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ORIGINAL ARTICLE
Facilitating parental engagement in school mathematicsand science through inquiry-based learning: an examinationof teachers’ and parents’ beliefs
Nicholas G. Mousoulides
Accepted: 18 July 2013
� FIZ Karlsruhe 2013
Abstract This study examined teachers’ and parents’
beliefs on the implementation of inquiry-based modeling
activities as a means to facilitate parental engagement in
school mathematics and science. The study had three
objectives: (a) to describe teachers’ beliefs about inquiry-
based mathematics and science and parental engagement;
(b) to describe parents’ beliefs about inquiry-based math-
ematics and science and their engagement in inquiry-based
problem solving; and (c) to explore the impact of an
inquiry-based learning environment comprising a model-
eliciting activity and Twitter. The research involved three
sixth-grade teachers and 32 parents from one elementary
school. Teachers and parents participated in workshops,
followed by the implementation of a model-eliciting
activity in two classrooms. Three teachers and six parents
participated in semi-structured interviews. Teachers
reported positive beliefs on parental engagement in the
mathematics and science classrooms and the potential
positive role of parents in implementing innovative prob-
lem-solving activities. Parents expressed strong beliefs on
their engagement and welcomed the inquiry-based model-
ing approach. Based on the results of this aspect of a four-
year longitudinal design, implications for parental
engagement in inquiry-based mathematics and science
teaching and learning and further research are discussed.
Keywords Parental engagement � Teachers’ beliefs �Parents’ beliefs �Model eliciting activities �Modeling
1 Introduction
Students, from a young age, are exposed to complexity on a
regular basis, as our global community has become gov-
erned by complex situations. Further, an appreciation and
understanding of the world as interlocked complex systems
is critical for making effective decisions about their lives as
individuals and community members (Lesh and Zawo-
jewski 2007). Students’ exposure to complex situations
further underlines the necessity to integrate group work in
classrooms, build on students’ existing knowledge, design
experiments and work with complex data, and share and
discuss ideas with peers. These practices (among others)
are collectively known as inquiry-based learning (IBL)
(Linn et al. 2004).
The complexity that appears in all forms of society, the
economy, and education, and the new technologies that
have been integrated in all forms of work, have led to sig-
nificant changes in the forms of mathematical and scientific
thinking that are needed beyond the classroom (Sriraman
and English 2010). Consequently, there is a demand to
further improve students’ abilities to use effectively these
new technological tools in dealing with complex problems
in school subjects and beyond. Taking into account these
demands, researchers and educational policy makers have
highlighted the need to promote students’ problem-solving
abilities, and their skills in designing experiments, setting
hypotheses, manipulating variables, working in teams, and
effectively communicating with others (Lesh and Zawo-
jewski 2007; Mousoulides et al. 2008).
Adopting an inquiry-based approach as a means to
achieve the above goals is not a straightforward process
(Linn et al. 2004). It conflicts with national curriculum
requirements and other constraints, such as the need for time,
the need for more resources, other curriculum constraints,
N. G. Mousoulides (&)
Department of Educational Sciences, University of Nicosia,
Nicosia, Cyprus
e-mail: [email protected]
123
ZDM Mathematics Education
DOI 10.1007/s11858-013-0524-4
and parental engagement. With regard to parental engage-
ment, several researchers have underlined the significance of
engaging parents in the implementation of innovations in
school mathematics and science (Deslandes and Bertrand
2005; Epstein et al. 2009; Hornby 2011). Parental engage-
ment has been also documented as a positive influence on
children’s achievement, attitudes, and behavior, regardless
of cultural background, ethnicity, and socioeconomic status.
However, this engagement is not easy to be maintained.
Teachers are encouraged to find appropriate methods to
engage parents, especially when it comes to use of innovative
methods, such as IBL, and schools have to take an active role
in developing collaborative relationships within parents and
communities (Barr et al. 2006).
While a significant number of studies have examined
various aspects of parental engagement, there is a lack of
studies that have focused on the role of parents in imple-
menting innovations such as IBL in the teaching and learning
of mathematics and science. To this end, the present study
examined teachers’ and parents’ beliefs with regard to IBL
and parental engagement. The study further explored how
parents’, students’, and teachers’ collaboration during the
implementation of an inquiry-based modeling activity could
contribute to improved parental engagement. The research
questions that guided the study were:
(a) What are teachers’ beliefs about inquiry-based learn-
ing in mathematics and science and parental
engagement?
(b) What are parents’ beliefs about inquiry-based math-
ematics and science and their engagement in inquiry-
based problem solving?
(c) What is the impact of an inquiry-based learning
environment comprising a model-eliciting activity
and technology tools for communication on parental
engagement?
2 Theoretical framework
The theoretical framework builds on two strands:
(a) instructional interventions to promote mathematical and
scientific inquiry, particularly in using a models and
modeling perspective (Lesh and Doerr 2003); and
(b) parental engagement with an emphasis on teachers’ and
parents’ beliefs.
2.1 A modeling perspective in inquiry-based learning
in mathematics and science
In studying complex situations and problems at elementary
school level mathematics and science, a focus on new
students’ abilities is needed. These abilities, for
conceptualization, collaboration, and communication, have
led to significant changes in the forms of mathematical and
scientific thinking that are needed, such as the abilities to
generate, analyze, operate on, and transform complex data
sets (Sriraman and English 2010). In achieving these
abilities, a number of researchers propose the use of
inquiry-based approaches in the teaching of mathematics
and science. In the present study we adopted Linn and
colleagues’ (2004) definition of inquiry-based learning
(IBL), as ‘‘the intentional process of diagnosing problems,
critiquing experiments, and distinguishing alternatives,
planning investigations, researching conjectures, searching
for information, constructing models, debating with peers,
and forming coherent arguments’’ (Linn et al. 2004).
