Formative Feedback in Mathematics Teacher Education: An Activity
and Affordance Theory Perspective
Said Hadjerrouit and Celestine Ifeanyi Nnagbo
a
Institute of Mathematical Sciences, Faculty of Engineering and Sciences, University of Agder, Kristiansand, Norway
Keywords: Activity Theory (AT), Affordance Actualization, Affordance Perception, Affordance Theory,
Computer-based Assessment System, Constraint, Formative Feedback, Numbas.
Abstract: The increasingly high number of students’ enrolment has necessitated the recent attention on the use of
computer-based assessment systems for feedback delivery to students for mathematical learning, such as
Numbas. However, little is known about the affordances of Numbas in the research literature. The purpose of
this study is to investigate the affordances of Numbas, their perception and actualization by students and
teachers, and their effects on mathematical learning from an activity and affordance theory perspective. The
study follows a qualitative research design using semi-structured interviews of six students and two teachers.
The results reveal the perception and actualization of several affordances at the technological, mathematical,
and pedagogical level. Conclusions and future work are drawn from the results to promote Numbas formative
feedback for teaching and learning mathematics.
1 INTRODUCTION
In recent years, emergent technologies like computer-
based assessment systems are gaining more attention
in mathematics education because they provide a
resource-efficient way to providing the much-needed
timely feedback to the students. Computer-based
assessment systems provide new learning potentials
for a large cohort of students by means of formative
and summative assessment. However, research on
computer-based assessment systems is still in its
infancy, especially in the area that assesses the added
value, affordances and constraints of such systems
(Csapó et al., 2012; Hadjerrouit & Nnagbo, 2021).
This study proposes a framework that captures the
affordances and constraints of Numbas in a
technology-based course at the University of Agder.
This study relates to previous research work on
affordances of Numbas in mathematics education
(Hadjerrouit & Nnagbo, 2021; Nnagbo, 2020). In
specific terms, the study aims to address the following
research questions:
1. What affordances of Numbas are perceived by
students and teachers?
a
C. I. Nnagbo defended his master’s thesis in mathematics
education in 2020 at the Institute of Mathematical Sciences,
University of Agder, Kristiansand, Norway.
2. How are the perceived affordances of Numbas
actualised by students and teachers?
3. What are the constraints for the actualisation of
Numbas affordances by students and teachers?
2 NUMBAS
Numbas is a computer-based assessment system for
mathematics and mathematics-related courses with
emphasis on formative assessment and feedback
(Lawson-Perfect, 2015). The primary use of Numbas
is to enable students to enter a mathematical answer
in the form of an algebraic expression, and then see
how Numbas feedback can impact students’
mathematical learning. Numbas allows several
question-and-answer types such as mathematical
expression, number entry, matrix entry, match text
pattern, choose one or several from a list, match
choices with answers, gap-fill, information only, are
supported by Numbas. The system shows the notation
instantly beside the input field, so as students are
inputting their answers, simultaneously they see how
Hadjerrouit, S. and Nnagboa, C.
Formative Feedback in Mathematics Teacher Education: An Activity and Affordance Theory Perspective.
DOI: 10.5220/0010937800003182
In Proceedings of the 14th International Conference on Computer Supported Education (CSEDU 2022) - Volume 2, pages 417-424
ISBN: 978-989-758-562-3; ISSN: 2184-5026
Copyright
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
417
the tool understands their expressions. Numbas
provides several capabilities to users.
Ease of Integrating Rich Content Materials:
Numbas supports videos and interactive diagrams to
be embedded on the editor before they are distributed
along with the final questions. The videos can be
uploaded directly, while the interactive diagrams
could be included in Numbas questions either by
embedding a GeoGebra applet or use JSXGraph.
Marking: Numbas uses marking to mark
mathematical expressions. For example, in
factorizing a quadratic equation, expected answers
are often in this form (x+a)(x+b) and not x^2+ax+b,
but Numbas marking algorithm is capable to
understand the later form, mark correctly and give
feedback accordingly.
Feedback: Numbas makes its feedback
immediate. In order to make the feedback effective,
there are multiple ways Numbas gives feedback to
both students and instructors. These include the
following options: submit answer, show steps, reveal
answers, try another question like this one (Figure 1).
Figure 1: Feedback options.
Submit Answer: Students get feedback when
they submit an answer. The feedback indicates with a
green color ‘good’ sign if the answer is correct, with
red color ‘bad’ sign indicating that the answer is
wrong, or partially correct. The students will also be
shown the maximum attainable score for each
question, and their own score for the question after
they have submitted the answer. The teacher may
choose to disable these feedback options.
