Queensland Association of Mathematics Teachers

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QAMTAC '00
Mathematics - Going for Gold?

Wednesday 27th - Friday 29th September 2000
Gold Coast, The Southport School

Conference Paper Abstracts

A new era in accomplishment and excellence - Teachers'PBs (personal bests) in an interconnected world
Being a mathematician
Qmaths feedback
Assessment and graphics calculators
Mathematics meets history – Building the pyramids of Egypt
Using schemas to provide a perspective for evaluating approaches to teaching algebra
Particular mental strategies for incorporation into primary mathematics programs
Particular mental strategies for incorporation into primary mathematics programs
Describing excellence in the teaching of mathematics: Why bother!
Maps & compasses website
The graphics calculator – A VAT (value adding technology) in the mathematics curriculum
Preservice mathematics teacher education – using video to push the boundaries
The graphical calculator in junior mathematics extension
Using mental computations for developing number sense
Lessons for the classroom from chance and data research
Mathplot
Applying technology in the maths classroom
Using computers as a tutorial tool
Catering for different types of learners in mathematics
The processes in a mathematical investigation
Robotics and data logging
Linking science and mathematics to Multiple Intelligences and Bloom's Taxonomy
Mathematical and scientific visual representations: Are they really worth 1000 words? MATHPLOT

Ref No. 32

Geiger, Vince - Hillbrook Anglican School

Ref. No. 60

A new era in accomplishment and excellence - Teachers'PBs (personal bests)in an interconnected world

While the act of teaching has been practised throughout time, teaching, in the sense we now know it, is an occupation whose origins can be traced to the beginning of the 20th century. The challenge to teachers in the new century is to establish standards of accomplishment and excellence that do justice to the respect we as teachers demand from the educational and wider communities, and to the tradition established by those who have gone before us. This address will highlight current and emerging issues which will set the scene for the future development of mathematics teachers as professionals including Professional Teaching Standards, the role of teachers as researchers, models for teacher professional growth, and the leadership role of teachers as managers of change. These provide windows into a vision of the future of the profession viewed from the practical perspective of teachers. Back to Top

Burton, Leone - University of Birmingham

Ref No. 57

Being a mathematician

In this presentation, Leone will outline what she learnt from a recent study in which she interviewed 70 research mathematicians about how they come to know mathematics. She will draw links between the new learning of these mathematicians when they do research and the learning of pupils in mathematics classrooms and outline what she sees as the implications for teachers of mathematics of this study.

Swift, Stephen - Victoria Point SHS

Ref No. 12

Qmaths feedback

Stephen is one of the authors of the Qmaths series of textbooks. he will present information on planning for the second edition as a result of the changes to the syllabus. Participants are invited to criticise, provide information and feedback about the present series and to make suggestions for the second edition. At this stage of planning, it is possible to make considerable changes in order to better accommodate the needs of teachers. Stephen himself is a classroom teacher and wants to make the texts as useful as possible for classroom teachers.

Boggs, Rex - Glenmore SHS

Ref No. 24

Assessment and graphics calculators

Access to graphics calculators in Maths B and Maths C, as mandated in the draft syllabuses, will have a significant impact on assessment. There are lessons to be learned from educational systems in Australia and overseas that have already mandated graphics calculators and have faced the same issues now facing Queensland secondary mathematics teachers.

Walters,Megan, Horsley,Katrina & Goos, Merrilyn - University of Queensland

Ref No. 21

Mathematics meets history – Building the pyramids of Egypt

Curriculum integration is one of a number of related reforms to middle schooling currently under way in Queensland government schools as part of Education Queensland’s Frameworks Project. These reforms involving curriculum (new basics), pedagogy (productive pedagogies) and assessment (rich tasks) are intended to draw together different disciplinary areas to enable students to tackle real world tasks in an intellectually rigorous learning environment. This workshop seek feedback on sample curriculum units that integrate mathematics and history at junior secondary school level. Participants will have the opportunity to try out classroom activities from one such unit, on the pyramids of Egypt.