By reflecting on these characteristics, a means to
develop students’ abilities is through future-oriented,
interdisciplinary problem-solving experiences that mirror
the IBL characteristics. The problems used in this study
draw upon the broad field of engineering, providing pow-
erful links between the school mathematics and science and
the real world, enabling students to apply their mathe-
matics and science learning to the solution of an authentic
problem (English and Mousoulides 2011; Kaiser and
Sriraman 2006). The use of such modeling activities in the
mathematics and science curriculum provides students with
opportunities to work with realistic, client-driven problems
that are based on the theoretical framework of models and
modeling (Mousoulides et al. 2008).
Engineering Model Eliciting Activities (EngMEAs)
provide opportunities for developing students’ creative and
flexible use of mathematical and scientific ideas within
interdisciplinary contexts, for creating, applying, and
adapting mathematical and scientific models in interpret-
ing, explaining, and predicting the behavior of complex
engineering problems (English and Mousoulides 2011;
Maass and Doorman 2013). EngMEAs aim to complement
and enrich the inquiry-based approach (which shares many
characteristics with the engineering design process) (Eng-
lish and Mousoulides 2011) by offering students opportu-
nities to repeatedly express, test, and refine or revise their
current ways of thinking as they endeavor to create a
structurally significant product—structural in the sense of
generating powerful mathematical, scientific, and engi-
neering constructs (Zawojewski et al. 2008). Thus, the
components of a modeling basic engineering design pro-
cess that students go through are: Ask (What is the prob-
lem? What have others done? What are the constraints?),
Imagine (What are some possible solutions?), Plan (What
diagram/sketch can you draw? Make a list of materials
needed), Create (Follow your plan and create a model; test
it out), and Improve (Discuss what works, what does not,
and what could work better; modify your design to make it
better; test it out) (Cunningham and Hester 2007).
N. G. Mousoulides
123
2.2 Parental engagement
Broadly, parental engagement refers to mutual collabora-
tion, support, and participation of parents, community, and
teachers in activities that directly and positively affect
student outcomes. Engagement can range from parents’
activities at home that support learning to parental activi-
ties in schools (Epstein and Van Voorhis 2001).
Parental engagement has been documented in a number
of studies as a positive influence on children’s achievement
and overall success of the student, socially, emotionally,
and academically (Epstein et al. 2009; Hornby 2011).
Active parental engagement, however, is quite difficult to
be maintained. Minner and Hiles (2005) have identified a
number of barriers impeding effective parental engage-
ment, including: (a) the status of science and mathematics
curricula, in which community and parental resources and
experiences are not taken into account; and (b) professional
development challenges and strategies. Parental engage-
ment strategies are rarely included in teacher professional
development courses and therefore teachers often do not
know how to effectively involve parents. Musti-Rao and
Cartledge (2004), in agreement with Minner and Hiles
(2005), concluded their study by proposing strategies
identified as appropriate for engaging parents. Among
others, they identified the establishment of clear commu-
nication between teachers and parents as a prominent one.
In strengthening the communication channels between
parents and teachers, Ramirez (1999) suggested the use of
technology, while Barr and Parrett (2003) identified the
importance of taking into account teachers’ and parents’
beliefs. The use of technology can reduce the time needed
for appropriate communication, while it can help teachers
individualize their communication to specific students’
needs. With regard to technology, the present study extends
Ramirez’s (1999) suggestion by employing Twitter, a
contemporary technological tool, as a means to facilitate
communication. With regard to beliefs, the study examines
teachers’ and parents’ beliefs with regard to IBL and
parental engagement.
The importance of parents’ beliefs was clearly high-
lighted by Miller (1989), who stated that: ‘‘The family can
socialize either a very positive or a very negative attitude
toward science. Parents want their children to study science
and mathematics and encourage that through … talk about
topics and problems that involve science and mathematics’’
(p. 177). Further, Barr and Parrett (2003) have identified
teacher beliefs as another barrier in creating relationships
between the home and school. When teachers do not feel
that parental engagement could have a positive impact on
students’ achievement and attitudes, they tend to exclude
parents from the schools’ activities and their children’s
learning (Epstein and Van Voorhis 2001). Often, the beliefs
and expectations between families and educators are not
shared collectively. In order for teacher beliefs to change,
more parental engagement training on how to work with
parents and communities is needed (Hornby 2011).
3 The present study
3.1 The purpose of the study
The purpose of the study was to explore teachers’ and
parents’ beliefs on parental engagement, with a focus on
implementing an inquiry-based modeling approach. We
hypothesized that the interactive learning environment
would have a positive impact on teachers’ and parents’
beliefs, and that it could further inform good practices on
parental engagement. We investigated teachers’ and par-
ents’ beliefs on parental engagement and IBL, and exam-
ined the impact of the learning environment on facilitating
parental engagement. More specifically, we investigated:
(a) teachers’ beliefs on IBL and parental engagement;
(b) parents’ beliefs on innovative approaches in mathe-
matics and science, such as IBL, and their engagement in
school; and (c) the impact of the inquiry-based environ-
ment, comprising EngMEAs and Twitter, on teachers’ and
parents’ beliefs.
3.2 Participants and procedures
The findings presented in this study are part of a larger
research design that included: (a) inquiry-based mathe-
matics and science instruction; (b) integration of engi-
neering model-eliciting activities as a part of the
mathematics and science instruction; and (c) examination
of various forms of parental engagement, including work-
shop participation, participation in classroom activities,
and communication with teachers. In the PRIMAS1 project,
a longitudinal four-year study, 62 teachers participated in
professional development courses and were provided with
teaching materials for integrating IBL in their day-to-day
teaching practices.
