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Technology, research and practice in mathematics education Technology, research and practice in mathematics education

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Technology, research and practice in mathematics education - PPT Presentation

Barry Kissane The Mathematics Education Research Group of Australasia Outline Technology in mathematics education What technology Policy statements Technology and research in mathematics education ID: 564802

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Slide1

Technology, research and practice in mathematics education

Barry Kissane

The Mathematics Education

Research Group of AustralasiaSlide2

Outline

Technology in mathematics educationWhat technology?Policy statementsTechnology and research in mathematics educationTrends over twenty years

Big pictures and big ideas

Technology, research and practice in mathematics education

(How) is practice informed by research?

(How) might we do better?Slide3

Clicker 1: Who are we today?

1. Classroom teacher (in a school)2. Head of department (in a school)3. Teacher educator (in a university)4. Researcher (in a university)5. Maths

teacher (in a university)

6. OtherSlide4

Technology in mathematics educationSlide5

Three roles for technology

ComputationalTo provide answers to mathematical questionsExperientialTo provide a means for students to interact with and explore mathematical ideas not otherwise available, to provoke and support mathematical thinking

Influential

To be considered as a significant factor when decisions are made about the nature of the curriculumSlide6

Policy positions on technology

ACARA Shape Paper on Australian Curriculum“An important consideration in the structuring of the curriculum is to embed digital technologies so that they are not optional extras.” (p.9)National Council of Teachers of Mathematics Position Paper “Technology is an essential tool for learning mathematics in the 21st century, and all schools must ensure that all their students have access to technology. Effective teachers maximize the potential of technology to develop students’ understanding, stimulate their interest, and increase their proficiency in mathematics. When technology is used strategically, it can provide access to mathematics for all students.” (2008)Slide7

AAMT statements

AAMT Statement on the Use of Calculators and Computers for Mathematics in Australian SchoolsIt is recommended that: “1. All students have ready access to appropriate

technology as a means both to support and extend their mathematics learning experiences” … (1996)

AAMT

Communiqué on graphics calculators and school mathematics

“There is a compelling case for the advantages offered to students who use graphics calculators when learning mathematics. They are empowering learning tools, and their effective use in Australia’s classrooms is to be highly recommended”. (2000)Slide8

Digital Education Revolution

Australian government initiative to provide laptops for studentsIncreased access to high speed broadband anticipatedMathematics Framing paper: Digital technologies allow new approaches to explaining and presenting mathematics, as well as assisting in connecting representations and thus deepening understanding. The continuing evolution of digital technologies has progressively changed the work of mathematicians and school mathematics (consider the use of logarithm tables and the slide rule), and the curriculum must continue to adapt. Digital technologies are now more powerful, accessible and pervasive. (p.9)Slide9

What technology for students?

Hand-held devicesFour-function calculatorsScientific calculatorsGraphics calculatorsCAS-enabled graphics calculators

Interactive devices

Casio

ClassPad

,

TI-

Nspire

PDA devices

iPod Touch,

iPhone

,

iPad

Computer software

Spreadsheets

Dynamic geometry

Cabri

Geometry

,

Geometer’s

SketchPad

,

GeoGebra

, etc.

Statistics

Fathom

,

TinkerPlots

, etc …

iPod Touch,

iPad

The Internet

Worldwide web

Learning online

(

HOTMaths

)

Maths

by Email

The

Le@rning

Federation

Social networking, Web 2.0, etc. Slide10

What technology for teachers?

Hand-held devicesAs for studentsWith demonstration versionsNetworked versionsComputer software

As for students

Demonstration software

E.g.,

Autograph

The Internet

The

Le@rning

Federation

Online learning

E.g.,

HOTMaths

As for students

Teaching technology

Interactive white boards

Graphics tablets

Audience response devices (‘clickers’)Slide11

Clicker 2: Mathematics, technology and me

Which one best describes you?1. I teach maths with technology and do

some research related to technology

2. I teach

maths

with technology but don’t

do research related to technology

3. I don’t teach

maths

with technology but

some of my research is related to technology

4. I neither teach

maths

with technology

nor do research related to technologySlide12

Computers, calculators, Internet, …

It is clear that there are large differences between what is ‘available’ to students and teachersSchools are differentially resourcedSome excellent software is expensiveStaff have preferences as well