Cooper, Peter - Nyanda SHS

Ref No. 48

Using schemas to provide a perspective for evaluating approaches to teaching algebra

Considerable evidence indicates that we use mental schemas to recognise, understand, and solve problems. Research suggests that successful problem solving requires either the application or adaptation of an appropriate schema. If we expect students to use algebraic methods to formulate and solve problems they will need to build schemas for this to occur reliably and efficiently. What would these schemas look like, and how well do current pedagogical approaches help students develop them?

Morgan, Geoff - Undurba State School

Ref No. 23

Particular mental strategies for incorporation into primary mathematics programs

The current emphasis on written methods of calculation, particularly the emphasis on standard written algorithms, needs to be reduced. The ability to calculate mentally is not merely a useful computational skill. More importantly, mental computation is closely related to number sense; this being a critical ingredient in an individual’s ability to use mathematics effectively. Mental computation is likely to be best developed through the exploration of idiosyncratic and teacher-introduced methods. The latter implies that mental strategies worthy of particular focus are able to be identified. Particular mental strategies for incorporation into primary mathematics programs The intention of this presentation is to identify some that could be focused upon.

Holland, Bill - Maleny State High School

Ref No. 30

Making basic facts easier

Analysing the basic facts and providing strategies, activities and games to assist teachers to achieve the recommended outcomes in this area.

Barbara Clarke - Monash University

Ref No.6

Describing excellence in the teaching of mathematics: Why bother!

What are the characteristics of an excellent teacher of mathematics? How might this be evaluated? These are some of the questions that a collaborative research project between AAMT and Monash University is attempting to answer. In this session, participants will engage in some stimulus activities to explore characteristics of excellent teachers of mathematics and discuss issues in relation to the development of National Professional Standards for Excellence in Teaching Mathematics.

Weil, Helen - Beerwah SHS

Ref No. 01

Maps & compasses website

An opportunity to demonstrate the many resources available on this website and others to which it is linked. There is so much of interest and practical application to the topics we teach in maths. Also, an opportunity to correct the problems experienced with Education Qld’s change of address. Teachers need to know about the Raybould websites and how to access them.

O’Brien, Gary - Cannon Hill Anglican College

Ref No. 34

The graphics calculator – A VAT (value adding technology) in the mathematics curriculum

Any new approach or technology can only be judged by its ability to improve student learning outcomes and to provide valuable learning experiences. This session will provide assessment items along with student responses. Some items will consider the extension in the students’ learnings that can be displayed through the use of graphics calculators on traditional tasks, leading to a discussion on what we value, should value or could value in a school mathematics curriculum. Others will consider the type of assessment tasks and perhaps learnings we can now value and expect our students to display.

Green, John - University of Southern Queensland

Ref No. 15

Preservice mathematics teacher education – using video to push the boundaries

I am currently experimenting with the use of video as a teaching and learning aid in the preservice teacher education context. The content area is Number and Operations in the primary school In each video episode there are two people assisting each other, sometimes with varying degrees of success, to elicit understanding in the third person, a child. One of the two people involved is a novice student teacher and the other person is myself. We are now in the concluding stages of a trial of this material with a group of 240 students here and a further 40 students who study off-campus. I would like to disseminate some of these ideas as a way of improving our practice within the faculty and as a way of investigating future possibilities in the inservice teacher education context.

Driver, David - Brisbane School of Distance Education

The graphical calculator in junior mathematics extension

As with most technology, following some initial reluctance, the graphical calculator is making inroads into Queensland mathematics classrooms. Although initially the preserve of Mathematics B and C classes, increasingly they are being used in Mathematics A and Junior Mathematics. This is partially attributable to the rapid decrease in cost of base model calculators. At Brisbane School of Distance Education, we are currently trialing their use in semester 2 Year 10 with students studying the extension material. This workshop will demonstrate how the calculator is being used as a supplement to traditional teaching approaches with this cohort.

Zevenbergen, Robyn - Griffith University

Ref No. 05

Using mental computations for developing number sense

This session explores the ways n which the curriculum in Queensland (Australia and most Anglo-centric countries) is based on a particular understanding of how children learn mathematics. Many European countries are underpinned by a very different set of assumptions. In particular, number sense is seen as critical to mathematical understanding and the study of formal place value is left until much later – no MABs until upper primary; informal methods very early, no hierarchies of learning. This provides us with some very interesting contrasts to how children learn mathematics. These differences, and some of the strategies used in Holland, will be discussed and demonstrated.

