MATE-BOOSTER: Design of an e-Learning Course to Boost
Mathematical Competence
Alice Barana
, Marina Marchisio
and Raffaella Miori
Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Torino, Italy
IIS “Eugenio Bona” di Biella, Via Antonio Gramsci 22, 13900 Biella, Italy
Keywords: Automatic Formative Assessment, Basic Mathematical Competence, Constructivist Learning Environment,
Learning Design, Problem Solving, Virtual Learning Environment.
Abstract: In the transition from lower to upper secondary education, Italian students are expected to have achieved a
level of competence which allows them to use knowledge and abilities to model and to understand scientific
and technical disciplines. Gaps or misunderstandings in basic knowledge can hinder the effort of students
who attend technical high schools, where the core subjects are based on Mathematics. This paper deals with
the design of a project conceived to strengthen mathematical competences of students attending the first year
of a technical upper secondary school through an online course named “MATE-BOOSTER”. The online
activities on the web-based platform have been developed using didactic methodologies founded on
constructivist assumptions, as problem posing and problem solving, collaborative learning, learning by doing,
automatic and adaptive formative assessment. In this work the process of design of MATE-BOOSTER is
shown, the methodologies chosen are discussed, and the online activities are analysed from a constructivist
Italian students completing lower secondary
education – which in Italy ends at 8th grade – are
supposed to have developed a positive attitude
towards Mathematics and to understand how
mathematical tools can be useful in many situations
to operate in the real world (MIUR, 2012). INVALSI
is the national institute in charge of verifying that the
learning outcomes are achieved: it administers
surveys and standardized tests in order to guarantee
the quality of Italian instruction and to make it
possible to be compared at international level. The
results of INVALSI surveys highlight how, at all
stages, but at the end of 8
grade of instruction in
particular, there are still difficulties in the deep
understanding of basic mathematical concepts, in the
ability of applying knowledge to solve problems in
real contexts and, above all, in the process of
argumentation, which shows the difficulty in
formalizing the intuitive knowledge (INVALSI,
2017). These gaps increase in importance when
students enrol to upper secondary school and they
have to approach scientific and technical subjects,
whose understanding relies upon their basic
mathematical competence. This problem is
particularly evident in technical upper secondary
schools, where specialized disciplines are studied at
an advanced theoretical level, though students’
average mathematical competence is lower than in
Lyceums, as the national surveys show (INVALSI,
2017). The ability to use mathematical thinking to
solve problems related to the real experience or to
other disciplines – in other words, mathematical
competence (MIUR, 2010; Pellerey, 2004) – thus
acquires relevance in the delicate period of transition
that young people go through when they enrol to
upper secondary school, when school successes and
failures are deeply interlaced with the shaping of their
characters (Debnam et al., 2014; Mariani, 2006)
The Head Teacher of the Technical Upper
Secondary School “Eugenio Bona” of Biella, together
with her team of Mathematics teachers, designed a
project aimed to strengthen the basic mathematical
Barana, A., Marchisio, M. and Miori, R.
MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence.
DOI: 10.5220/0007721702800291
In Proceedings of the 11th International Conference on Computer Supported Education (CSEDU 2019), pages 280-291
ISBN: 978-989-758-367-4
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
competences of first year students with the support of
an e-learning platform and digital materials. The
project, called “MATE-BOOSTER”, has been
implemented in collaboration with the department of
Mathematics of the University of Turin, which has a
long experience in the development of virtual
environments for learning Mathematics, especially to
prevent school failure (Barana et al., 2017b; Barana
and Marchisio, 2015) and to support students in the
transition from lower to upper secondary school
(Barana et al., 2016). The project started in September
2018 and it is currently developing.
This paper focuses on the design of the project;
the methodologies chosen in relation to the students’
needs are deeply discussed and the process which led
to the realization of innovative digital materials is
shown and exemplified.
