Why has Digital Culture and Secondary Mathematics in Australia been Asymptotic to Date?

Peter Gallagher

Abstract

Take a moment to think about your high school maths class. Remember the screech of the chalk as unending formula were engraved and expounded by your aging educator in their monotonal mutter? Remember drifting off during algebraic fractions and carving indentations in your wooden desk with your metal ruler instead of copying furiously, HB in hand, into your exercise book? You smile at that memory but also sigh in relief that students today do not have to endure such lacklustre and lifeless teaching but in its place are encircled by learning environments and technologies that enhance their understanding of mathematics. Or are they? Have maths teachers embraced the technology in which their ‘digital native’ students frolic?

The need for a renewed digital culture in the study of Secondary School Mathematics in Australia has never been more evident. Since the introduction of computers into educational campuses, a strong integration between mathematics and digital technologies has been expected. This union, however, has failed to wed and today we find many mathematics classrooms very much the same as they were 30 years ago. Through examining research papers, online articles and the writings of influential thinkers, this paper will examine possible explanations for this gap between promise and delivery, how digital technologies have attempted to influence the pedagogy of classrooms, as well as looking at opportunities to further assimilate a digital culture into the teaching of mathematics.

For more than 30 years, Australia has been moulded and changed by the technological revolution, along with the growing emergence of a digital culture. As a result, the vehicles used for learning by students today are very different to that of their parents. As a whole, students are interfacing with their laptops, smart phones and tablets and accessing the internet to obtain instantaneous and contemporaneous knowledge and insight into topics. Students seemingly already know what Groom (2012, p. 15) postulates when he states that “the internet is no longer about knowing web addresses, but knowing where to find other people who curate, exchange and analyse potentially useful ideas, methods and information to amplify, consolidate and improve performance”. However Australian mathematics teachers as a whole appear to shy away from such a medium and underutilise its potential in the classroom.

Goos and Bennison (2008, p. 102) recognised this promise of a world where mathematics teachers embrace new technology, stating “for some time education researchers have recognised the potential for mathematics learning to be transformed by the availability of digital technologies”. For decades, the relevance and authenticity of both mathematics content and its teaching in the Australian classroom has been questioned. In 1988 Richard Noss (p.251) identified that there was “a cultural gap between the mathematics that children do as part of their everyday experience and the mathematics that they learn at school”. Barak and Asad (2012, p. 81), when investigating the writings of Dewey (1963), Bandura (1975) and Bruner (1996), found that “educators widely agree that one of the keys in fostering learning in school is linking subject matter and instructional methodology with students’ real-life situations, experiences and interests”. Noss (1988, p. 265) suggested that the solution for mathematics education and its relevance for students was to “alter the content of the mathematics we teach”. It appears that this counsel has gone unheeded.

Not only was it identified early that the content needed to change, but the delivery too, as recognized by Kinnane (2008, p. 33) who warns that “the traditional chalk and talk pedagogy of the past will not work as the sole method of instruction for this generation of students”. This sentiment is echoed by Franciosi (2012, p. 243) who found that “the common theme suggested by the literature is that the traditional model … is unworkable in the digital culture”. Unfortunately Goos and Bennison (2008, p. 102), report that “recent international research shows that technology still plays a marginal role in mathematics classrooms”. Despite a slow start, mathematics teachers need to shrug off the real and perceived challenges of the emergence of digital cultures to our schooling system and embrace “the potential of technology to develop students’ understanding, stimulate their interest, and increase their proficiency in mathematics” (National Council of Teachers of Mathematics, 2011, para. 1). However in order to improve the effective amalgamation of digital culture and mathematics, we need to not only examine the digital technologies introduced but also the successful delivery of these technologies by our teachers, one of their said challenges.

Noss (1988, p. 263) affirms this notion when he asserts, “the introduction of the computer in the learning environment entails more than simply a technological component (hardware and software)… there is a pedagogical component”. Apperley and Walsh (2010, p. 125) are sympathetic to the mathematics teachers plight when they state that “digital technologies are not ‘teacher proof’ tools: they require thoughtful and thorough integration into pedagogy, in a manner that reflects carefully articulated instructional and learning goals”. However many teachers find this process of integration to be quite daunting and time consuming for as Robinson (2008, p. 50) points out “many teachers are too busy with the day-to day challenges of educational practice to keep up”. Educators also find themselves as somewhat out of touch with these ‘new technologies’, lamenting that they are forever developing and changing, a view reiterated by Kinnane (2008), when discussing to the work of Prensky (2001), who identifies teachers today as ‘digital immigrants’, those for whom this same language is a second language, something new to be learned (p. 32). This idea is reiterated by Groom (2012, p. 15) finding “resources … can be complex to implement as teachers struggle to learn how to use systems and resources that are embedded inside digital culture”.

