THE ROLE OF ICT IN DEVELOPING MATHEMATICAL RESILIENCE
IN LEARNERS
Mary Lugalia1, Sue Johnston-Wilder2 and Janet Goodall3
1,2,3
The University of Warwick, Institute of Education, Coventry (UNITED KINGDOM)
M.A.Lugalia@warwick.ac.uk, sue.johnston-wilder@warwick.ac.uk,
janet.goodall@warwick.ac.uk]
Abstract
Reports on the impact of ICT upon learning suggest that the impact has not always been positive, and
certainly not as positive as it was initially suggested it would be. Luckin et al (2012) posit that what is
needed is a fundamental shift in pedagogy, a shift that transforms teaching and learning by focusing
on the learning experience. Grid Algebra is an example of educational software whose design is
underpinned with theory about learning (Hewitt, 2009). In this paper, we explore the changes in
learning mathematics experienced by Kenyan students given a brief course using Grid Algebra. We
examine the impact on 45 of the students over a one month period within the course, showing ways in
which understanding was improved and the experience was positive for the learners. We use the
construct of ‘mathematical resilience’ (Johnston-Wilder and Lee, 2010), a description of what is
required to promote effective learning of mathematics, to analyse why this example of ICT use was
effective. In this way, we explore what theory says about the mathematical activities using ICT that are
likely to add positively to a learner’s experience of mathematics and their consequent attainment. We
also identify some features of mathematical activities that would be expected to reinforce
mathematical helplessness and anxiety. Our analysis leads us to particularly emphasise the role of the
social setting within which the ICT is used. We comment on the nature of the ICT environment and we
note the critical role played by the feedback provided by the software for the learner. In conclusion, we
make some observations about the required pedagogy and how the software design relates to this
Keywords: ICT, mathematics, mathematical resilience.
1
INTRODUCTION
The introduction of Information and Communications Technology (ICT) into the teaching and learning
of mathematics has been reported to have an effect, at least in some instances, in terms of enhancing
pupil participation, motivation, pace and productivity, as well as progression in learning ([1], [2]). Over
the years, societal preoccupation with the integration of digital technologies into education, for
example as depicted in 2010 on the ICT in schools website, Department for Children, Schools and
Families, United Kingdom, has persistently been steeped in the much-touted claims of the
transformative potential of these technologies on teaching and learning ([3], [4], [5]). Colossal
investment has been, and continues to be dedicated to this venture, devoid of rigorous researchbacked evidence about what causes positive, negative and neutral impact on learning ([3], [4]). The
apparent lack of extensive and systematic reviews of the real impact of digital technologies in
education may be attributed to the challenge posed by the plethora of applications in diverse settings,
compounded by issues related to policy and practice [4]. In this paper, we discuss a particular ICT
tool, Grid Algebra, which was designed around how pupils learn; we used the tool in a social setting of
collaborative working, and we demonstrate positive impact on both conceptual and affective
development.
1.1
Learning Mathematics with ICT
Luckin et al present a damning indictment of currently prevalent practices in the education sector, in
which technology is used to support existing pedagogies. The teaching of school mathematics is
dominated by didactic, textbook-based classroom practices, which favour procedural presentation of
abstract knowledge, thus significantly limiting many learners’ conceptual agency [6]. The emphasis on
memorisation of rules and repetition of procedures, at speed, to arrive at correct answers, rather than
thinking about the underlying reasons why and when the procedures may be applied in concepts,
would be expected to reinforce helplessness and anxiety in pupils. Luckin et al advocate a
fundamental shift in pedagogy that transforms teaching and learning by focusing on the learning
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experience [3], arguing that technology on its own has no impact on learning. Instead, its impact
depends on the application rather than on the type of technology used. Luckin et al urge harnessing
the promise and potential of the digitally rich environment by designing educational technology around
how pupils learn in order to support that learning, and underline the vital role played by the context
within which technology is used.