Show Steps: When show steps is chosen,
Numbas will give the general solution to that task.
This is a way of reminding the student to have a look
at the general solution and retry solving the task. This
does not give the exact solution to the particular task.
Try Another Question Like This One: With this
option, students have the opportunity to attempt
similar questions many times until they feel
confidence to move to the next question.
Reveal Answer: This option provides a step-by-
step solution that is personalized to the question, but
the students lose all the marks and cannot re-attempt
the exact question. This option may be disabled by
teachers.
Statistics: Numbas stores data of students
performance. Teachers can track how well the
students understand the topic through their
performances, and they can equally identify the tasks
students perform below expectations and
reemphasize on them in the next class if necessary.
3 THEORETICAL FRAMEWORK
Activity Theory (AT) is coupled with affordance
theory to form the theoretical framework of this
study. AT is found to be a source of useful concepts
for describing how Numbas interacts with other
elements of the learning context, including students,
teachers, and the physical environment (Day &
Lloyd, 2007).
AT is combined with affordance theory (Volkoff
& Strong, 2017) to explicate the concepts of
emergence, perception, actualisation, and effects of
Numbas affordances on teaching and learning
mathematics. More precisely: (a) The emergence or
existence of Numbas affordances; (b) The perception
of Numbas affordances; (c) The actualisation of
Numbas perceived affordances; and (d) The effects of
Numbas affordances on learning and teaching.
3.1 Activity Theory (AT)
AT has its root in the cultural-historical psychology
work of Vygotsky, Leont’ev, and Engeström. The
primary ideas of the theory rests on the social-cultural
perspective of learning in which learning is conceived
as an offshoot of a dynamic relationship between the
learner and the environment. With other words,
learning is an appropriation of knowledge through a
feedback relation between the learner and the
environment (Vygotsky, 1978).
A fundamental concept in AT is the word
‘activity’ itself (Engeström, 2014). Leont’ev (1978)
defines an activity as any purposeful interaction
between a subject (which could be an individual or
collective), and an object. Leont’ev (1978) further
describes activity as the most basic unit of life; that
subject and object have no noticeable properties if
there is no activity. Thus, when activity is not studied
and understood, it may be difficult to deduce how an
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418
artefact affords a subject. The underlying assumption
of the theory is that an artefact or tool mediates the
interaction between subject and object to give the
desired outcome.
3.2 Affordance Theory
The term affordance’ was proposed by James J.
Gibson to describe what the environment offers the
animal (Gibson, 1986, p. 127). He argues that
affordances (henceforth, in plural or singular form)
can be seen from the properties of the environment
that are relative to the animal in question. He further
stresses that affordances must be peculiar to the
animal they afford; not just any property of the
environment or whatever the environment can offer.
In the world of Human-Computer Interaction, the
term “affordance” (Norman, 1988) refers to a goal-
oriented action potential that emerges as result of
interaction between subjects (e.g., students and
teachers) and an object (e.g., Numbas). Affordance is
neither the property of an object in isolation nor that
of the subject. Instead, it emerges as an offshoot of a
dynamic relationship between the subjects (students
and teachers) and the object (Numbas). It is perceived
(i.e., students and teachers are aware of the existence
of the action potential of Numbas) in many ways and
actualized (i.e., students are able to turn the potential
of Numbas into action) to produce effect (i.e.,
feedback delivery) depending on many factors that
include Numbas platform, its user interface,
capability of the students and their level of
preparedness. Moreover, the actualization of Numbas
affordance is either facilitated by some enabling
conditions or mitigated by some constraints.
Given the emergence of Numbas affordances, it is
important to ask how the affordances are perceived.
As such, when students interact with Numbas to
facilitate feedback delivery on some mathematics
concepts they do so conveniently with the aid of the
technological features of the tool. During this process,
they become aware of the affordances that emerged
during the interaction in terms of feedback delivery.
The next issue is how they can actualize these
affordances. Affordance actualization is a process of
turning action potentials (affordances) into real
actions to bring an effect in using a particular tool
(Anderson & Robey, 2017; Bernhard et al., 2013). To
turn a possibility into an action, it is expected that the
user has the ability and capability to harness the
potential and there are enabling conditions to
facilitate the process. Affordance actualization may
vary from one individual to another because it is goal-
oriented and a process of specificity. Two or more
students may interact with Numbas and actualize (or
not) different affordances of the tool depending on
their respective individual differences and choices.