The present study followed three of these teachers, who
worked in two sixth grade classes from one public K-6
elementary school in the urban area of Nicosia, the capital
of Cyprus. One class of 22 and one class of 19 eleven-year-
olds, their parents, and the three teachers worked on the
‘‘Water Shortage’’ activity, during the second year of the
project. The activity was the third one in a sequence of four
1 PRIMAS, Promoting Inquiry Based Learning in Mathematics and
Science, focuses on enhancing students’ inquiry skills in mathematics,
science, and engineering (e.g., decision making) and on exploring
students’ development of modeling competences.
Facilitating parental engagement in school mathematics
123
modeling activities that were implemented. All activities
required students to develop models for solving engineer-
ing-based problems. Chronologically, the order of the
activities was: ‘‘Office Spaces,’’ ‘‘House Temperature,’’
‘‘Water Shortage,’’ and ‘‘Bridge Design.’’ Parents were
engaged in two of the activities, namely ‘‘House Temper-
ature’’ and ‘‘Water Shortage,’’ and the results from their
engagement in the second activity are presented here.
Results from the other activities have been reported else-
where (see English and Mousoulides 2011).
3.2.1 Teachers’ and parents’ workshops
Prior to working with modeling activities in their class-
rooms, all 62 teachers attended three 5-h workshops in
afternoon or Saturday sessions. More detailed information
on the structure and the implementation of the PRIMAS
professional development courses can be found in other
contributions in this volume (e.g., Maass and Doorman
2013; Dorier and Garcıa 2013). A fourth workshop focused
on the use of Twitter and on parental engagement good
practices. Parents participated in two workshops: one that
focused on IBL in mathematics and science; and a second
on the use of Twitter. Out of the 41 parents who were
invited to participate, only 28 accepted the invitation.
Seventeen parents held university or college degrees (10
females and 7 males), while the remainder had earned high
school degrees (6 females and 5 men).
The workshops were designed and conducted by PRI-
MAS personnel. During workshops, teachers were actively
involved as they shared questions, suggestions, and
examples from their own practice. Some teachers experi-
enced in working with modeling activities shared the
challenges and constraints they faced in implementing
model-eliciting activities in their classrooms. Participating
parents expressed their willingness to learn more about IBL
and how IBL approaches might improve students’
achievement and attitudes towards mathematics and sci-
ence. They also welcomed the PRIMAS initiative, as an
opportunity to explore with researchers and teachers
appropriate ways to be engaged in their children’s learning.
The first workshop (for both parents and teachers) pro-
vided an introduction to IBL and parental engagement.
Emphasis was given to effective inquiry instruction that
requires a balance of teacher guidance and student initia-
tive, as teachers make the decisions about when and how to
foster student responsibility depending on students’ prior
experience with inquiry and the difficulty of inquiry tasks.
A discussion on appropriate strategies for parental
engagement also took place during the first workshop.
During the second and third workshop teachers were
introduced to model-eliciting activities and worked with
PRIMAS materials. Teachers had opportunities to work in
small groups, in which they discussed appropriate ways to
implement open-ended, and student-centered activities.
A more detailed presentation of model-eliciting activi-
ties and an introduction to the ‘‘Water Shortage’’ activity
took place during the fourth workshop. Teachers and par-
ents formed groups and worked on the activity. Teachers
formed groups and reflected on possible ways of imple-
menting the activity, while parents formed their own
groups, trying to find possible ways to be engaged during
the implementation of the activity. In the second part of the
workshop participants (teachers and parents) were intro-
duced to Twitter and how it could be used in the mathe-
matics and science classrooms. Twitter is an online
technological tool which can break down the rigid class-
room schedule barriers and allow teachers, students, and
parents to collaborate. Participants familiarized themselves
with Twitter; they created accounts, shared tweets (mes-
sages), followed others, sent direct messages, and created
lists. Parents and teachers were also introduced to a free
service for shortening website links (urls) (as tweets are
limited to 140 characters, users often have to shorten long
urls).
3.2.2 The implementation of the ‘‘Water Shortage’’ activity
The ‘‘Water Shortage’’ activity (see Appendix) entailed:
(a) a warm-up task comprising a mathematically rich
‘‘newspaper article’’ designed to familiarize the students
with the context of the activity; (b) ‘‘readiness’’ questions
to be answered about the article; and (c) the problem to be
solved, including the tables of data. This activity asked
students to assist the local authorities in finding the best
country for supplying Cyprus with water. As water short-
age was one of the biggest problems Cyprus faced, students
were very familiar with the problem situation.
The activity was implemented by the author and the
classroom teachers. Activity implementation lasted
3 weeks. Working in groups of three to four, the children
spent five 40-min sessions in solving the activity. Two
sessions took place during the first week, two during the
second week, while the last session took place during the
third week of the implementation.
During the first two sessions the children worked on
the newspaper article and the readiness questions and
familiarized themselves with Google Earth and spread-
sheets (software used in creating the models appropriate
for solving the activity). During the first session students
individually read the newspaper article and answered the
related questions. They then discussed in groups the
importance of water shortage and submitted a relevant
tweet (one Twitter account was created for each group of
N. G. Mousoulides
123
students2). Twelve parents commented on students’
tweets, by agreeing that this was indeed among the
country’s most important problems and by providing
additional sources of information. During the second
session students reviewed the parents’ comments. Stu-
dents accessed the provided resources and reached a
conclusion on the importance of the water shortage
problem. They were then introduced to Google Earth.
Core functions and commands of the software were pre-
sented and discussed with students, with a focus on
commands like ‘‘Fly to’’ for visiting a place, ‘‘Add
Placemark’’ and ‘‘Ruler’’ for calculating the distance
between two points, and ‘‘Path’’ for drawing a path
between two points. In contrast to regular maps, Google
Earth could help students in making accurate calculations,
being precise in drawing tanker routes, and in observing
each country’s ports and landscape. Since the great
majority of students were familiar with spreadsheets no
specific introduction to the software was provided.
