning objective. Figure 2 shows
the other possible extreme where each task is associated equally
with all learning objectives.
When tasks are not weighted toward specific learning objec-
tives, we cannot derive relative weights or relative performance
for learning objectives. Because of the centrality of the align-
ment between assessments and learning objectives for good
course design, it can be argued that a course without this align-
ment may require reconsideration of the learning objectives. If
the evaluation of one learning objective always entails equally
weighted evaluation of all other objectives, we should probably
rethink our course design.
For example, consider a Genetics 101 course with the expecta-
tion that, upon completing the course, students should be ableto:
• Describe natural selection mechanisms and implications for
disease resistance in humans.
• Describe natural selection mechanisms and implications for
disease resistance in primates.
Since these knowledge areas overlap, there is a good chance
that graded tasks in this course would have very low specificity
(similar to Figure 2). This may prompt us to rearrange the course
objectives so that, upon completing the course, students should
be able to:
• Describe natural selection mechanisms in primates.
• Describe natural selection implications for disease resistance
in primates.
This would probably yield much higher task specificity and,
we believe, better learning objectives.
Mixed-Specificity Case
Our experience has been that even for well-designed course
objectives, some tasks may not be 100% specific to a single learn-
ing objective. Figure 3 depicts such a realistic scenario.
In this particular case, the points allocated to each task
are split, in the proportions specified by the matrix, across the
objectives. Learning objective one receives 63 points (90% x 70
points) from task one and six points (20% x 30 points) from task
two for a total of 69 points, or 69% of grading in this course.
This demonstrates that even when tasks are not 100% specific,
the results can still be quite useful.
Note that we can derive grading weights for the learning
objectives even before the course has begun. This allows instruc-
tors to modify the course design by adjusting the mix of tasks to
better ref lect the relative importance of learning objectives.
Using Rubrics and Subtasks to Align Assessment With
Learning Objectives
Even when a task as a whole is not specific to learning objec-
tives, a rubric may provide separate evaluation criteria that,
when aligned with learning objectives, can significantly increase
assessment specificity (Suskie, 2009; Walvoord & Anderson,
1998). For example, a rubric for evaluating a paper may provide
separate grades for writing, critical thinking, and knowledge of
ethical principles. Similarly, although a final exam as a whole
may not be specific to learning objectives, each question within
the exam may be quite specific.
When a single task generates separate grades for different cri-
teria or subtasks, we should record and treat the grade for each
criterion or subtask as a separate assessment with its own weight.
This would preserve useful information and increase our ability
to align assessments with specific learning objectives.
From Task Grades to Learning Objective
PerformanceScores
Although we can derive grading weights for the learning
objectives even before the course has begun, tasks must be graded
before we can assess how well our students performed on each
learning objective. Figure 4 shows how ta sk grades are tran sformed
Derived weight
Objective Matrix Max points Weight
LO one 50% 50% 50 50%
LO two 50% 50% 50 50%
Task one Task two
Max points: 70 30
Figure 2: A Matrix That Includes Tasks That Do Not Align
With Specific Objectives
Derived weight
Objective Matrix Max points Weight
LO one 90% 20% 69 69%
LO two 10% 80% 31 31%
Task one Task two
Max points: 70 30
Figure 3: A Matrix That Includes Tasks Which Are Partially
Specific to Multiple Objectives

16 Quality Approaches in Higher Education Vol. 6, No. 2asq.org/edu
through the GBO matrix
into performance scores for
the learning objectives.
On average, students in
this course scored 60% on
task one and 90% on task
two. This means that out of a
maximum of 70 points, stu-
dents averaged 42 points on
task one, and out of a maxi-
mum of 30 points, students
averaged 27 points on task
two. Multiplying these task
performance points (TPPs)
by the allocation percentages in the GBO matrix
allows us to split and recombine these points into
learning objective performance points (LOPP). For
example, learning objective one accumulates 90%
of the 42 TPPs from task one and 20% of the 27
TPPs from task two for a total of 43.2 LOPPs.
