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Using coding to teach mathematics: Results of a pilot project

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Abstract

The Australian Curriculum: Digital Technologies provides an opportunity for teachers to integrate coding and computational thinking within their STEM teaching practices. However, this opportunity has proven to be a challenge for many teachers, as their self-efficacy with respect to teaching these new skills is often low. This research explores the implementation of a professional development program that focussed on the integration of coding and computational thinking within the teaching of mathematics in primary school classrooms. In particular, we study changes in teacher selfefficacy with regards to coding and computational thinking before and after participating in the program. Using the validated Teachers’ Self- Efficacy in Computational Thinking (TSECT) instrument as well as focus group data, we analyse the experiences of 15 primary school teachers in New South Wales, Australia. We conclude that the program, based on the ScratchMaths resources developed in the UK, was successful in improving teachers’ self-efficacy towards both computational thinking and the integration of mathematics and coding. Our qualitative analysis of the focus group conversations also highlighted teachers’ positive perceptions of student engagement and the need to make the mathematics concepts underpinning the ScratchMaths modules more explicit.
Integrated EducaƟon for the Real World
5th InternaƟonal STEM in EducaƟon Conference
Post-Conference Proceedings
hosted by the Queensland University
of Technology, Brisbane, Australia,
21st to 23rd November 2018
Page 152
Holmes, K., Prieto-Rodriguez, E., Hickmott, D., & Berger, N.
USING CODING TO TEACH MATHEMATICS: RESULTS OF A PILOT PROJECT
Professor Kathryn Holmes
Western Sydney University,
Australia
K.Holmes@westernsydney.edu.au
Dr Elena Prieto-Rodriguez
The University of Newcastle
,
Australia
elena.prieto@newcastle.edu.au
Daniel Hickmott
The University of Newcastle
,
Australia
daniel.hickmott@uon.edu.au
Dr Nathan Berger
Western Sydney University,
Australia
N.Berger@westernsydney.edu.au
ABSTRACT
The Australian Curriculum: Digital Technologies provides an opportunity
for teachers to integrate coding and computational thinking within their
STEM teaching practices. However, this opportunity has proven to be a
challenge for many teachers, as their self-efficacy with respect to teaching
these new skills is often low. This research explores the implementation of
a professional development program that focussed on the integration of
coding and computational thinking within the teaching of mathematics in
primary school classrooms. In particular, we study changes in teacher self-
efficacy with regards to coding and computational thinking before and
after participating in the program. Using the validated Teachers’ Self-
Efficacy in Computational Thinking (TSECT) instrument as well as focus
group data, we analyse the experiences of 15 primary school teachers in
New South Wales, Australia. We conclude that the program, based on the
ScratchMaths resources developed in the UK, was successful in
improving teachers’ self-efficacy towards both computational thinking
and the integration of mathematics and coding. Our qualitative analysis of
the focus group conversations also highlighted teachers’ positive
perceptions of student engagement and the need to make the mathematics
concepts underpinning the ScratchMaths modules more explicit.
Keywords: Teacher professional development, computational thinking, integration of coding and
mathematics in STEM.
GOALS AND OBJECTIVES
Computer programming has been utilised as a pedagogical tool to facilitate
understanding of mathematical concepts since computer languages were made widely
available through personal computers. Early examples of using computer programming to
explore mathematics concepts through the process of ‘testing and debugging’ are found in the
literature as early as the 1960s (Feurzeig, 1969), although perhaps the most salient case of
advocacy for this pedagogical approach has been the one proposed by Seymour Papert.
Papert, a mathematician, posited that young people learn best when they are engaged in
the construction of digital and/or physical artefacts that are personally meaningful to them
and that can be shared with others (Papert, 1980). During the late 1980s, personal computers
were introduced in schools in the United States of America (USA) and the United Kingdom
(UK), which, in turn, allowed for the teaching of programming languages in mainstream K-
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12 education (Agalianos, Whitty, & Noss, 2006). The use of Papert’s ideas, including their
integration into mathematics classrooms, has been the object of notable studies since that
time (Benton, Hoyles, Kalas, & Noss, 2017; Hoyles & Noss, 1992; Kafai & Burke, 2015;
Kafai & Harel, 1991; Wilensky & Resnick, 1999).
Many countries, such as the UK, the USA and New Zealand, have recently introduced
STEM curricula in compulsory and post-compulsory schooling, and there is often a focus on
teaching coding and computational thinking within STEM (Bell, Newton, Andreae, &
Robins, 2012; Brown, Sentance, Crick, & Humphreys, 2014; Fisher, 2016). However,
introducing coding and computational thinking into compulsory education undoubtedly
presents challenges for teachers, as the learning of these skills has not usually been part of
their formal education. This is particularly true for primary school teachers, as they are
unlikely to have completed a technology major at university, are usually generalist teachers,
and often possess low levels of self-efficacy in relation to coding and computational thinking
(Bean, Weese, Feldhausen & Bell, 2015).