Students worked on solving the problem in the next two
sessions. They developed a number of appropriate models,
which they shared with their teachers and parents. During
model development students were prompted by teachers to
share their ideas and their models with the parents. To better
facilitate communication a public Wiki was created, in
which students could easily upload their files and docu-
mentation, and share links to their files by sending tweets to
the parents. Almost all parents provided feedback, by
replying to these tweets. During model development parents
and teachers sent more than eighty tweets, a quite impres-
sive number. However, the majority of these tweets (around
80 %) just encouraged students to continue the good work
(e.g., ‘‘Your solution is very good; continue like this’’),
while only few tweets (around 20 %) provided constructive
feedback and identified weaknesses in students’ models
(e.g., ‘‘There is an error in the Excel file. Check your cal-
culations!’’ ‘‘You did not use port facilities in your model.
Why?’’). During the last session students wrote letters to
local authorities, in which they documented their models/
solutions. The activity ended with a class discussion, which
focused on the key mathematical ideas and relationships
students had generated while working on the activity.
3.2.3 Interviews
The three teachers (2 females and 1 male) and six parents
(3 females and 3 males) who were randomly selected
participated in individual interviews that took place after
the activity implementation. Each interview lasted between
45 and 60 min and all interviews were audio recorded and
later transcribed.
Semi-structured interviews (Corbin and Strauss 2008)
were used to allow the researchers to be flexible and adapt
the questions to each particular interview session. Three
areas of interest, following the research questions of the
study, were investigated during the interviews: (a) partici-
pants’ (teacher or parent) beliefs on IBL and the imple-
mentation of the EngMEA; (b) parental engagement in
mathematics and science, with an emphasis on IBL; and
(c) participants’ experiences with regard to collaboration
and communication during the activity implementation.
With a list of topics to cover and suggested questions the
researchers introduced the topics of conversation and
through questions steered the course of the interview. The
questions that guided the interview protocol are presented
in Fig. 1.
3.2.4 Data analysis
After the interviews were transcribed, the author and one
teaching assistant examined the transcripts for themes.
With each interview, the researchers followed an open data
exploration and theoretical sampling technique (Corbin and
Strauss 2008), which encouraged the gathering of data
based on evolving concepts, to elucidate the varying
dimensions of beliefs on IBL and parental engagement
among the teachers and parents participating.
How do you feel about inquiry in the mathematics and science classroom?
How do you evaluate the possible contribution of IBL in studentlearning outcomes in mathematics and science?
What is your opinion on the use of modeling activities in themathematics and science curriculum?
Can you remember a positive and a negative experience in workingwith IBL and inquiry activities in your classroom?
Did you have any professional development courses on IBL andmodeling?
What do you think of parental engagement?
Did parental engagement assist you during the implementation of the modeling activity?
Did this experience affect your attitudes towards IBL and/orparental engagement?
Did you find this setting appropriate enough for your engagementin your child learning at school and home?
How did you find the communication between you and thestudents? Between you and the teachers?
Was engaging in school mathematics a positive or a negative experience for you?
What else would you like to experience as part of your engagementin school?
Fig. 1 The interview questions
2 Students’ groups and parents’ Twitter accounts were ‘anonymous’
(Parent 1, Parent 2, … Student Group 1, etc.) so as to better facilitate
the process. Since some parents did not participate, we did not want to
exclude their children from being actively involved in the activity.
Further, we aimed to avoid direct communication between parents
and their child only.
Facilitating parental engagement in school mathematics
123
Following Corbin and Strauss (2008), the two major
levels of coding—open coding and axial coding—were
employed. At the beginning of coding interview data,
researchers were engaged in the process of open coding or
‘‘breaking data apart and delineating concepts to stand for
blocks of raw data’’ (Corbin and Strauss 2008, p. 195).
This approach allowed for exploration of the ideas and
meanings that were contained in the raw data, and resulted
in creating codes. In determining the potential codes, the
researchers had discussions regarding the theoretical
framework that guided the study and the themes that arose
in the data collected through the interviews. At first, both
researchers worked on providing codes for the same
interview. In a discussion that followed, different inter-
pretations of the data were discussed until we had a con-
sensus. Once codes were created using open coding,
researchers proceeded to analyze them through the process
of axial coding. This higher level of coding enabled
researchers to identify the connections that existed between
codes and to build families of codes (themes). Axial coding
was done by using AtlasTI, a content analysis tool designed
for qualitative assessment, where themes were identified
and clustered. Examples of the codes generated are pre-
sented in Table 1.
4 Results
The presentation of the results is structured around the
three research questions that guided the study. Within each
research question, the results are presented in terms of the
themes that arose from the analysis of the data. With regard
to the first question (What are teachers’ beliefs about
inquiry-based mathematics and science and parental
engagement?), the results are organized in two themes,
namely the goals of inquiry in the mathematics and science
teaching and the teachers’ beliefs with regard to parental
engagement in school mathematics and science.
Results that revealed parents’ beliefs about inquiry-
based mathematics and science and engagement in inquiry-
based problem solving (second question) are organized in
two themes, namely parents’ beliefs on the role of inquiry
and beliefs on their engagement in school mathematics and
science. Finally, the examination of the impact of the
learning environment on parental engagement (third ques-
tion) is presented.
4.1 Teachers’ beliefs about inquiry-based mathematics
and science and parental engagement
4.1.1 Goal of inquiry in mathematics and science teaching
Teachers’ responses to the questions related to the goals of
an inquiry-based approach could be summarized in three
broad categories: (a) student cognitive goals and teaching
effectiveness; (b) student affective goals; and (c) con-
straints of using IBL.