External constraints can be dominant (especially in senior secondary school)

Graphics calculators’ portability, cost and exam acceptability

Home Internet access is very high, and rising for many communities, but still SES differencesSlide13

A big picture 1990-2010

Seymour Papert in the early 1980’s observed that the computer laboratory was School’s defence against technology.Graphics calculators were designed solely for mathematics education and broke down this

defence

(for many)

Software available on all computers (i.e. spreadsheets) began to be used too

Purpose-built software for mathematics education was developed

The Internet

Laptop computers and home access to technologySlide14

The big picture 2010-2030Slide15

A personal opinion about graphics calculators

My engagement with graphics calculators began in 1986, when it was clear that there was no more efficient way of ensuring access to technology in many, if not most, US schools.It continues to be the case in 2010 that a technology that is individually affordable (to many), flexible, powerful, portable and acceptable to high-stakes exam authorities offers the best prospect of taking technology seriously and thinking of universal access.

Despite its many limitations

This will not always be the caseSlide16

Technology examples?

Not really timeMany are familiarGraphics calculatorsCASInteractive devicesGeometry

Statistics

InternetSlide17

The Internet

There is a large and increasing number of opportunities for students to engage with mathematics on the webSlide18

Some iPod examplesSlide19

Some more examplesSlide20

Technology and research in mathematics educationSlide21

Technology and research: A naïve

questionTeachers (and others) would like an answer to the naïve question: “Does it work?”That is, if we use this technology with students, will they learn mathematics (better)?

Yes?

No?

Of course, it is never that simple …Slide22

Does it work?Slide23

Why does it work?Slide24

Why doesn’t it work?Slide25

Why does it work only sometimes?Slide26

Why does it work only sometimes with my Year 10 class?Slide27

Why does it work only sometimes with Jane Smith’s Year 10 class?Slide28

Would it work with Jane Smith’s Year 10 class?Slide29

Would it work with Jane Smith’s Year 10 class in NSW?Slide30

Technology and research: Does it work?

It depends… on many thingsThe classroomThe teacher

The curriculum

The student

The technology itself

There is no panaceaSlide31

Changing research perspectives on technology in Australasia

MERGA’s RIMEA series1988-1991: Calculators and computers in teaching and learning of mathematics

1992-1995: ??

1996-1999: Technology-assisted instruction in mathematics education

2000-2003: Computers, multimedia and the Internet in mathematics education; Calculators and computer algebra systems

2004-2007: Teaching and learning with technology:

Realising

the potential

2008-2011: ??Slide32

Stages in research on technology

Developmental work, drawing on research in various disciplinesEarly empirical studies concerned with proof of conceptCase studiesComparative studies involving quasi-experimental designs

Larger studies with

randomised

, controlled trialsSlide33

A balance of approaches

“While research in a wide range of areas could directly or indirectly facilitate the effective utilization of educational technology within our nations K-12 schools, much of the research that the panel believes to be most important falls into one of the the following three categories:

1. Basic research in various learning-related disciplines and fundamental work on various educationally related technologies;

2. Early-stage research aimed at developing new forms of educational software, content and technology-enabled pedagogy; and

3. Empirical studies designed to determine which approaches to the use of technology are in fact most effective. (PCAST, 1997, Executive Summary)” (

p

. 443)

Ferrini

-Mundy, J. & Breaux, G.A. (2008) Research, policy and technology use. In

Blume

,

Glendon

W. &

Heid

, M. Kathleen (2008

) Research on technology and the teaching and learning of Mathematics: Volume 2: Cases and perspectives

. (pp 427-448) USA: Information Age, NCTM. Slide34

Should technology have a role in school mathematics?

“In the Panel’s judgement, the principal goal of such empirical work should not be to answer the question of whether computers can be effectively used within the school. The probability that elementary and secondary education will prove to be the one information-based industry in which computer technology does not have a natural role would at this point appear to be so low as to render unconscionably wasteful any research that might be designed to answer this question alone. (PCAST, 1997, Section 8.3: Priorities for Future Research)” (

p

. 444)

Ferrini

-Mundy, J. & Breaux, G.A. (2008) Research, policy and technology use. In

Blume

,

Glendon

W. &

Heid

, M. Kathleen (2008

) Research on technology and the teaching and learning of Mathematics: Volume 2: Cases and perspectives

. (pp 427-448) USA: Information Age, NCTM. Slide35

What might research offer us?

An opportunity to understand things betterBut rarely an unambiguous answer to important questions of teaching and learningAn opportunity to explore the boundaries of

relevance of a theoretical framework to understand practice

An opportunity to put (competing) theories to a test

New phenomena to explore

Most research projects generate as many fresh questions as answers

“Further research is needed to …”Slide36

Problems with research on technology in particular

A moving target, as the technology is changing (very rapidly), as Jim Kaput remarked in 1992:“Anyone who presumes to describe the roles of technology in mathematics education faces challenges akin to describing a newly active volcano — the mathematical mountain is changing before our eyes, with myriad forces operating on it and within it simultaneously.” (

p

. 515)

Unavoidable novelty effects

Teacher effects

Curriculum (including external examination) effects

especially in senior secondary school and undergraduate mathematics?

Time span (longitudinal research?)

Up-scaling and

generalisability

problemsSlide37

The place of reviews of research

For some of the foregoing reasons, research results rarely (if ever) lead to uncomplicated, unequivocal ‘solutions’ to problemsThe gold standard of empirical scientific research, the randomised experiment, is clearly unattainable in this field (yet)

… if in any branches of mathematics education …

So, systematic reviews of research are important, and meta-analyses even more important, to try to reconcile differences in findings

These are major undertakings (

eg

RIMEA)Slide38

What does research tell us? Some sources

RIMEA seriesEvery four years, focusing on AustralasiaNCTM Handook

of Research

Key constructs

NCTM

Research Syntheses

volumes

Systematic, structured compilations

MERGA conferences and journals

Some recent highlightsSlide39

RIMEIA 2004-2007:Some big pictures

Thomas, M. & Chinnappan, M. (2008) Teaching and learning with technology: Realising the potential. In H.

Forgasz

, A.

Barkatsas

, A. Bishop, B. Clarke, S.

Keast

, T.S. Wee, T. S. & P. Sullivan (Eds.)

Research in Mathematics Education in Australasia 2004-2007

. (pp 165-193). Rotterdam: Sense Publishers.

“… a high level of enthusiasm from both students and teachers to embrace a variety of technologies …”

A focus on “… the crucial role of the teacher when employing technological tools…”Slide40

Organising constructs

AffordancesE.g., Presence of technologyConstraintsStudent or teacher instrumentationTime available

Curriculum content

Pedagogical technology knowledge (PTK)

“principles, conditions and techniques required to teach mathematics through the technology” (p.167)Slide41

Teacher variables

Metaphors for technology (Goos, Galbraith, Geiger, et al)MasterServantPartner

Extension of self

Professional development variables

Teacher confidence

Technical expertise

PTK

Use of CAS

Teacher privileging

CAS as a conceptual tool, not just a crutchSlide42

Some big pictures?

“One factor that consistently needs attention is whether the success reported in studies can translate to teachers in general, or whether the research participants are exceptional in some ways.” (p. 170)“Research and teaching community are enthused … but teachers need support and guidance in classroom implementation”

Both pre-service and in-service. (

p

. 183)

Conflicting results regarding CASSlide43

A perspective of constructs

This recent major review of the field suggested a number of constructs as organisers of the research, evolved from collections of studies.

Rose Mary

Zbiek

, M. Kathleen

Heid

,

Glendon

W.

Blume

& Thomas P. Dick (2007) Research on technology in mathematics education: A perspective of constructs. In

F. K. Lester Jr. (ed.)

Second handbook of research on mathematics teaching and learning.

(pp 1169-1207). USA: Information Age, NCTM.Slide44

Which constructs?

Technical and conceptual activitiesCognitive toolsTools and mathematical activityExternalised representationMathematical fidelity

Cognitive fidelity

Student-Tool relationships

Instrumental genesisSlide45

More constructs

Students and mathematical activityExploratory activityExpressive activityMethods of workingTechnology and practice

Pedagogical fidelity

(Teacher) privileging

Technology and curriculum: Constructs that capture the opportunities for change in curriculum facilitated by technology

Representational fluency

Mathematical concordance

Amplifiers and

reorganisers

Sequencing and emphasis:

Microprocedures

and

macroproceduresSlide46

Research syntheses

Heid, M. Kathleen & Blume,

Glendon

W. (2008

) Research on technology and the teaching and learning of Mathematics: Volume 1: Research syntheses

. USA: Information Age, NCTM.

Rational number

Algebraic understanding

Geometry

Calculus

Mathematical

modelling

Practice

EquitySlide47

Algebra

“Technology in conjunction with technology-based curricular approaches can effectively change the content and processes of school algebra.” (p. 97)“Technology in conjunction with technology-based curricular approaches can affect the processes of mathematical activity in an algebraic setting. Many of these effects are related to the representational capacity of technology.” (

p

. 97)

“Technology in conjunction with technology-based curricular approaches can affect the acquisition of algebraic concepts and procedures” (

p

. 98)

Heid

, M. Kathleen &

Blume

,

Glendon

W.

(2008) Algebra and function development. In

Heid

, M. Kathleen &

Blume

,

Glendon

W. (Eds.

) Research on technology and the teaching and learning of Mathematics: Volume 1: Research syntheses

. (pp 55-108) USA: Information Age, NCTM. Slide48

Geometry

“There is evidence that computer environments can support learning and teaching in geometry in new and dynamic ways, as well as complementing and enriching traditional strategies.” (p. 141)“There is not yet a critical amount of research devoted to long-term teaching with regular use of DGS. Moreover there is currently a lack of computer-supported geometry teaching.” (

p

. 191)

“The computer provides a window on student’s [geometric] understandings.” (p.189)

“In a DGS, construction tasks induce the need to use geometrical knowledge.” (

p

. 190)

“DGS offers a new perspective in addressing the issue of the teaching and learning of proof.” (

p

. 190)

Hollebrands

, K.,

Laborde

, C. &

Straser

, R. (2008) Technology and the learning of geometry at the secondary level. In

Heid

, M. Kathleen &

Blume

,

Glendon

W. (Eds.)

Research on technology and the teaching and learning of Mathematics: Volume 1: Research syntheses

. (pp 155-205) USA: Information Age, NCTM. Slide49

Probability and statistics

Statistics was not mentioned in the Research Syntheses publication, and Friel’s chapter emphasises

the relative

recency

of attention to research on statistics education

RIMEA 2004-2007 review also noted relative dearth of research about statistics with technology in Australasia (at that time)

Research with educational software (such as

Fathom

and

TinkerPlots

) is relatively new, with results (case studies, design studies) informing conceptions of an appropriate curriculum.

Technology is an assumed part of the developing EDA conception of statistics, with a focus on understanding data.

Friel

, S.(2008) The research frontier. In

Blume

,

Glendon

W. &

Heid

, M. Kathleen (Eds.)

Research on technology and the teaching and learning of Mathematics: Volume 2: Cases and perspectives

. (pp 279-331) USA: Information Age, NCTM. Slide50

Teachers and technology

Survey research has provided some helpful information about secondary mathematics teacher use of technology and professional development needs The best recent example is: Goos &

Bennison

(2008) Surveying the technology landscape: Teacher’s use of technology in secondary mathematics classrooms.

Mathematics Education Research Journal

, 20(3), 102-130.

Computers, graphics calculators and the Internet

Clear effects of mandatory use of technology (graphics calculators)

More use of technology in senior school than below

Marginal use of computers and the Internet

Professional development is important and can be influential

Bennison

&

Goos

(

MERJ

, 2010) note that “effective integration remains patchy”, with a number of teacher issues identified

Thomas surveys (1995 & 2005) in NZ highlight access issues for computersSlide51

The Internet (and beyond)

There seems to be relatively little empirical research yet on the use of the Internet by students and teachersInternet as a source of information about mathematics seems to have no place in the curriculum? (yet seems likely to be of interest to many students?)

There are

very

rapid changes in technology outside mathematics classrooms

Web 2.0 and the ubiquitous Internet

Mobile phones with computer capabilities in an interconnected world

Podcasts and video

A curriculum that seems oblivious or impervious to these must seem increasingly quaint to students

How does research keep up?Slide52

Undergraduate teaching

In many places, it seems that the use of technology in early undergraduate mathematics differs sharply from the use of technology in schoolsWood, L. (2008) University learners of mathematics. In H. Forgasz, A.

