MY MATHS STORY: AN APPLICATION OF A COMPUTER-ASSISTED
FRAMEWORK FOR TEACHING MATHEMATICS IN THE LOWER
PRIMARY YEARS
Nasrin Moradmand
School of Computer Science & Software Engineering, The University of Western Australia
nasrin.moradmand@grs.uwa.edu.au
Amitava Datta
School of Computer Science & Software Engineering, The University of Western Australia
amitava.datta@uwa.edu.au
Grace Oakley
Graduate School of Education, The University of Western Australia
grace.oakley@uwa.edu.au
Abstract: The development of interactive educational multimedia applications that are
grounded in accepted pedagogical principles, in terms of both learners’ and teachers’ needs, is a
challenging and complex undertaking. This paper presents a new educational framework for
teaching mathematics, which is based on Bloom/Anderson’s taxonomy and current pedagogical
views of mathematics education. With this underpinning framework, along with the capability
of multimedia technology for presenting multiple representations, and using children’s
literature for teaching mathematics, it has been possible to design and develop interactive
multimedia educational software that appears to meet the needs of both students and teachers in
junior primary classrooms. This application was trialled for teaching various mathematics
concepts in five different primary schools in Australia for approximately one school term. A
detailed analysis of the development process and various components of the application are also
presented in this article, followed by the pedagogical and technological results of using the
application in classroom settings.
Introduction
In an ever-advancing technological world, the use of Information and Communication Technologies (ICTs)
has become very common in all aspects of daily life. Within education, the development of digital media and
computer skills has resulted in significant changes in the way that teachers teach and children learn in school.
The appropriate use of technology has proven to have broad pedagogical affordances and invaluable potential
to change teaching and learning (Oliver, 2002; Ongori & Mburu, 2010; Pramanik, 2011; Yelland, Australia. Dept. of
Education, & Affairs, 2001) in a variety of content areas. In this context, ICTs in general, and multimedia
applications in particular, open up a whole field of possibilities in the world of mathematics teaching. There is no
question about whether teachers should integrate technology into their existing practices; in fact, the main issue now
is how teaching can be transformed by technology (Angeli & Valanides, 2009) to encourage mathematics learning
without the technology ‘getting in the way’.
Along with other countries, in Australia the integration of ICTs across the curriculum has become a priority,
and there have been education policy shifts to include ICTs in the schooling system (ACARA, n.d.; Ministerial
Council on Education, 2008). ICTs now have a firm place in education and access to computer-based technology in
schools and classrooms has increased. However, many of the computer-based applications that are currently used in
Australia originate from the USA, and in recent years more have been coming from the UK (Bingimlas, 2009; Eng,
2005; Yelland et al., 2001). Subsequently, educational packages are mainly based on the curricula of these countries,
and their teaching philosophies and methods. Thus, in many cases, sourcing computer based technology and
software applications to facilitate learning in a pedagogically acceptable manner has become an area of challenge for
Australian teachers.
This study took place with the aim of designing and developing interactive multimedia educational software
based on a sound mathematics education framework and meeting the requirements of the new Australian Curriculum
(ACARA, n.d.) to assist in the teaching of mathematics concepts in Australian junior primary school classrooms.
The first section of this paper reviews the potential of using multimedia technology to present multiple
representations and outlines the rationale for using children’s literature for teaching mathematics in the lower
primary classroom. This is followed by the presentation of a new framework, which is based on current pedagogical
views of mathematics education and a cognitivist learning theory. By using this underpinning framework, interactive
multimedia software for teaching various mathematics concepts in Australian primary school classrooms (K-4) was
designed, developed and trialled in schools for approximately one school term. Also in this paper, the pedagogical
and technological results of using the new application (My Maths Story) in school settings are discussed.
Literature review
Computer-based technology has been growing rapidly and it has been claimed that the use of educational
software can increase the mathematical achievement of children in pre-school and primary grades (Clements, 1993;
Heid, 2005; Masalski, 2005; Saracho & Spodek, 2009). According to the research literature, the largest gains in
mathematics learning so far appear to have been through the use of interactive mathematical application and practice
software (Chang, Wu, Weng, & Sung, 2011; Clements, 1987, 2002; Manches, O’Malley, & Benford, 2010; Yelland
et al., 2001). With the help of interactive technology, it is claimed that students are able to learn more deeply,
receive feedback on their performance, test their ideas and revise their understandings (Chang et al., 2011; Kozma,
2003; Mayer, 2003). Although several educational software packages and applications for teaching mathematics are
available, many of them have not been successfully used in school settings. Evidence shows that most educational
software is commercially produced and is not widely accepted by educators, policy makers and researchers
(Kingsley & Boone, 2008). Studies have suggested that software is rarely designed with an appropriate pedagogical
framework in mind (Laurillard, 2009; Mumtaz, 2000; Patten, Arnedillo Sánchez, & Tangney, 2006) and that, also,
much of it has inadequate consideration for the teaching contexts in which it is supposed to be used (Hinostroza &
Mellar, 2001; Robin, 2008).