2.1 Web based Constructivist Learning
The choice of the methodologies for developing the
learning materials has been made on constructivist
assumptions, according to which knowledge is
situated, being a product of the activity, context and
culture in which it has been developed and used
(Brown et al., 1989). Learning is seen as a lifelong
active process of knowledge building mediated by
experiences and relations with the environment and
the community (von Glasersfeld, 1989); thus
constructivist learning environments should provide
authentic activities and real world problems which
can engage students. In Mathematics education this
theme has been investigated by many researchers, as
Schoenfeld who suggests that Mathematical thinking
should be a tool to interpret quantitative phenomena
of the outside world and it should be developed at
school through meaningful modellization activities
(Schoenfeld, 1992).
One of the main implications of the constructivist
idea of the learner creating his or her own knowledge
is the shift from a teacher-centred to a student-centred
approach. If students become the protagonists, the
teachers need to leave the stage and move aside,
changing their role from leaders to mentors, and their
task from knowledge transmission to the creation of a
suitable environment for learning (Cornelius-White,
The community where the learner is integrated in
is a core element as well. The sharing of opinions
opens the mind and favours the process of knowledge
building. Thus a constructivist learning environment
should facilitate collaboration and activities should
require discussion and interaction among peers (Lave,
Moreover, activities should be rooted in
assessment with a formative value in order to inform
both teachers and students about progresses (Scriven,
1966). Assessment and metacognition are deeply
interlaced: frequent and well-structured feedback
helps learners understand where they are going and
how they are going, giving information not only about
how the task has been performed (task level), but also
about the process that should have been mastered
(process level), and enabling self-regulation and self-
monitoring of actions (self-regulation level) (Hattie
and Timperley, 2007).
Strategies as formative assessment, collaborative
learning and relevant problem solving are also
indicated by several researches as useful enablers of
learners’ engagement, which is related to high
learning achievements (Ng et al., 2018). Improving
engagement is particularly important in students with
challenging backgrounds, learning difficulties or low
scholastic performances; in these contexts,
interventions that only focus on the reinforcement of
basic knowledge are often little effective, if they don’t
rely on approaches which promote interest,
motivation and self-efficacy (Haberman, 2010).
Technology can support the creation of
constructivist digital environments, as it can provide
computer mediated communication, computer
supported collaborative work, case based learning
environments, computer supported cognitive tools
(Jonassen et al., 1995), as well as instruments for self
and peer assessment (Kearns, 2012) and for automatic
evaluation (Barana et al., 2015).
The analysis of the implementation of web based
constructivist learning environments has involved
many authors in literature in the last twenty years and
several models have been designed to engage students
of different school levels, in e-learning or blended
modality, in learning several disciplines (Alonso et
al., 2005; Czerkawski and Lyman, 2016; Lefoe, 1998;
Sangsawang, 2015). Their results mainly deal with
the relations between strategies, media and tool used
and processes activated. Constructivist instructional
designers generally accept as a valid and well-
established framework for building learning
environments the seven learning goals devised by
Cunningham, Duffy and Knuth in 1993 and
illustrated by Honebein (1996); they are:
1. to provide experience with the knowledge
construction process;
MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence
2. to provide experience in and appreciation of
multiple perspectives;
3. to embed learning in realistic and relevant
4. to encourage ownership and voice in the
learning process;
5. to embed learning in social experience;
6. to encourage the use of multiple modes of
representation; and
7. to encourage self-awareness in the knowledge
construction process.
2.1 Automatic Formative Assessment
In a virtual learning environment, formative
assessment can be easily automatized in order to
provide students immediate and personalized
feedback. There are several Automatic Assessment
Systems (AAS) that allow the creation of questions
for STEM (Science, Technology, Engineering and
Mathematics); those which are based on a Computer
Algebra System (CAS) support the creation of
automatically graded open Mathematical answers,
such as formulas and equations, but also sets, vectors
and graphs, which are accepted for their meaning, not
only for their form.
These tools can be usefully adopted to enhance
learning, master problem solving strategies,
improving metacognition, facilitate adaptive teaching
strategies and support teachers’ work (Barana et al.,
in press).
Using Moebius AAS (Moebius Assessment,
2018), the Department of Mathematics of the
University of Turin has designed a model for the
formative automatic assessment for Mathematics,
based on the following principles (Barana et al.,
1. availability of the assignments to the students,
who can work at their own pace;
2. algorithm-based questions and answers, so that
at every attempt the students are expected to
repeat solving processes on different values;
3. open-ended answers, going beyond the
multiple-choice modality;
4. immediate feedback, returned to the students at
a moment that is useful to identify and correct
5. contextualization of problems in the real world,
to make tasks relevant to students;
6. interactive feedback, which appears when
students give the wrong answer to a problem. It
has the form of a step-by step guided resolution
which interactively shows a possible process
for solving the task.
The last one consists of a step-by-step approach
to problem solving with automatic assessment, but it
is conceptualized in terms of feedback, highlighting
the formative function that the sub-questions fulfil for
a student who failed the main task. The interactive
nature of this feedback and its immediacy prevent
students from not processing it, a risk well-known in
literature which causes formative feedback to lose all
of its powerful effects (Sadler, 1989). Moreover,
students are rewarded with partial grading, which
improves motivation.
This model relies on other models of online
assessment and feedback developed in literature, such
as Nicol and MacfarlaneDick’s principles for the
development of self-regulated learning (Nicol and
MacfarlaneDick, 2006) and Hattie’s model of
feedback to enhance learning (Hattie and Timperley,
The MATE-BOOSTER project was conceived with
the aim of strengthening basic mathematical
competence of first-year students of a technical upper
secondary school, acting with methodologies and
tools able to activate students’ motivation and
engagement, in order to prevent failures in scientific,
technological and economic subjects which are at the
core of their curriculum. The main feature of the
project involves the creation of a web-based course in
a virtual learning environment where students can
revise the contents in a self-paced way or under their
teachers’ guide, both in the classroom and at home.
Materials have been created according to didactic
methodologies which are in line with the theories of
constructivism and formative assessment outlined in
the previous paragraph.
The project involves 202 students of nine classes
with their seven teachers of Mathematics, plus one
teacher in charge of coordinating the works from
inside the school.
MATE-BOOSTER has been developed following
a model of learning design of “ASSURE” (Heinich et
al., 1999), which includes the following steps:
1. Analyse the learners;
2. State objectives;
3. Select methods, media and materials;
4. Utilize media and materials;
5. Require learner participation;
6. Evaluate and revise.
The whole design process has been conducted by
researchers from the Department of Mathematics of
the University of Turin in close collaboration with the
CSEDU 2019 - 11th International Conference on Computer Supported Education
teachers of Mathematics of the nine classes involved.
In fact, it has been considered essential that teachers
share the instructional strategies, approve the didactic
materials and are consulted at each step of the design;
otherwise they couldn’t present the project to their
students in a convincing way that make them take part
in the online activities.
4.1 Analysis of the Learners
The analysis of the learning needs, preceding the
development of the course, was carried out with two
different aims:
to examine students’ competence in
Mathematics, and the gaps in their knowledge;
to inquire about students’ motivations to the
study in general and to the study of
Mathematics in particular.
Two different tools have thus been chosen for
these objectives: an entry test to assess the initial
competence and a questionnaire to understand their
The entry test was composed of 20 multiple
choice questions to be answered in 45 minutes. For
each correct answer students got 5 points, 0 for
incorrect or ungiven answers. It has been
administered online with an automatic assessment
system. All students took the test on the same day (8
October 2018); some settings were added to the test
to prevent students from cheating: the questions and
the choice of the answers were shuffled, there were
some random numeric parameters, there was only one
attempt available with an automatically set time limit,
so that the test automatically quitted after 45 minutes.
Few days before the date of the test, students were
given the log in data to access the platform where the
test would take place; there, they could find a sample
test with the instructions to navigate through the
Questions were distributed among the core topics
studied in the lower secondary school, in proportion
to the time generally dedicated to each one. Each
question referred to one of the main content areas of
the curriculum (numbers, space and shapes, functions
and relations, data and predictions), moreover there
were two questions about simple logic reasonings.
More details are shown in Table 1.
Questions were built in order to verify the
comprehension of particular concepts or processes,
not just to check the memorization of rules or
Table 1: Content areas and topics of the questions.
Number of
Number 8 Rational numbers,
number estimation,
fractions, percentages,
Space and
4 Perimeter and area of
plane figures.
4 Symbolic computations,
equations, proportions.
Data and
2 Tabular and graphic
representation of
2 Simple logic reasonings
involving order
relations and set theory.
The results of the test have been statistically
treated using the difficulty index, which corresponds
to the ratio between the number of correct answers
and the sample size, and the discrimination index,
which is the difference between the difficulty indexes
of the best performing group and the worst
performing one, where the two groups are equal sized
and cover the whole sample (Ebel, 1954). The test
reliability has been assessed through the Cronbach
Results of the entry tests were not particularly
good, with an average score of 41/100, meaning that
the level of difficulty was quite high, at least for the
students of this school. Nobody scored more than 80
out of 100, while the lowest registered score was
5/100. If aggregated by classes, the average score
varied significantly, from a minimum of 34/100 to a
maximum of 54/100; the belonging to a specific class
explains the 18.5% of the variance of test results
(square eta = 0.185, p<0.0001). It can be noticed that
the best performers attend a curriculum which is more
rooted in Mathematics than the worst performers.
Results aggregated by content areas show the same
trend as INVALSI tests: space and shapes turned out
to be the most difficult area, with an average index of
difficulty of 0.27; it was followed by logic reasonings
(0.36), whilst data and predictions was the easiest one
(0.60). Results for numbers and relations hung around
The difficulty of questions ranged from 0.22 to
0.87; only 4 out of 20 questions can be considered
“easy”, reaching more than 50% of correct answers.
The majority of questions can be considered coherent
with the general test, since the discrimination index is
greater than 0.25 for the 75% of the questions.
Questions with a low discrimination index have been
qualitatively analysed: they include frequent
MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence
misunderstandings among the incorrect options or
high-level reasonings that caused also the most
skilled students to make mistakes (Tristan Lopez,
1998). The test Cronbach Alpha was 0.65; it was
negatively influenced by these questions which
hindered the students. Our claim is that this test is
quite efficient for grade 9 students, but in general
students who enrol to a technical secondary school
like this one have low-level competence in
Mathematics, that the test highlighted.
The questionnaire was composed of 33 statements
where students were asked to state their level of
agreement with Likert scale from 1 to 4 (completely
disagree – completely agree) or from 1 to 5
(insufficient – excellent). It was administered online
on the same platform where the entry test took place.
The questionnaire is inspired by the student
questionnaire of 2012 PISA survey, when
Mathematics was the main focus (OECD, 2013). It
was aimed to measure attitudes and behaviours
towards school and Mathematics, in particular
intrinsic motivation (shown by students that study
mathematics because they like it), instrumental
motivation (shown by students that study
Mathematics because it will be useful for their
future), perseverance, openness to problem solving,
perceived control over success in Mathematics, ethic
and respect of school roles, mathematical activities
outside school. Moreover, it was asked if students
have an internet connection and a device
(tablet/computer) at their home. It emerged that
students’ intrinsic motivation is not so high (the
average is 2.6 in a scale from 1 to 4), although it varies
widely (standard deviation: 0.9), while instrumental
motivation is higher (the average is 3.1 in a scale from
1 to 4, standard deviation: 0.5). All students have the
possibility to use a computer with internet connection
for large part of their time at home. Deeper analysis
on the answers to the questionnaire will be carried out
later in the project; the information gained will be
used to better interpret the outcomes.
4.2 Statement of the Objectives
In the light of the results of the entry test and of the
questionnaire, during a focus group researchers and
teachers listed the learning outcomes of the course.
The choice of the topic that the course should cover
was made considering the contents needed to
understand the scientific courses of the first years
(Mathematics, Computer Science, Economy,
Science, Physics). They are the following:
fractions (operating with rational numbers);
proportions (calculating the unknow term of a
proportion, to solve problems involving direct
and inverse proportionality in real contexts);
percentages (calculating percentages in real
powers (knowing the meaning of
exponentiation and applying the properties of
mathematical formulas and functions (working
with symbols and formulas and with their
graphical representations);
equations (reading and building equations,
solving linear equations in one unknown);
plane geometrical shapes (knowing and
calculating measures of angles, triangles and
statistics and probability (managing data,
descriptive statistics indexes and graphical
representations, calculating elementary
probabilities in real contexts);
mathematical language (understanding and
using different registers of representation:
verbal, symbolic, graphical, geometrical,
logics (managing simple logic reasonings using
Boolean operators).
4.3 Selection of Methods, Media and
The choice to create an online course which students
can use at home in a self-paced modality has been
validated by their availability of technological
devices to access the material, expressed in the
questionnaire. Moreover, in all the classrooms of the
school there is an Interactive White Board (IWB) that
teachers can use to show students the platform and to
complete the activities together; the school has three
computer labs and several tablets that allow students
to work with the course activities even at school. As
a Virtual Learning Environment, an integrated
Moodle platform has been adopted, managed by the
ICT services of the Department of Computer Science
of the University of Turin, in collaboration with the
Department of Mathematics, the same platform where
the entry test and the questionnaire have been
delivered. MATE-BOOSTER has been inserted on an
instance of the Moodle platform that the University
of Turin commonly adopts for e-learning and that
often hosts school teachers and students for
educational projects (Barana et al., 2017a, 2017c;
Barana and Marchisio, 2016a; Giraudo et al., 2014;
Marchisio et al., 2017). It is integrated with an
Advanced Computing Environment (Maple) for the
CSEDU 2019 - 11th International Conference on Computer Supported Education
creation of interactive materials, and with Moebius
Assessment for automatically graded assignments.
The didactic methodologies for the development
of the contents have been selected on the base of the
constructivist framework and of the evidence gained
during previous experiences of e-learning courses
(Barana and Marchisio, 2016b). They are the
Problem posing and problem solving:
assuming the social-constructive insight of
problem solving, problems are considered as
learning environments where mathematical
knowledge is created in a collaborative
discussion starting from a problem. The top-
down order traditionally used to study
Mathematics is inverted: from the analysis of a
real-world situation, paths to the solutions are
drawn, in a constructive approach toward the
discipline. Afterward, the solving steps are
synthetized and generalized, introducing the
typical rigor of Mathematics. Learning
technologies are used both for online
cooperation and as a mean of representation of
the solving process: freed from the burden of
calculations, students can focus on the solving
strategy, find relationships and better
understand the solutions (Brancaccio et al.,
Collaborative learning: in a Virtual Learning
Environment, collaboration can be fostered
through activities for synchronous or
asynchronous discussion; it enhances students’
comprehension of problems and of
Mathematical concepts. Moreover, positive
collaborations affect the quality of the
environment and they are reflected on students’
motivation. Collaborative virtual learning
environments force the shift of the teachers’
role, who let students create their own learning
– but carefully monitoring it (Barana and
Marchisio, 2017).
Learning by doing: interactivity enhances
students’ engagement and contributes to
increase their motivation. Feedback that
students get from activities help them control
their learning and move forward (Gossen et al.,
Automatic formative assessment: implemented
with an AAS specialized for STEM, it allows
students to practice at their own pace and to
obtain immediate feedback to acknowledge
their own level of preparation. Questions and
assignments can be enhanced by varying them
in a random controlled form, inserting parts
expressed in a special programming language.
This allows a great variety of assessment
modalities which strengthen reasoning until it
is mastered: students can obtain different data
or graphics at every new attempt, the system
can adaptively suggest guided resolutions,
feedback and questions can automatically be
proposed on the base of previous answers
(Barana et al., 2018).
The process of creation of the materials took place
in a “Management course”, where school teachers
could access and follow the work, propose ideas and
suggestions, get in touch with the researchers.
The structure given to the course is modular,
according to the general guidelines for the creation of
e-learning course (Rogerson-Revell, 2007), each
module corresponding to a different topic, to the
purpose of addressing students through the course
topics and to show at a glance the whole content.
Figure 1 shows the course homepage with the 11
modules in a grid format, chosen for its graphical
impact on the learner.
All the modules have a fixed structure, composed
of submodules containing:
1. materials with theoretical explanation of the
fundamental concepts in the form of e-book,
that students can read online or download in
pdf. Explanations begin with problems and are
correlated with examples, graphics and images;
2. interactive materials for the exploration of the
concepts illustrated in the e-book, which help
students to put theory into practice, to visualize
Figure 1: Homepage of the course with the modules in grid
MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence
and analyse different representations of the
same mathematical structures when parameters
3. automatically graded assignments to check the
understanding of the concepts presented and of
the related abilities.
At the end of every module there are:
4. one or more real-world problems which require
the use of the contents of that unit to be solved;
5. a final test, automatically graded, to verify the
achievement of the learning objectives
expected for the module.
Figure 2 shows an example of course module.
Taking into account the methodologies chosen
and the needs of the students, their frequent
misunderstandings emerged both in the entry test and
from teachers’ experience, the didactic materials have
been created to populate the modules. As an example,
in the entry tests one of the most difficult questions
was about the properties of powers, in which students
had to choose the only wrong answer between 4
equalities (difficulty index: 0.34). A set of questions
were developed, focused on the most frequent
mistakes in the applications of the properties of
powers, on the scheme of the question shown in
Figure 3. Initially, students are asked to decide
whether an equality involving properties of powers
was correct or incorrect. They can earn half the score
if they answer correctly; after that, they are asked to
fill two subsequent sections which refer to the general
rule to apply, through which they can earn up to the
remaining half of the score. The last two sections can
have a double function: justifying the choice, if the
student had answered correctly to the first part, or
showing a reasoning process, if the student had given
the wrong answer (or guessed by chance) to the first
step. Once they finish the test, students can try it again
and find questions with a similar structure but
different examples of applications of the same and
other power properties. This is an example of
question with interactive feedback: after the first
Figure 2: Structure of a module.
Figure 3: Example of a question with interactive feedback.
section the student receives a first feedback in a form
of green tick or a red cross depending on whether he
answered correctly or not; the following sections are a
feedback about how he was supposed to develop his
reasoning in order to reach the solution. The feedback
is interactive, because the student has to complete step
by step the sub-questions, following the proposed
Figure 4 shows an example of problem solving
question developed with the automatic assessment,
related to the module about mathematical formulas and
functions. A real-world problem is given and students
can explore different solving strategies: a numerical
solution through an interactive table; a symbolic
solution through an open-ended response area which
offers the possibility to enter formulas through a
symbolic equation editor, and a graphic solution, made
possible through the graph of the function entered by
the students generated by the system. Students can
compare the different mathematical representations of
the real world situation and deepen their understanding
of the involved concepts, namely functions and their
zeros. When they try the question again, students will
find different values that allow them to repeat the
process and to acquire awareness of the meanings
laying behind abstract mathematical objects.
Within the online course there are also a forum of
discussion for students, a progress bar, through which
learners can visualize their learning steps, and a link to
the gradebook, where all the assignments results are
CSEDU 2019 - 11th International Conference on Computer Supported Education
Figure 4. An example of real world problem with automatic
4.4 Utilization of the Materials
Once the course was completed, it has been
duplicated in 9 single courses, one for each class, so
that teachers can easily control the progress of their
own students and give them personalized support and
Courses were opened to the students at the end of
October 2018, and they are currently ongoing; they
will be active until Spring 2019, even though students
will be able to access the contents successively to the
estimate end of the project.