Teachers reported positive comments on the impact of
IBL in students’ cognitive gains. They reported that stu-
dents had opportunities to design experiments, handle
variables, set hypotheses, and use their critical thinking,
decision-making, and problem-solving skills. This empha-
sis on inquiry and critical thinking was evident in one
teacher’s comment: ‘‘This open approach got the children
to think critically, set their own questions to reach a
solution, and become independent in solving quite complex
problems.’’ A second teacher reported: ‘‘I really enjoy
teaching when I have the feeling that students work like
real mathematicians. This is the only way to teach higher
order thinking and problem-solving skills.’’ She further
referred to an impact on herself: ‘‘I spent a lot of time in
preparing the activity. It was challenging, and even helped
Table 1 Sample codes, definitions, and examples
Code Description Example
Active parental engagement Teacher/parent makes direct/indirect reference to
specific actions that are considered to promote
active parental engagement and consequently have
an impact on the teaching–learning process
‘‘Workshops helped parents to get involved […]
It helped them realize that […] their role was
crucial […] to the success of the activity.’’
Student cognitive goals Teacher/Parent states or alludes to a belief that
inquiry-based learning has an impact on student
cognitive goals
‘‘This open approach got the children to think
critically, set their own questions to reach a
solution, and become independent in solving
quite complex problems.’’
Student affective goals Teacher/Parent states or alludes to a belief that
inquiry-based learning has an impact on student
affective goals
‘‘I have students who rarely participate in more
traditional lessons; their behavior in PRIMAS
activities is completely different.’’
Modeling referencing Teacher makes direct/indirect reference to (aspects
of) the model-eliciting activity and its positive
impact on parental engagement
‘‘This approach was a good example. We clearly
need more good examples in engaging parents
in mathematics.’’
N. G. Mousoulides
123
me to increase my own mathematical knowledge […]
although I sometimes had the fear that students might ask
something I could not answer.’’ The third teacher added: ‘‘I
strongly believe that my teaching is more effective now.
Perhaps I do not cover so many curriculum objectives, but I
am impressed with how well students work with the
activities and solve problems.’’ She continued: ‘‘I am
confident that you [PRIMAS personnel] should promote
these activities [referring to PRIMAS materials] to other
teachers as well. They [teachers] will benefit and their
[teaching] approach will change.’’
Teachers were also very emphatic in commenting on the
affective goals. They mentioned that such approaches could
help students in developing ‘‘a love for mathematics and
science’’ and getting students ‘‘excited about problem
solving.’’ One teacher commented: ‘‘I really like watching
average [ability] students working so hard. It is obvious that
they enjoy what they are doing … and their results are often
impressive.’’ A second teacher added: ‘‘I have students who
rarely participate in more traditional lessons. Their behavior
in PRIMAS activities is completely different; they repeat-
edly told me that they really like these activities.’’
Teachers also reported a number of concerns regarding
the constraints related to using IBL approaches. Time
constraints were mentioned in all teachers’ responses. For
instance, a teacher commented: ‘‘I wish I could use more
inquiry in my lessons, but there is so little time for extra-
curricular activities. I assume we are lucky because our
principal and inspector are in favor of such approaches in
mathematics … more time would be much appreciated.’’ A
second teacher commented on the ‘fragmented nature’ of
the curriculum. He said: ‘‘At least in elementary school we
can integrate subjects and adopt a more interdisciplinary
approach. Things are worse in middle school. My wife
[also a PRIMAS teacher] has great difficulties in using
modeling activities in her lessons. How can you complete
even a part of it [modeling activity] in 45 min?’’
4.1.2 Teachers’ beliefs on parental engagement
Teachers shared various ideas on how to engage parents in
school mathematics and science. They reported that
parental engagement was important in improving a
school’s results, and that parents should help their children
at home with their homework. One teacher mentioned that
it was the school’s responsibility to teach parents various
ways of helping their children with their homework. All
three teachers stressed that parental engagement was
important for student success in school and they underlined
that the great majority of parents in their school expressed
their willingness to be more engaged.
Teachers explicitly expressed that active involvement
was more than volunteering at school events. Teachers also
acknowledged that practices like those adopted in PRIMAS
provided good examples of active parental involvement.
One teacher commented: ‘‘Moving beyond workshops [for
engaging parents] was appropriate. Parents had ideas to
discuss with their children at home … some of my students
were so active and almost every day we had discussions
based on their interactions with their parents at home.’’ A
second teacher added: ‘‘Workshops helped parents to get
involved, and assigning parents with specific tasks was
appropriate. It helped them realize that everyone was val-
ued and their role was crucial and critical to the success of
the activity. But of course this was not easy; only half of
them participated, right? And I am not sure how many of
them spent much time at home finding resources and pro-
viding accurate feedback to students’ solutions.’’ Another
teacher shared the same belief, that parental engagement
was an ongoing process and that careful planning and
organization was needed.
Another theme that arose in teachers’ interviews was the
impact of parental engagement on students’ growth and
involvement. The great majority of students were actively
involved in the activity and tried their best in solving the
problem. Teachers reported that the activity could not be
the same without the active engagement of the parents,
which was clearly positive and constructive. Teachers
further proposed: ‘‘This approach was a good example. We
clearly need more good examples in engaging parents in
mathematics, which, I believe, will be beneficial for stu-
dents’ achievement.’’ Another teacher pointed out: ‘‘Is
there a better way to engage parents both at school and
home? I do not think so. I am confident that such appro-
priate engagement practices will help their children to
improve their grades and attitudes towards mathematics
and science.’’
