Can Formative Assessment Practices Appear Spontaneously during
Long Distance Learning?
Giorgio Bolondi
1
, Agnese Del Zozzo
2
, Federica Ferretti
3
, Marzia Garzetti
1
and George Santi
1
1
Faculty of Education, Libera Università di Bolzano, Viale Ratisbona, 16, Bolzano, Italy
2
Department of Mathematics, Università degli studi di Trento, Via Sommarive, 14, Trento, Italy
3
Department of Mathematics, Università di Ferrara, Via Macchiavelli, 30, Ferrara, Italy
GeorgeRichardPaul.Santi@unibz.it
Keywords: Formative Assessment, Long-Distance Learning, Mathematics Education, Eye of the Theoretician.
Abstract: Within the context of Long-Distance Learning (LDL) during the first Italian lockdown due to Covid-19
pandemic, our eye as researchers in mathematics education looks at the modification of student-teacher
interactions regarding the exchange of feedback. We claim that digital-technology based environment fostered
the spontaneous emergence of teaching and learning practices that can be associated with formative
assessment. Through the analysis of answers to a questionnaire and the observation of a class during LDL we
outline the relation between the theoretical construct of formative assessment and observed practices. This
analysis allows to highlight what factors of digital-technology based environment shape class interaction and
what directions can be taken to exploit the potential of digital technologies in teaching and learning context,
in particular within mathematics education field.
1 INTRODUCTION
Starting from February 2020 Italy has been
overwhelmed by the Covid-19 pandemic. This
resulted in a strong national lockdown that lasted until
June 2020. To maintain the educational relationship
teachers and students have adapted their practices to
long-distance learning (LDL): this adaptation process
was not neutral nor painless and has brought to a deep
change in teachers-students interaction modalities.
LDL allowed the emergence of many relevant
spontaneous phenomena. Within this context, our eye
as researchers in mathematics education look at the
modification of student-teacher interactions
regarding the exchange of feedback: on the one hand,
feedback from the teacher on student's work, on the
other hand, feedback for the teacher on what the
student has understood, or on the acquired skills. We
focus on the modification of these exchanges and
their reason, which we identify as the use of certain
digital technologies to mediate student/teacher
communication. We can conceive this change as an
emerging phenomenon characterized by an enormous
density of didactical information. In this position
paper, we claim that such emerging phenomenon,
often perceived by teachers as overwhelming, can be
shaped using the theoretical construct of Formative
Assessment (FA). We also believe that the FA
construct can not only be a lens but also a tool for
managing such a phenomenon. In order to support our
claim, we propose to think about it as an example of
an eye of a theoretician in Radford’s (2010, p.4) sense:
Mathematicians’ eyes have been culturally
educated to organize the perception of things in
particular rational ways [...] The domestication of the
eye is a lengthy process in the course of which we
come to see and recognize things according to
“efficient” cultural means. It is the process that
converts the eye (and other human senses) into a
sophisticated intellectual organ – a “theoretician”.
According to his perspective, in this work, the
observer, or the eye, is the researcher in mathematics
education who knows the FA construct, the observed
phenomenon (thus, the perceived thing) is the
spontaneous didactical practice during pandemic
induced LDL, and the theoretical lens that
domesticates the eye is FA. Not all the involved
teachers were aware of the construct of FA, anyway,
as we are going to show, some widespread
spontaneous practices in managing the huge amount
of “didactical data” during LDL can be linked to some
theoretical features of FA.
Bolondi, G., Zozzo, A., Ferretti, F., Garzetti, M. and Santi, G.
Can Formative Assessment Practices Appear Spontaneously during Long Distance Learning?.
DOI: 10.5220/0010475506250632
In Proceedings of the 13th International Conference on Computer Supported Education (CSEDU 2021) - Volume 1, pages 625-632
ISBN: 978-989-758-502-9
Copyright
c
2021 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
625
The paper is organised as follows: in Section 2 we
introduce the construct of FA and we specify how we
use it in our analysis, then in Section 3 we specify our
claim in the light of the theoretical framework. In
Section 4 we present some data, in Section 5 we
clarify our approach to these data then in Section 6
we analyse them in order to support our claim. In the
last Section 7 we outline how and why this work can
be valuable both for teachers and researchers to
analyse and exploit the experience of LDL.