As a result, mathematics teachers tend to revert to their comfortable ‘tried and true’ practices, which in turns sees them, their school and their students “becoming more disconnected from the reality of the changing world” (Barak & Asad, 2012, p. 82). Unfortunately, this reticent adoption by teachers seems to be one of the major stumbling blocks to the effective use of digital technologies in mathematics.

A survey conducted by Merrilyn Goos and Anne Bennison entitled Teacher’s Use of Technology in Secondary Mathematics Classrooms found that a “substantial proportion of teachers reported attitudes that suggested they remained unconvinced of the benefits of computers for students’ learning”(2008, p. 106). This idea, however, is juxtaposed with that of Borwein (2008, p. 55) who found that technology assists the “teacher to provide enriched material (say, on fractions, binomials, irrationality, fractals and chaos) to the brightest class while allowing more practice for those still struggling with the basics”. Therefore, rather than apportioning the blame on teachers, perhaps we need to agree with Wiske (2001, p. 69) who maintains that teachers “shape the impact of computers in schools more than the features and software. If we want to understand how to improve learning in schools, we need to pay more attention to the conditions affecting the culture and profession of teaching”.

Although having been developed in the mid-1980s, a technological device that has been readily accepted by mathematics educators nationally in recent years are calculators, both scientific calculators and graphics display calculators. This adoption is reported by Goos and Bennison (2008, p. 103) may be due to “various Australian state and territory curriculum statements and syllabuses now permit, encourage, or require use of digital technologies in secondary school mathematics”. In a further study, Goos (2010, p. 67) found that “calculator use has either a positive or neutral effect in students’ operational, computational, conceptual and problem-solving skills”. Noss (1998, p. 264) applauded the use of calculators in classrooms suggesting that calculators “used in suitable ways, can expand what it is possible to do, learn and teach in mathematics classrooms”. Borwein (2008, p. 33) now encourages mathematics teachers to at least graduate to the use of the personal computer within the classroom, as he purports that “computers are a very helpful, if not essential, component of a constructivist approach to the mathematics curriculum”. He continues, “The power of the modern computers matched with that of modern mathematical software and the sophistication of current mathematics is changing the way we do mathematics” (2008, p. 34).

But what of today’s technology? When examining which digital technologies may assist in the teaching and learning of mathematics in the Australian classroom, Wiske (2001, p. 70) advises educators that three important conditions be met:

1. The technology must afford significant educational advantage

2. The technology must be readily affordable, networked and portable

3. Technology alone does not change school practice

In terms of technologies currently available to meet these conditions, we can divide them into two categories; software-based and internet-based applications (although it is noted that internet-based are developed from some form of software). Examples of software-based include: TI-Nspire software, Autograph, Graphmatica, Microsoft Math, EFOFEX, MathType, MATLAB, and SAS.

These more traditional forms of technology, however, may be deemed by students as ‘archaic’ in so far as they do not provide instant results or feedback and there use must be first learnt. Osbourne, Dunne and Farrand (2013, p. 3) see the technology issue as “something of a moving target. As the digital world matures, traditional models of technology use in education are being challenged”. Therefore we must turn our attention to internet-based applications, for which most students are already aware of and possible use everyday. Applications like: YouTube, Flickr, Twitter, Facebook, Google and Google Scholar, View, Moodle, Blackboard, as well as digital libraries, websites, blogs, wikis, webcasts, RSS feeds, applets and games. Apperley and Walsh (2010, p. 126) see these applications as beneficial as there use “increases participation in the learning process [and] deliver positive outcomes for students with different learning styles”, a sentiment backed by Walshaw (2012, p. 405) who argues through the use of aforementioned applications, “alternative approaches to mathematizing and alternative mathematical thinking might emerge”.

Not only do schools require modern programs and applications to improve the mathematical learning of students, resources for teacher and students alike need to be developed so as to meet the growing demands of our digital culture. The National Council of Teachers of Mathematics (2011, para. 4) believes that these resources should “take advantage of technology-rich environments and the integration of digital tools in daily instruction, instilling an appreciation for the power of technology and its potential impact on students’ understanding and use of mathematics”.

Teachers need to be working side by side with students in the pursuit of effective mathematical learning, not in front or behind them. Students will play their part, for as Robinson (2008, p. 54) sees it “maybe we should be inviting students to teach the new digital culture to their teachers”. Nevertheless, teachers are crucial to the process, as Goos (2010, p. 70) quite eloquently articulates it “in their hands lies the task of enacting a truly future-orientated curriculum that will prepare students for intelligent, adaptive and critical citizenship in a technology-rich world”.