It is proposed in this article that learning through technology, especially when it enables content to be
presented in multimodal formats (multiple representations) and incorporates children’s literature (storytelling), can
offer children powerful new ways of exploring abstract mathematical concepts that have not been possible through
traditional means of teaching and learning.
Using children’s literature (storytelling) to teach mathematics has proven to be an effective method (Elia, van
den Heuvel‐Panhuizen, & Georgiou, 2010; Tucker, Boggan, & Harper, 2010). Mathematics is part of everyday life,
and children’s literature can be used as a bridge for children to connect the abstract and symbolic language of
mathematics to their own world through engaging and meaningful conversations. The US National Council for the
Teachers of Mathematics considers communication as an essential component of learning mathematics ((NCTM),
2000) and the mathematical achievement of children is highly correlated with their ability to use language to
communicate their maths idea (Tucker et al., 2010; Ward, 2005). Using literature can enable children to
communicate mathematically through listening, reading, writing and talking about mathematics ideas, leading to
increased depth in their understanding of difficult concepts as well as their ability to talk about and represent the
ideas.
Engaging in multiple representations can enable learners to better understand, develop, and communicate
different mathematical attributes of the same object or operation, along with connections between them (Carpenter,
Fennema, Franke, Levi, & Empson, 1999; Harries & Barmby, 2007; Mishra & Sharma, 2005). Research studies on
teaching mathematics have shown that multiple representations have an important role in developing children’s
understandings of mathematics concepts (Carpenter et al., 1999; Gray, Pitta, & Tall, 1997; Harries & Barmby, 2007;
Mishra & Sharma, 2005; I. Thompson, 1999) and can serve as useful teaching aids for learners, because each
representation contains important information. There is a variety of ways in which multiple representations can be
used to convey mathematics concepts, and computer-based technology has been identified as being capable of
providing this (Goldin & Shteingold, 2001; Milovanović, Takači, & Milajić, 2011). The use of multimedia and
computer-based tools can facilitate the learner’s abstract thinking and allow multiple representations to be linked
dynamically between concrete and symbolic representations; for instance, changing a formula that can instantly
change a graph, or showing a numeral and having multiple representations of the relevant number available in
pictures, sounds and even animation. This study used these two powerful approaches (storytelling and multiple
representations) in teaching mathematics as a basis for designing new interactive multimedia software for teaching
and learning mathematics in the lower primary classroom.
Theoretical framework
The project being reported here draws on a cognitivist approach to learning, which focuses on mental
processes and how learners attend to, manipulate and remember information during learning. Cognitive education in
the teaching and learning process encourages learners to think and analyze a particular topic in gradually more
complex ways (Bruner, 1990; Cooper, 1998; Krause, Bochner, & Duchesne, 2006).
The Bloom/Anderson taxonomy is a hierarchical model for cognitive learning objectives, ranging from lower
levels of learning (i.e. knowing and understanding) to higher levels of thinking, which require a more sophisticated
evaluation and analysis of content (Benjamin, 1956). This is a useful learning model which is widely used as a
planning tool in educational settings (Krause et al., 2006), and has also been applied in higher education domains
such as engineering, structuring assessments and computer science for course design and evaluation (Thompson,
Luxton-Reilly, Whalley, Hu, & Robbins, 2008). However, it appears that the approach has seldom been used for
designing computer-based educational mathematics applications for schools.
In the study being discussed here, the Bloom/Anderson taxonomy has been used to inform the design of a
mathematics educational framework. We propose a new framework for designing mathematics software to capture
all elements of the Bloom/Anderson taxonomy (Figure 1a), and this framework has underpinned the design and
development of a computer-based application to facilitate the teaching of various mathematics concepts to children
in lower primary school classrooms.