Given that the maximum LOPPs for the first objec-
tive is 69, we can compute an overall performance
score of 63% for learning objective one. Similarly,
learning objective two accumulates 10% of the 42
TPPs from task one and 80% of the 27 TPPs from
task two for a total of 25.8 LOPPs. Given that the
maximum LOPPs for the second objective is 31, we can compute
a performance score of 83% for learning objective two.
Even though the tasks are not 100% specific to single objec-
tives, this procedure provides useful information. We would be
justified in concluding that students are struggling to attain
learning objective one but are doing quite well with learning
objective two. The instructor may then investigate the reasons
for the poor performance on learning objective one and change
the design of the course to address these deficiencies.
Summative Versus Formative Tasks
According to Allen (2005), the validity of a measure of stu-
dent performance (e.g., a grade) is diminished if measures of
behavior, effort, or practice are included. Thus, when measuring
academic performance using the GBO method, we recommend
focusing only on summative assessments scores, such as exams,
end-of-topic assignments, and final papers because these types of
assessments are designed to determine the level at which students
achieved the learning outcomes at the end of a unit or course.
In such a case, we should exclude formative assessments, such
as practice quizzes or early paper drafts, which are designed to
provide feedback and help students improve.
Yet, when we move from the measurement of academic per-
formance to a broader objective of course diagnostics, we may
include metrics for formative assessments. Keeping both types
of graded tasks in the matrix (and classifying each as summa-
tive or formative) would provide useful information such as the
relative assessment attention each learning objective receives in
terms of summative assessments, formative assessments, or both.
For example, the scatter chart in Figure 5 highlights a diver-
gence between the summative and formative assessment weights
for two out of four learning objectives. Learning objective one
receives high summative but low formative assessment atten-
tion, while learning objective two receives low summative but
high formative attention. These disparities may or may not be
appropriate for these learning objectives. In any case, the GBO
method would help make such disparities visible to the instruc-
tor, who can then make modifications if necessary.
Ancillary and Mixed Grades
Just as formative grades should be excluded when assessing
the achievement of learning objectives, so should grades deal-
ing with non-academic performance. Allen (2005, p. 220) states
“grades should not be a hodgepodge of factors such as student’s
level of effort, innate aptitude, compliance to rules, attendance,
Derived weight
Objective Matrix Max points Weight Actual points Performance
LO one 90% 20% 69 69% 69 69%
LO two 10% 80% 31 31% 31 31%
Task one Task two
Max points: 70 30
Performance 60% 90%
Actual points 42 27
Figure 4: Deriving Performance Scores for Learning Objectives
Weight
Summative Formative
LO one 35% 15%
LO two 15% 35%
LO three 20% 20%
LO four 30% 30%
Figure 5: Summative Versus Formative Assessment Weights
10% 20% 30% 40%
LO one
LO four
LO three
LO two
10%
20%
30%
40%
Summative weight
Formative weight

17 Quality Approaches in Higher Education Vol. 6, No. 2asq.org/edu
social behaviors, attitudes, or other nonachievement measures.”
However, Allen (2005, p. 119) also claims that “although ancil-
lary information such as effort and attitude could be part of an
overall student report, they should not be part of a grade that
represents academic achievement” (Tombari & Borich, 1999).
Thus, instructors may choose to award points to non-academic
behaviors for motivational purposes, but these points should be
excluded from the GBO matrix if it is to represent a valid mea-
sure of student performance.
A Case in Point
For several semesters, one of the authors has used the GBO
technique in a senior-level undergraduate course on busi-
ness intelligence. A sanitized version (no student names) of
the grading spreadsheet with the integrated GBO technique is
available for download from: https://dl.dropboxusercontent.
com/u/38773963/Grading_By_Objectives_Sample.xlsx.
The spreadsheet starts with a row-wise listing of the learn-
ing objectives. The intersection of learning objective rows with
assessment columns (cells J7 to AS9) is used to indicate how each
assessment is allocated across the learning objectives. Since each
assessment must distribute all its weight across the learning objec-
tives, each column in that range adds up to 100% (J10:AS10). The
maximum points value for each learning objective is computed by
multiplying the assessment points for each assessment (J14:AS14)
by the percent allocated for that learning objective and summing
across all assessments. The weight % column is then computed by
dividing the maximum points value for each learning objective
by the sum of maximum points across all objectives. In Figure 6,
the weight % column shows that 50% of the assessment in this
course is allocated to the third learningobjective.
The class performance on each assignment is converted to
percent scores (J1:AS1) by dividing the average score for each
assessment by its maximum points. Multiplying these actual
scores by the allocation percentages for each learning objective
and summing across all assessment provides the actual points
(G7:G9) scored for each learning objective. Finally, dividing
actual points by maximum points provides the percentage of max-
imum metrics (H7:G7) and reflects how well the class performed
on each objective. Similar logic is applied to compute how well
individual students performed across the learning objectives. In
Figure 6, the percentage of maximum column shows that the
class performed on the first learning objective was lower (75%)
compared to the other two learning objectives (89% and 88%).
When the method was first used, the second learning objec-
tive (suggest and design improvements) had a grading weight of
just 17%. This revelation was a surprise to the instructor who
then added two new assignments and several exam questions to
bring the grading weight for that objective to its current value
of 31%. This supports and demonstrates Frazer's (1992) claim
that self-evaluation is necessary to achieve quality in higher
education, and that a mirror is required for teachers to become
"self-critical and reflective" (p. 18).
In this particular course, there were more than 20 graded
tasks. This explains how even an experienced instructor might
be unaware that an important learning objective is not subject to
sufficient assessment. We believe that the GBO method becomes
even more helpful when a course has many graded tasks.
Integrating Grading by Objectives Into Learning
Management Systems
The increasing popularity of learning management systems
provides an opportunity to embed the computational logic of the
GBO method in the software already used by instructors to set
up tasks, assign relative points to these tasks, and record grades.
The GBO method would simply require that instructors specify
learning objectives, allocate each task across these learning objec-
tives, and classify each task as formative or summative.
Once these aspects are embedded within a learning man-
agement system, we estimate the extra input required from the
instructor would demand no more than 20 minutes per course.
This does not count the time to interpret and act upon the reports
generated by the method. However, since this feedback would
help instructors improve their course designs, we believe most
instructors would welcome it. In cases where the same course
is taught by different instructors, reports from the system can
highlight metrics with significant differences. For example, an
instructor whose students are struggling with a particular learn-
ing objective would be able to seek advice from the instructor
whose students are performing best on that particular objective.
Using Grading by Objectives for
Program-Level Assessment
Although course grades are not appropriate metrics for learn-
ing outcomes assessment, scores on specific tasks within a course
that align with program-level objectives are appropriate methods
for providing evidence that students are meeting the program
Figure 6: Sample Grading by Objectives Spreadsheet

18 Quality Approaches in Higher Education Vol. 6, No. 2asq.org/edu
objectives. Thus, the GBO method provides an added benefit
for instructors teaching courses in which assessments for one or
more learning objectives will be used as evidence that students
have met program-level objectives. The embedded formulas will
automatically generate a percentage that represents the extent to
which students have met a particular objective. This result can
then be included in the program assessment report and discussed
by program faculty as part of the process.
Limitations
The proposed methodology assumes proper learning objec-
tives can be identified for courses. Yet, several researchers cast
doubt on the ease and advisability of establishing such objectives.
A good review of such objections is provided by James (2005).
We need to exercise care and proper balance in establishing
learning objectives:
If learning outcomes are defined too broadly, they lose their
capacity to assist in comparison across cases and over time.
Defined too narrowly, they become impotent, in the sense
that they refer to so little of a de facto learning process that
they are simply uninformative, powerless to generate or even
signal improvement. (James 2005, p. 90).
Although instructors may welcome access to GBO metrics
and reports, one sensitive consequence of this method is that it
would make problem areas visible to administrators and, possibly,
to other instructors. This tension between "external control and
internal improvement" (Padró, p. 2) is an issue for any assessment
initiative. However, since the GBO method uses grades as input,
it raises the threat that instructors might be tempted to assign
higher grades to escape negative attention from administrators
and peers. To avoid such unintended consequences, it may be wise
to restrict detailed feedback to constructive use by the instructor.
Allen (2005) warns “grading systems used by teachers vary
widely and unpredictably and often have low levels of valid-
ity due to the inclusion of nonacademic criteria used in the
calculation of grades.” The GBO method strives to remove
non-academic criteria by exclusively using summative grades for
assessing the achievement of learning objectives. Still, there is a
remaining concern about the reliability and consistency of sum-
mative grades. To reduce possible instructor bias, subjectively
scored tasks, such as essays, papers, or presentations, should be
scored using well-developed rubrics, which make scoring more
accurate, unbiased, and consistent (Suskie, 2009). Close atten-
tion should also be paid to creating reliable objective tests such
as multiple choice tests, which requires significant effort (Suskie,
2009). Also, a grade lift reporting system (Millet, 2010) may pro-
mote grading consistency across faculty members.
Future Research
Future research may investigate the impact of using the
proposed GBO methodology on teaching practices, grades,
academic performance, and student satisfaction. It would also
be important to collect feedback from instructors who are early
adopters of the technique. Such feedback may include overall sat-
isfaction, suggestions for improvements, and level of impact on
course and assessments designs.
As mentioned earlier, establishing proper learning objectives is
an essenti al yet challen ging aspect of any lea rning asse ssment effort.
Future research is needed to establish guidelines for the creation of
effective learning objectives for various educationalcontingencies.
Another interesting question relates to the proper balance
between formative and summative assessment. As depicted in
Figure 5, the GBO methodology provides descriptive information
about that balance as reflected by graded tasks. However, we lack
prescriptive insight. What type of balance is conducive to achiev-
ing different types of learning goals in different situations? For
example, do undergraduate students require a greater proportion
of formative tasks? Do students benefit from a greater propor-
tion of formative tasks for learning objectives at higher levels of
Bloom’s taxonomy, such as analysis or evaluation (Bloom, 1956)?
Do courses with a higher proportion of formative tasks lead to
better long-term knowledge retention? What is the impact on stu-
dent engagement and performance when formative task grades
are downplayed in computing final grades? Answers to these and
other questions associated with the impact of formative assessment
on student performance would benefit our educational systems.
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PA1&source=gbs_toc_r&cad=4#v=onepage&q&f=false.
Ido Millet, Ph.D. is a professor of manage-
ment information systems at the Sam and Irene
Black School of Business, The Pennsylvania
State University-Erie. His research interests
include the analytic hierarchy process, online
reverse auctions, business intelligence, and use
of academic data to support faculty and stu-
dents. Millet’s industrial experience includes
systems analysis, project management, con-
sulting, and software development. His
business intelligence software packages have
been purchased by more than 5,600 organi-
zations. For more information, contact him via
email at ixm7@psu.edu.
Suzanne Weinstein, Ph.D. is director of
instructional consulting, assessment, and
research at the Schreyer Institute for Teaching
Excellence at Penn State University. She also
holds a courtesy appointment in the depart-
ment of psychology. Weinstein joined the
teaching and learning support community at
Penn State in 2002 as an assessment special-
ist. Her assessment expertise ranges from
single courses to multi-course projects to uni-
versity-wide learning outcomes assessment.
Contact her at swd107@psu.edu.
Ido Millet
Suzanne Weinstein
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