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Automated Grading of Parametric Modelling Assignments: A Spatial Computational Thinking Course

  • White Lioness Technologies

Abstract and Figures

This paper describes the implementation and deployment of an automated grader used to facilitate the teaching of a spatial computational thinking course on the online education platform, edX. Over the period of a course on the platform, more than 3000 assignments were graded. As an evaluation of the grader, examples of assignments and statistical results are presented and discussed.
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A Spatial Computational Thinking Course
1,2,3National University of Singapore
Abstract. This paper describes the implementation and deployment
of an automated grader used to facilitate the teaching of a spatial
computational thinking course on the online education platform, edX.
Over the period of a course on the platform, more than 3000 assignments
were graded. As an evaluation of the grader, examples of assignments
and statistical results are presented and discussed.
Keywords. Automated Assessment; Parametric Modelling; MOOC.
1. Introduction
The rise of the web provides people new ways to interact and learn. In recent
years, Massive Open Online Courses (MOOCs) have allowed students to receive
a quality education through the web. Some institutes have since taken up a “flipped
classroom” approach in their pedagogy, where curricular content was taught
outside the formal system and in affiliated online systems. Industry professionals
alike make use of such platforms to keep themselves updated with the relevant
skills. In the spatial discipline, Spatial Computational Thinking is increasingly
being recognised as a fundamental skill. This paper describes the application of
an automated online grader used to facilitate the teaching of Spatial Computation
principles on a MOOC.
The use of a web-based grader is common in online learning platforms for
learning programming. Numerous studies have highlighted the advantages of
automated formative assessment (Lewis & Davies 2004, Douce et al. 2005,
Nicol & Macfarlane-Dick 2007, Baranaa & Marchisioa 2016). Automated
formative assessment provides a system where students can conveniently test their
understanding of taught concepts, which is synchronous with the pedagogical
objectives of a MOOC.
Approaches for assessing programming assignments may be summarised into
two categories: dynamic analysis and static analysis (Ala-Mutka 2005). A
submitted file is executed in a dynamically assessed assignment and not executed
in a statically assessed assignment. The former checks for functionality and
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Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong.
efficiency of the code while the latter checks for programming styles and design.
Numerous systems for automating assessment have been developed for learning
textual programming languages. One of the earliest systems was the AGSICP for
Cobol Programming (Aaronson 1973). More recently, two popular systems are
Web-Cat and Stepic.
For parametric modelling, no automated assessment approaches have been
developed. In general, the approach could be similar to existing approaches using
automated assessment for learning textual programming languages. However, for
parametric modelling, the output of the program may be a complex 3D model.
A more advanced approach is therefore needed for assessing the validity of such
The paper describes the development of an automated grader for parametric
modelling assignments. The contents of this paper are organised as follows.
Section 2 sets the premise the grader was designed for. Section 3 describes our
implementation of a grader for parametric modelling assignments. Section 4
provides an example of how the grader is used in a MOOC. Finally, Section 5
concludes the paper.
2. Context
The Automated Grader was used in a second-year module, “Spatial Computational
Thinking” at the National University of Singapore. The module consisted
of 150 students, most of whom did not have prior scripting or programming
knowledge. The module focused on the development of algorithms for generating
complex, parametric 3D models. It was taught on the edX MOOC platform using
videos and online exercises. The modelling assessments were all performed in
the web-based parametric modelling tool developed by the authors (reference
removed). The Automated Grader was developed on the Amazon Web Services
(AWS) infrastructure, allowing large numbers of assignments to be graded in
For each assignment, the instructors created a detailed problem description on
the edX platform, and a model representing the correct answer was uploaded to
the Amazon Simple Storage System (S3) object storage. Students then performed
the modelling assignment and uploaded their models through the edX platform.
In the edX platform, the student models were added to a grading queue, from
which the AWS server would fetch the models and grade them using an AWS
Lambda function, returning the grade and any feedback to the edX server. Within
a maximum of 20 to 30 seconds, students would see the grade and feedback
displayed on their browser.
The modelling assignments increased in complexity as the semester
progressed. At the start of the semester, the assignments started quite simple.
As the students learnt new concepts and techniques, the assignments also grew
in complexity.
The automated grading process meant that these assignments could not be
open-ended. Each student was expected to submit a model that, given certain
inputs (such as parameter values), produced ‘correct’ outputs. The way that the
models were implemented could still differ from one student to the next. However,
the outputs were required to be the same for all students. This, of course, meant that
individual creative freedom was quite limited. In order to overcome this limitation,
the final assignment of the semester was open-ended and was manually graded.
Nevertheless, it is noted that automated grading freed up a significant amount of
time that allowed instructors to spend more time helping students with their final
3. 3D Model Grader
The grader was designed to be an extension of a web-based parametric modelling
tool developed by the authors. A similar approach could be developed for
other existing parametric tools. However, for commercial software issues with
commercial licenses would have to be resolved if parallel execution of the grader
would be required.