2 THEORETICAL FRAMEWORK
Our reflections embrace the idea of promoting the use
of FA as a tool for improving the mathematics
teaching-learning process. To frame our observation,
we refer to the theoretical framework of LLP-
Comenius Project FAMT&L Formative
Assessment for Mathematics Teaching and Learning
(Bolondiet al., 2016). One of the main objectives of
the FAMT&L project was to improve the skills of
mathematics teachers in the use of FA as a tool for
methodological quality in mathematics teaching
(Ferretti, Michael-Chrysanthou, & Vannini, 2018;
Gagatsis et al., 2019) and one of the outcomes of the
project was the following definition of FA in
mathematics (Ferretti et al., 2018, p.33):
The FA is connected with a concept of learning
according to which all students are able to
acquire, at an adequate level, the basic skills of a
discipline. The learning passes through the use of
teaching methodologies which can respond
effectively to different learning time for each
student, their different learning styles, their zones
of proximal development.
The FA is an assessment FOR teaching and
learning.
In line with the FAMT&L framework (Ferretti et al.,
2018), we embrace the idea that the FA: i) is part of
the teaching-learning process and regulates it; ii)
identifies, in an analytical way, the strengths and
weaknesses of student’s learning, in order to allow
teachers to reflect on and may modify their own
practices; iii) allows in a form of formative feedback
to establish a dialogue between teacher and student
and to design educational interventions aimed to the
recovery; iv) promote and foster the learning of all
students through differentiated teaching that ensures
each student different rhythms and different teaching
and learning strategies; v) involves the student in the
1
https://docs.google.com/document/d/1gjlm-hSpV7t10iN
RX1FsyApzZaB6376qSy_ywt3jktU/edit?usp=sharing
analysis of own errors/weaknesses and own ability to
promote self- and peer-assessment and active
participation in the teaching-learning process. In
particular, our approach of FA is in line with the
definition given by Leahy, Lyon, Thompson, &
Wiliam (2005) and Black & Wiliam (2009), where
FA criteria and strategies are also highlighted:
S1. Clarifying and sharing learning intentions and
criteria for success.
S2. Engineering effective classroom discussions and
other learning tasks that elicit evidence of student
understanding.
S3. Providing feedback that moves learners forward.
S4. Activating students as instructional resources for
one another.
S5. Activating students as the owners of their own
learning.
In the following, we simply refer to these as five
FA strategies or as S1, S2, S3, S4, S5. Starting from
these strategies, within the FAMT&L project, the
structured FAMT&L Grid, a specific video analysis
tool was designed, built and used.
The FAMT&L Grid was developed starting from
the international debate on FA, and it is composed of
several indicators. For our work, we considered a
subset of 72 indicators, chosen in agreement with two
of the authors of the grid as the more suitable, to
detect FA within the LDL context. Moreover, we
decided to categorize these indicators according to S1,
S2, S3, S4, S5. The result of this work is a table,
which we make available in an external online
document
1
. The table has taken the role of a
theoretical tool of analysis, and it enabled us to
highlight what aspects of the lesson could be linked
to specific features of the construct of FA, and to
better understand how some phenomenon, typical of
the digital environment, could be related to strategies
of FA.
3 CLAIM
In line with the eye of a theoretician perspective
(Radford, 2010), the theoretical framework allows us
to redefine the initial claim as it follows: a researcher
in mathematics education, observing some
spontaneous practices in LDL, if carried out with
appropriate platforms, can recognise features that
create a fertile ground for FA. Especially, we argue
that teaching and learning practices conducted in
some digital-technology based environment have
CSEDU 2021 - 13th International Conference on Computer Supported Education
626
characteristics that can be associated with at least
three out of five FA strategies, in particular:
1. Immediacy and automaticity of storage and
collection of documentation, which allows
monitoring over time of the students' path, related
to S1 and S2.
2. Individualisation of didactics: the increased
documentation about the student’s work allows
the teacher to give more individualised feedback
and to enhance more individualised strategies,
related to S3.
4 DATA
The data we consider for this work are part of a
research on LDL teaching and learning practices in
Italian schools of different order and grade during the
lockdown. In this context, our focus is on some
questions of a questionnaire administered to teachers
and on ethnographic observation of teaching-learning
practices in a grade 12 class, both conducted during
the first Italian lockdown. We highlight that this is not
a data collection specifically designed to support our
hypothesis but, rather, it is the sharing of some of the
evidence in favour of the thesis that we wish to
introduce here.
