Barbie Bungee Jumping, Technology and Contextualised Learning of
Mathematics
Aibhin Bray and Brendan Tangney
Centre for Research in IT in Education (CRITE), School of Education and School of Computer Science & Statistics,
Trinity College Dublin, Dublin, Ireland
Keywords: Mathematics Education, Post-primary Education, Technology, Contextualised Learning.
Abstract: There is ongoing debate about the quality of mathematics education at post-primary level. Research
suggests that, while the capacity to use mathematics constructively is fundamental to the economies of the
future, many graduates of the secondary-school system have a fragmented and de-contextualised view of the
subject, leading to issues with engagement and motivation. In an attempt to address some of the difficulties
associated with mathematics teaching and learning, the authors have developed a set of design principles for
the creation of contextualised, collaborative and technology-mediated mathematics learning activities. This
paper describes the implementation of two such activities. The study involved 24 students aged between 15
and 16 who engaged in the activities for 2.5 hours each day over a week long period. Initial results indicate
that the interventions were pragmatic to implement in a classroom setting and were successful in addressing
some of the issues in mathematics education evident from the literature.
1 INTRODUCTION
Research suggests that, while the capacity to use
mathematics constructively will be fundamental to
the economies of the future, the view that many
graduates of the secondary-school system have of
the subject is fragmented and lacking in context,
leading to issues with engagement and motivation
(Gross et al., 2009; Grossman, 2001). This study
looks at how the affordances of readily available
digital technology can be exploited to create
mathematical activities that address common issues
in mathematics education.
There is strong evidence in the literature that an
approach to mathematics education encouraging
contextualised, collaborative solving of
mathematical problems is beneficial (Hoyles and
Noss, 2009; Olive et al., 2010). Following an
extensive review and analysis of the recent literature
on technology-enhanced mathematics learning
interventions, the authors have devised a set of
guidelines to assist teachers in the design and
delivery of such interventions, a number of which
have been piloted in an experimental learning
environment in the authors’ institution. Following
from these pilot interventions, a larger scale set of
activities has been implemented in a conventional
school setting, the preliminary results of which will
be discussed in this paper.
The overarching research in which this study is
situated follows a design-based methodology
(Anderson and Shattuck, 2012; Mor and Winters,
2007), in which a series of technology-mediated
mathematical tasks are developed in tandem with the
theory and principles that underpin them. The design
principles for the activities are evolving from the
ongoing literature review and classification process,
in conjunction with analysis of empirical findings
from teaching experiments in natural and
exploratory settings.
This paper is consists of two main parts. In order
to contextualise the current research within the
broader field, a literature review and background to
the current work is presented. The paper then
describes a week-long intervention in a conventional
co-educational school setting, involving 24 mixed-
ability students. Preliminary findings from the
intervention will be discussed, along with its impact
on the design principles and future work.
2 BACKGROUND
In order to ground this research within the wider
context, this section includes a literature review of
the general issues in mathematics education, as well
206
Bray A. and Tangney B..
Barbie Bungee Jumping, Technology and Contextualised Learning of Mathematics.
DOI: 10.5220/0004945802060213
In Proceedings of the 6th International Conference on Computer Supported Education (CSEDU-2014), pages 206-213
ISBN: 978-989-758-022-2
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
as specific topics relating to the use of digital
technology in the field. A synopsis of the
development and analysis of the classification
system, and the development of the design principles
and related activities is also provided.
2.1 Issues in Mathematics Education
There is an unfortunately prevalent view of
mathematics as a collection of unrelated facts and
rules, and a related belief that learning mathematics
involves memorisation and execution of procedures
leading to unique, correct answers (Ernest, 1997); an
assumption that mathematics is “hard, right or
wrong, routinised and boring” (Noss and Hoyles,
1996, p. 223). This formal, abstract and assessment
driven approach to mathematics education remains
dominant in many countries (Ozdamli et al., 2013)
contributing to behaviourist and didactic tendencies
in teaching and learning, with an emphasis on
content and procedure over literacy and
understanding. In this context, mathematical
creativity is not prized and students are rarely
encouraged to seek out their own alternative
solutions (Dede, 2010). The authority of the teacher
is perceived as absolute, their job to transmit
information to the students.