Moreover, it is expected that following the
actualization of Numbas affordances are some
effects, which may be “intended by the user and/or
those by the original creator of the artefact as well as
unintended effects” (Bernhard et al., 2013, p.6). Thus,
it is expected that when affordances are perceived and
actualized, then some effects are generated in terms
of feedback delivery to students.
Drawing on this view, Engeström (2014) asserts
that the subject of any activity system uses a
combination of both physical and psychological
tools. As such, the mediating artefact in the present
study is Numbas. It is important to remark that there
is a thin line between the mediating artefact (Numbas)
and the object (feedback delivery) in this study
because the former encloses the latter. Unlike,
physical classroom objects such as whiteboards and
pointers that are used to mediate learning content.
Therefore, it is argued that the outcome of a
dynamic interaction between the subject (e.g.,
student), the object (feedback delivery), and the
mediating artefact (Numbas) are the affordances of
Numbas. In other words, Numbas affordances are not
an exclusive property of the tool and not completely
determined by the subject. Instead, they emerge from
a dynamic interaction between the tool and the
subject. A key issue is that the interaction between the
subject and object is considered from a socio-cultural
perspective following the lines of thought of Gibson
(1986).
Figure 2 shows the theoretical framework that
captures the emergence, perception, and actualisation
of Numbas affordances, and their effect from an
activity theorical perspective. The perception of
Numbas affordances concerns its awareness by a
goal-oriented user during the interaction. Affordance
actualisation is a process of turning action potentials
(affordances) into real actions to bring an effect in
using a particular tool (Anderson & Robey, 2017;
Bernhard et al., 2013). In specific terms, affordance
actualisations are “the actions taken by actors as they
take advantage of one or more affordances through
their use of the technology to achieve immediate
concrete outcomes” (Strong et al., 2014, p. 70).
Moreover, it is expected that following the
actualisation of Numbas affordances are some effects.
It is important to highlight that actualisation of
Numbas affordances does not happen in isolation. In
fact, affordances are not without constraints; these are
facilitated by enabling conditions and hindered by
constraints. As captioned by Hadjerrouit (2020)
Formative Feedback in Mathematics Teacher Education: An Activity and Affordance Theory Perspective
419
affordances and constraints are inseparable because
they complement each other, and not opposite.
Figure 2: Perception, actualisation, and effects of Numbas
affordances from an Activity Theory perspective.
4 METHODS
A case study design approach (Yin, 2009) is chosen
to understand and analyze the affordances perceived
by both students and teachers while interacting with
Numbas, and how they actualize the perceived
affordances. Data collection was done from two set of
participants: Two teachers and six students from a
mathematics teacher education class of a Norwegian
university. The two teachers were considered and
selected because they are actively making use of
Numbas for formative assessment in their respective
classes. The second cohort is six out of about twelve
students from one class who willingly volunteered to
participate in the study. These participants are
master’s degree students taking a course entitled
“Digital tools in mathematics teaching”.
A thematic approach is used to analyze the data
by identifying themes or codes within the data set
(Bryman, 2016). The analysis takes both a deductive
and inductive approach by following the pre-defined
framework in search for meaningful interpretation of
the empirical data. Rom is given for the data to
express itself by creating new codes that emerge from
the data inductively. The development of codes
follows reading and rereading of the data carefully
and annotating same to identify topics, which are
refined and validated by checking whether these are
repeated or highlighted by different participants as an
important topic (Hennink et al., 2020).
5 RESULTS
Figure 3, which is an extension of figure 2, shows the
results achieved so far. The figure shows both
students’ and teachers’ activity systems in interaction,
and the affordances (and constraints) that emerged,
are perceived, and actualized, and their effects on
teaching and learning. Three types of affordances are
perceived: (a) Technological (e.g., ease-of-use and
navigation); (b) mathematical (e.g., varied
mathematical representations); and (c) pedagogical
(e.g., learner autonomy, motivation, formative
feedback, etc.). A subset of the perceived affordances
is actualized, and some of these have an effect on
teaching and learning. Space is limited to report on all
affordances. Therefore, the paper focuses on the three
types of affordances highlighted above.
Figure 3: Students’ and teachers’ activity systems in interaction, and the affordances that emerged, are perceived, actualized,
and their effects on teaching and learning.
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5.1 Technological Affordances
The findings reveal that both teachers and students
globally share the same views regarding
technological affordances. They perceived and
actualized affordances related to technological issues
such as ease-of-use and navigation, accessibility, and
facility to contain mathematical contents.