4.1 Questionnaire
The questionnaire has been administered during the
month of April 2020 in order to gain information on
a fluid process started a month earlier and that was
settling itself day by day. The questionnaire contains
32 questions, both open-ended and multiple-choice
ones, organized in five sections according to the aim.
For a detailed description of the entire questionnaire,
we refer the reader to Del Zozzo, Garzetti, & Santi
(2020).
We selected a convenience sample: the need to
reach teachers during a fixed period has guided the
selection, we spread the questionnaire through
mailing lists of teachers that collaborate with us in
other projects, asking, when possible, to share it with
others. Overall, from secondary school teachers, we
obtained 99 answers. In this study we consider only
the following three questions in order to give a
broader picture in relation to the phenomenon we are
discussing.
2
https://edu.google.com/products/gsuite-for-education/ G
SE is now called Google Workspace for Education.
3
https://support.google.com/meet/?hl=en#topic=7306097
One item of a question where teachers are asked
to express their agreement/disagreement with
different items: I can give feedback to each
student for every task she sends me, and it seems
to me that some students are improving.
Two subsequent questions where teachers are
asked to rank the differences in feedback
restitution between LDL and physical classroom
and to explain the reason of the difference.
These data allowed us both to notice that practices
that could be related to FA were emerging among
teachers, and to shape the classroom observation. We
found consistency between teachers’ word in the
questionnaire and observed teachers’ practices.
4.2 Classroom Observation
From 11
th
of May until the end of classes (between 5
th
and 10
th
of June), we had the opportunity to conduct
ethnographic observation in several classes of
different school grades during LDL.
In this paper, we refer to one of the observed
classes: a grade 12 class of a Technical Institute
enrolled in the G Suite for Education
2
(GSE). It
appears important to highlight how the analysed
didactical practices did not consist in a controlled and
planned intervention organised by the researchers,
and thus the involved teachers were not aware of FA
construct. Here, we do not go into the methodological
details of this observation, for which we refer to
Ferretti, Del Zozzo & Santi (2020). Nevertheless, it is
important to remark that, as far as classroom practice
in the context of LDL is concerned, each virtual
classroom is dichotomous, and it has two components:
one synchronous and one asynchronous. When our
observation began, we were provided with a link to
access the synchronous component - implemented
with Google Meet
3
(GM) - and access to the
asynchronous component - implemented with Google
Classroom
4
(GC). In particular, regarding GC, two of
us were added to the class in the platform with the
role of additional teachers. This choice allowed us to
access the entire archive of materials and all the
message exchanges (both public, with the whole class,
and private between the teacher and each student) that
had taken place since the beginning of the creation of
this class in GC, the 27
th
of February. Thus, our
observation was conducted as follows. Regarding
classroom dynamics in the synchronous component,
it was indirect (since we only know what is reported
4
https://support.google.com/edu/classroom/?hl=en#topic=
10298088
Can Formative Assessment Practices Appear Spontaneously during Long Distance Learning?
627
or described in GC) for what happened between 27
th
of February and 9
th
of May, direct from 11
th
of May
until the end of the school year, on 5
th
of June.
Regarding the classroom dynamics in the
asynchronous component, we had the opportunity to
analyse the entire teaching flow from the first day of
class creation in GC (27
th
of February) to the last day
of interaction between teachers and students in the
platform (12
th
of July).
For clarity, in GC there are different areas of work
and interaction with different functionalities and
permissions for action and access among teacher and
students; the main areas we considered are the Stream
page, the Classwork page, and the Assignment space.
In the following, using "episode" we mean what
happens in the virtual classroom, in both its
synchronous and asynchronous components, in a
fixed time starting with a teacher's assignment on a
certain set of exercises or tasks, and ending with the
assignment of a new task on a different set of
exercises. With respect to the aim of the present work,
we focus on the following three episodes, that we
consider as paradigmatic of the teaching and learning
practices we observed: episode 1 between 17
th
and
20
th
of March, episode 2 between 24
th
and 30
th
of
March, and episode 3 on the 18
th
of May.