Efforts to address some of these issues have met
with limited success. Attempts to introduce problem-
solving and realistic context to mathematics teaching
and learning are particularly pertinent to this
research. However, as Boaler (1993) suggests, such
problems are frequently uninteresting from the point
of view of the students as they are generally
formulated in such a way as to be routine problems
with just a veneer of the ‘real-world’. In an attempt
to reduce complexity, the activities are overly well-
defined, furnishing all of the information required to
solve the problem, without excess. The learner is
reduced to following the standard procedure of
inserting data into appropriate formulae in an
attempt to get the ‘correct’ answer (Dede, 2010).
2.2 ICT and Mathematics Education
The use of digital technologies in mathematics
education has the capacity to open up diverse
pathways for students to construct and engage with
mathematical knowledge, embedding the subject in
authentic contexts and returning the agency to create
meaning to the students (Drijvers, Mariotti, Olive, &
Sacristán, 2010; Olive et al., 2010).
Noss and Hoyles (1996) propose that technology
has the potential to bring meaningful mathematics
into the classroom. It can facilitate an emphasis on
practical applications of mathematics, through
modelling, visualisation, manipulation and more
complex scenarios (Olive et al., 2010).
Many authors contend however, that although
use of technology in the classroom is increasing, its
potential to enhance the learning experience lags
behind its implementation in the classroom (Geiger
et al., 2010; Hoyles and Lagrange, 2010). While
students may engage in the creative use of digital
technologies on a daily basis, they do so less
frequently in an educational context (Oldknow,
2009; Pimm and Johnston-Wilder, 2004).
Jonassen, Carr, and Yueh (1998) contrast
technologies that attempt to instruct the learner, with
what they describe as mindtools - technological tools
that students learn with, rather than from – which
support knowledge construction by engaging them
in critical thinking. Thus technology becomes a
mediator of the learning experience, facilitating
reflective, discursive and problem-solving skills.
In this research, we are attempting to facilitate
the use of digital technology as ‘mindtools’ to
encourage the development of the desired skill set
by scaffolding implementation through the emerging
design principles.
2.3 Analysis of Empirical Interventions
At the outset of the research process, it became clear
that a system of classification would be beneficial in
order to put a framework on the current trends in the
literature relating to technology usage in
mathematics education.
An ongoing, systematic review of recent
literature in which technology interventions in
mathematics education are described is used as the
foundation of such a system of classification, a
detailed analysis of which can be found in (Bray and
Tangney, 2013b). Trends emerging from the
analysis of the classification are used in conjunction
with a broader literature review, to inform a set of
design principles for the development of
interventions in the field.
Through the classification it is evident that a
wide range of technologies are being researched in
different environments, with different agendas and
from varying theoretical standpoints. What most
interventions have in common is a trend towards
social constructivism and a desire to create engaging
environments in which the technology is used to
increase the students’ interest, motivation and
performance. The pervasive perception of
mathematics education emerging from the papers
BarbieBungeeJumping,TechnologyandContextualisedLearningofMathematics
207
focuses on understanding of relations, processes and
purposes, as opposed to the requirement to learn a
fixed body of knowledge. There is a move towards
connection, coherency and context as important
aspects of mathematics education that can be
facilitated by technology.
2.4 Emerging Design Principles
Analysis of the classified papers, along with a
general literature review, provides the theoretical
foundations for a set of design principles for the
development of innovative, technology-mediated,
mathematical activities. Using a first iteration of the
design principles, a number of activities have been
devised and trialled in an exploratory environment.
The results of these pilot studies have fed back into
theoretical foundations of the research, leading to
refinement of the classification and design
principles. Our intention in developing these
guidelines and activities is to increase student
engagement and motivation with mathematics and to
increase teacher awareness of how to support
learning within these scenarios.