Each parametric model has a set of input parameters. Setting the values for
these parameters and executing the model will result in a 3D geometric output,
which we refer to as the output model. Each assignment was accompanied by an
answer model and a number of input parameter sets. The grading process then
consisted of the following steps:
The parameters in the parametric answer model were compared to the
parametric submitted model. If the submitted model had missing parameters,
the grader would exit and assign a zero grade.
For each set of input parameters:
The parametric answer model and parametric submitted model were both
executed, thereby producing two output models: the submitted output model
and the answer output model. These two output models were compared to one
another, and a grade was calculated.
One complication that had to be addressed was the normalization of the output
models. The ordering of the geometric objects and entities in an output model
should not impact the correctness of the model. For example, the answer output
model may contain two polygons. If the submitted output model contains the same
two polygons, it should be marked as correct, irrespective of the polygon ordering.
The same applies to the ordering of other geometric entities, including vertices.
Thus, in order to be able to compare models, they first needed to be normalized,
so that the model representation could be guaranteed to be deterministic.
The normalization process consisted of two stages. First, the vertex order
within individual objects was normalized. Second, the order of the objects in the
model was normalized.
For the normalization of vertex ordering, a few different rules were applied.
For open polylines, they were modified in order to guarantee that the coordinate
values for the start vertex were always less than the end vertex. For polygons and
closed polylines, they were modified in order to guarantee that the first vertex was
always the vertex with the lowest coordinate values. For polygons with holes,
additional rules developed.
For the normalisation of object ordering, a fingerprint was generated for each
object in the model. The fingerprints were generated from the data constituting that
object, including the coordinates of the vertices. (For the fingerprinting process, all
numerical values were rounded to 8 significant digits. This accounted for rounding
errors that could result from different computing hardware and operating systems.)
For entities that were not exact clones, each fingerprint was guaranteed to differ.
The normalisation process then sorted all entities according to their fingerprints.
Figure 1. Schematic flow of information in an assessment with five parameters and three tests.
In each test, the object (points, polyline, and polygons) in the answer output model
were matched against the objects in the submitted output model. If a match was
found, then the score was incremented by 1. The matching process required an
exact match between objects, using the same fingerprinting process as was used
for model normalization. To encourage efficient solutions, extra objects found in
the submitted output model result in 1 mark being deducted (equation 1).
Figure 2. equation 1.
Figure 3. equation 2.
Figure 4. equation 3.
The score awarded to each test is the fractional result from the sum of all
the number of congruent points, polylines, polygons, and model attributes in the
submitted model against the total number of entities and attributes in the answer
model (equation 2). The final grade given to an assessment is determined by the
average of the test scores (equation 3). For example, consider an answer generated
model has 10 polygons. If only 8 of those polygons can be matched against entities
in the submission generated model, then the grade would be 8/10, or 0.8. An
example breakdown of the grading is detailed in Section 4.1.
Feedback messages highlight to the students how marks were lost and allow
them to rectify and receive a better grade in their subsequent tries. Such
information returned from an automated assessment is essential in the facilitation
of a self-paced course. The key feedback messages are listed as follows:
Entities could not be found
Extra Entities
Model Attribute not found
Incorrect model attribute value
Missing start node parameters
In the web parametric modeller the authors have created, entities may be assigned
with attributes. Attributes define the types of data that may be attached to entities
in the entire model. They exist in key-value pairs in which the user can specify
data to be stored under a name key. Materials are assigned to entities through the
use of attributes. The materials of a submitted model may also be checked.
A submitted model with missing entities translates to a parametric model with
wrong procedures. A submitted model with extra entities would be another with
redundant procedures. In addition, the grader was able to pick up translational and
directional errors in the geometries which would be highlighted to the student in
the returned feedback.
4. Spatial Computational Thinking
The learning outcome of the course was to gain theoretical knowledge and practical
skills in applying spatial computational thinking as a way of generating 3D models,
building upon elementary critical and logical thinking aptitude. The key concepts
tested and the weekly assignments are listed as follows:
W1 - Variables and Operators: Hello World (Console-Based).
W2 - Lists, Control Flow, and Functions: Printed Hash Checkerboard
W3 - Entities and Attributes: Debugging Generated Geometry (Static
W4 - (break)
W5 - Rendering and Geometric Constraints: Windows (Parametric Geometry)
W6 - Search Spaces, Vectors, and Planes: Parametric Stairs (Parametric
W7 - Loop Updates and Transformations: Parametric Stair Runs (Parametric
W8 - Vector Arithmetic and Graphing Polylines: Solar-Responsive Roof
(Parametric Geometry)
To familiarise the students with procedural thinking, the earlier assignments were
simple 1-part tasks. In the later weeks when more complex concepts were
introduced, each assignment was broken up into smaller steps to guide the students
into creating the final model while building up their capacity to deconstruct a
spatial problem.
The assignment for Week 1 was a simple 1-part task that required the students
to submit a file with a single parameter. The console should print “Hello
__parameter_value__” when executed. In Week 2, the students were given another
1-part task which required them to submit a file with a single parameter that
defined the size of a printed checkerboard. The students were first introduced
to geometry in Week 3. For their assignment, they were given a file that generated
an extruded model and they were tasked with changing the arguments and values
in the procedures to achieve another extruded result.
The assignment for Week 5 was a 3-part task that broke the creation of a
window into the creation of a polygon, the creation of a grid of panes, and finally
the extrusion of the frame. In Week 6, the students created a flight of stairs. They
were first tasked with creating a staggered polyline that was then translated to the
profile of the stairs. Next, they were required to create the volume of the stairs.
Finally, the railings are created. This 4-part task will be discussed in detail in
Section 4.1. The students were tasked with another stairs assignment in Week
7. In this 4-part assignment, the students first had to create a run of steps on a
plane. Next, the last step was modified into a landing. Then, they were required to
create runs of steps one after another. The model was required to be able to change
direction based on a parameter. Finally, the number of steps in each run was made
variable by a parameter. The final assignment in Week 8 looked at the creation of
a parametric solar roof that reacted to the direction of the incoming sun rays. The
assignment was broken down into three parts. The first required the students to
create a series of arches. Next, the students created a barrel vault. Finally, glass
panels with varied sizes were installed on the vault. Panels with direct exposure
to the incoming rays were smaller in size.
The parametric stair model served as an introductory modelling task to more
advanced concepts like transformations with vectors and planes. As an example
of a typical submission to the automated grader, the task featured in the course has
been chosen to be described in detail.
Figure 5. The 4 parts of the assignment (Tasks 1 to 3). Example of an erroneous submission in
Task 4.
Figure 6. The 4 parts of the assignment (Task 4). An example of an erroneous submission.
This assignment was divided into four parts (Figure 5 and 6). First, the students
were tasked to create a staggered polyline which would translate to the profile
of the stair. Step depth, height, and number were set as parameters. Next, the
cross-section polygon was extruded in the direction of its normal based on another
parameter. Finally, the polyline rails were added. The height of the rails was also
defined by another parameter.
Following the submission through edX, the model was run through three tests
and each generated model was positionally compared to the one generated by the
answer algorithm (Figure 1). The fractional score calculated from the average of
the three tests was returned to edX, where the final grade was converted into the
edX weighted grade.
Figure 6 also shows the most commonly detected error for the task. A polygon
with a reversed list of positions was determined to have its normal pointed in the
opposite direction and was treated as a different polygon. As seen in the figure,
the face opposite to its normal is rendered with a darker shade in the viewer. With
1 polygon missing in a model with 56 entities, a score of 55/56, or 0.98, was given
for the first test. Similarly, the submission generated model was scored 34/35, and
40/41 in its next two tests respectively. The task was awarded a final score of 0.98.
Amazon CloudWatch was set up to log all submission processes. Over the period
of the course, over 3000 submissions were registered. The authors used the
collected information to make incremental improvements to the grader feedback.
Negative scoring of extra entities was introduced in Week 6, along with detailed
suggestions for missing entities. A gradual decrease in the number of submissions
with extra entities over the subsequent weeks can be seen in the data (Figure 6).
This suggests an improved quality in the submissions.
Figure 7. Frequency of Errors for Parametric Geometry Assignments.
In general, the automated grader achieved the desired results. It gave students
immediate feedback on their parametric modelling assignments, allowing them
to learn at their own pace. However, feedback from students also highlighted
that they often did not understand why a model was being marked as incorrect.
For example, for the common error of the reversed polygon mentioned above, the
grader only reports that one of the polygons is incorrect. It does not explain why
it is incorrect.
In order to tackle this issue, a set of additional checking algorithms were
implemented to detect common errors. For example, if a student model was
missing a polygon, the algorithm would check if the reversed polygon was present.
If it was present, it could then feedback to the student that the polygon was
reversed. Many other checks were performed, for example, polygons that were
correct in shape and orientation, but that were placed in the wrong location (often
due to some small offset). However, as models became larger, this checking
process got increasingly complex and slow to execute. In the end, the decision was
taken to reverted back to simpler checks that were faster to execute. Nevertheless,
in order to achieve the pedagogical objectives, it is important that students are able
to understand why their models are being graded as incorrect. Our investigations
into this are ongoing.
5. Conclusions
Our ongoing research aims to investigate the extent to which the visual
programming language can support computational thinking concepts required
for constructing complex parametric models. This research paper focuses on
an extension of our web-based parametric modeller for automated assessment
of parametric modelling assignments, and a framework using modern cloud
technologies which may be replicated on other web-based parametric modelling
The grader is being further developed and improved. Three key areas are being
worked on. First, the grader currently only gives textual feedback to the students.
We are investigating approaches whereby the grader might be capable of giving
visual feedback. Second, the grader currently requires all students to be given
the same problem, which causes problems with plagiarism. We are investigating
approaches whereby questions can be randomized so that each student will receive
a variant of the question, which will require a slightly different answer. Third, the
grader is currently only grading the geometric output model that is generated. We
are investigating how the grader could support performative grading. For example,
the assignment may be to create a space with certain daylight and solar radiation
requirements. In such a case, students will be able to submit different models,
and as long as the model meets the performative requirements, the model will be
marked as correct.
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