Episode 1: First Assignments on GC. During
episode 1, only asynchronous exchanges on the GC
platform are considered. On 17
th
of March, a task is
assigned to be completed by March the 20
th
, and in
this time frame, we consider the interactions between
T and students that occurred in the various spaces of
the platform. In the following, the unfolding of
episode 1 is presented, with the aim of showing how
the different spaces interact with each other during
the different activities. In the descriptions of the
remaining episodes, we do not repeat this pattern and
only highlight the changes in the structuring of the
activities involved. T indicates the mathematics
teacher, and the class was composed of 29 students.
17
th
of March. In GM: 2-hour synchronous lesson.
In GC: on the instruction page a homework
assignment (exercises from the textbook) is published
with deadline 20
th
of March; in the Stream, it appears
the notification of the assignment with the link to
access it.
18
th
and 19
th
of March. In GC: one student
communicates in her workspace that she has not the
textbook. Consequently, in the instruction page T
modifies the assignment by adding the scanning of
the pages of the book in which the exercises are
presented. Also, public exchanges between students
and T appear in this space. Contextually, in other
students’ workspaces, we see private exchanges
between students and T about the assignment and we
also see that 24 out of 29 turn in their homework by
sending photos of their notebooks.
20
th
of March. In the Stream of GC, a reminder of
the meeting on GM is posted with the related topic:
homework correction. Then, in GM: 1-hour
synchronous lesson is conducted in which the
exercises are corrected. After the lesson, in GC, in
students’ workspaces, there are requests for feedback
on the correction carried out synchronously during
the meeting. In particular, one student sent her own,
report of correctly completed exercises and of errors,
and uploaded photos of her corrected work with
corrections marked in red. We see that this practice
becomes a routine for the whole classroom from
episode 2.
Episode 2: The Institutionalisation of Self-
correction. Episode 2 opened with an assignment on
GC, like episode 1. The difference with episode 1 is
the institutionalisation of a process of correction of
the assignment which will be maintained until mid-
May: the teacher asked for the assignment to be
handed in on 27
th
of March and on that date, she
published videos with the correction of the exercises.
She then assigned as a task on GC the correction of
the exercises already done, asking the students to do
it on the text of the exercises already done in a
different colour than the one used previously.
Throughout the process, there are synchronous
lessons and many asynchronous exchanges between
T and individual students.
Episode 3: Peer Assessment on GM. Episode 3
occurred in GM: for the entire duration of the episode,
the teacher shared the screen. It is a planned assessment
session involving four students. The session consisted
of three phases. In the first phase, the teacher asked
them to carry out a function study in a document shared
with and editable by the whole class: each of the 4
involved students carried out a part of the exercise and
corrected the work of the previous students. In the
second phase, the teacher asked the whole class to draw
the graph of a function given certain characteristics,
and then she shared and analysed the answers of the
four involved students. In the third phase, it took place
the correction of one of the exercises assigned to the
whole class and conceived as preparation for the
assessment period. The correction discussion involved
all four students and was triggered by the solved
exercise of one of them.
So far, we described the data, without making
explicit our intentionality as researchers in
mathematics education. Now we try to systematize
our process in support of our claim referring to
Radford’s work.
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628
5 OUR APPROACH
Using the metaphor of the eye of the theoretician
(Radford, 2010), quoted in Section 1, we recall the
structure of our work as it has been conducted and
will be presented in the first analysis. We emphasize
that a crucial point is the objectification process
(Radford, 2008) in which the students encounter the
object of knowledge. In our case the object is FA, the
theoretical eye is our eyes as researchers, and the
students are the teachers involved in the project.
Table 1: Parallelism with Radford’s quote (p.4), continuing
from section 1.
Radford’s quote In our context
[...] The domestication of the
eye is a lengthy process in the
course of which we come to
see and recognize things
according to “efficient”
cultural means. [...]
In the observed practices,
the researchers recognized
features that are consistent
with the FA construct.
I am not saying that the
students did not see two rows.
They surely did. But they did
not deem it important to
recognize the figures as being
divide
d
into two rows.
The teachers who do not
intentionally perform FA,
but the researcher links
teachers’ practices to a
construct she is aware of,
the construc
t
of FA.
the capacity to intuit and
attend to them in certain
manners rather than others,
belongs to those sensibilities
that students develop as they
engage in processes of
objectification.”
Teachers can develop their
sensibility as they engage in
a process of objectification
of FA.