Watson, Jane - University of Tasmania

Ref No. 11

Lessons for the classroom from chance and data research

This workshop will present several ideas for classroom lessons arising from recent research related to the chance and data part of the mathematics curriculum. Potential experiences for students in the middle and secondary years of schooling have arisen from interview protocols used with students in grades 3, 6 and 9 and a media survey used with grades 6 and 9. These are associated with understanding issues of fairness and sample size in various settings, with understanding average as used in different contexts, and with representing data sets and relationships in graphical forms.

Rook, Robert - Sebastopol Secondary College

Ref No. 52

Mathplot

This session will display the use of Mathplot, a graphing package that has been designed by Robert Rook, a teacher of mathematics for 15 years. The package can produce many types of 2D and 3D graphs. There are also forms that display topics such as Complex Numbers, Linear Programming, Matrices, Mensuration, Tessellations, Regression and Statistics, Vectors, and much more. Everyone attending these workshops will receive a fully registered copy of the program.

Finnemore, Mary & Levings, Mark - ISIS Communications

Ref No. 50

Applying technology in the maths classroom

Technological innovations are having a tremendous impact on our society and represent an important vehicle for stimulating the development of schools into learning communities. Possibly the most powerful reason is the very rate of change and access available to the information economy and in particular the Web. As teachers we must be pro-active in our response to these changes and embrace them to ensure we guide the future of education through this period of change. Understanding the Internet and embracing its enormous potential can only be of benefit. This workshop will outline some of the pedagogical benefits of Internet use in the classroom and also offer an opportunity to explore XSIQ, a suite of multimedia curriculum resources, and its application to mathematics education.

Luxton, Ian - The Southport School

Ref No. 05

Using computers as a tutorial tool

Students are becoming increasingly demanding on the way lessons are presented. This is not new. However, now they are demanding an increase in tutorial work on a self help basis which also needs good presentation.

Dunne, Trudy - Downlands College

Ref No. 13

Catering for different types of learners in mathematics

How do I cater for students who do not grasp a concept when it is first taught, who may have been absent, or who simply wish to work when it suits themselves? I increasingly seem to be addressing this problem in my Senior Mathematics classroom. One possible solution has led me to the use of a PowerPoint display for the introduction of a topic. This presentation includes a display for the topic Hypothesis Testing, my reasoning for developing the display, and the advantages for students and the teacher.

Reid, Sue - Redbank Plains SHS

Ref No. 51

The processes in a mathematical investigation

A mathematical investigation can take many forms, from simply gathering data in a survey to devising a complex mathematical model that describes a situation involving many variables. In the classroom, investigations provide opportunities for student-centred learning, group work, active involvement in learning and communication of mathematical findings. As a result of the investigation used in this workshop, a mathematical model can be developed to describe a particular situation, This is a professional development exercise, which puts participants in the place of a group of students undertaking an investigation. The aim of the workshop is to identify the processes employed within the group while undertaking the task and to enable participants to reflect on these processes and on their own mathematical learning. As a result, teachers may gain an insight into the experience of mathematical investigations, group work and how they may assist students undertaking a similar exercise.

Moore, Libby - Moore Educational

Ref No. 27

Robotics and data logging

The RCXTM is a programmable LEGO brick which can control motors, lights and process input from sensors. You will have a blast while seeing how to construct and program real robots using the RCX unit. You will be taken step by step through the programming from the simplest to more challenging activities. In this session you will explore the teaching material which provides information about real life robotic systems including their design, control and behaviour. (Max 20 participants)

McMahon,Bronwyn & Kennedy, Mick - St Anthony's Primary School

Ref No. 09

Linking science and mathematics to Multiple Intelligences and Bloom’s Taxonomy

Successful planning, teaching and assessment of units of work in science and mathematics can be achieved using a matrix that incorporates Multiple Intelligences and Bloom’s Taxonomy. This workshop features how science and mathematics for the upper primary can be integrated with Multiple Intelligences and Bloom’s Taxonomy and still be structured to maximise learning from students who have a range of needs in the regular classroom.

