Analysis of Assessment Alignment
Dr Dengsheng Zhang1
Before we address the assessment alignment issue, it is instructive to identify assessment
purposes. Swearingen characterizes seven purposes of assessment [1]:
ƒ Assist student learning,
ƒ Identify students’ strengths and weaknesses,
ƒ Assess the effectiveness of a particular instructional strategy,
ƒ Assess and improve the effectiveness of curriculum programs,
ƒ Assess and improve teaching effectiveness,
ƒ Provide data that assist in decision making,
ƒ Communicate with and involve students.
An effective and quality assessment has to deal with authenticity, variety, validity and
reliability. Assessment that is aligned with the classroom objectives and reflects realworld applications is called authentic assessment. Another method of insuring quality
assessment is to use a variety of assessment techniques like true/false questions, multiple
choice questions, essays and projects. Validity refers to the notion that a measurement
should bear a strong and direct relationship to its intended use. Simply put, timbers
measured as longer should actually prove to be longer when compared to timbers
measured as shorter [2]. Reliability means that when an assessment is applied to students
of the same achievement level, it should produce similar results. Hence, the hallmark of
assessment reliability is the reproducibility of assessment results.
To design assessment tasks, we start by referring to the educational objectives. Above
everything else is the need for the assessment tasks to align with our objectives. The
assessment tasks must be designed to be opportunities for students to demonstrate their
attainment of our subject/unit’s intended learning outcomes. However, the assessment
should be aligned with learning objectives at different levels rather than in a single level.
In the following, I analyze the hierarchy of the learning objectives of a teaching topic and
how to align assessment tasks to assess these different levels of objectives. The
hierarchical levels of learning objectives I will use are based on Bloom’s cognitive
taxonomy.
Subject: Computer Models for Business Decisions
Teaching duration: Week 2~Week 4
Teaching topic: Linear Programming
• Linear programming model formulation
o Model Formulation
o Maximization Model
o Minimization Model
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This work is done under the Graduate Certificate in Higher Education Course
1
•
•
o Graphic Solutions of Linear Programming Models
o Irregular Types of Linear Programming
o Characteristics of Linear Programming Problems
Linear Programming: Computer Solution and Sensitivity Analysis
o Computer solution
o Excel Spreadsheet Solutions
o QM for Windows Solutions
o Sensitivity analysis
o Objective Function Coefficient Ranges
o Changes in Constraint Quantity Values
o Constraint Quantity Values Ranges
o Shadow Prices
Integer Linear Programming
o Integer Programming Models
o Total Integer Model
o 0-1 Integer Model
o Mixed Integer Model
o Integer Programming Graphical Solution
o Computer Solution of Integer Programming
o Solving Integer Problems with Excel and QM for Windows
The learning objectives for the linear programming topic in terms of Bloom’s taxonomy
are as following:
1. At the knowledge level, be able to
1.1 Understand the concepts and physical meaning of linear programming
1.2 Learn the basic algebraic knowledge in need of solving linear programming
problems
1.3 Name two basic types of linear programming problems: maximization of profit
and minimization of cost
1.4 Differentiate integer programming problem from linear programming problem
1.5 Distinguish three types of integer programming problems: total integer
programming, 0-1 integer programming and mixed integer programming
1.6 Identify the objective, decision variables and tabulate the data/parameters in a
linear programming problem
1.7 Formulate the linear programming model consisting of objective function and
constraints
1.8 Identify real world problems which can be solved as linear programming model
2. At the comprehension and application level, be able to
2.1 Solve the formulated linear programming model manually and graphically
2.2 Solve the linear programming model using Excel software in computer
2.3 Interpret the solution and make simple business decisions
2.4 Summarize the procedures of linear programming solution
2.5 Summarize the procedures of computer solutions using Excel
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2.6 Apply linear programming model to given business problems
2.7 Understand the significance of linear programming model in solving business
problems
At the analysis, synthesis and evaluation stage, be able to
3.1 Identify the components of linear programming model
3.2 Recognize the characteristics of linear programming problems
3.3 Do different types of sensitivity analysis of linear programming models
3.4 Read sensitivity analysis report
3.5 Optimize resources and make alternative decisions based on sensitivity analysis
report
3.6 Relate linear programming model with different real world business operations
3.7 Propose and do case study of variety of business problems
3.8 Understand the limitations of linear programming model
Assessment task1
Warragul Angel Fabric produces two types of cotton cloth—denim and corduroy.
Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw
cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of
corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours.
Although the demand for denim is practically unlimited, the maximum demand for
corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000
hours of processing time available each month. The manufacturer makes a profit of $2.25
per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how
many yards of each type of cloth to produce to maximize profit.
Assignment questions:
a. Formulate a linear programming model for this problem.
b. Transform this model into standard form.
c. Solve the problem graphically. How much extra cotton and processing time are left
over at the optimal solution? Is the demand for corduroy met?
d. What is the effect on the optimal solution if the profit per yard of denim is increased
from $2.25 to $3.00?
e. What will be the effect on the optimal solution if Warragul Angel could obtain only
6,000 pounds of cotton per month?
f. Solve the problem using computer. If Warragul Angel can obtain additional cotton or
processing time, but not both, which should it select? How much? Explain your
answer.
g. Identify the sensitivity ranges for the objective function coefficients and for the
constraint quantity values. Then explain the sensitivity ranges for the demand for
corduroy.
Assessment task 2
3
A steel mill in Melbourne supplies steel to manufacturers in eight other Victoria cities via
truck, as shown in the following network. The travel time between cities in hours is
shown along each branch. Determine the shortest route from Melbourne to each of the
other eight cities in the network. Formulate the shortest route problem as linear
programming model and solve it using computer.
Wandin
4
Noojee
2
6
3
Powelltow
Melbourne
4.5
7
5
3
1
4
3
9
2.5
3.5
4
4
3
5
3
Neerim
8
Berwick
Drouin
3
4
2
6
3
Lang Lang
Cranbourne
Learning objectives 1.6, 1.7, 2.1, 2.2, 2.3, 2.6, 3.3, 3.4, 3.5 are all directly assessed
through the two tasks, and the difficulty is appropriate. 1.1~1.5, 2.4~2.5, 3.1~3.2 are
indirectly assessed, because in order to solve the two problems, students need to
understand these objectives. Objectives 1.8, 2.7, and 3.8 are not assessed because they
have been discussed in class. The ‘bare pass’ students only need to be able to formulate
the problems into linear programming model and integer programming model, solve them
graphically, do some simple manual sensitivity analysis and make sensible decisions.
Students attempt to achieve higher grades need to present computer solutions and do
more complex sensitivity analysis.
References:
[1] R. Swearingen, A Primer Diagnostic, Formative, & Summative Assessment.htm,
Heritage College, 2004.
[2] Assessing Learning and Evaluating Teaching, Unit Book of GCHE, Higher Education
Development Unit, Monash University, 2004.
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