Section 4 outlines the data collected, now we need
to start the process of justification described in the last
two rows of Table 1: in this respect we introduce the
analysis of the data and the first results obtained both
from the questionnaire and from the observation.
6 ANALYSIS
6.1 Analysis of the Questionnaire
Working Methodology. Our starting point has been
the answers to the questions in which teachers
highlighted how their way of giving feedback to
students was changed. Looking at the answers we
could find a relation between the tools used for LDL
and the changes, but we could also find some
examples of the changes. More precisely, we selected
the ones where we found coherence between the
content of the answer and at least one of the five
strategies of FA.
Analysis Outcome. Most teachers declared changes
in the way they were giving feedback (79%) to
students, and almost 60% of the involved teachers
agreed with the claim I can give feedback to each
student for every task she sends me, and it seems to
me that some students are improving.
This phenomenon found a first explanation in the
open answers to question Q24: How did it change [in
the way you give feedback]? In the answers, 41 out of
99 of the teachers referred to individualization of
feedbacks and to an increased possibility to check on
students’ work giving personalized corrections. The
results show a strong presence of the strategies S2 and
S3. Indeed, globally, watching at the 41 selected
answers we see that at least one between S2 or S3 is
present. As some of the teachers affirm, this can be a
direct consequence of the technological environment
involved in LDL, which structurally leads to the
dematerialization of didactical materials, including
students' work. Indeed, there are at least two
important common features of such technological
environment: one is the automatic storage of the huge
amount of data exchanged by participants and the
other is the ease of access to these data. We see in this
sense a parallelism with Goody’s observation (1977,
p. 37) regarding the invention of writing and printing:
It changed the nature of communication beyond
face-to-face contact as well as the system for the
storage of information. […] No longer did the
problem of memory storage dominate man's
intellectual life; the human mind was freed to
study static "text" (rather than be limited by
participation in the dynamic "utterance").
The questionnaire provides an overview of an
emerging phenomenon, that we, as researchers in
mathematics education, associate with FA: this does
not mean that it is FA, but that it shares some
characteristics of FA, related to S2 and S3.
6.2 Analysis of Classroom Observation
Working Methodology. Starting from our
theoretical framework we tried to define an
observation tool grounded in the definition of FA
given by the literature that could detect the specific
practices observed during LDL. In order to do so, we
first needed to redefine some of the usual classroom
practices in the new environment. The definitions we
present here clarify the effect of some of the structural
features of the classroom in a virtual environment
during the lockdown, that is, the structure given by
the mediation of digital technologies that allows
Can Formative Assessment Practices Appear Spontaneously during Long Distance Learning?
629
maintaining the educational relationship between
students and teachers in that context.
The result of our work is in the following: we
indicate the aim of an action in the classroom, then
we show the instantiation of that action in LDL
classroom with GSE tools in comparison to the class-
room in the school building.
Action: Positioning in the classroom.
School Building: Desk/teacher desk, objects used,
body/physical presence, etc.
Virtual Classroom: It is multiple: on one side the
physical workstation with objects used (pen,
notebook, hardware...), on the other the software used,
and the different accounts, etc.
Action: Communicative interaction in the
classroom.
School Building: written and oral communication,
deictic language, gestures, etc. Oral interactions are
mostly public, and the exchanges can have different
objectives (explanation, evaluation, feedback,
affective-relational), etc.
Virtual Classroom: written and oral
communication, via mail, private messages, public
messages, videoconferencing; content exchange in
class subgroups or pairs. In the case of the
asynchronous component in GC, any activity
assignment that the teacher makes to the whole class
(or to a group of students) also implies that this
activity is sent to each student in the class (or
belonging to the group). The need to mediate
communicative intentions and deictic language by
using "additional" devices (e.g., indicating becomes
moving the mouse in a screen that is situation visible
to the other), etc.
Action: observing student’s work.
School Building: rotating between desks; calling
to the teacher’s desk, etc.
Virtual Classroom: flexible mode depending on
the software used: grid view on GM, scrolling
through delivered tasks on GC, use of collaborative
documents and/or applications that allow you to see
the work being done, asking for screen sharing, etc.
Action: to collect/send materials.
School Building: delivery on paper, writing on the
blackboard (or teacher's PC screen projection), use of
textbook and other resources, use of electronic
register, etc.