The design principles resonate with a view of
mathematics as a problem-solving activity and of
mathematics education as involving students in
constructing their knowledge via the social
formulation and solution of problems. A need for the
development of tasks that are transformed through
the use of technology, providing contexts that are
relevant and of interest to the students, and which
have compelling goals is evident (Confrey et al.,
2010; Laborde, 2002; Oldknow, 2009).
Technologies that outsource the burden of
computation have proven to be an interesting area of
research, not only improving speed and accuracy of
students engaged in procedural tasks, but also
allowing increasing emphasis to be placed on
meaning as opposed to routine operation (Geiger et
al., 2010; Oates, 2011). The use of a variety of
accessible, free technologies is an important issue,
not only due to matters of equity, but also to
engender flexibility amongst students and teachers
(Oldknow, 2009; Sinclair et al., 2010).
2.5 Initial Learning Activities
A number of activities have been designed in
accordance with the design principles, and have
been piloted with groups of students and teachers in
an exploratory learning centre, Bridge21, at the
authors’ institution. The centre is designed to
support a model of collaborative, technology-
mediated and project-based learning (Lawlor et al.,
2010). The teacher is seen as orchestrator rather than
director of the learning, building on a model of peer
learning and collaboration originating in the patrol
system of the World Scout Movement (Bénard,
2002). Post-primary students are released from
school to attend workshops in the centre, of between
four and five hours duration.
The activities that have been tested to date
include The Human Catapult (projectile motion,
functions, angles and velocity) and The Scale
Activity (estimation, orders of magnitude and
scientific notation) described in (Bray and Tangney,
2013a), as well as Probability and Plinko
(independent events, normal distribution, Pascal’s
triangle, probability, binomial distribution), the Pond
Filling Activity (problem-solving, estimation and
volume) (Tangney and Bray, 2013), and the Barbie
Bungee (collecting, representing and analysis of
data, linear functions, line of best fit, correlation,
extrapolation). The interventions have provided data
relating to the practicality of the tasks and a starting
point from which to begin the iterative process of
development.
The results of the pilot interventions have
provided the justification for further investigation in
authentic classroom environments. This study
reports on initial trials in an actual classroom setting.
3 THE INTERVENTION
The school in which the study took place is a co-
educational private school in an urban area and is
one of a network of schools cooperating with our
institution in an attempt to adapt the Bridge21 model
for use in mainstream schools. These schools are
favourably disposed towards a collaborative,
technology-mediated approach. In addition,
participating students have had prior exposure to
workshops in which they have been introduced to
the Bridge21 model of learning, thus increasing their
understanding of the processes involved in
teamwork and project-based learning. When it
comes to tackling the mathematical activities, they
should therefore be well versed in the methodology
and in a position to concentrate on the task.
The school in this study has re-modelled its
approach to teaching and learning in line with the
Bridge21 methodology. In light of this, the year 10
(age 15/16) timetable has been restructured in order
to accommodate a 2.5 hour block of curriculum-
related project work in the middle of the day. For the
Contextual Mathematics intervention the 1
st
author
CSEDU2014-6thInternationalConferenceonComputerSupportedEducation
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had access to students for this project block each day
for one week. During this period, the author acted as
primary teacher, or facilitator, with one classroom
assistant. The class consisted of 24 students (12 male
and 12 female), of mixed ability, who were assigned
to 6 groups of 4 students each. The groups were
assigned in order to balance abilities and gender.
The environment was made up of two adjoining
rooms with double doors between them. Each team
had an allocated area, or workstation, with access to
at least one computer, where they could work
together. Laptops, cameras and other props were
provided by the researchers. Students had
permission to leave the school premises when the
activity required.
3.1 Methodology
As described in the introduction, the overarching
research project employs a design-based
methodology (Anderson and Shattuck, 2012; Mor
and Winters, 2007) whereby the mathematical
activities and the theory that underpins them are
developed in a complimentary and iterative manner.