Kidman, Gillian & Nason, Rod - QUT

Ref No. 17

Mathematical and scientific visual representations: Are they really worth 1000 words?

In this workshop, mathematical and scientific visual representations from two Integrated Learning Systems (ILS’s) will be analysed using a set of principles generated from a review of the research literature from the fields of mathematics education, science education, cognitive science, computer-aided learning, computer graphic design and semiotics. Based on this analysis, the participants will discover that visual representations found in ILS’s and other educational software may be visually attractive, but may also be useless and seditious.

Rook, Robert - Sebastopol Secondary College

Ref No. 52

Mathplot

50 5.8 Finnemore, Mary & Levings, Mark TBA (Online learning) ISIS Communications TBA 41 6.1 QUT Casio bursary winners TBA QUT Preservice students present graphing calculator activities 19 6.2 Fuller, Milton Modelling growth, decay and periodic phenomena for senior mathematics Central Queensland University This workshop will allow participants the opportunity to use the HP38G graphics calculator to develop models using exponential and periodic functions.

14 6.3 Ousby Joseph What can you reasonably expect? Brisbane Grammar School In the past two years I have run workshops for all of the Year 10 students at Brisbane Grammar School on probability. Initially, during this workshop you will participate as the Year 10 students do, ‘buying tickets’, ‘placing bets’, etc. For our Year 10 students this is intended mainly as motivational. While it does tidy up our position on gambling, it leaves many mathematical threads untied. We will take up these threads: investigating both their application to the proposed revision of the Maths B classroom level.

49 6.4 O’Brien, Gary TBA (Casio graphing calculator) Cannon Hill Anglican College TBA 29 6.5 Cavanagh, Jan The mathematics of science Jan Cavanagh Consultancy With outcomes based syllabi, it makes sense to link the skills learned in mathematics with the content of science. Science provides rich contexts, and mathematical skills are required to make comparisons and analyses. This will be a hands-on workshop with practical classroom activities.

28 6.6 Moore, Libby Gearing up for the Olympics using LEGO DACTA P-8 resources Moore Educational This workshop is an overview of the range of resources available from LEGO DACTA, the educational division of the LEGO group, to implement in your school programs. We will be investigating, designing, and evaluating systems incorporating gears, pulleys, levers, wheels and axles and structures all related to the 2000 Olympic Games.

44 6.7 Geiger, Vince Conducting mathematics learning using “Interactive” Hillbrook Anglican School TI-Interactive is the first of a new breed of software that integrates the communication tools of word processing and email, mathematical tools such as graph plotting and CAS, and the information tool of a web browser. Interactive allows students and teachers to make use of all of these tools within one software package with the effect of a student or teacher conducting an orchestra made up of different tools with a computer mouse as a baton. This package will allow students and teachers alike to read, write and create mathematics within a single environment. This session will demonstrate some of the facilities and potential of this application.

58 7 Watson, Jane Statistical literacy – Going for gold! University of Tasmania The purpose of this talk is to explore how we can bring Australian students to the gold-medal level in statistical literacy. Three steps in the process will be explored, The first is to look at some research on today’s students’ statistical literacy skills in contexts provided by the news media. The second is to explore what teachers can do in the classroom today using the media and available technology to increase levels of statistical literacy. The third is to suggest some possibilities for future uses of technology to challenge and extend students’ understandings.

10 8.1 Geiger, Vince & Goos, Merrilyn Students’ presentations using technology – Another ingredient in a rich pedagogical soup Hillbrook Anglican School & The University of Queensland There has been much recent attention to the advantages offered by graphics calculator technology to the teaching and learning of mathematics. The focus, however, has tended to be on he way graphics calculators can be used to enhance students’ concept development or range of skills via the ever expanding number of facilities offered by these devices. Little has been done to advise teachers about the issues of pedagogy that must be addressed when teachers make greater use of mathematically enabled technologies in their classrooms. This workshop will discuss the potential of graphics calculator technology to enhance collaborative and student centred approaches to the teaching/learning of mathematics through problem focused role play.