4.2 Parents’ beliefs about inquiry-based mathematics
and science and their engagement in inquiry-based
problem solving
4.2.1 Parents’ perceptions on the role of inquiry
All parents welcomed this type of activity in the mathe-
matics and science classrooms. They explicitly mentioned
that such activities were challenging, not only for their
children, but also for them. One parent who was actively
involved in the activity commented: ‘‘I was always good in
math and I never had any problems in helping my son with
his homework. But this activity opened new horizons for
me. I did not have to ask every day: ‘What do you have for
homework?’ I frequently visited the Wiki and commented
on students’ tweets. It was great! And my son also liked it
very much. Believe it or not, he even discussed the activity
with his cousins.’’ Another parent, a civil engineer
Facilitating parental engagement in school mathematics
123
professional, expressed: ‘‘Well, students were invited to act
like real engineers … taking into account real constraints,
working with complex data, drawing assumptions. Ok, it
was not like the actual problem, but I am impressed how
well they did.’’ In addition, a third parent commented:
‘‘Such activities will help our children to develop important
skills, needed beyond school … in the society. I am not
sure that all of my colleagues have these skills [works as a
salesperson] … I am very happy that we use such
approaches in our school.’’
Less positively, two parents mentioned that the activity
was interesting, but rather difficult. One parent mentioned
that the activity was quite complicated, even for him. He
added that sometimes his daughter was frustrated and
confused: ‘‘Well, I could not know for sure that the solution
was correct, and that was somehow annoying. Perhaps
more guidance from you [PRIMAS personnel] and the
teacher could be helpful.’’
4.2.2 Parents’ beliefs on parental engagement
To improve parental engagement in schools, parents
seemed to agree unanimously that good communication
and active engagement were key. Parents suggested a
number of different events and strategies that could assist
all parents to be engaged. One parent noted: ‘‘Attending
lessons is not bad, but it cannot be the only way to engage
parents. I enjoyed the two workshops very much, although
I had to leave from my work earlier … we should have
[such] workshops more often.’’ Another parent added:
‘‘Working with our children was great. Perhaps we could
have Math Afternoons or Nights to discuss with our chil-
dren and teachers at school math and science problems. I
am sure she [her daughter] would love that.’’ Another
parent mentioned a strategy currently employed in the
school: ‘‘Last year children had to work on two projects.
Those projects were not focused on math, but required
some math and science. I would like to see more projects
like these, in which I can work with my child at home.’’
All parents underlined the necessity for open commu-
nication in order to improve parental engagement. One
parent noted that open communication was the key to
accessibility. He stated: ‘‘Teachers should be nice to par-
ents, welcome them when they show up, and not make
them feel like they are intruding.’’ Another parent added:
‘‘Parents should feel comfortable enough with the teachers
to ask content-related questions, and even spend time on
working on activities, if we are expected to assist our
children at home.’’ A third parent highlighted the impor-
tance of constant communication: ‘‘Every parent wants to
be involved in his child’s school … you only need to know
that you are welcome and that you can freely communicate
with teachers. An appropriate atmosphere is needed for
successful parental engagement. I guess we are lucky to
have it here.’’
Although quite satisfied with the situation, parents
explicitly mentioned that it was expected for school and
teachers to do more in order to enhance parental engage-
ment. It was revealed that a school’s climate and culture
impacted the overall effectiveness of parental engagement
efforts in a significant way. From parents’ responses a
number of suggestions emerged for what schools should do
in order to better encourage and enhance parental
engagement. One parent mentioned that schools should
promote parental engagement using various methods, and
not just expect parents to be engaged. She said: ‘‘Schools
and teachers must actively seek and promote parental
engagement. Not all parents are engaged by default.’’
4.3 The impact of the learning environment on parental
engagement
All teachers emphasized the positive impact of the ‘‘Water
Shortage’’ modeling activity. At first, teachers indicated
that PRIMAS materials had an impact on the way they
structured their lessons in mathematics and science and
consequently had an impact on parental engagement.
Teachers reported that in this new setting there was more
focus on discussion, both in the classroom and at home (as
reported by parents), more time for group work, and stu-
dents’ cooperative learning roles (with their peers at school
and with parents at home) improved. Teachers reported the
‘‘Water Shortage’’ activity to be a good example of active
student involvement, in which discussion fostered oppor-
tunities for critical thinking. For instance, one teacher said:
‘‘Students had to collect information and data from multi-
ple sources … that helped them to further develop their
critical skills. It was very challenging for them when some
parents suggested somehow contradictory [however cor-
rect] resources. That was real problem solving!’’ Two
parents also shared the same feeling; they mentioned that
parents also got involved in real problem solving, since
they had a crucial role in providing students with extra data
and resources.
A second teacher characterized the activity as ‘pure
inquiring.’ He explained: ‘‘I was so impressed to see how
many questions students asked … well, some were naive,
but in general they asked very precise and appropriate
questions.’’ Another teacher added: ‘‘In the first two ses-
sions some students were somehow afraid to even answer a
question, because they thought they were going to be
wrong.’’ Parents also reported that questions were central
while working with their children at home. A parent noted
that she encouraged her daughter to ask questions, during
class discussion, but also using Twitter, since ‘‘precise
questions are important for understanding a real problem.’’
N. G. Mousoulides
123
Another dimension of teachers’ comments on the
appropriateness of the learning environment focused on the
use of technology. All three teachers described technology
as having a very positive impact on students’ solutions and
on the communication between teachers, students, and
eventually parents. With regard to the use of Twitter, one
teacher described his initial worries and how his beliefs
gradually changed as: ‘‘To be honest, during the workshop
I was very skeptical. I could not think of many ways to use
Twitter. At the beginning of the activity I was impressed by
parents’ involvement and how that [involvement] benefited
students’ work … I really liked the way Twitter was used
and I will continue using it in my lessons, when possible.