Students received an e-mail at their institutional
e-mail address with the indications to log in the
platform and to access the materials. Interactive
instructions about how to use the automatic
assessment were provided to the students directly
through the platform. The teachers were also asked to
repeat the instructions to the classes at school and to
show through the IWB how to use the materials. The
learning materials can thus be used by students who
need to revise basic skills at their own pace, but it is
also suitable to class activities of different kind when
teachers need to introduce new topics based on
previous knowledge or assign differentiated activities
to different group of students.
4.5 Requirement of Learner
Aware that little motivated students won’t be too keen
on autonomously doing online mathematical
activities in their spare time, some expedients have
been taken in order to assure their frequency to the
The main one is the certification: students who
initially have low grades will be required to present,
by the month of April, the certificate of completion of
the course. The certificate can be automatically
downloaded from the platform, at the condition that
all the activities will figure as completed. So, they are
forced to use the materials.
If the certification acts as “external” motivational
lever, the learning methodologies chosen to develop
the materials contribute to the development of
intrinsic motivation. The real contexts, the immediate
feedback, adaptivity and interactivity make all the
materials engaging and useful to get prepared, so that
students who try the activities can acknowledge their
usefulness and go on with the modules. The
interactive feedback provided through automatic
assessment help them understand solving strategies
and processes, contributing to the development of
self-regulation. Through a progress bar they can be
made aware of their position in the learning path and
be motivated to complete it.
In addition, all teachers have been asked to
present the course to their classes, to invite them to do
the activities as homework and to recall the problems
during lessons. In fact, students need to see the course
as linked to their study and not as an external and
additional duty; the more they are convinced of the
usefulness of the online course for their learning, the
more easily they will participate. The collaboration
with the teachers could also have the positive effect
to renew their teaching practices, introducing the use
of the didactic methodologies and technologies
adopted in the online course. As a consequence, not
only the online course, but the whole school
experience with Mathematics could be more
engaging for the students, who can be facilitated in
the development of interest for Mathematics.
4.6 Evaluation and Revision
In April 2019, when the time limit for the course
completion will come, an evaluation of the course
will be performed in several modalities.
The achievement of the learning outcomes will be
assessed through a final test, similar to the entry one,
for all the students. The appreciation of the course
MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence
will be evaluated via a questionnaire, which
investigates the appreciation and perceived
usefulness of the online activities to get a better
understanding of the contents. Teachers will be
interviewed to express their point of view about
students’ performances.
Data collected through the two tests, the two
questionnaires, platform usage and students’ scores
and teachers’ interviews will be cross-checked in
order to understand key strengths and limits of
MATE-BOOSTER for future implementations of the
The project is at a too early stage to get results from
students. Nevertheless, the appreciation from the
teachers involved is very high, since they perceive the
online course as a valid support for their didactic, for
reducing failures and motivating students.
The design of the course, made according to
constructivist directions, actually respects the seven
goals for building constructivist learning
environments theorized by Cunningham, Duffy and
1. Real-world problems offer students a learning
environment in which to create mathematical
knowledge starting from a specific case;
exploration activities let students build and
associate meanings to mathematical concepts;
adaptive questions with step-by-step guided
solutions help them manage a complex
resolution following their own ideas. Thus,
students get to experience the very
knowledge construction process.
2. Interactive exploration materials show
Mathematics from different points of view; the
resolution of the problems is often discussed
offering more than one solving process; peer
discussions ask students to come to terms with
different opinions and ways of understanding.
These features can provide learners with
experience in and appreciation of multiple
3. Not only all the problems, but also great part of
the automatically graded questions and of the
interactive materials are contextualized in real-
world situations, interesting and challeging for
students. In this way learning is embedded in
realistic and relevant contexts.
4. When opening the online course, students can
choose their own path between the offered
topics and materials. They are at the center of
their own learning. All the activities do not
flow automatically in front of students’ eyes:
they have to autonomously get into each one
and browse pages and questions with a click,
thus enhancing their commitment. In this way
ownership and voice in the learning process
can be encouraged.
5. Students’ work, their problems and successes
are not isolated: they can share them with other
learners through the forum. Moreover, MATE-
BOOSTER is inserted in a blended context,
where students actually meet every morning at
school and teachers are adviced to discuss the
activities during the lessons, to the purpose of
embedding learning in social experience.
6. Exploring activities often present the same
concept with different registers (in words,
symbolic, graphic, tabular, and so on) and try
to simplify its understanding via a shift of
register. The same approach is applied in the
automatically graded assignments and in the
problems, in order to encourage students to
the use of multiple modes of representation.
7. Immediate feedback facilitates students’
acknowledgement of their preparation;
moreover, the tracking of activities and the
progress bar offer them a visual insight of the
learning path that they have undertaken.
Automatically graded open answers and
interactive feedback ask students to explain
processes, not only to give results. Hence, the
course activities pursue the goal to encourage
self-awareness in the knowledge
construction process.
Thus MATE-BOOSTER can be a suitable
learning environment where students can reinforce
their knowledge with a constructivist approach.
In the design of the course a special attention has
been dedicated to feedback, considered a core
element for promoting success. MATE-BOOSTER
feedback works at three levels: at task level, when it
informs students whether the task has been performed
correctly or knowledge has been achieved; at process
level, when it explains how the task should be
performed; and at self-regulation level, when it helps
learners monitor their own learning. Table 2 shows
the MATE-BOOSTER features and activities which
provide the three kinds of feedback.
CSEDU 2019 - 11th International Conference on Computer Supported Education
In summary, MATE-BOOSTER has been conceived
with the aim of supporting students in the transition
from lower to upper secondary school by strengthening
basic mathematical competences. The project has been
managed using a design method of ASSURE kind
(Analyse the learners; State objectives; Select
methods, media and materials; Utilize media and
materials; Require learner participation; Evaluate and
revise). The core action of the project involves the
implementation of an online course that students can
use at their own pace as a support to their study. The
design of the virtual learning environment has been
carried out according to constructivist assumptions,
and under the seven goals for building constructivist
learning environments theorized by Cunningham,
Duffy and Knuth (to provide experience with the
knowledge construction process; to provide experience
in and appreciation of multiple perspectives; to embed
learning in realistic and relevant contexts; to encourage
ownership and voice in the learning process; to embed
learning in social experience; to encourage the use of
multiple modes of representation; and to encourage
self-awareness in the knowledge construction process).
The learning methodologies used are problem posing
and problem solving, collaborative learning, learning
by doing and automatic formative assessment.
In the course design, the collaboration of the
researchers with the school teachers of Mathematics is
a key strategy to maximize learners’ participation,
since the presentation of the course is filtered by the
teachers’ voice.
The course is currently open to students and the
results, in terms of teachers’ and students’ satisfaction
and competence achieved, will be analysed as soon as
they will be available and used for perfecting the
course and proposing it again.
Table 2: Analysis of the feedback provided by MATE-
Level of
Task level
Immediate feedback from automatic
grading; interactions with peers and
Process level
Interactive feedback; resolutions of
the problem; interaction with peers
and teachers
Automatic assessment, tracking of
activity completion, progress bar,
gradebook, certification.
Since in Italy schools and teachers need to offer
paths for the revision to students who get low marks,
including individualized courses and further
assessment, similar courses could have a double
effect on the optimization of scholastic resources:
firstly, they could reduce failures at their root, as they
are often due to gaps in the basic knowledge that
cause difficulties in learning new things; secondl,
they can be used as part of the paths of content
revision, because the topics included within the
course are those which are required in advanced for
understanding the first year course, and they are
usually object of the revision courses. Thus, schools
using online courses as MATE-BOOSTER could
save human resources in delivering revision courses
and collocate them elsewhere, such as in projects for
the innovation of methodologies and curricula. This
procedure could be even promoted by the Ministry of
Education, maybe proposing a format that schools
can customize. The project could be extended to other
core disciplines, such as Italian and Foreign
Languages, with the collaboration of experts in these
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MATE-BOOSTER: Design of an e-Learning Course to Boost Mathematical Competence