Virtual Classroom: sending photos of paper
materials, using shared collaborative documents,
sharing web resources via links (i.e., text string
5
https://docs.google.com/document/d/1l2Yu5Lth6QAmB
MHdJxxmU1XyOfGJ1BeXlQp0nSmU6MA/edit?usp=s
haring
sharing, indeed, each web resource associated with a
link), etc.
As a second step, we analysed the three episodes
using the chosen FAMT&L indicators categorised
according to the five FA strategies, as we describe in
the theoretical framework (Section 2). It is worth
mentioning that the FAMT&L table was created for
the analysis of video recordings of lessons in the
physical classroom. Nevertheless, we assume that it
is legitimate to use it to analyse the unfolding of a
possible lesson on LDL in a non-experimental
environment for which we have documentation. Each
of the three selected episodes in the classroom was
analysed individually by two researchers: the aim was
to find out which practices were implemented
according to the ones in the table. After the individual
selection the inter-rater reliability was calculated
through Cohen’s K (Landis & Koch, 1977) obtaining
good concordance for all the three episodes
(respectively 0,69, 0,63 and 0,69 for episode 1,2 and
3). The union of the indicators selected by each
researcher has been chosen as the final option after a
discussion about the indicators on which the
researchers initially disagreed. We provide the reader
with the three coding tables of episode 1,2 and 3 in an
external online document
5
; the analysis which follows
refers to such tables. In the external document also
examples taken from each episode are given.
Analysis Outcome. We observe that out of 72
considered indicators, 38 are detected in episode 1,
taking place mid-March, 49 are detected in episode 2,
taking place at the end of March, and 53 in episode 3,
which takes place the 18th of May. Moreover, we also
see a distribution of the detected indicators along the
five FA strategies. This makes our assumption well-
founded: we can affirm that FA can be used as a lens
to look at some of the emerging phenomena in LDL,
when implemented with the described tools. In
particular, looking at the 30 indicators present in all
the three episodes, we find that 9 of them can be
considered a consequence of the use of a specific
LDL environment, in this case some tools of the GSE.
We comment on them briefly.
1.T fixes with the students the date for the
assessment.
13.T distributes the text of the test/task.
When considering the platform GC, together with
any assignment, not only the assignment is sent to the
students, but also notifications and reminder related
to the task. Moreover, once an action is done in the
CSEDU 2021 - 13th International Conference on Computer Supported Education
630
platform, every person that is part of that GC class
and has the right to see that action can immediately
access to and interact with it.
26. T asks questions to the whole class.
27. T asks questions to a single student.
These two indicators can be stackable on some
occasion on GC: for example, when an assignment is
sent to the whole class, each student receives it
individually and has at his disposal a private space of
interaction with the teacher.
36. T uses a structured tool of observation.
37. T takes some record of the behaviour of
one/all student/s.
38. T takes some record about how much the
students have achieved to handle the content of the
test/task.
39. T takes records from her/his desk.
40. T takes records passing among the students.
These five are related to the structure of the
technological environment which leads to the
dematerialization of didactical materials, including
students 'work, and their automatic archiving for its
own design, as affirmed also by some of the teachers
involved in the questionnaire.
We affirm that these 9 indicators, which we have
seen as being structural to some tools used for LDL,
are sufficient to create a fruitful ground for FA
practices. Actual practices of FA then obviously
depend on the teacher's intentions.
Considering the observed teacher T, she managed
all the information granted by the environment she
was in, in specific ways during LDL, and especially
along the three analysed episodes. Observing her
actions with our theoretical tool, we noticed that
among the other indicators that were presented in all
the three episodes, 11 could be related to the 9
previously listed: they effectively represented her
specific way to manage the information she was
getting from students through the media used. Thus,
the spontaneous emerging of FA practices can be
related to this managing of the structural
characteristics of the considered LDL environment:
we can say that at least the following 11 indicators
make the teacher’s practices in LDL readable as
effective FA practices:
4. T asks some questions to the students to verify
if the students understood the aims of the assessment.
8. T asks some questions to the students to verify
that the students understood the test/task instructions.
20. T provides advices or suggestion during the
test/task.
22. T gives enough time so that every student can
work through the test/task (without anxiety).
30. T asks a new question based on a wrong
answer to the previous one.
31. T asks a new question based on the previous
one.
42.T illustrates the results of the test/task to the
whole class.