Well, this is obvious from the number of my tweets! [He
submitted a significant number of tweets, replying to both
students’ and parents’ messages].’’ Another teacher added:
‘‘I love it! It is great when students and parents are
involved. I had the impression that the lesson was ongoing,
24 h a day. This is teaching!’’
In line with teachers’ comments, all six parents explicitly
highlighted how the activity assisted in building a partner-
ship climate between parents and teachers. The activity
opened a whole new space for fruitful collaboration and
created better communication channels among parents,
teachers, and children. ‘‘I had the feeling that we [parents
and teachers] were equal partners,’’ one parent commented.
She continued: ‘‘It was far better than sitting at the back [in
the classroom] and watching a lesson. We were actively
involved and we had constant communication with our
children and the teacher. It was really good.’’ Another
parent added: ‘‘I was following the teacher’s comments and
suggestions and tried to build on these, by discussing at
home with my child … yes, it helped the communication
between all of us.’’ A third parent commented: ‘‘I found
those messages [tweets] a much more appropriate method
of communication than signing tests … I knew exactly what
my child did in the activity, and even better I could now
observe the process, not only the results. I would definitely
prefer [my child] to have more activities like this one.’’
Another parent claimed: ‘‘Such activities [‘‘Water Short-
age’’ activity] are one of the best ways to engage parents,
because their children are also engaged. When the children
are excited and discuss their mathematics and science work,
parents are more inclined to be engaged.’’
5 Discussion
The purpose of this study was to examine teachers’ and
parents’ beliefs with regard to parental engagement in
mathematics and science teaching, with a focus on mod-
eling as an inquiry-based approach. The study aimed to
inform research by exploring teachers’ and parents’ beliefs
on collaborating during the implementation of a modeling
activity, and by examining how a communication-rich
environment could facilitate parental engagement. Building
on previous research and by linking teachers’ IBL-related
beliefs and practices to their beliefs on parental engage-
ment, and to parents’ beliefs, we have gained new infor-
mation about how model-eliciting activities might serve in
improving teachers’ and parents’ partnership climate and
how positive relationships between them might be related
to improved students’ engagement. In this section, con-
clusions stemming from the results are discussed, followed
by implications for parental engagement practices and
recommendations for further research.
The first aspect of the study focused on examining
teachers’ beliefs with regard to IBL and parental engage-
ment. The results, in line with previous research, supported
the expectation that inquiry-based approaches are likely to
affect teachers’ and parents’ partnership in mathematics
and science and possibly student outcomes (Epstein et al.
2009). Further, the activity used here facilitated students’
engagement in a creative and innovative problem-solving
approach and increased students’ awareness of the different
aspects of real-world problems (English and Mousoulides
2011). The environment generated provided opportunities
for students to elicit their own mathematical and scientific
ideas as they worked on the problem, and to collaborate
with their teachers and parents. The study also showed that
teachers welcomed a refocus on their teaching, so as to
better respond to students’ ideas and needs, and parents
responded positively to their new roles as engaging part-
ners in their children’s learning.
During interviews, teachers emphasized the importance
of IBL and expressed their positive beliefs towards IBL,
although they identified challenges, demands, and other
institutional constraints. Teachers reported that adopting a
modeling perspective provided an opportunity for a more
interdisciplinary, real-world-based approach, in which
students’ role was central and parents’ impact had the
potential to be positive. With regard to parental engage-
ment, teachers expressed positive beliefs. Clearly, teachers
can play a significant role in bridging the gap between
home and school, and their beliefs are important in deter-
mining parental engagement in their classrooms. Positive
teachers’ beliefs and attitudes are needed to maintain the
best possible parental engagement, and to build mutual
understandings and collaboration for the improvement of
mathematics and science teaching.
The second aspect of the study focused on parents’
beliefs on their engagement in school mathematics and
science, and on their beliefs on IBL. Interviews with par-
ents revealed that they held positive beliefs and attitudes
towards innovations in mathematics and science, such as an
IBL modeling perspective.
Facilitating parental engagement in school mathematics
123
The third aspect of the study focused on the impact of the
learning environment on parental engagement. An essential
component of the learning environment was the enhance-
ment of communication among the key players. The use of
Twitter not only facilitated this communication, but also
assisted in generating a safe, shared knowledge space, in
which parents gained insights into their children’s learning,
and assisted the children in developing better solutions. This
new setting also allowed teachers to find more appropriate
methods to engage parents beyond classroom observations
and meetings. Students accessed a whole new space, by
having their parents and teachers as partners in challenging
problem solving, beyond the traditional classroom bound-
aries (English and Mousoulides 2011).
In extending the findings of the present study, the next
research steps in involving Twitter in parental engagement
programs (in IBL in mathematics and science, and beyond)
should take account of a number of constraints. First,
involving larger numbers of parents is not a solution; this
might result in a complete avalanche of tweet ‘data’ that
would be impossible to cope with or to identify how par-
ents’ engagement assisted students and resulted in improved
models and solutions. Second, analysis of parents’ data
should carefully take into consideration issues related to the
representativeness of the tweeters, and avoid only focusing
on more articulate and interested parental groups.
There were a number of limitations to this study, which
therefore does not allow us to proceed to many general-
izations. One limitation was the number of the participating
teachers. Only three out of the 62 teachers who participated
in PRIMAS’ professional development courses in Cyprus
participated in this study. Further, all three teachers came
from one high socioeconomic status school. However,
although biased, we can claim that the sample of the three
teachers provided useful insights into teachers’ beliefs with
regard to IBL and parental engagement, and thus met the
needs of the study. A second limitation was the number of
parents involved in the interviews. Due to time constraints,
only six out of the 26 parents involved in the study were
interviewed. Although the six-parent sample was randomly
selected and the beliefs reported in the interviews could be
generalized for the whole sample, we cannot claim that the
activity had a significant impact on their beliefs. Further,
although a limitation, the fact that the majority of parents
appear to be highly educated might also lead to a recom-
mendation for further research amongst less educated
parents, and in schools with lower socioeconomic status. It
would be beneficial to examine how parents’ education
might impact their engagement in school mathematics and
science, and which strategies might better support the less
advantaged parents.