Interestingly, one of the approaches suggested for helping prepare teachers for teaching
coding and computational thinking is to integrate them into the STEM subjects they are
currently teaching, for example, mathematics (Barr & Stephenson, 2011). This approach to
teacher professional development constitutes the essence of the ScratchMaths project, led by
Hoyles and Noss (Benton et al., 2017), currently underway in the UK, designed to help
prepare primary school teachers undertake the challenging task of bringing the new digital
technologies curriculum in an integrated manner to their classrooms.
This paper reports on a pilot project centred on adapting ScratchMaths materials to the
Australian mathematics and digital technologies curricula and exploring its implementation
with 15 primary school teachers in the State of New South Wales (NSW), Australia. Our
research questions are:
x Does participant teachers’ self-efficacy with regards to coding and computational
thinking increase after learning and using the adapted ScratchMaths resources?
x Does their self-efficacy with regards to using coding to teach mathematics also
increase?
STUDY DESIGN
ScratchMaths is a project that incorporates the programming language Scratch. Scratch
is a visual programming language designed for introducing students to computing, which was
developed at MIT Media Lab (Resnick et al., 2009). Scratch is used widely by Australian
primary school teachers as a way to introduce coding in their classroom, and its pedagogical
possibilities in mathematics in Australian schools are currently being explored (Miller &
Larkin, 2017).
ScratchMaths is a two-year computing and mathematics-based curriculum for Key
Stage 2 in the UK (equivalent to Years 4 and 5 in Australia). Its aim is to enable students to
engage with and explore important mathematical ideas through coding in Scratch. The
ScratchMaths curriculum contains 6 modules of work and incorporates teacher guides,
classroom presentations, Scratch starter projects, additional challenges and reference posters.
For the Australian pilot project reported in this paper, we conducted professional
development in ScratchMaths with Stage 3 (Year 5 and 6) teachers. The pilot project ran for
roughly 8 weeks, commencing with a 2-day professional development workshop and ending
with a final showcase where teachers shared their experiences and samples of students’ work.
We also offered support during the interim classroom implementation period. The aim of the
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pilot project was to explore participant teachers’ perceptions of their ability to facilitate
students’ learning processes to develop mathematical ideas through coding, and how those
perceptions varied after an eight-week intervention.
The concepts covered in the workshops included sequencing and repetition (loops),
which are present in the Australian Digital Technologies curriculum (Australian Curriculum
and Reporting Authority [ACARA], 2017) and have been identified in the literature as
essential computational thinking concepts for students in the later stages of K-6 education
(Brennan & Resnick, 2012; Rich, Strickland, Binkowski, Moran, & Franklin, 2017).
The ScratchMaths investigations used in the workshops introduce or reinforce a couple
of computational and mathematical concepts and often build on concepts introduced in the
preceding investigations. In Figure 1, an example of a stack of Scratch blocks from
ScratchMaths is shown next to the tile pattern that results from these blocks being followed.
This example includes some of the computational and mathematical concepts present in the
investigations.
Figure 1. A stack of Scratch blocks and the resulting tile pattern
METHODOLOGY
To evaluate the effectiveness of our adapted resources, we used Social Cognitive
Theory and its concept of self-efficacy (Bandura, 1993). Our choice was based on our belief
that for teachers to embrace new concepts and pedagogies, they need to feel a certain amount
of confidence in their ability to impart these concepts and utilise the pedagogies. In order to
evaluate the change in teachers’ self-efficacy, we utilised the Teachers’ Self-Efficacy in
Computational Thinking (TSECT) instrument.
This instrument was developed by Bean et al. (2015) to evaluate very similar initiatives,
contains nine items, and has a high reliability (Chronbach’s Alpha = 0.935). Out of these nine
questions, we used only seven, as two of the original items relate to US Common Core
Standards and are irrelevant in the Australian context. We measured teachers’ perception of
their ability to facilitate their students’ development of mathematical ideas using coding,
using three validated questions from the ScratchMaths research project in the UK. All items
are shown in Table 1.
Research data was collected via two main methods. We conducted pre- (n=15) and
post- (n=8) intervention surveys linked through an identifier. The eight teachers who
completed the post-intervention survey had also completed it prior to the commencement of
the project. The surveys contained a range of Likert items as described above.
We aggregated each of the two scales into two variables by calculating mean scores.
These mean scores were considered non-categorical variables for analysis purposes. A small
number of open-ended questions were included in the surveys. These open-ended questions
asked about the methods of integration of mathematics and coding that participant teachers
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were already employing. Questions were also asked about the use of digital technologies for
teaching mathematics.
The workshops were conducted in two different locations in NSW. Participating
teachers came from a range of regional and metropolitan schools and across school sectors.
Four teachers attended the 2-day workshop in the regional location, and eleven in the
metropolitan location. Participating teachers were mostly female (n = 11) and their years of
teaching experience ranged from less than 5 years to over 20. The schools where they taught
were within the public and Catholic systems and had students with a very wide range of
socioeconomic backgrounds.
At the end of the school term we invited the teachers to showcase their students’ work
at each of the two project locations. After each of the showcases, we conducted two focus
group interviews. The total number of teachers participating in the focus groups was six: two
in the regional location and four in the metropolitan location. Both focus groups were audio-
recorded and approximately one hour in duration. Questions focused on teachers’ experience
teaching coding, computational thinking and mathematics; pedagogies preferred for teaching
in these areas; professional learning to date; and details on their implementation of
ScratchMaths.
RESULTS AND DISCUSSION
We observed gains in participants’ confidence with teaching across both areas (see
Table 1). All items were presented in a 5-point scale from Strongly Disagree (coded as 1) to
Strongly Agree (coded as 5). In terms of statistical significance, a paired-samples t-test was
conducted to compare teachers’ perceptions prior to attending the workshop and after
attending (n = 8).
There was a change in teachers’ perceptions of their ability to teach mathematics with
programming before (M = 3.3, SD = 0.47) and after the intervention (M = 4.5, SD = 0.08); t
= -5.09, p = 0.037. There was also a statistically significant difference in their self-efficacy
with regards to coding and computational thinking before (M = 3.2, SD = 0.78) and after the
intervention (M = 4.3, SD = 0.23); t = -5.05, p = 0.002.
Table 1. Pre- and post-survey results (items in Mathematics scale preceded by an asterisk)
Pre
Gain
I feel confident using simple programs for the computer.
4.60
0.11
I know how to teach programming concepts effectively.
2.67
1.48
I can promote a positive attitude towards programming in my students.
4.13
0.44
I can guide students in using programming as a tool while we explore other
topics.
2.93
1.50
*I can guide students in using mathematical thinking as a tool when
programming.
3.13
1.30
I feel confident using programming as an instructional tool within my
classroom.
2.67
1.50
I can adapt lesson plans to incorporate programming as an instructional tool.
2.93
1.35
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I can create original lesson plans, which incorporate programming as an
instructional tool.
2.87
1.28
*I understand how mathematics concepts relate to programming concepts.
3.00
1.43
*I appreciate the value of teaching mathematics and programming in an
integrated manner.
3.87
0.70
After attending the professional development workshops, teachers trialled the resources
with their students over a period of up to eight weeks. In the follow-up showcase and focus
group sessions with teachers, they all expressed positive sentiments about ScratchMaths.
Teachers presented student work samples, including students’ reflective comments on
ScratchMaths and unanimously reported that the students were engaged in learning and
looked forward to the ScratchMaths sessions each week. They also elaborated how the
resources were very well scaffolded and facilitated collaboration and social support for
learning.
With regards to our research questions, participant teachers reported an increased level
of self-efficacy with mathematics and coding. One teacher reflected: “mathematics has
always been my area of weakness, as a kid I had enormous anxiety in maths [but I could use
the resources because] it was very practical and made the 2D shapes understandable”.
Another teacher, who had a high level of self-efficacy from the commencement of the
project, said “maths is probably my favourite, I drive kids crazy ‘cos there’s no downtime in
maths classes [but] with coding you don’t know everything and the [resources were] prepared
so you could go back to the classroom and feel supported”.
Regarding the integration of mathematics and coding, teachers reflected that while
there was strong evidence for sustained student engagement with ScratchMaths, not all
students were actively engaged with the mathematical concepts underpinning the activities.
When this issue was discussed in the focus groups, the teachers agreed that the mathematical
aspects of the activities were not adequately understood by all students, and that in future
they need to be more explicit in directing students to engage with the mathematical
components of the module.
In the focus group conducted in the regional location one of the teachers commented
“the maths was a lesser learning outcome than the coding for us”, and the other responded,
“yes, some of them didn’t quite get the concepts. In the beginning some of them didn’t get
that they could do [360 degrees using a loop], so there was a lot of repetitions”. In the focus
group in the metropolitan area, teachers commented that in many cases students were taking a
‘trial and error’ approach to completing the patterns involved in the module, rather than
working through their solutions mathematically. They all agreed, however, that the activities
were “a good practical way to reinforce concepts” already taught.
CONCLUSIONS AND SIGNIFICANCE OF THE STUDY
Many argue that the term ‘computational thinking’ popularised by Jeannette Wing a
decade ago (Wing, 2006) is in no way different to logical thinking, a pedagogical construct
that is inherent in mathematics education (Grover & Pea, 2013). Thus, it would seem that
coding and mathematics are interlinked through shared conceptual ideas and therefore lend
themselves to an integrated pedagogical approach. In this pilot study we found that
participant teachers self-efficacy in relation to integrating mathematics and coding improved
significantly after a relatively short period of engagement with ScratchMaths.
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While this is a pilot project and the results on self-efficacy are not generalisable, the
observations made by participants have implications for future ScratchMaths professional
development sessions. Most of the participating teachers were coding novices, but through
the professional development sessions they readily learned the basics of coding and were able
to teach these skills to their students. However, for future professional development sessions,
more emphasis needs to be placed on the mathematical skills underpinning the ScratchMaths
modules and the pedagogical approaches that can be used to balance the mathematics and
coding content. We intend to modify the professional development we provided in this pilot
project to address the issues outlined above in order to continue our evaluation of
ScratchMaths in the context of a larger scale project.
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