1.2
Context
Mathematics teaching in Kenya is largely based on the traditional textbook approach, which is
inherently teacher-centred [7] and restricts the success of manoeuvres towards pupil-centred learning,
group work and learner agency; digital technologies are yet to be embraced. Recently, the Centre for
Mathematics, Science and Technology Education in Africa (CEMASTEA) launched an initiative to
promote the application of 21st Century methods in teaching and learning in ways which are richly
enhanced by the use of ICT. The research we report here aims to build on this initiative; the Kenyan
secondary school in which the study was conducted is designated as a training centre for both primary
and secondary schools. The study investigates the introduction of Grid Algebra, and seeks to address
the research question:
What effect will the introduction of Grid Algebra in a social setting of working in small groups have on
pupils learning algebra in a Kenyan school?
Despite being central to the secondary mathematics curriculum, algebra is a topic many pupils
disengage with and regard as ‘difficult’ ([8], [9], [10]). Algebra, as a symbolic language, is important in
providing a means of expressing generalities ([10], [11], [12]). However, failure to develop symbol
awareness while in school, compounded with certain classroom practices, can have a negative impact
on many pupils’ motivation towards learning mathematics, and can lead them to feeling generally
inadequate in mathematics ([13], [5]).
1.3
Mathematical Resilience
Since access to various concepts in algebra is considered difficult, it is imperative for pupils to develop
a positive, adaptive stance towards mathematics in general that will allow them to persist in learning,
despite the difficulties and barriers. We term this stance ‘mathematical resilience’, a description of
what is required to promote effective learning of mathematics [14]. Development of mathematical
resilience calls for the adoption of teaching approaches that have been shown to nurture resilient
behaviours in pupils as well as to convert mathematics classrooms into positive learning environments
where barriers to pupils’ access to mathematical concepts may be overcome [15]. In addition to having
a growth mindset [16], three factors are key to the development of mathematical resilience: learner
agency to make choices and decisions within the classroom; the learners experiencing themselves as
becoming part of a community of practice; and each individual learner feeling themselves to be
included in the learning process, in terms of both personality traits and values. In such environments,
pupils are motivated to persevere when faced with difficulty, and to recognize the value of working
collaboratively with their peers, acquiring language skills to express their mathematical
understandings, explore any questions, and a firm belief that effective, additional effort on their part
leads to higher achievement (the ‘growth’ mindset). For effort to be both effective and safe, it needs to
be focused on the learner remaining safely within the ‘zone of proximal development’ (ZPD) with
support from more knowledgeable others, learning but avoiding the danger of becoming overly
stressed or anxious. Due to our additional consideration of emotion to the notion of ZPD, and the fact
that emotion only appeared explicitly in Vygotsky’s later work [17], in this paper, we will call the ZPD
simply the ‘growth zone’ (see Fig. 1). It can be argued that ICT and peers can at times contribute to
the role of ‘more knowledgeable other’, and that using ICT with agency and in pairs or groups enables
the learner to keep themselves safe and ensures that the learning will be appropriately scaffolded for
each learner.
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Figure 1: Learning ‘growth’ zone
1.4
Learning with Grid Algebra Software
To many pupils at secondary school, arithmetic and algebra appear quite removed from each other
[11]. Through appropriate use of ICT in the learning process, pupils can benefit by receiving a more
meaningful introduction to algebra, including the use of letters for variables and formal algebraic
notation ([18], [19]). The pupils have been seen to take ideas they obtain in the computer environment
and apply them to pen-and-paper settings. Learning algebra with computers can potentially support
pupils to make a break from arithmetic while at the same time employing arithmetic ideas as a basis
for algebra ([19], [10]).