35 8.2a Cretchley, Patricia, McDonald, Christine & Fuller, Anne Why do students choose to study mathematics at university? The role of the teacher, and other factors University of Southern Queensland & University of Wollongong This talk describes an investigation of the factors which influence students in their choice to study mathematics at tertiary level. The primary questions were: what are the factors behind their choice, how are they ranked, and are there gender and regional differences underpinning these choices? The rankings of 541 first year students at four Queensland universities suggest that the strongest factors are strength and interest in the subject, but that the role of the teacher is also high, and comparable with that of career prospects. The significance of these findings is noted, and their implications for promoting the study of mathematics are discussed.

20 8.2b Fuller, Milton UNILEARN Mathematics – a second chance for success Central Queensland University This paper describes the preparatory course UNILEARN Senior Mathematics available through the Queensland Open Learning Network. UNILEARN Senior Mathematics has been endorsed by the Queensland Tertiary Admissions Centre as meeting the requirements as a prerequisite subject equivalent to Queensland Senior Mathematics B. Thus another opportunity now exists for students who, for various reasons, do not completer Senior Mathematics B but wish to undertake a course for which that subject is a prerequisite.

37 8.3 Paul Sutton Simple modelling with simple data Ingham State High School This hands on workshop uses simple body measurements to build a predictive model for height using graphics calculators – bring your own or use one of the ones available at the workshop. We investigate the reliability of the model by analysing the differences between the predicted height and the real height. This highly integrative activity uses measurement, data collection and analysis, graphing and graphics calculators in an interesting real context. It can be run equally as well on a spreadsheet and could be done as a group activity by a whole class.

56 8.4 Bill Holland The Melbourne Cup – A statistical analysis Maleny SHS We use statistical procedures to analyse the past thirty Melbourne Cups and then use this knowledge to predict (select) this year’s winner. (Good news – it is an application of statistics to a real life situation. Bad news – it has not picked the winner yet!)

22 8.5 Price, Peter Making sense of numbers: Do MABs really help? Christian Heritage College Recent research by the presenter shows that conventional use of concrete materials to teach children about numbers may not be as effective as has been believed. In particular, use of MABs can lead to the development of faulty mental models for numbers, including face-value and independent-place constructs. Evidence for these claims will be shown in this session. Teachers attending will take part in practical activities involving the use of concrete materials and receive suggestions for helping children to develop meaningful mental models for numbers. Examples will be given of typical textbook questions that may either hinder or promote such models.

08 8.6 Zevenbergen, Robyn Using open-ended tasks for teaching, learning and assessment Griffith University In this workshop, participants will explore the use of open-ended tasks for use in classrooms. The value of open-ended tasks is that they can be used in teaching situations, for learning about student learning, and for assessment. Participants will work together to develop more open-ended tasks that can be used in their own work contexts.

45 8.7 Hamilton, Elaine & Graham, Dave Virtual Schooling Service demonstration Virtual Schooling Service and Access Ed A demonstration of the Virtual Schooling Service in Maths C. The range of tools employed to teach via data conference and voice to multi-points will be displayed.

33 9.1 O’Brien, Gary Whirlybirds – A mathematical journey in flight Cannon Hill Anglican College Assessment items that cover a number of content areas, that require active student participation, incorporate the use of technology and allow students to display their understanding and teachers to assess student progress are to be encouraged, This workshop will involve participants working through this item, including the analysis, followed by a discussion of student work received for this item. A whirlybird is a flying device whose time of flight can be varied by altering its dimensions. Participants will attempt to optimise the time of flight of a whirlybird. The use of Casio graphics calculators will feature in this workshop.

25 9.2 Sobb, Christopher Teaching and learning mathematics using the Casio 9850 GB+ Casio A hands on workshop using a graphics calculator to perform investigations involving various mathematical concepts. These will include statistics, graphing, probability, measurement and financial maths.

02 9.3a Boyce, Rick A beginners guide to using the internet in assessment in mathematics in secondary schools Ferny Grove SHS The paper will detail the experience gained so far at Ferny Grove using the internet as a tool in assessment. Some examples of assessment instruments will be presented. There will be a discussion on the best way to start, some traps to avoid and some hints on how to get you and your school started without too much pain.

