Digital Technologies refer to a wide range of devices which combine the traditional elements of hardware (processing, memory, input, display, communication, peripherals) and software (operating system and application programs) to perform a wide range of tasks. They include: technical applications; communication applications; consumer applications and educational applications (The Joint Mathematical Council of the United Kingdom, 2011, p.3)
The tools of the twenty-first century are already allowing learners to shift from being ‘consumers of knowledge’ to ‘creators of knowledge’. More and more devices and services allow learners to work more creatively and collaboratively than ever before. Helping them to develop their skills that allow them to work collaboratively, innovatively and to interact with a truly global audience is key to develop more independent and interdependent learners.
The future will bring tools and services that allow learners to create even more personalised content and interact with the digital world in ever more immersive and engaging ways.
Read the following two statements made by The Joint Mathematical Council of the UK in 2007 (p.5).
The vast majority of young people are involved in creative production with digital technologies in their everyday lives, from uploading and editing photos to building and maintaining websites. They acquire many skills which will be relevant in their careers, but which are not drawn on during their time in school. They acquire new skills rapidly, and share their knowledge with their peers – but rarely in an educational context.
Whereas digital technologies are the ‘tools of the trade’ of the modern scientists, technologists, engineers and mathematicians, young people are not likely to use digital technologies for the creative production of science, technology and mathematics in their everyday lives.
Do you agree? Do you think the situation has changed since 2007? If so, how? Why?
In a report by the National Centre for Excellence in Teaching Mathematics (September 2010), it concluded that mathematics teachers’ concerns about the use of digital technologies related to:
- a lack of confidence with digital technologies
- fears about resolving problems with the technology
- fears about knowing less than their learners
- access to digital technologies
- inappropriate training
- lack of time for preparation
- a lack of awareness of how technology might support learning
- not having technology use clearly embedded into schemes of work.
Within a survey conducted by the National Institute of Adult Continuing Education (NIACE) in 2011, it noted that technology in the teaching of literacy and numeracy is widespread. However, this use focused predominantly on the technologies most widely used in daily life: the Internet, Microsoft Office Suite applications and digital cameras. The ‘untapped potential’ of the following technologies was identified.
- The use of social media for learners to create content and to interact online (although inhibited by safeguarding concerns, lack of training for teaching professionals and institutional ‘blocking’ of social media sites).
- The use of open access educational resources.
- Distance learning opportunities.
- providing learners with access to an online learning space through a virtual learning environment (VLE)
- training to provide the skills and confidence to experiment with new technologies and how to manage a ‘connected classroom’
- improved access to equipment and connectivity
- institutional vision which encourages experimentation and allows for staff to ‘learn from mistakes’
- ease of access to resources (including ‘games’ and online video content).
1. Use the following list to ‘audit’ your current use of digital technologies in teaching numeracy.
|Mathematical software (e.g. a graphing program)|
|DVDs or CD-ROMs|
|Visualiser or web-camera|
|Data logging equipment|
|Tablet device (with apps)|
|Robot (e.g. roamer, beebot)|
|Virtual manipulative (e.g. onscreen version of a calculator, protractor, fraction wall)|
|Online video content|
|Social media websites|
2. Consider the concerns identified by teachers in the NIACE survey (2011), the ‘untapped potential’ of technologies and the factors which might support the integration of digital technologies in numeracy learning and teaching. Reflect upon these in relation to your own teaching in your professional reflective journal.
Hwb – the all-Wales learning platform
A new digital learning platform for all learners aged 3–19 in Wales was launched in December 2012. Hwb (external link) is a bilingual all Wales virtual learning environment which allows teachers and learners to access online resources anywhere, at anytime and from any internet enabled device. It includes all the content from the NGfL Cymru website.
The virtual learning environment made up of an integrated collection of online tools and services for teachers, learners, governors, parents/carers and other stakeholders, will support learning and teaching. This includes support for developing numeracy across the curriculum.
Teachers and learners are able to create and share their own resources, to work collaboratively, and to have access to tools and content hosted across the web. Schools and colleges also have the opportunity to create and host their own local platforms, tailored to their own needs through Hwb+. This will be a secure area which only they can access.
- View this YouTube video which provides a visual overview of the Hwb+ online portal (external link) .
- Now read this article about Hwb+ (external link). What key issues are raised in the article? What potential impact might this online portal have for creating a numeracy friendly learning environment – for learners? For teachers?
Mobile technologies and the numeracy classroom
Kearney and Maher (2013) explore mobile learning in teacher education contexts as part of a growing body of research into ‘m-learning’ approaches. They highlight the potential hand-held devices have in supporting collaborative and contextualised learning. They suggest that their use may help teachers to move away from overly-didactic approaches to mathematics/numeracy teaching or de-contextualised tasks which are removed from ‘real-world settings’ (p.77).
Tangney et al (2010) present the view that learners in secondary schools are seldom exposed to real world data, situations or problems as part of mathematics teaching and therefore experience difficulties in relating their learning to aspects of the daily life. However, in their study they provide examples of how smart phone applications are used as the foundation for building learning scenarios in real-life contexts. This approach based upon social constructivist principles encourages learners to use ‘apps’ to explore concepts such as trigonometry and fractions, rather than presenting a series of mathematical rules or procedures.
Attard and Curry (2012) state that one of the most significant influences on learner engagement is the teacher’s pedagogical practices, including the incorporation of technology into the learning and teaching of mathematical concepts and procedures. However, support for professional development is required if such use is to have a positive impact on learning and teaching.
The small-scale study described by Attard and Curry uses the ‘TPACK framework’ (i.e. Technological Pedagogical Content Knowledge) developed by Mishra and Koehler (2006) which builds on Shulman’s pedagogical content knowledge framework (1986). Mishra and Koehler argue that there are three essential components which lead to effective teaching with technology: content, pedagogy, and technology
Reproduced by permission of the publisher
© 2012 by tpack.org
It requires an understanding of the following:
- The representation of concepts using technologies.
- Pedagogical techniques that use technologies in constructive ways to teach content.
- Knowledge of what makes concepts difficult or easy to learn.
- Knowledge of how technology can help to redress some of the problems that learners face.
- Knowledge of learners’ prior knowledge.
- Knowledge of how technologies can be used to build on existing knowledge to develop new knowledge.
(Koehler and Mishra 2009)
Niess et al (2009) recognise that teachers require guidance in the development of their ability to effectively use technology to enhance the teaching and learning of mathematics (or numeracy). They present a model which identifies five steps that teachers progress through when integrating a new technology such as a tablet device.
1. Recognising (knowledge)
Recognising that a specific technology can be used in learning and teaching, but not yet integrating it into the learning and teaching of mathematics.
2. Accepting (persuasion)
Teachers form either a favourable or unfavourable attitude towards learning and teaching mathematics with an appropriate technology.
3. Exploring (implementation)
Teachers actively integrate learning and teaching of mathematics with an appropriate technology.
4. Adapting (decision)
Teachers engage in activities that lead to a choice to adopt or reject learning and teaching mathematics with an appropriate technology.
5. Advancing (confirmation)
Teachers evaluate the results of the decision to integrate learning and teaching mathematics with an appropriate technology.
Reflect upon your own use of mobile technologies in the classroom.
- How has this come about?
- Have you used mobile technologies in teaching numeracy?
- How is this the same or different to using technologies in mathematics?
- Have you experienced the five-step progression that Neiss et al (2009) present? Was this a linear process?
- Have you received professional development in order to effectively integrate technology into your teaching?
- How might you further develop the use of mobile technologies in order to develop learners’ numeracy skills?
Record your reflections in your professional reflective journal.
An example of how mobile technology is being used by one primary school is found in sub-topic 3.2 Effective learning and teaching in numeracy.
Exploring the Use of iPads to Engage Young Students with Mathematics (external link)
Attard and Curry’s small-scale study (2012) of the impact of using iPads in a Year 3 primary classroom in Sydney, New South Wales.
Beetham, H. and Sharpe, R. (2007) (Eds). Rethinking Pedagogy for a Digital Age: Designing and delivering e-learning. Oxon: Routledge
The National Centre for Excellence in the Teaching of Mathematics (NCETM) report, ‘Mathematics and Digital Technologies: New Beginnings’ (external link) (September 2010) provides a useful overview of essential equipment and features of the mathematics classroom. This provides a good starting point for considering what resources should be available in a numeracy learning environment.
Attard, C. and Curry, C. (2012) Exploring the Use of iPads to Engage Young Students with Mathematics. New South Wales: Mathematics Education Research Group of Australasia Inc. (accessed 30 September 2013).
Kearney, M. and Maher, D. (2013) Mobile learning in maths teacher education: using iPads to support pre-service teachers’ professional development. Australian Educational Computing, 27 (3).
Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper S. R., Johnston, C., Browning, C., Özgün-Koca, S. A., & Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education [Online serial], 9(1).
Tangney, B., Weber, S., Knowles. D, Munnelly, J., Watson R., Salkham, A., and Jennings, K. MobiMaths: An approach to utilising smartphones in teaching mathematics. MLearn. Malta. Jan. 2010.
Promoting and supporting the integration of ICT (PDST) Technology in Education promotes supports the integration of ICT in learning and teaching. It is part of the national support service, the Professional Development Service for Teachers, which operates under the Department of Education and Skills. The PDST is managed by the Dublin West Education Centre (DWEC).
Technological Pedagogical Content Knowledge (TPACK) Framework (external link)
A description of the TPACK Framework developed by Koehler and Mishra which presents their view of the nature of knowledge required by teachers for effective technology integration in their teaching.