45.T gives back the results in a short time.
46.T describes the mistakes as an occasion to
learn.
68. T analyses the data she/he collected in the
classroom.
70. T writes the profiles with respect to knowledge.
We care to mention one last practice that was
implemented by T during episode three. In two
different moments T, who has at her disposal the
solution of the same task as made by the student,
decides to communicate with one student upon her
answer using the answers of other students producing
a sort of dialogue between answers. This dialogue
involves T, the students, and their written productions:
it elicits evidence of student understanding (S2) and
it activates students as instructional resources for one
another (S4), and for this reason can be considered a
practice of FA. However, it cannot be easily tracked
by FAMT&L’s indicators because, as far as we
noticed, it is strictly linked to the structure of a digital
technology-based environment and especially storage
and ease access we mentioned in Section 6.1.
Recalling our claim, we argue that teaching and
learning practices conducted in digital-technology
based environment have characteristics that can be
associated with at least three out of five FA strategies
and can therefore be a starting point to enhance
practices of FA. Thanks to classroom observation we
were able to better understand the emergent
phenomenon, dividing what is structural to the used
tools, and what is specific to the teacher’s actions and
choices. More precisely, we structured our perception
of observed classroom dynamics during the lockdown
with the lenses of FA, and with the five FA strategies
and the selection of indicators we described in the
theoretical framework (Section 2).
Summarising, we noticed that there are 9 out of 72
FAMT&L indicators of FA whose existence is a
consequence of the digital tool used for the teaching
environment (e.g., GC). These 9 indicators are
associated with the strategies S1 and S2 regarding the
possibility to elicit evidence of student understanding
and the clarification of learning intentions and criteria
for success. Observing T’s agency and its unfolding
under the lens of FA and our theoretical tool, we were
able to see that a specific managing of the effect of
the 9 indicators leads to practices readable as
effective FA practices according to our construct.
Can Formative Assessment Practices Appear Spontaneously during Long Distance Learning?
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7 CONCLUSIONS
Digital technologies have allowed the realization of
LDL during the first Italian lockdown, resulting in a
massive use of such technologies for almost the entire
school population over three months. On the one hand,
the possibility of collecting and sharing information
in an efficient way is a known effect of digital
technologies. On the other hand, during the first
lockdown in our country, the widespread use of
digital technologies has become constitutive of any
didactical practices, generating a huge amount of data
at the disposal of students and teachers. Despite the
undeniable difficulties encountered, this period will
result in a wealth of experience on which teachers and
students can decide to work, making the most of it.
Within this work, we tried to shape this wealth of
experience using the construct of FA, that guides our
eye as researcher in mathematics education and limits
the multiple phenomena we observed during LDL.
More precisely, we structured a theoretical tool based
on FA theoretical framework in order to link FA
indicators to spontaneous teachers’ and students’
actions and behaviours we observed. We found that
the listed above 9 out of 72 indicators can be ensured
simply by being in a digital-technology based
environment and they are responsible for the huge
amount of didactical data that can be managed.
Nevertheless, not every teacher takes advantage of
this possibility in the same way, some of them feel
overwhelmed by all the received information. One
way to manage the increased workload could be the
intentional use of FA construct in its entirety, and FA
practices. For example, the use of S4 and S5 would
allow the teacher to redistribute workload between
her and the students. We could say that is the
management of the effect of the 9 indicators that led
to the emerging of practices that could be associated
with the FA construct. We have evidence of at least
one teacher whose spontaneous didactical agency can
be described using more than half of the FA indicators,
widespread along with the five FA strategies and we
believe that other teachers can take advantage from
this work. Indeed, every teacher that implemented
asynchronous practices, or that recorded her
synchronous lessons during LDL, has at her disposal
a huge amount of data of the same kind we analysed
about her didactical practices, and can eventually
analyse them herself. Moreover, professional
development on FA from now on could work not only
on shared experiences and individual practices, but
also in the direction of a decreasing of the workload
thanks to intentional use of FA from the teachers’ side.
As we show in the analysis of classroom observation,
some peculiarities of such environment impact the
deepest feature of human interaction, for instance, we
can refer to the storage and access to data introduced
in section 6. Thus, another direction seems to be of
high relevance within the context of digital-
technology based environment: the study of the
specific instantiations of known theoretical constructs
of mathematics education.
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