References

Alves, D. B., & de Souza Júnior, A. J. (2013). Mathematics Education in a Digital Culture. Journal of Mathematical Modelling and Application, 1(8), 32-41. Retrieved from http://gorila.furb.br/ojs/index.php/modelling/article/view/3354/2469

Apperley, T., & Walsh, C. S. (2010). Digital culture & education: classroom perspectives. Digital Culture & Education, 2(2), 124-127. Retrieved from http://oro.open.ac.uk/27766/1/dce_classroom_perspectives.pdf

Bandura, A. (1975). Social learning & personality development. New York, NY: Holt, Rinehart & Winston.

Barak, M., & Asad, K. (2012). Teaching image-processing concepts in junior high school: boys’ and girls’ achievements and attitudes towards technology. Research in Science & Technological Education, 30(1), 81-105. doi: 10.1080/02635143.2012.656084

Borwein, J. (2006). Implications of experimental mathematics for the philosophy of mathematics. In B. Gold & R. Simons (Eds.), Current issues in the philosophy of mathematics from the viewpoint of mathematicians and teachers of mathematics: Mathematical Association of America. Retrieved from http://docserver.carma.newcastle.edu.au/280/1/implications.pdf

Bruner, J. (1996). The culture of education. Cambridge, MA: Harvard University Press.

Dewey, J. (1963). Experience and education. The Kappa Delta Pi Lecture Series. New York: Macmillan.

Franciosi, S. J. (2012). Transformational leadership for education in a digital culture. Digital Culture and Education, 4(2), 235-247. Retrieved from http://www.digitalcultureandeducation.com/cms/wp-content/uploads/2012/09/dce_4001_franciosi.pdf

Goos, M. (2010). Using technology to support effective mathematics teaching and learning: What counts? Australian Council for Educational Research. Retrieved from http://research.acer.edu.au/cgi/viewcontent.cgi?article=1067&context=research_conference

Goos, M., & Bennison, A. (2008). Surveying the technology landscape: Teachers‘ use of technology in secondary mathematics classrooms. Mathematics Education Research Journal, 20(3), 102-130. Retrieved from http://eric.ed.gov/?id=EJ836455

Groom, D. (2012). Evolvability: a world of persistent ambient digital culture. Scan 31(1), 14-17. Retrieved from http://search.informit.com.au.libraryproxy.griffith.edu.au/fullText;dn=191033;res=AEIPT

Kinnane, A. (2008). Who Are We Teaching Again?: Teaching in a Digital World. Literacy Learning: The Middle Years, 16(2), 32-33. Retrieved from http://search.informit.com.au.libraryproxy.griffith.edu.au/fullText;dn=168994;res=AEIPT

National Council of Teachers of Mathematics (2011). Technology in Teaching and Learning Mathematics. Reston, VA: Author. Retrieved from http://www.nctm.org/Standards-and-Positions/Position-Statements/Technology-in-Teaching-and-Learning-Mathematics/

Noss, R. (1988). The computer as a cultural influence in mathematical learning. Educational Studies in Mathematics, 19, 251–268. Retrieved from http://www.jstor.org.libraryproxy.griffith.edu.au/stable/pdf/3482577.pdf?acceptTC=true

Osborne, R., Dunne, E., & Farrand, P. (2013). Integrating technologies into ‘‘authentic’’ assessment design: an affordances approach. Research in Learning Technology, 21. Retrieved from http://www.researchinlearningtechnology.net/index.php/rlt/article/view/21986http%3A

Prensky, M. (2001). Digital natives, digital immigrants. On the Horizon, 9(5). Retrieved from http://search.informit.com.au.libraryproxy.griffith.edu.au/fullText;dn=141401;res=AEIPT

Robinson, K. (2008). The Other Climate Crisis: Digital Culture, Demography and Education. Media International Australia, 128, 49-58. Retrieved from http://search.informit.com.au/documentSummary;dn=914332253168502;res=IELLCC

Walshaw, M. (2012). Book Review: Interpreting how students come to understand mathematics in the digital environment. Nigel Calder (2011). Processing mathematics through digital technologies: The primary years. Educational Studies in Mathematics, 81(3), 401-405. Retrieved from http://download-v2.springer.com/static/pdf/959/art%253A10.1007%252Fs10649-012-9403-0.pdf?token2=exp=1429325429~acl=%2Fstatic%2Fpdf%2F959%2Fart%25253A10.1007%25252Fs10649-012-9403-0.pdf*~hmac=f8830bd84fb2950b1bc3796bfee1cac2350c4ca84180d2c7ceb4a7c44465ebdb

Wiske, S. (2001). A new culture of teaching in the 21st century. In D. T. Gordon (Ed.), The digital classroom (pp. 69-77). Cambridge, MA: Harvard Education Letter.

Link Introduction page: