Grammar Gazette- Issue 2, 2008

Curriculum

Curriculum

History’s Lessons Our staff present seminars to Queensland History teachers

Technology in Mathematics Education

Mathematics courses expose students to twenty-first century technologies. Dr Peter Jenkins discusses how they fit within the traditional notions of mathematics education.

History is an important course of study because by investigating the past students can make sense of the present and obtain critical insights for future possibilities.

In an age characterised by the ubiquity of technology, mathematics as a mode of thought, expression and discovery is evolving. Increased computing power and the development of sophisticated mathematical software have had the dual benefit of enabling mathematical ideas to be applied to more complex real-world problems, and enabling previously difficult mathematical concepts—for example, the visualisation of multi-variable functions—to be better understood by students. Despite this evolution, care must be taken when deciding how to incorporate technology in the mathematics classroom. The use of handheld calculators, for example, has always been controversial. Numerous educators (such as Perso, 2006, and Shuard, 1992) believe that there is little point teaching students mental or pencil and paper algorithms for arithmetic tasks since students will always have access to calculators or computers. Furthermore, they reason that the ease with which students can perform procedural tasks with a calculator frees the mind to focus on higher order thinking. Such attitudes ignore the hierarchical nature of mathematical concepts and imply that the steps in mathematical procedures are arbitrary and worthless. This is simply untrue. Consider the example of adding two fractions: important concepts such as equivalent fractions, highest common multiples, and the need for equivalent denominators in order to add the numerators, are consolidated each time a student performs

the algorithm. I believe only when a level of automaticity is reached with these concepts, will a student be able to understand more complex concepts such as the simplification of algebraic fractions. How then can technology be used to aid conceptual understanding instead of hindering it? The well-respected neuropsychologist and mathematician Stanislas Dehaene (1999) believed that educators must use technology to help students observe patterns, see connections, and observe the ‘fascinating regularity’ which so often appears in mathematics (p.135). At Brisbane Girls Grammar School, mathematics teachers use this rationale when creating dynamic geometry and algebra demonstrations using software such as Geogebra and Autograph, and helping students discover properties of functions and statistical data using their graphics calculators. One of the more recent developments in technology usage in mathematics education is the emergence of drill and practice software. Such software is designed to be used by students at home to gain additional practice at mathematics problems. Initially, such software packages were found to have little effect on student performance. Salomon (2000) states that ‘The use of review and practice applications is merely a repackaging of traditional teaching methods, with the content being displayed a bit faster and a bit nicer.’ (p.2). However, more recent versions of drill and practice software have

incorporated elaborate feedback loops which include additional explanations, and change the types of questions presented to the student based on previous mistakes. This incorporation of dynamic feedback to students has led to significant improvements in student performance (see Hill, 2007, for example). Brisbane Girls Grammar School students currently use the Mathletics and QAX software packages to gain additional practice solving mathematics problems. The educational rationale behind technology implementation in mathematics classes is clearly more important than the technology itself. Rather than attempting to adapt current curricula to suit the introduction of new technology (as is suggested in Kilderry et al., 2003), mathematics educators should instead focus on adapting the use of technology to better elucidate mathematical concepts. Dr Peter Jenkins Mathematics Faculty

Brisbane Girls Grammar has had a long and mutually rewarding connection with the Queensland History Teachers’ Association (QHTA).This connection dates back to the 1990s and has involved, among other things, Girls Grammar opening its doors and facilities to other Brisbane schools, private and public, for a series of QHTA History seminars. In the past eminent tertiary educators such as Associate Professor Russell Cowie fromThe University of Queensland and Dr Brian Hoepper from Queensland University of Technology (QUT) have addressed full audiences in the Gehrmann Theatre on topics related to modern history. This year for the first time Girls Grammar hosted both the QHTA Modern and Ancient History Student Seminars for central and north Brisbane schools. These seminars focused on popular topics drawn from the Senior Queensland Modern and Ancient History syllabuses.

History at Brisbane Girls Grammar and Vice-President of the QHTA, spoke about the rise of Hitler and the Nazi Party as a warning from history. Ms Hennessey cited the sobering words of Professor Ian Kershaw when he said that ‘Nazism cannot be regarded with detachment or seen as simply the arena for scholarly debates. Its history belongs to all of us. Its lessons should be heeded by all of us.’ (1997, p7). Nazism continues to be in our midst and this was dramatically illustrated by the Brisbane based flyer ‘Blood & Honour’ (see illustration) which was found at the bus stop between Boys and Girls Grammar some years ago.

hypothesis that people are the same regardless of time or place. She presented a range of evidence from Ancient China, India, Greece and Rome to encourage students to think about ancient people’s behaviour, ideas and emotions. Excerpts from the contemporary films Troy and Death at a Funeral were compared with extracts from the Hindu epic Mahabharata and the Funeral Oration of Pericles, the classical Greek statesman. Key to Ms Bolton’s presentation was the notion that history can give us a fuller understanding of ourselves and our common humanity. Collectively the presentations from the 2008 History Student Seminars illustrated the endless chain of history which links past, present and future. History is an important course of study because by investigating the past students can make sense of the present and obtain critical insights for future possibilities. Ms Julie Hennessey Head of History

References 1. Dehaene, S. (1999). The Number Sense. London: Penguin Books.

In one of the 2008 Modern History seminars, Ms Julie Hennessey, Head of Foreword by Professor Ian Kershaw in Rees, L. (1997). The Nazis: AWarning from History. London: BBC. In the 2008 Ancient History seminars, Ms Samantha Bolton, former Head of Ancient History and Head of Woolcock House at Girls Grammar, explored the

2. Hill, S. (2007). Mathletics - Improvement Analysis. Retrieved June 21, 2008, from http://static.3plearning.com/mathletics/www/ImprovementAnalysis_AUS.pdf 3. Kilderry, A., Yelland, N., Lazaridis, V., & Dragicevic, S. (2003). ICT and Numeracy in the Knowledge Era: Creating Contexts for New Understandings. Childhood Education, 79 (5), 293-298. 4. Perso, T. (2006). Issues concerning the teaching and learning of mathematics and numeracy in Australian schools. Australian Mathematics Teacher, 62 (1), 20-27. 5. Salomon, G. (2000). It’s not just the tool but the educational rationale that counts. Keynote address presented at Ed-Media, Montreal, Quebec, Canada. Retrieved June 21, 2008, from http://construct.haifa.ac.il/~gsalomon/edMedia2000.html 6. Shuard, H. (1992). CAN: Calculator use in the primary grades in England andWales. In J.T. Fey, & C. R. Hirsh (Eds.). Calculators in Mathematics Education: 1992 Yearbook. NCTM, Reston: VA.

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