Data from individual case studies, collected by way
of observation, semi-structured interview and
questionnaires, helps to inform and refine both the
design principles and the activities themselves.
The Mathematics and Technology Attitudes
Scale (MTAS) (Pierce et al., 2007) was used as a
pre- and post-questionnaire, giving a quantitative
measure of confidence levels in mathematics and
technology, behavioural engagement, affective
engagement, and attitudes to using technology in
mathematics. Qualitative data was gathered from
student journals, written comments and a semi-
structured interview with 5 of the 6 team leaders. At
this stage only preliminary results are available from
the qualitative data as the process of coding and
theming is in its early stages.
3.2 Outline of the Activities
In this section, an outline of the weeks’ activities is
provided. Every day followed the same general
structure, based on the learning model developed in
the Bridge21. Each session began with an initial
plenary discussion in which previous work was
reviewed and the mathematical problems and
activities for the day were presented. This was
followed by a team planning, after which team-
leaders met to discuss possible solution strategies
with the facilitator and assistant. Once the plans
were approved, the groups were free to implement
them. As the teams worked, the facilitators
interacted with the students, scaffolding their
exploration of the mathematics and technology. At
the end of the session, each group presented their
work, discussing what individual team members had
been responsible for, what had been accomplished,
and what mathematics they had understood. After a
final whole group discussion, take-home problems
were assigned. These were short questions designed
to be thought provoking and interesting, and
requiring the students to be creative with their
solving strategies.
The first day consisted of warm-ups, team-
building activities and Fermi-type problems. These
are exercises in estimation and approximation,
encouraging problem-solving and mathematical
creativity. The ‘correct’ answer is not the primary
goal, and many approaches to the solution are
acceptable. Examples used include the following.
Estimate the number of blades of grass in
the local park.
Estimate the average walking speed of
people outside the local park.
Estimate how many seconds old you are.
The teams had permission to use the internet,
giving them access to Google maps, grid overlay
tools etc. Each team was also furnished with a
measuring tape and a camera.
Day 2 marked the beginning of the program of
activities that were the primary focus of this study.
Although the concept of a Barbie Bungee is not a
new in mathematics education, embedding it a
loosely scaffolded, technology-mediated and team-
based environment has lent it a novel and innovative
perspective.
Each group was provided with a Barbie doll, a
box of rubber bands, a camera, a laptop with the free
video analysis software Kinovea and a spreadsheet
program. They were asked to estimate the number of
rubber bands needed to give Barbie an exhilarating,
but safe jump, from a first floor window. Trial and
error was not permitted, and they were not initially
allowed to leave the room to measure the distance of
the fall. Particular incentive was given by making
the testing of their hypotheses into a competition.
The groups used diverse methods of tying the bands
and adding weights to the dolls. All but one of the
teams made use of the available digital technology
to video the bouncing Barbie in order to accurately
capture the distance she dropped. Each group
recorded their data in a spreadsheet and used the
capabilities of the technology to create a scatter plot
and generate a line of best fit. Most of the teams had
reached this point in time for the wrap-up session at
BarbieBungeeJumping,TechnologyandContextualisedLearningofMathematics
209
the end of the day.
Day 3 began with a very interesting discussion
about functions, correlation, causality and
extrapolation. The groups then estimated the
distance the Barbie would need to drop from the first
floor window and returned to the functions that
described their line of best fit. Once the dolls were
attached to their bungees, the knockout competition
began and two by two the teams competed to see
whose doll got closest to the ground without hitting
it.
Figure 1: Barbie Bungee Competition.
Once the winning team was decided and the
prizes were distributed, the discussion regarding the
next activity began.
The Human Catapult activity is an investigation
into projectile motion. Teams use an oversized
slingshot, foam balls, cameras and the free video
analysis software Tracker (www.cabrillo.edu/
~dbrown/tracker), and GeoGebra (www.geogebra.
org), to investigate concepts such as functions,
angles, rates of change and velocity.
After a plenary session in which the optimal
approach to video recording for the purposes of
generating quadratic functions was discussed, the
groups spent the second half of the 3
rd
day in the
local park recording their team members using the
catapult to fire a foam ball.
The plenary session that began the 4
th
day
highlighted the mathematical connections that
underpin the Barbie and Catapult activities.
Although the methods of data collection differed –
manual measurement and plotting of points on a
graph, or automatically generated functions through
frame-by-frame video analysis – the approach of
using the line/parabola of best fit for modelling and
generalisation was common to both activities. In
addition, the concept of correlation and causality
that had been introduced with the Barbie activity
was explored in significant depth through the graphs
of the functions generated by the catapult. The initial
graph discussed was the pictorial representation of
the flight of the ball through the air, in which the x-
axis represents horizontal distance and the y-axis
represents height.
Figure 2: Tracker Generation of Initial Graph.
On discussing whether there was a causal
relationship between these two variables, one of the
students remarked: “well, if the distance is counted
as time there is”, which allowed for the
deconstruction of the original graph into the two
more meaningful graphs of height with respect to
time and horizontal distance with respect to time.
The groups used the video analysis and best-fit
functionality in Tracker to generate relevant
functions, which were then analysed in GeoGebra.
After initial technical difficulties, most of the teams
managed to generate the functions and begin their
modelling. While calculating the angle of projection
and maximum height were straightforward tasks,
estimation of the initial velocity of the ball is quite
an involved concept and this part of the activity was
left for the final day.
Once the concept of initial velocity and possible
approaches to its calculation were explained, the
teams were given time to try to work it out before
using a simulation on phet.colorado.edu to gauge the
accuracy of their mathematical model. Once again, a
competition was used to incentivise the efforts and a
final showdown, in which the actual distances were
compared against the simulated distances, was used
to judge the endeavour. Once preparation of the final
presentations was complete, the groups took turns to
talk about what they had achieved.
3.3 Preliminary Analysis of Results
While results presented in this section are in the
early stages, preliminary analysis indicates some
interesting outcomes.
21 of the 24 students completed both a pre- and
post-questionnaire, which was designed to highlight
changes in their attitudes to mathematics and
technology, and their levels of behavioural and
CSEDU2014-6thInternationalConferenceonComputerSupportedEducation
210
affective engagement over the course of the
intervention. The questionnaire used was the
Mathematics and Technology Attitudes Scale
(Pierce et al., 2007) – a 20 item questionnaire with a
likert-type scoring system that measures
mathematical confidence, technological confidence,
behavioural engagement, affective engagement and
attitude to using technology in mathematics. There
was a small increase in behavioural engagement and
in attitudes to using technology in mathematics, and
a slight decrease in mathematical and technological
confidence. However, a 6% increase in affective
engagement was recorded.
As short-term significant changes are hard to
achieve, and these changes have not yet been tested
for statistical significance. However, from the
qualitative data it seems that the drop in confidence
levels relates to the change from the typical,
formulaic approach to mathematics education to the
use of messy data with no absolute “correct” answer
to the activities.
At this stage of the analysis, we have decided to
use a word-cloud of the most frequently recorded 50
words of 4 or more letters to provide a feel for the
qualitative data that has emerged from the
intervention. This graphical representation of word
frequency is not meant as a substitute for traditional
content analysis – which is ongoing at the time of
writing – but as a visually rich way to enable readers
to get a feel for the data at hand (Joubert, 2012;
McNaught and Lam, 2010). In a word-cloud the size
of the word relates to the number of times it occurs.
The data was gathered from student post-
questionnaire comments, individual journals, and
from the transcription of a 25 minute, semi-
structured focus group interview. Before running the
word frequency analysis on the data, usage of the
word “like” as a vocalised pause was removed from
the transcript of the interview so that it would not
pollute the data. This usage of the word is common
among teenagers as a meaningless interjection, to
keep conversation flowing.
The relatively large size of positive attitudinal
words such as “like” (used to represent enjoyment),
“enjoy” and “interesting” support the increase in
affective engagement recorded in the quantitative
data. Additional support is found in quotes such as:
“I found using maths in a practical
environment and in everyday life interesting
and enjoyable.”
“It was definitely better than normal school
maths. It was far more engaging.”
“I felt that leaving us to it and letting us go out
was great.”
Figure 3: Word Cloud.
“I liked this week; it did not feel like maths in a
way, it felt like fun. It felt different from school
maths but I still learned things.”
Even students with negative initial attitudes seemed
to have a positive experience:
“[I am] shaken in my absolute use of the term
‘hate’ [relating to mathematics] and more on
the side of ‘mildly dislike’”.
The focus group interview involved team leaders
from five of the six groups (one team was
unavailable) and the 1
st
author, and shed light on
many of the positive and negative aspects of the
intervention. One student felt that the aim of the
approach was to create a more engaging and
involving way to learn mathematics, encouraging
students to “think outside the box”. When queried as
to whether he meant problem solving, he replied:
“it's not just simple problem solving, like when you
get this big long-winded question, and... you know
it's simultaneous equations, or you know it's going to
be graphs. This is like, it doesn't tell you what it is,
you just have to figure it out yourself”. Another
student found using the facility of the technology to
outsource the calculation was very beneficial: “using
the computers was really handy, because it meant
that I could understand it and have fun with it,
without having to stress about getting it wrong”. All
of the students agreed that the emphasis was more
on understanding of concepts as opposed to
procedures and content. When questioned about the
development of new understanding, a number of
them pointed out that prior to the intervention, they
had not realised the extent of relationships between
different areas of mathematics, and how, in many
cases, what are often presented as diverse topics are
simply different modes of representation. Others had
developed a deeper understanding (or in some cases
‘an’ understanding) of functions.
There were contrasting reactions to the usage of
technology in the groups. Some of the students felt
BarbieBungeeJumping,TechnologyandContextualisedLearningofMathematics
211
that it gave them freedom to understand and
manipulate the mathematics, while others preferred
more concrete, hands on activities: “I didn't like…
when we were using GeoGebra. That's why I liked
the Barbie thing, because you can hold it. I liked
seeing it in my hands and being able to pull it and
see what happens and that, but on a computer it
seems very abstract”.
4 DISCUSSION
While digital technology has the potential to open
new routes for students to construct and comprehend
mathematical knowledge and new approaches to
problem-solving, this requires a change in the
pedagogical approach in the classroom in terms of
student engagement with learning (Drijvers et al.,
2010). Olive et al. (2010) highlight that “it is not the
technology itself that facilitates new knowledge and
practice, but technology’s affordances for
development of tasks and processes that forge new
pathways” (p154).
The need to conduct research into the design and
development of tasks and activities that provide
engaging environments, in which the mathematics
are seen as relevant by the students, with goals that
they find compelling (Confrey et al., 2010; Laborde,
2002; Oldknow, 2009) is the motivating factor for
this work. In this study, technology has facilitated
research, data gathering and analysis, outsourcing of
computation and mathematical modelling, all of
which have permitted a level of engagement with
mathematical concepts that would not otherwise
have been possible. This is reflected in the increase
in affective engagement recorded in the MTAS
scores, but perhaps more significant is the sense of
student ownership and the understanding of
connections, mathematical context and relevance
that is evident from the students’ qualitative
responses.
Kieran and Drijvers (2006) contend that
mathematical tasks that make use of technology
should not be studied without also paying careful
attention to the classroom environment and the role
of the teacher. Flexibility with regard to routine and
environment are necessary in order to fully exploit
the potential of technology in the teaching and
learning of mathematics; the block structuring of the
timetable in the School in which the study took place
facilitated real student engagement with the
activities. If the activities were to be conducted
within the confines of a more conventional
timetable, with periods of between 35 and 90
minutes, the experience would have been more
fractured and, while it may still be possible, it is
unlikely that the same level of engagement would
have been achieved.
Means (2010) points out that higher learning
gains are associated with classrooms in which an
established routine is in place for moving between
technology-mediated and traditional activities.
Orchestration of the classroom and technological
difficulties relating to network access and up-to-date
software emerged as an issue that needs serious
consideration and contingency planning before
further interventions of this kind are undertaken.
The week-long intervention in an authentic
school setting has provided a positive view of the
approach to integrating technology in mathematics
education proposed in this research. The initial
results indicate that there is real potential for
increased engagement and conceptual understanding
emerging from participation with activities designed
in accordance with the design principles
REFERENCES
Anderson, T., & Shattuck, J. (2012). Design-Based
Research A Decade of Progress in Education
Research? Educational researcher, 41(1), 16-25.
Bénard, D. (2002). A method of non-formal education for
young people from 11 to 15. Handbook for Leaders of
the Scout Section. World Scout Bureau, Geneva.
Boaler, J. (1993). Encouraging the transfer of
‘school’mathematics to the ‘real world’through the
integration of process and content, context and culture.
Educational studies in mathematics, 25(4), 341-373.
Bray, A., & Tangney, B. (2013a). The Human Catapult
and Other Stories – Adventures with Technology in
Mathematics Education. 11th International
Conference on Technology in Mathematics Teaching
(ICTMT11), 77 - 83.
Bray, A., & Tangney, B. (2013b). Mathematics, Pedagogy
and Technology - Seeing the Wood From the Trees.
5th International Conference on Computer Supported
Education (CSEDU2013), 57 - 63.
Confrey, J., Hoyles, C., Jones, D., Kahn, K., Maloney, A.
P., Nguyen, K. H., . . . Pratt, D. (2010). Designing
software for mathematical engagement through
modeling Mathematics Education and Technology-
Rethinking the Terrain: The 17th ICMI Study (Vol. 13,
pp. 19-45): Springer.
Dede, C. (2010). Comparing frameworks for 21st century
skills. In J. Bellanca & R. Brandt (Eds.), 21st century
skills: Rethinking how students learn (pp. 51-76).
Bloomington, IN: Solution Tree Press.
Drijvers, P., Mariotti, M. A., Olive, J., & Sacristán, A. I.
(2010). Introduction to Section 2. In C. Hoyles & J. B.
Lagrange (Eds.), Mathematics Education and
CSEDU2014-6thInternationalConferenceonComputerSupportedEducation
212
Technology - Rethinking the Terrain: The 17th ICMI
Study (Vol. 13, pp. 81 - 88): Springer.
Ernest, P. (1997). Popularization: myths, massmedia and
modernism. In A. J. Bishop, K. Clements, C. Keitel, J.
Kilpatrick & C. Laborde (Eds.), International
Handbook of Mathematics Education (pp. 877-908).
Netherlands: Springer.
Geiger, V., Faragher, R., & Goos, M. (2010). CAS-
enabled technologies as ‘agents provocateurs’ in
teaching and learning mathematical modelling in
secondary school classrooms. Mathematics Education
Research Journal, 22(2), 48-68.
Gross, J., Hudson, C., & Price, D. (2009). The long term
costs of numeracy difficulties. Every Child a Chance
Trust. Retrieved from http://www.northumberland.
gov.uk/idoc.ashx?docid=c9aee344-23be-4450-b9aa-
41aaa891563a&version=-1.
Grossman, T. A. (2001). Causes of the decline of the
business school management science course.
INFORMS Transactions on Education, 1(2), 51-61.
Hoyles, C., & Lagrange, J. B. (2010). Mathematics
education and technology: rethinking the terrain: the
17th ICMI study (Vol. 13): Springerverlag Us.
Hoyles, C., & Noss, R. (2009). The Technological
Mediation of Mathematics and Its Learning. Human
Development, 52(2), 129-147.
Jonassen, D. H., Carr, C., & Yueh, H. P. (1998).
Computers as mindtools for engaging learners in
critical thinking. TechTrends, 43(2), 24-32.
Joubert, M. (2012). Using digital technologies in
mathematics teaching: developing an understanding of
the landscape using three “grand challenge” themes.
Educational studies in mathematics, 1-19.
Kieran, C., & Drijvers, P. (2006). Learning about
equivalence, equality, and equation in a CAS
environment: the interaction of machine techniques,
paper-and-pencil techniques, and theorizing. In C.
Hoyles, J. B. Lagrange, L. H. Son & N. Sinclair
(Eds.), Proceedings of the Seventeenth Study
Conference of the International Commission on
Mathematical Instruction (pp. 278-287): Hanoi Institute
of Technology and Didirem Université Paris 7.
Laborde, C. (2002). Integration of technology in the
design of geometry tasks with Cabri-Geometry.
International Journal of Computers for Mathematical
Learning, 6(3), 283-317.
Lawlor, J., Conneely, C., & Tangney, B. (2010). Towards
a pragmatic model for group-based, technology-
mediated, project-oriented learning–an overview of the
B2C model. Technology Enhanced Learning. Quality
of Teaching and Educational Reform, 602-609.
McNaught, C., & Lam, P. (2010). Using Wordle as a
supplementary research tool. The qualitative report,
15(3), 630-643.
Means, B. (2010). Technology and education change:
Focus on student learning. Journal of research on
technology in education, 42(3), 285-307.
Mor, Y., & Winters, N. (2007). Design approaches in
technology-enhanced learning. Interactive Learning
Environments, 15(1), 61-75.
Noss, R., & Hoyles, C. (1996). Windows on mathematical
meanings: Learning cultures and computers (Vol. 17):
Springer.
Oates, G. (2011). Sustaining integrated technology in
undergraduate mathematics. International Journal of
Mathematical Education in Science and Technology,
42(6), 709-721. doi: 10.1080/0020739x.2011.575238.
Oldknow, A. (2009). Their world, our world—bridging
the divide. Teaching Mathematics and its
Applications, 28(4), 180-195.
Olive, J., Makar, K., Hoyos, V., Kor, L. K., Kosheleva, O.,
& Sträßer, R. (2010). Mathematical knowledge and
practices resulting from access to digital technologies
Mathematics Education and Technology - Rethinking
the Terrain: The 17th ICMI Study (Vol. 13, pp. 133-
177): Springer.
Ozdamli, F., Karabey, D., & Nizamoglu, B. (2013). The
Effect of Technology Supported Collaborativelearning
Settings on Behaviour of Students Towards
Mathematics Learning. Procedia-Social and
Behavioral Sciences, 83, 1063-1067.
Pierce, R., Stacey, K., & Barkatsas, A. (2007). A scale for
monitoring students’ attitudes to learning mathematics
with technology. Computers & Education, 48(2), 285-
300.
Pimm, D., & Johnston-Wilder, S. (2004).
TECHNOLOGY, MATHEMATICS AND
SECONDARY SCHOOLS: A BRIEF UK
HISTORICAL PERSPECTIVE. In S. Johnston-Wilder
& D. Pimm (Eds.), Teaching secondary mathematics
with ICT (pp. 3-17).
Sinclair, N., Arzarello, F., Gaisman, M. T., Lozano, M. D.,
Dagiene, V., Behrooz, E., & Jackiw, N. (2010).
Implementing digital technologies at a national scale
Mathematics Education and Technology-Rethinking
the Terrain: The 17th ICMI Study (Vol. 13, pp. 61-
78): Springer.
Tangney, B., & Bray, A. (2013). Mobile Technology,
Maths Education & 21C Learning. 12th world
conference on mobile and contextual learning
(Mlearn2013), In Press.
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