In addition, taking into account the qualitative nature of
the study, and therefore the inability to proceed to further
generalizations, we can only make claims as to the success
and the novelty of the implementation of the modeling
activity as a means to improve parental engagement and to
turn teachers’ and parents’ beliefs into more positive ones.
So, while the limitations are present, it is believed that
much could be gained from examining the impact of the
implementation of inquiry-based modeling activities in
improving parental engagement, as long as the limitations
are made clear at the outset.
Like many other studies, the present study generated
more questions than it answered. Among the new research
questions that can be considered in follow-up studies are:
(a) How might the different levels of interest and/or com-
mitment displayed by different parents or parent groups
impact their beliefs and their communication and collab-
oration with teachers? (b) What are effective strategies to
engage those parents who are not interested or able to
participate? (c) How can different genres of technology be
used to facilitate parental engagement and to improve
parents’ beliefs? (d) If the approach used here is extended
to mathematics and science as a whole what will be the
impact on parental engagement? At least some of these
questions raised are targeted within the PRIMAS project.
While this study presented results from one activity, our
continued research will examine the extent to which the
positive teachers’ and parents’ beliefs and strategies
towards IBL and parental engagement might become
manifest in the teaching and learning of mathematics and
science. The analysis of the data presented here not only
unveiled aspects of effective parental engagement from the
perspective of parents and teachers, but the research has
also revealed characteristics that schools and communities
must possess to help strengthen and sustain parental
engagement.
Unquestionably, students need high-quality instruction
to improve mathematics and science learning. However, if
schools, teachers, and parents work together in creating
appropriate, collaborative environments, they are more
likely to see higher students’ learning outcomes.
Acknowledgments This paper is based on work within the project
PRIMAS—Promoting Inquiry Based Learning in Mathematics and
Science across Europe (http://www.primas-project.eu). Project coor-
dination: University of Education, Freiburg (Germany). Partners:
University of Geneve (Switzerland), Freudenthal Institute, University
of Utrecht (The Netherlands), MARS—Shell Centre, University of
Nottingham (UK), University of Jaen (Spain), Konstantin the Phi-
losopher University in Nitra (Slovak Republic), University of Szeged
(Hungary), Cyprus University of Technology (Cyprus), University of
Malta (Malta), Roskilde University, Department of Science, Systems
and Models (Denmark), University of Manchester (UK), Babes-Bol-
yai University, Cluj Napoca (Romania), Sør-Trøndelag University
College (Norway), IPN-Leibniz Institute for Science and Mathemat-
ics Education at the University of Kiel (Germany). The research
leading to these results/PRIMAS has received funding from the
European Union Seventh Framework Programme (FP7/2007–2013)
N. G. Mousoulides
123
under Grant Agreement no. 244380. This paper reflects only the
author’s views and the European Union is not liable for any use that
may be made of the information contained herein.
Appendix
There is a trouble in paradise: severe water shortage
problem in Cyprus
Part of background information
Nicosia. Alex Chris, a landscape gardener working for
several foreign embassies and private estates in Nicosia,
said many of the capital’s boreholes are now pumping mud.
‘‘I installed one expensive garden with 500 meters of irri-
gation pipe in Nicosia a few months ago,’’ he said. ‘‘Last
week they called to tell me the system had stopped and
their trees and lawns were dying. I found that sludge had
been pumped through the pipes and then solidified in the
heat. It was like cement.’’ […]
Emergency water rationing as well as a request to import
water from nearby countries was ordered as a result of a
severe water shortage due to a drought over the last 4 years.
Reservoir reserves have plunged dangerously low and
desalination plants cannot keep up with a growing demand
for water. Cyprus has two desalination plants running at full
capacity, with a third due to come on stream in June. The
island is increasingly relying on desalinization plants for
water, but they can only provide 45 % of demand, and their
operation is energy heavy. Further, there are several con-
cerns on the environmental impact of their use. […]
Cypriot officials decided to sign a contract with a nearby
country, to import more than 12 million cubic meters over
the summer period starting at the end of June. Officials will
also sign a contract with a shipping company to use oil
tankers for supplying Cyprus with water. The tanker supply
program will continue until a permanent solution to the
problem has been reached.
Sample of readiness questions
1. How many desalination plants are currently in Cyprus?
2. Why did the Cyprus government decide to not build
more desalination plants to cover the country’s water
needs?
3. Which solution did the Cyprus Water Board decide to
adopt for solving the water shortage problem?
The problem
Cyprus Water Board needs to decide from which country
Cyprus will import water for the next summer period.
Using the information provided, assist the Board in making
the best possible choice.
Lebanon, Greece, Syria, and Egypt expressed their
willingness to supply Cyprus with water. The Water Board
has received information about the water price, how much
water they can supply Cyprus with during summer, oil
tanker cost, and the port facilities. This information is
presented below.
Write a letter explaining the method you used to make
your decision so that the Board can use your method for
selecting the best available option not only for now, but
also for the future when the Board will have to take similar
decisions.
Country Water
supply per
week
(metric
tons)
Water
price
(metric
ton)
Tanker
capacity
(metric
tons)
Tanker
oil cost
per
100 km
Port
facilities
for
tankers
Egypt 3,000,000 € 4.00 30,000 € 20,000 Average
Greece 4,000,000 € 2.00 50,000 € 25,000 Very
good
Lebanon 2,000,000 € 5.20 30,000 € 20,000 Average
Syria 3,000,000 € 5.00 30,000 € 20,000 Good
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