The mathematics-specific software, Grid Algebra, is based upon the idea of making ‘journeys’ across
a ‘multiplication grid’, both ‘journeys’ and ‘multiplication grid’ being supportive ‘met-befores’ in the
words of Tall [20]. The software is designed in two modes, and invokes the ‘Play Paradox’, a belief
that play facilitates learning [21]. One benefit of incorporating ‘play’ in education is that it can engender
pupil engagement, which in itself is a contributing factor to effective learning [22]. The Interactive Grid
Algebra mode of the software offers pupils an environment in which the notion of ‘play’ takes the form
of allowing users to enter numbers or letters into a cell and then drag this cell across a grid
horizontally or vertically, observing what happens. In the use of the multiplication grid in this mode, the
rows are pre-determined but which columns are in use is initially undetermined and is set by userinteraction with the grid. Each movement, right, left, down and up, represents one of the basic
mathematical operations: addition, subtraction, multiplication and division respectively. The software
represents these movements algebraically on the screen, providing instant feedback in the form of a
representation of each single journey (see Fig. 2).
Fig. 2 shows what happens on the grid using a variety of starting points. For example, letter “a” in Row
1 moved two cells to the right makes “a+2”, which then moved down to Row 3 makes “3(a+2)”.
Number “12” in Row 6 moved one cell to the left makes “12-6”, which then moved to Row 3 makes
“(12-6)/2”. The desired effect is that users associate a particular movement across the grid with a
particular mathematical operation, and algebraic ‘equivalence’ with different routes to the same endpoint. This association directs attention to the structure of the resulting algebraic expressions [18].
The other mode of the software provides Tasks, twenty-six in total, each consisting of questions on
various concepts in algebra at varying levels of difficulty. Pupils can work through the levels in each
task according to a group-negotiated pace, as part of a learning community.
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F
Figure 2: Grid Algebra
The teacher is enabled, by the design of the software, to give the pupils responsibility for solving
problems. As they do this, the pupils make choices and decisions; they have the freedom to make
and follow connections and to build ideas for themselves. In this way, the pupils can be enabled to see
the ‘why?’ and ‘how?’ of the mathematics they learn in addition to the ‘what?’ [6].
Hewitt [18] reports findings from a study conducted using Grid Algebra in England with 21 pupils of
mixed-ability in Year 5, who had never previously been taught any formal algebra; he highlights the
issue of deliberate pedagogic decisions in directing pupils’ attention to particular aspects of what is
being discussed in mathematics lessons. After four hours of combining working with Grid Algebra and
pen-and-paper tasks, the pupils in that study were generally found to accept formal algebraic notation
and to apply it within their written work [18]. The study whose findings are reported in this paper was
undertaken using the same piece of software on computers with older, secondary school pupils in
Kenya, and using less time, to provide them with an alternative medium of presentation to support
their algebraic conceptual understanding.
In this paper, we use the term ‘ICT’ to refer collectively to the computer itself, the related peripherals
and the computer programs. In “putting learning first” and making learning more social [3], we sought
to foster a classroom practice that encourages pupils to be actively engaged in and take ownership of
their own learning, with support, in order to gain meaningful access to concepts.
2
METHODOLOGY
Data reported here are drawn from a mixed-method study of a Form 2 mathematics class (pupils aged
14 to 15 years) at a public (state-run), girls-only, boarding school in Kenya. The 45 girls were
participants in a pilot study conducted with the principal purpose of testing data-collection instruments
to be used in a larger research project. The girls had a varied range of achievement in tests and
examinations, and they followed the Kenyan national secondary mathematics curriculum. The pupils
had already been introduced to formal algebra both at primary school and in Form 1 at secondary
school.
2.1
Description of the Study
The usual procedure in these pupils’ mathematics classrooms was for the teacher to work through a
few examples on the blackboard before the pupils worked individually on textbook exercises, with
whole-class marking and discussion of ‘difficult’ questions on the following day. However, this study
sought to inject the element of collaborative working in small groups using Grid Algebra software
loaded on 13 computers in the school computer laboratory rather than in the usual classrooms.
Two one-hour sessions were conducted, on consecutive days, during which the pupils first worked
collaboratively on software-generated tasks after which they worked on pen-and-paper tasks on
worksheets. All the pupils were then invited to complete a pupil questionnaire administered to collect
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their individual perceptions of their experience of using Grid Algebra in their mathematics lessons.
Semi-structured interviews were conducted, with two individual pupils and three groups of four pupils,
to probe their responses. Other data were collected also, but these are not discussed in this paper.
Instead, we will focus on the mathematics-with-ICT sessions, pupil questionnaire responses and
interview data.
2.2
Session 1
The pupils gathered around thirteen computers in groups of at most four. The researcher drew pupils’
attention to the display of a Grid Algebra screen on the whiteboard, and invited the pupils to describe
what they could see as she introduced them to various features of the software. Each pupil had the
worksheet of their marked responses to a set of ten questions on algebra, on which they could record
their ideas and thinking. The researcher then led the class in a discussion on the following: Starting
with the letter ‘b’, divide by 4, add 2, and then multiply the result by 5. Write down the final algebraic
expression.
The pupils offered their suggestions of operations the researcher was to perform in terms of
movements across the grid as they watched the resulting expressions form on the screen. The pupils
appeared to appreciate seeing for themselves the structure of the final algebraic expression given by
the software.
From the Tasks mode, the researcher selected Task 22: ‘Substitution’ and chose ‘Difficulty Level 3:
Expression with 3 operations’ and asked the pupils to read the instructions accompanying the
question, which asked the user to find the value of an algebraic expression involving x, for a given
value of x. The algebraic expression was contained in a red cell while the value of the letter was in a
blue cell. The question required the predicted value of the expression to be selected from the ‘Number
Box’ and dragged into the red cell.
Low murmurs erupted in the room as pupils worked out the question, some individually, while others
discussed softly amongst themselves. Hands were raised as pupils indicated their willingness to be
selected to offer their answers; the rules of engagement in this classroom required everyone to listen
to a single contribution at a time. One pupil was randomly selected to offer their answer, which the
researcher dragged into the highlighted cell; the rest of the class watched the feedback offered by the
software. A correct answer gave way to the next question. When a wrong answer was offered to a
subsequent question, a ‘No Entry’ sign appeared on the cell with the expression, and a bin showed at
the bottom right of the screen. At this point, the researcher requested the contributor to explain how
they arrived at their answer. A class discussion ensued as other pupils were invited to identify the flaw
in the reasoning and possibly to correct it. A further click of the mouse resulted in the wrong answer
being ‘binned’. This process was repeated through an entire level of questions, at the end of which the
software offered a summative score with a brief comment, and the option either to repeat the task at
the same level of difficulty or to select the next level or to quit the program. The pupils responded to
the experience of predicting and reflecting by actively debating why a contributor’s answer worked or
did not work.
The pupils were then asked to turn, in their groups, to the software on their own screens, to select the
relevant task and to work through the questions; the software marked their work and offered them
instant feedback. In this session, the pupils worked through two software tasks.
•
Task 1: ‘Calculating’
This task consisted of a series of questions, each involving numbers only, in a highlighted cell in the
grid. The pupils practised their arithmetic skills with motivation to manipulate the software as they
negotiated and discussed their reasoning in groups [3]. The software promptly marked their answers,
providing instant, non-judgmental feedback that encouraged the pupils to make predictions, test them,
discuss the outcome and, if necessary, modify their mathematical ideas.
•
Task 21: ‘Simplify’
This task offered questions with an algebraic expression consisting of both numbers and letters in a
highlighted cell in the grid and an ‘Expression Calculator’. The pupils were required to type into the
calculator a simpler expression equivalent to the one that was given; then the software gave them
feedback on their responses. As the control of the activity is accomplished through manipulation of the
computer’s mouse, the pupils were allowed to drag numbers and letters across the grid and to
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observe the structure of the resulting representations on the screen. In this way, the pupils worked
with agency and received non-judgmental feedback.
2.3
Session 2
The same procedure as that used on the previous day was used as pupils worked on the following
tasks.
•
Task 13: ‘Make the expression (letters)’
This was a timed task that required the pupils to create prescribed algebraic expressions by dragging
a letter across the grid within a given time frame: ten seconds for difficulty level 1 and twenty for
difficulty level 2. Pupils earned marks if successful and none if they were time-barred. As members of
a learning community, the pupils were expected to consult each other on which movements
represented the correct operations to create the given expressions.
•
Task 25: ‘What is the expression?’
In this task, the pupils were presented with a journey made by a letter on the grid, and were asked to
type the algebraic expression representing the journey in the ‘Expression Calculator’ starting with the
given letter.
Each of these tasks required the pupils to have associated each movement across the grid with a
particular operation. The pupils had to put their thinking into action to create the required expressions,
and the software allowed them to undo wrong movements, as long as it was within the given time
frame in the case of Task 13. In this way, the pupils experienced that it was acceptable to make
mistakes whilst learning.
At the end of this activity, the pupils were given worksheets with four questions, each showing a
journey on the grid, and asked to write down the resultant algebraic expressions. From the responses
collected, 26 of the 45 pupils successfully observed symbol convention in writing the expressions.
Some of the other 19 pupils had not yet grasped the association of movement on the grid with the
mathematical operations. Others seemed to have forgotten that the rows were pre-determined and
that therefore horizontal movements on different rows would add or subtract different values.
However, we consider this outcome very encouraging, after only two sessions with the software,
especially given the willingness of the pupils to keep working at the tasks.
3
DISCUSSION
The evidence of impact of this brief study that emerged from the questionnaire and interview data
indicated enjoyment, greater access to mathematical concepts, increased engagement, participation
and interest in the learning of mathematics, as well as changes in attitude, motivation and confidence
on the part of the pupils.
Impact on Affect: 22 of the 45 pupils considered the Grid Algebra lessons enjoyable and fun, while
others used the terms ‘exciting’, ‘fascinating’, ‘amazing’ to describe the experience. Others reported to
‘love’ or ‘like’ their mathematics-with-ICT lessons. This suggested that the change in the learning
environment had an impact on the pupils’ affective domain and consequently on their learning of
mathematics [5]. In terms of the mathematical resilience model, the pupils felt included.
I like it because it expose us first to technology, like now we are able to use the computer even more,
because like in this world, it is a must to know computers so that you can go far, and most people like
when we were being taught these concepts in class, most of us just could not see it because it is
boring, but since we love computers, we engage more in the learning of mathematics (P41)
Agency: 44 pupils (98%) welcomed learning algebra on computers, believing that the computer activity
was beneficial and had a positive effect on the learning environment, indicating a high computer
motivation [5] despite the fact that some had little experience with computers. Through collaborative
working and the change of the learning medium, the pupils had agency.
I got to use something I had never used before, a software, and think about how I am learning (P45)
Because being in class is so monotonous and gets boring, by using Grid Algebra, the environment
changes and the fact that we love computer, learning tends to be fun (P10)
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These pupils were clear about the value they placed on using computers in the lessons, stating they
felt very much part of the “new generation” in taking advantage of the available new technology while
still learning mathematics as part of their normal schooling activities. This was irrespective of whether
they were getting all the exercises right or wrong. In contrast, one pupil suggested the activity may
make one lazy, with the computer taking over doing the work.
I prefer doing maths manually on a working-out paper. This helps me exercise my brain and know how
fast I am in maths…you feel like it is your own work, you are being helped to do it, that you can
actually do the sum without the help of the computer and you have your own speed…(P3)
This comment prompted the researcher to probe further through a follow-up, individual interview which
revealed that the pupil may already have been in her safe learning zone (see Fig.1) in algebra, since
the same learner also stated “it is really exciting to use the computer when learning maths”.
Learning community: A majority of the pupils appeared to value working in groups on computers,
discussing and sharing views as they learned mathematics. In terms of the mathematical resilience
model, the pupils were being members of a supportive community of practice.
Personally I thought it was a good way of helping us work as a team and working together, not without
backing, but doing things with other people. Most of the time… we put our heads together and think as
one, not as separate people...that helped us, I think, to get the tasks right, and we felt like we had
achieved something (P5)
It was nice to hear other people’s opinions, get other points of views other than just my own, and hear
people debate…it was fun working together because most of the time we are just alone! (P43)
It helped us work together as a group and enjoy ourselves when doing mathematics, and not many
people get to do that at all. It gives you a chance to debate and give your points of view, and you are
able to learn more from others, unlike in class, when you are calculating, you are on your own (P40)
We argue that discussion-based classroom activities offer pupils autonomy and choice, as well as
opportunities to articulate and share their mathematics, enabling them to be active, resilient
participants with responsibility for their own learning. The pupils felt this dimension gave them deeper
insights into the concept of reading and writing algebraic expressions. However, not all the pupils
embraced this way of working:
Okay, if we are discussing after having attempted the work on our own, not when we do it together,
because everyone gets their own answers, everyone has their own methods. After you get your
answer, you can discuss to see who is correct. (P3)
This pupil appeared to have a distinctive view of the role of a learning community. Not all pupils
socialize in the same way; others may be reluctant to change, having become habituated to receiving
knowledge from figures of authority, either the teacher or the textbook, and being quite content to
remain in their comfort zone (see Fig. 1) by mastering procedures and arriving at the correct answers
[6].
Deeper understanding: The pupils expressed a belief that using Grid Algebra enhanced their learning
by enabling them to make and see useful links within algebra and with other areas in mathematics, an
indication of high computer-mathematics interaction [5] and increased learner agency in terms of the
mathematical resilience model.
It showed us the steps of getting to the answer rather than having some examples by the teacher on
the board and you would not really understand why, like writing algebraic expressions (P28)
I gained a lot, and helped me know about Integers, that I now understand even more about negative
numbers since I was not getting the concept before the lessons with Grid Algebra (P24)
Twenty of the pupils indicated their appreciation of the provision of variety in their learning activities;
variety afforded them an opportunity to explore with the tool that served to enhance their grasp of
concepts through curiosity and mental challenge.
It makes you curious to know what happens next, and it also expands your thinking because you have
to think about what would happen if I drag it this way, how it goes when you drag it down… (P1)
Motivation changed: There was a marked change in pupil motivation towards their learning as stated
by 21 of the study pupils, which they attributed to the ICT-enabled interactivity and feedback that
encouraged them to engage with the learning process with increasing competence and confidence.
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I learnt how to use the Grid Algebra program which I did not even know, had never heard about. That
encourages me that I can do better by learning and understanding more. It was lovely because people
got to concentrate on maths because they were working on computers, and it made people to
concentrate more in class (P44)
Change in perception of self in relation to algebra: 12 of the pupils stated that they no longer
considered the topic ‘difficult’ or ‘hard’ nor themselves ‘poor’ in algebra, indicating a changed
relationship with the topic and with mathematics as a subject. In terms of the mathematics resilience
model, this indicated increased inclusion due to increased accessibility.
These lessons helped me realize that algebraic expressions are not as hard as everyone thinks. It has
shown us that algebra is not that hard (P13)
It gives all the simplicity of mathematics, which sometimes seems complicated when we do it in class.
It makes maths appear more simple than how we see it… and helps us understand better, also to
apply it. It gave me the psyche to do more, practice more to see if I have really understood. (P36)
Raised interest: The pupils underscored the importance of being allowed to be active learners; 18
members of the group expressed an increase in interest in their learning of algebra and mathematics
Maths became an interesting subject when we used the computer to do algebra. I got to see the fun
part of maths as we were doing it practically as a group, thus helping each other to understand (P30)
Grid Algebra is easy to understand and simple enough for anyone to use and makes learning more
fun. Now at least I find algebra more interesting and fun (P37)
Acquisition of new skills and attitudes: Despite the brevity of the intervention, there were explicit
expressions of changed attitudes by 12 of the pupils, and 10 pupils commented that they had acquired
new skills in both mathematics and computing.
It has helped me improve both my mental calculations in math, and computer skills, and also given me
a positive attitude towards algebra (P11)
I have a positive attitude towards algebra now and it’s simpler so am able to take my assignments
especially in algebra and do it with a positive mind (P16)
Inclusion: Some of the pupils appeared particularly to value ‘connected knowing’ [6] in applying their
secure ‘met-befores’ [20] through discussion as they shared the tasks in the sessions.
We got to understand deeply the basics of expressions, how they come to be in a more real manner
(P32)
Grid Algebra makes learning fun, interesting and easy to learn and understand. I am now able to
understand algebra better and to see it practically (P1)
By understanding what is taught since it is not easy to forget because the grid reminds you. Through
Grid Algebra, I was able to understand algebra more, and see how easy it is (P9)
4
CONCLUSION
The introduction of Grid Algebra as an environment, allowing pupil agency, combined with
collaborative working in small groups, was designed to inculcate agentic, social learning into these
pupils’ mathematics lessons. The activities were learner-centred, with the pupils taking control of the
tasks in which they actively participated with a shared sense of excitement and curiosity in their quest
for higher attainment. The opportunity for peer interaction contributed to a relaxed atmosphere within
which the pupils articulated their mathematical reasoning; articulation of itself supported their growing
understanding. The pupils were encouraged to compare each other’s ideas and decisions against the
computer’s representation of a contributor’s input, the computer taking the role of ‘more
knowledgeable other’ at such times. By drawing upon pupils’ knowledge of the multiplication table
underpinning the grid, the symbolic representation by the software served to scaffold the pupils’
development of a structural conception of algebra within an arithmetic context.
This software challenged the pupils to solve problems, and allowed them the freedom to make and
correct their mistakes; when pupils entered a solution, the software immediately provided pupils with
non-judgmental feedback. The researcher’s observations revealed that pupils were able to build upon
what they already knew by linking algebraic representation to familiar movement, which enabled pupils
to experience a sense of inclusion in algebra. Both the software environment and the organisation of
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interactions within the classroom were designed to reduce feelings of frustration and anxiety that are
often experienced by pupils in algebra lessons. The support provided by the software, and the
positive nature of the group interactions in this lesson, were intended to dispel any feelings that a pupil
might have brought to the lesson that algebraic ideas are inaccessible. In addition, the teacher and
researcher, as adults, were available in the classroom to support the pupils, facilitating the pupils’
learning by enforcing social norms of interaction and by intervening to address any apparent
misconceptions. In this way, the learning environment was intended to ensure that pupils remained
safely within their individual growth zones (see Fig.1) and did not stray into anxiety, thereby affording
the pupils spontaneous, accessible and effective learning through collaboration, reflection, culture and
agency.
In a short study such as this, we cannot claim that the changes observed in the pupils would persist.
However, a group of five pupils from this class later acted as a team of ‘teachers’ to display an exhibit
for the School’s Open day, and revelled in explaining the learning of algebra using ICT to pupils from
other classes, teachers, parents and the School’s Principal. It seems that at least these five pupils
members may have changed their stance towards algebra more permanently, supported both by
peers and by ICT that used secure ‘met-befores’, feeling secure in making errors, and finding ‘it wasn’t
so hard after all’. Data from the subsequent, more extensive study will be reported in due course.
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