31 9.3b Driver, David Who do you teach using a graphical calculator Brisbane School of Distance Education Current mathematics syllabuses emphasise the use by teachers of a wide variety of teaching approaches. The concept of preferred learning styles and its influence, in conjunction with teaching style, on student achievement have been acknowledged since the early 1980s. McCarthy defines four learning styles based on how we perceive information and how we process that information. Given a graphical calculator, students with differing learning styles will prefer to learn how to use it in different ways. We need to be sensitive to our students’ preferences and give them opportunity to learn how, and then use the calculator in a way which with they’re comfortable.

46 9.4 Burton, Leone Being a mathematician University of Birmingham This workshop will be an interactive follow-up to the keynote address entitled Being a Mathematician. In it, participants will be asked to engage in debating and planning requirements for their classrooms if activities are to encourage pupils to be mathematicians rather than to learn mathematics. The hazards as well as the pleasures of the approach will be discussed. Leone will offer some activities as starters, but participants are encouraged to bring activities to the workshop that they would like to offer as starting points.

47 9.5 Cavanagh, Jan Pattern is mathematics: Mathematics is pattern Jan Cavanagh Consultancy TBA 39 9.6 QSCC Maths Team TBA QSCC 38 9.7 Delroy, Chris T.B.M. (Trade & Business Mathematics) How to do I.T. (Information Technology) Tullawong State High School This computer lab session will be totally interactive using mathematics IBM software and the web to develop Thought-Revealing Activities for students. The need for Vocational Education bound students to understand and be able to use the mathematics in their everyday life has never been greater. Expected outcomes include: • creating new models for documenting student achievements • employing technology for students/teachers to pursue new challenges for teaching, learning, problem solving • activities will encourage/engage students to look at problems from a mathematical viewpoint • reduce behaviour management issues in the classroom

06 10.1a Nothdurft, Lyn Enhancing learning: Developing a community of learners St Patrick’s College Gympie This paper discusses strategies which have been used with senior secondary students to make learning mathematics more rewarding through increasing understanding and making learning more enjoyable. The students have been encouraged to act as a community of learners who can work collaboratively, reflect on their learning strategies, and behave autonomously.

03 10.1b Blum, Kathy Curriculum reform St John Fisher College Examines how mathematics curricula should be changed in order to equip students truly with another useful way of viewing their world. Endeavours to show the importance of a mathematical lens through which to view current world problems.

18 10.2 Fuller, Milton Sequences, series and financial models – A learning experience with the graphics calculator Central Queensland University This workshop will enable participants to use the HP38G graphics calculator, with Aplets, to investigate sequences, series and difference equations in developing financial models for loan repayments and investments.

43 10.3 Baldry, A. & Callum, B. School trail The Southport School Come for a walk around the TSS grounds in which various “practical” mathematics activities are explored. The activities are aimed at students from Years 7-9. The main purpose of the walk is to introduce and enhance students’ mathematics through practical experience. The walk explores mathematics around the pool, the chapel, the dining hall and the river. This walk finishes with a treasure hunt around the school. So come along, pick up a few ideas, a worksheet or two and maybe win a prize in the treasure hunt.

26 10.5 Cooper, Tom Structure of mathematics and effective teaching of number and pre-algebra QUT This workshop will focus on practical classroom activities to effectively teach whole number, decimals, fractions, percent and rate and ratio which are based on the structure of mathematics. Participants will experience, “hands on” with materials, activities which illustrate the theoretical points being made. The workshop will conclude with activities which show how this work can lead in to algebra.

16 10.6 Zevenbergen, Robyn, Sullivan, Peter & Mousley, Judy Making classroom practice more open Griffith University, ACU, Deakin University The potential for open-ended tasks to enhance learning may be restricted by the background of students. Using a series of videotape extracts from classrooms, the workshop explores aspects of practice that may cause difficulties for students from various equity target groups.

04 10.7 O’Brien, Mark Resources for secondary teachers Eastern Hills SHS (WA) Mark is a Western Australian secondary maths teacher who has been producing resources while teaching. He now runs ‘Online Teachers’ Resource Network’ and will be showing some of the resources available via OTRNET, how to access them, or how to market your own.

59 11 Penrose, Bevan TBA Marsden SHS TBA

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Email: qamt@qut.edu.au

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