As is mentioned above, using children’s literature is an effective approach in mathematics education for
young children and is at the core of the proposed framework. As shown in Figure 1b, storytelling constitutes the first
level of the framework (lower section), where the whole class can be engaged in a story involving mathematics
concepts. Here, there is substantial teacher involvement (modeling and explaining) to focus children’s attention and
build comprehension. The storytelling method can assist learners with reference to the recall of facts, terms and
concepts, and can encourage them to imagine and sequence story scenes (Braddon, Hall, & Taylor, 1993; Krause et
al., 2006; Tucker et al., 2010). This ties in with the first category (Remember) of the Bloom/Anderson model. Also,
storytelling can assist with the comprehension of a subject through processes such as explaining the scenes, retelling
the story, asking ‘why’ and ‘how’ questions, and having children describe scenes and characters (which should
contain mathematics concepts) in their own words (Krause et al., 2006; Tucker et al., 2010). This aligns with
"Understand" categories of the Bloom/Anderson model. It can be seen that storytelling clearly relates to both
“Remembering” and “Understanding” in the Bloom/Anderson model.
The middle section of the framework focuses on skill building in individual students through the application
of knowledge and understandings already gained through the first level. Skill building (fluency building) can be
described as a way of learning by developing a capacity to retrieve basic facts from memory quickly and effortlessly
(with automaticity) (Mercer & Miller, 1992; Tait-McCutcheon, Drake, & Sherley, 2011). This can be achieved
through practicing, repeating (Tait-McCutcheon et al., 2011) and accomplishing. This aligns with the “Apply”
category of the Bloom/Anderson model, although it should be acknowledged that practicing could also help children
remember (the lowest level of the model).
Problem solving is a “higher-order cognitive process” (Chiou, Hwang, & Tseng, 2009; Goldstein & Levin,
1987) that entails the ability to recognize, understand and analyze a problem. All of the components of the problem
then need to be evaluated and incorporated to create a new form or representation. This can be related to the last
three categories (“Analyze”, “Evaluate” and “Create”) of the Bloom/ Anderson model, which require a higher order
of thinking by learners (Anderson et al., 2000). As is presented in Figure 1b, this is the upper level of the proposed
framework, where students can work either individually, in pairs or in small groups to analyze and find solutions to
mathematics problems. When using this framework, teachers and learners have the opportunity to move back and
forth between the three levels (of the framework), as required. The conceptual ties between the Bloom/Anderson
model and the proposed framework provide a strong theoretical basis for designing a computer based mathematics
educational application (Figure 1).
Figure 1: The conceptual ties between the Bloom/Anderson taxonomy (a) and the proposed framework (b).
Methodology
As noted above, the educational application that has been developed as part of this study is based on a
cognitivist theoretical perspective and applies the Bloom/Anderson learning objectives through the use of interactive
multimedia technology. The application, My Maths Story, which we developed in a computer science lab, places a
special emphasis on the use of multimedia and interactivity for teaching and learning mathematics concepts in the
primary school classroom. All parts of the application were designed to be used by the teacher in the classroom, as well
as by children; children can use the software independently, in pairs or in small groups. The application offers teachers
many opportunities to model and share with children, and discuss a range of mathematical concepts for various ability
levels, within the motivational context of a storybook that links mathematical concepts to real world events and
settings. In and through this application, mathematical language is reinforced and extended, and cross curricular links
are made with literacy. Moreover, the application can be adapted to multiple grade levels and can be used to target a
range of different learning objectives throughout the school year.
Based on a review of existing mathematics concept books and discussions with teachers and other mathematics
educators, we chose an engaging mathematics concept book, “One is a Snail, Ten is a Crab”, a counting by 'feet' book
written by April Pulley Sayre, Jeff Sayre, and Randy Cecil (2003) 1. This picture book is about counting animals with
various numbers of feet; e.g. “5 is a dog (with 4 feet) and a snail (with 1 foot)”. With permission from the publisher, we
used this book as a basis of the multimedia software.
After completion of the software and before trials in classrooms, we presented the application to 32 pre-service
teachers and 4 early primary mathematics educators in a Western Australian university. Each pre-service teacher and
mathematics educator accessed different parts of the application for approximately 15-25 minutes (Figure 2). Through
this process, the application was submitted to critical judgment. Pre-service teachers and educators’ comments and
suggestions, which were collected via survey and interview, were analyzed and the necessary changes were introduced
to improve the application. Once this process was finalized, the application that would be assessed by junior primary
mathematics teachers in Western Australia was produced.
Figure 2: Pre-service teachers testing the application.
In order to demonstrate the value of the application in facilitating mathematic teaching and learning, the
application was offered to five different primary schools in Western Australia (three public, one private and one
specialist school for English as a Second Language students), from areas with different social and economic
demographics, for approximately one school term in 2012. We presented the software to participating teachers in
individual training sessions or small group workshops for demonstrations and examples of use. Participants also had
time for self-directed exploration and learning, and for designing their classroom mathematics lesson plans using
different components of the application.
Twelve teachers and 284 students in multiple grade levels (K to Year 4) used the application in their classrooms
for the teaching and learning different mathematical concepts. The application was used in classrooms (on interactive
whiteboards) for whole class engagement and in school computer labs (on personal computer and laptops) for
individual and small group work.
Participant teachers used the different components of the application for teaching counting, place value, number
sense, number relationships and basic addition for younger children, while they used it to teach skip counting, counting
by sets of 2’s, 4's, 10's, even and odd numbers, addition, subtraction and multiplication in different ways for older
1
From ONE IS A SNAIL, TEN IS A CRAB: A COUNTING BY FEET BOOK. Text copyright © 2003 April Pulley Sayre & Jeff Sayre. Illustrations
copyright © 2003 Randy Cecil. Reproduced by permission of Walker Books Australia on behalf of Candlewick Press.
children throughout the term. Teachers created various interactive stories by choosing scenes, characters (e.g. a snail,
person, dog, insect, spider, crab) and appropriate multimedia such as sound and text (Figure 3 – left photo) and
emphasized the intended learning outcomes or objectives by explaining the scene, retelling, and asking ‘why’ and
‘how’ questions. This helped students to recall facts, terms and concepts by remembering, describing and explaining
(the "Remember" and "Understand" categories of the Bloom/Anderson model-lower level of the proposed framework).
Through interacting, manipulating, and creating various stories, students practiced their fluency skills by calculating
answers, finding various answers and recalling factual knowledge and concepts readily (the "Apply" category of the
Bloom/Anderson model – middle section of the proposed framework) (Figure 3 – middle photo). The software was also
used for more complex concepts, through teachers generating a story or a mathematics word problem and asking
students to analyze, explain and solve a problem individually or in pairs (the "Analyse", "Evaluate" and "Create"
categories of the Bloom/Anderson model – upper level of the proposed framework) (Figure 3 – right photo).
Figure 3: Different components of the My Maths Story application: teacher using the software on an interactive whiteboard in the
classroom (left); a student using the software independently (middle); and students using the software in pairs for solving a
mathematics word problem (right).
One of us (the researchers) was present in the classrooms as an observer throughout the school term but did not
actively participate in the classroom activities. This allowed her, through a systematic method, (field notes, video and
audio recording) to observe and record the interactions of teachers and learners with the application (usability) in real
world settings, for the purpose of pedagogical and technical evaluation.
Toward the end of the school term, individual and semi-structured interviews with the participant teachers
occurred. A series of questions were asked in order to carry out a pedagogical and technical evaluation of the
application, some of which were directly answerable and others were open-ended to allow for in-depth responses
(Punch, 2009). The questionnaire had four parts, beginning with some general questions which were mainly related to
the teachers’ experiences in using the My Maths Story software and associated teaching aids, any challenges they may
have faced during the use of the software, and how they thought the software designers might minimize these
challenges. In the second part of the interview, participants were asked about the technical features of the software and
factors associated with technology integration, including questions about the interface and layout design, the
multimedia elements and functionality. The third part of the interview focused on the pedagogical evaluation of the
software, which included questions about how well the application might assist teachers to demonstrate mathematical
concepts to children and to raise “why and how” questions related to the mathematics concepts being taught.
Furthermore, teachers were questioned about their students’ engagement in the mathematics activities and how they
shared and discussed a range of mathematical concepts when using the application independently or in pairs. The
interviews ended with several concluding questions that elicited teachers’ responses to the possibility of using the
application in their classroom again in the future, and whether they would use it instead of, or alongside, a traditional
book. Furthermore, teachers were asked to complete a survey (the same survey that was used for the pre-service
teachers).
Results and discussion
Interview and survey results indicated that teachers were satisfied with the technical aspects of the software.
They responded that the design elements and layout were clean, simple, consistent and well structured. Teachers
thought that it had been possible to present multiple representations of mathematics concepts creatively and clearly
through the use of the multimedia components in the application. All participant teachers endorsed the flexibility of
changing and modifying the software to address a range of mathematics topics and to fit their students’ diverse needs.
Easy to find and use multimedia elements, the ability to change and modify mathematics activities to suit students’ skill
levels, visual and graphical appeal (to children), and the ability to use it with an interactive whiteboard for whole class
engagement, as well as its suitability for use individually or in pairs, were highlighted as advantages of the application
by all participant teachers. Table 1 shows participant teachers’ responses to technical features of the software. However,
some teachers requested new features in some parts of the application, such as the ability to move the text box around
the screen or change the story characters’ size.
Rating (%)
Technical features of the My Maths Story software
A. Strongly disagree, B. Disagree,
C. Undecided, D. Agree, E. Strongly agree
A
B
C
The software has a professional look/presentation.
The screens are well-structured and the design is clear.
Menu, graphic, animation, audio and general layout interface are consistent.
It is easy to navigate through the application.
Multimedia elements are easy to find and use.
The application is enjoyable to use.
D
E
12%
38%
12%
25%
36%
12%
%88
62%
88%
75%
64%
88%
Table 1: Participant teachers’ responses to questions about technical features of My Maths Story
In response to questions about their pedagogical beliefs and the teaching activities facilitated through the use
of the application, teachers stated that they were able to use the software to demonstrate and explain targeted
mathematical concepts to their classroom. They indicated that the presentation of mathematics concepts within a story
in a multimodal way, and having a chance to choose pictures, audio and video to tell the mathematics concept story,
helped them to express various mathematics concepts much easier and faster than in traditional ways. Modifying the
original story by changing characters or settings, explaining the scenes, retelling the story, and asking ‘why’ and ‘how’
questions through variations of the story were highlighted as strengths of using the application in the classroom. Many
teachers reported that their students showed increased comfort levels in talking about their understanding of
mathematics concepts through making their own story and sharing and discussing it in the classroom. Opportunities to
interact with the familiar characters from the story in order to create mathematics exercises for various levels, and even
for students to pose their own problems and find answers individually, in pairs or small groups, were revealed as
advantages of using the application (Table 2).
A 100% agreement can be seen among the participant in-service teachers and pre-service teachers in response to
the question as to whether they would, in the future, use the software instead or alongside traditional books in their
classroom. However, teachers suggested variations to the software, such as using different characters and story themes,
which leads this research to another stage; the development of a more complex and dynamic environment.
Rating (%)
Pedagogical features of the My Maths Story software
A. Strongly disagree, B. Disagree,
C. Undecided, D. Agree, E. Strongly agree
A
B
C
Through the use of this application, learning mathematics concepts could be more enjoyable,
engaging and motivating for children than when using other resources.
Through the use of this application, the teacher could explain and demonstrate mathematical
concepts.
Through the use of this application, the teacher could explain ‘why and how’ questions relating to
the mathematics concepts being taught.
Through the use of this application, the teacher could facilitate collaborative learning.
Young students (Years 1 to 4) could navigate the software.
It would be easy for student to create a simple mathematics concept story, through the use of this
application.
Through the use of this application, students could practice number facts.
If you could choose, would you use this software and the teaching aids in your classroom?
Table 2: Participant teachers’ responses to some pedagogical questions
8%
D
E
12%
88%
25%
75%
26%
66%
12%
10%
88%
90%
12%
88%
12%
88%
100%
Conclusions
In this paper we have presented a new framework, based on the Bloom/Anderson cognitive learning
objectives, to guide the use of multimedia technology to present multiple representations and children’s literature for
the teaching of mathematics in the lower primary school. Based on the framework, and taking into account current
pedagogical views of mathematics education as well as the new Australian Curriculum, the My Maths Story interactive
multimedia educational software was developed. This application was trialled for one school term in five different
junior primary schools in Australia to gauge its usefulness for teaching various mathematics concepts. The results
indicate that the application, because of the strong theoretical and pedagogical underpinnings, may not share the
limitations of many existing mathematics software packages. The My Maths Story application appears to hold
considerable potential for teaching mathematics in junior primary mathematics classrooms through storytelling and the
use of multimedia technology to present multiple representations. This research supports the claim that, when is based
on appropriate pedagogical principles, the use of multimedia for teaching abstract subjects such as mathematics can
provide successful teaching and learning experiences for both teachers and learners.
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