Regarding ease-of-use and navigation, one of the
students pointed out that “(…) anything you see there
is understandable; they are not complex. I think
everything is ok, I don’t have any problem with it. I
think the graphics are ok. It's just simple to use, there
are not much confusing buttons, every icon in the
interface is self-explanatory. It's just attractive”.
Another student added the navigations were fairly
easy, the buttons are visible with good inscriptions,
just click on it and see what is inside. Like I said there
are not too many icons, so anywhere you want to
move to, it’s easy to find, and navigate there.”.
One of the teachers said: it’s very much simple
to use, especially when compared with MyMathLab,
the main feedback from my students was that they
could see the mathematical expressions when they
write it in Numbas, they could see how the program
understands what they feed in, unlike in other
programs, so they committed fewer errors in Numbas
than in MyMathLab”.
The effect of ease-of-use and navigation is that
the students’ motivation and engagements increased;
they became curious and eager to solve more
formative assessment in Numbas.
The study finding clearly shows that the
perception of technological affordances such as
navigation and ease-of-use supports the perception of
and actualization of other affordances - which depend
to a large extent on the technological features of the
tool - such as learner autonomy, differentiation,
collaboration, and variation. If students or teachers
find the interface of Numbas difficult to use, they may
likely not use the tool to achieve their pedagogical
purpose. If the navigation buttons are hidden, the user
might not be able to move to the feedback pages,
thereby not getting the desired help.
However, reverse is the case when the teachers
themselves interacted with Numbas for the purpose of
creating tasks. Their responses seem to suggest that
creating tasks in Numbas is difficult, especially when
the task is a complex one. This can be seen from the
response given by one of the teachers "I will say that
could probably be better, once you start to getting the
grips on, I will say that using the basic things if you
want to create a simple task is quite easy, but again
as soon you start on more complicated questions, on
what to do more, (…), I will say it's not that intuitive
then you really need to go into the guidance because
there is a lot of boxes to check out if you want to do
that and you could".
Finally, the findings reveal some, mostly
technological constraints both for students and
teachers, such as insufficient navigation buttons, poor
internet connection when solving tasks, lack of
teachers’ knowledge and skills, e.g., programming
skills and lack of time for teachers.
5.2 Mathematical Affordances
Both teachers and students perceived the
mathematical affordance “varies mathematical
presentations”. With this affordance, teachers can
create formative assessment tasks using different
representations - diagrams, graphs, matrices, multiple
choices etc., also they can create the associated
feedbacks in various forms that may cover students’
misconceptions. Formative feedbacks that Numbas
give in these forms are found useful and motivating
by the teachers and students.
One of the students stated: I think the
presentation of math contents in Numbas is of high
quality. Many things including graphs, diagrams,
videos, formulars, numbers, signs are well presented
…I think it's very nice”.
Another student suggested: “I have also come
across in Numbas some questions that contain
GeoGebra pages and graphs, that show how
sophisticated Numbas is, and that makes
presentations of mathematical contents really
pleasing”. Therefore, the possibilities of increased
variation, including supporting embedment of third-
party software, are high in using Numbas. The tool
was also found to be useful in terms of enhancing pen
and paper skills of students.
Likewise, another student indicated that yes,
again as I said before, you often need your pen and
paper to do the calculations on Numbas. ...you have
to solve the tasks on paper especially the difficult
ones, by doing so, your pen and paper skills are
developing”.
The findings from the students’ perceptions are
similar to teachers’ views. One of the teachers thinks
that thepresentation of mathematical contents like
graphs, interactive diagrams, videos, GeoGebra
work well too... You can put in video and everything,
or link to YouTube channels or different pages and it
shows the video, you can play it within the program”.
Formative Feedback in Mathematics Teacher Education: An Activity and Affordance Theory Perspective
421
5.3 Pedagogical Affordances
Both teachers and students perceived and actualized
several pedagogical affordances, such as learner
autonomy, collaboration, differentiation, and in
particular formative feedback. Most perceived
affordances were actualized with effect on
motivation, engagement, learning and
misconceptions (see Figure 3).
Basically, formative assessment requires setting
learning and monitoring progress towards achieving
the goals. This type of feedback provision helps to
achieve learning goals. Similarly, Numbas feedback
gives the students the opportunity to access the level
they are in a learning process, what the learning goals
are, and how to achieve them. Findings reveal that
Numbas promotes formative assessment to both
students and teachers in a timely fashion in four
different forms:
a) It provides feedbacks to the teachers in form of
the statistical report of students’ activities
b) It provides support for students to test their
knowledge and exercises as much as they want
c) It helps students improve their learning, and
stay on track to meet their goals
d) It gives other types of feedbacks in different
forms, e.g., instant feedbacks, reveal answers,
show steps, or try another question like this one
Firstly, with statistical reports, time is saved for
teachers and students. From the teacher point of view,
the feedback in form of statistics containing students’
problem-solving strategies and ways of thinking
identifies their current performance level, areas of
difficulties and strengths are useful to the teachers for
conducting diagnostic teaching. Both teachers
expressed satisfaction with Numbas, particularly
because the tool is equipped with randomization
mechanisms, which means that it can generate
unlimited similar tasks with corresponding
feedbacks. This saves teachers a lot of time. They do
not need to spend days preparing tasks for formative
assessment. It also offers students the opportunity to
solve many tasks until they master the topic.
Secondly, teachers think that students have shown
motivation by asking for an opportunity to do more
exercises in Numbas, even when they have reached
the threshold. This can be seen from one teacher’s
response: “(...) I think the instant feedback is
motivating for the students”. The other teacher
suggested that “for most of them, at least for the way
I do it with this kind of programs they need (…) to
pass a certain amount of test to be able to attend
exam, ... and most of them will do it again even though
they have passed the test, because they want to
improve...I have got students that write to me asking
can you open the test again, I want to get 100%”.
Thirdly, in terms of quality feedback, one of the
students responded: “…with the two equations, there
was a movie, and it was sort of helping because it
assured me that I was doing it in the right way. The
third one, it was helping because it was the rule you
were supposed to use”. Another student explained
that “… it gives you a lot better feedback, than most
of that kind of programs …So that feedback is good,
and as I said, when you write, the next box shows you
how the program interprets, that program is really
good”. Students seem to appreciate the feedbacks,
including the video hints. The response from one
student does not only show that the video helped her,
but it also encouraged and motivated her to solve the
task. As a result, her confidence increased. Another
student tried to compare the feedback to that of other
similar tools and she found it better than other
programs she had used. She was particularly
overwhelmed that Numbas could instantly show how
it understands her answers.
Finally, in terms of instant or immediate
feedbacks, hints, and reveal answers, findings show
that the students equally found Numbas feedbacks
helpful and motivating. Teachers state that their
students “do get stuckand when they do, that “most
of them chose to show hints and the tips, (and) the
other feedback options from the program”. They also
think that the feedbacks motivate the students.
Findings also reveal that engagement in Numbas
enhances students’ motivation. Students identified
among others, the instant feedback to be very
motivating. However, they believe that bulk of the job
lies on the teachers’ ability to create tasks that would
take into consideration students’ misconceptions
about a particular task.
They further expressed concerns that the
feedbacks, no matter how good it may be, may never
be sufficient to get some students going, especially
the low achieving students. This can be seen from one
of the teachers responses I would say that the
feedback does help them but again for the strongest
students, it’s helpful for them but the weaker students,
I think they need the teacher actually to tell them what
they have done wrong, it’s not enough for them to see
the feedback or the examples.”
6 DISCUSSION
The purpose of this paper is to explore how Numbas
promotes formative assessment for mathematics
teaching and learning by analyzing the affordances
CSEDU 2022 - 14th International Conference on Computer Supported Education
422
and constraints that emerge from interactions
between teachers/students and Numbas.
The main essence of formative assessment
according to Weeden et al. (2002) is to identify
students’ current performance that will hopefully lead
to improvement in learning and teaching. Therefore,
formative feedback is vital to improving mathematics
education (Pereira et al., 2016).
Feedbacks from teachers to students regarding
their performances, challenges and difficulties are
aimed at encouraging and helping them to identify
their misunderstandings and misconceptions
regarding the topics, concepts, and ways to improve.
Many studies have linked feedback as one the most
powerful ways to increase students learning and
achievement (eg. Hattie & Clarke, 2018; Hattie &
Timperley, 2007). However, delivering it on time is
often challenging to the teachers.
This is the reason why formative feedback is done
while Numbas is on-going. It is to identify how far
teaching and learning goals have been achieved.
Teachers and their students mostly undertake this
kind of assessment to obtain vital information in form
of formative feedback that they will apply to modify
and improve the ongoing teaching and learning
activity (Black & Wiliam, 2010).
Figure 2 and 3 show that achieving the goal
(formative feedback delivery), which is needed to
improve teaching and learning of mathematics
subject depends on the perception and actualization
of the emerged affordances of Numbas by students or
teachers. If they fail to actualize the affordances, the
intended goal may not be achieved.
The object is the mathematical knowledge in the
form of formative feedback while the subject is the
student/teacher, and the mediating artefact is
Numbas. Then, the outcome of a dynamic interaction
(activity) between the subject (student/teacher), the
object (formative feedback), and the mediating
artefact (Numbas) is the affordance of Numbas. Thus,
the goal of students is to receive formative feedback
from Numbas. However, the desired goal (formative
feedback delivery) does not manifest straight away.
In fact, it manifests as an effect of the actualized
affordances of Numbas.
In an activity system, teachers and students are the
subjects, and the goal of the teachers in their
relationship with students is to give feedback to the
students or receive feedback about the students
performance through Numbas. While the goal of
students is to receive feedback from teachers through
Numbas. Therefore, formative feedback delivery is
the common goal, but the ultimate goal, which is the
effect of the formative feedback delivery is to
improve teaching and learning of mathematics.
According to the theoretical framework, the desired
goal (formative feedback delivery) does not manifest
itself directly, but as an effect of actualization of
Numbas affordances. Moreover, the emergence of
Numbas affordances is viewed as an offshoot of a
dynamic relationship between students/teachers and
Numbas, and the perception of the emerged
affordances concerns its awareness by
students/teachers. Whereas actualization is the action
taken by the students/teachers to take advantage of
the perceived affordances.
When students and teachers actualize some
required affordances, then the effect will lead to
achieving the goal (formative feedback delivery) and
by extension improves teaching and learning. For
example, when a student wants to solve mathematical
problems at home using Numbas, her/his goal is to
achieve formative feedback through the mediation of
Numbas. However, she/he must first of all actualize
the affordance of accessibility (amongst other
affordances needed). If the student faces constraint of
internet connection, then the effect will be that she/he
will not achieve her/his goal (formative feedback
delivery) because she/he could not actualize an
important affordance required. But if the student
actualizes the affordance by accessing the internet,
she/he may achieve the goal (formative feedback
delivery), however this is subject to actualizing other
feedbacks (like ease of use, navigate, etc.) she/he
might also need to successfully achieve the goal.
7 CONCLUSIONS
The main contribution of this paper is the
development of a theoretical framework drawing on
a combination of AT and affordance theory. AT has
proved to be useful for arguing that the emergence of
Numbas affordances is a result of a dynamic
relationship between a goal-oriented user and the
assessment tool. Likewise, affordance theory has
shown to be a useful in explaining the distinctiveness
of the perception and actualisation processes of
affordances. However, the framework as presented in
this study is not intended to map all affordances and
constraints, but it is open enough to capture potential
affordances. This is the reason why the deductive-
inductive approach to data analysis is so important for
the emergence of affordances. Moreover, Csapó et. al.
(2012) posited that large-scale implementation of
computer-based assessment systems still needs
further investigations in real education settings.
Formative Feedback in Mathematics Teacher Education: An Activity and Affordance Theory Perspective
423
Summarizing, the findings show that Numbas is
basically a useful tool for assessing mathematical
concepts and problem-solving. However, there are
issues related to the feedback, which can act as a
source of motivation for a few students while
demotivating other students. Numbas may be
included in the Norwegian curriculum with the sole
intention of identifying possible problems and
effecting necessary modifications along with
improving the learning of students and teachers. For
teachers, it is important to ascertain their role in using
their skills and expertise for adding new tasks of
formative assessment, and identifying students’
learning progress, while for students, it is important
to focus on using Numbas as a practice, learning, and
feedback tool. However, the role of Numbas should
be clearly defined along with the role of teachers.
From a practical point of view, the study has two
limitations. Firstly, the participants (N=8) are
master’s students and their teachers (N=2) from a
teacher education program of one university. A larger
number of participants from several universities
could have been more desirable to make better
generalization. Nevertheless, the chosen number of
participants with a large set of information seems to
be justifiable for addressing the research questions.
The second limitation is that the participative
students are not the ‘end users’ of Numbas. Though
they have sufficient knowledge of Numbas, and used
the tool for assessment, but in a limited form.
However, it is difficult to generalize their views to
encompass students using Numbas regularly in their
studies. Students from other study programs using
Numbas for day-by-day activities may have a
different perspective about perception of affordances
and actualization processes. Future research studies
involving such set of students would be relevant to
compare with findings of the present study to achieve
more reliability and validity of the results.
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