Barkatsas

, A. Bishop, B. Clarke, S.

Keast

, T.S. Wee, T. S. & P. Sullivan (Eds.)

Research in Mathematics Education in Australasia 2004-2007

. (pp 73-97). Rotterdam: Sense Publishers.

“On computing tools, the majority of authors espouse the use of professional software and hardware tools. Such as Excel, CAS and computers rather than teaching-only tools such as graphics calculators.” (

p

. 91)

“There is a distinct split between universities that

favour

computing tools for mathematics learning and those who work only with pen and paper.” (p.91)Slide53

Proficiencies and technology

The draft Australian Curriculum – Mathematics identifies four ‘proficiencies’:UnderstandingFluencyProblem solving

Reasoning

Teachers might reasonably expect to see clear guidance, advice and descriptions about the (different) role of technology in theseSlide54

The nature of the curriculum

There seems to be limited evidence of technology influencing the nature of the curriculum (at least in the Australian Curriculum drafts,

in my personal opinion

)

Technology is mostly

interpreted as ‘pedagogy’ and thus the prerogative of the teacher?

Computation is

recognised

, and there is encouragement to use ‘available technology’ to change the teaching and learning experience

Coherence

of teaching, learning and assessment is worthy of closer research, as it seems highly likely that what is used in assessment is likely to determine what is generally used for teaching and learning.Slide55

K-10 draft, Australian Curriculum

Information and communication technologies (ICT) allow students to solve problems and perform tasks that previously have been onerous. Calculators of all types from the simple four operations versions to the more complex graphical and CAS calculators allow students to make calculations, draw graphs and interpret data in ways that previously have not been possible. There are spreadsheets, dynamic geometry programs and other software that can engage students and promote understanding of key concepts.

It is expected that mathematics classrooms will make use of all available ICT in teaching and learning situations.

[ACARA, 2010; emphasis added]Slide56

11-12 draft, Australian curriculum

The Shape of the Australian Curriculum – Mathematics states that available technology should be used for teaching and learning situations. Technology can include computer algebra systems, graphing packages, financial and statistical packages and dynamic geometry. These can be implemented through either a computer or calculator.Technology can aid in developing skills and allay the tedium of repeated calculations. For example a technology can be used to complete recursive calculations.

The decision about using technology in assessment programs is not within the province of the curriculum, jurisdictional assessment agencies will make that decision.Slide57

Adding-on technology?

Fey, J.T., Hollenbeck, R.M. & Wray, J.A. (2010) Technology and the mathematics curriculum. In Reys, B.J., Reys, R.E. & Rubenstein, R.

NCTM 72

nd

Yearbook: Mathematics curriculum.

(pp 41-49). Reston, VA: NCTM offered an opinion on this question:

Curriculum specialists and other interested parties should examine objectives to determine whether technology can enhance students’ learning of mathematics.

However, technology should not be an add-on to curricula.

Using technology to cover topics that are just as accessible through other approaches may actually interfere with learning and undermine the benefits of technology. Given the urgency of providing strong mathematical preparation for students who will enter and live in a technologically sophisticated society and workplace, such study and experimentation by all involved in the enterprise of mathematics teaching should be a high priority for our field. (2010, p.48) (Emphasis added.)Slide58

Some examples of curriculum influence?

E.g., changing the emphasis in statistics from mathematical statistics to data analysis, using real data and real problems, using suitable technology toolsE.g., approaches to probability beyond the formal classicist approach (in terms of sample spaces and equally likely outcomes, sets and combinatorics

); study of ‘risk’

E.g., numerical approaches to ‘calculus’ problems such as finding relative

extrema

or numerical solutions to differential equations

E.g., Focus on construction and interpretation of integrals, rather than methods of integration, in an age of CASSlide59

Some more examples

E.g., explorations with geometric software to encourage and motivate conjecturing, reasoning and proofE.g., some focus on numerical solution of equations rather than only on exact solutions of equationsE.g., use of reducible interest (which is what occurs in practice) rather than simple and compound interest (which usually don’t occur in practice)

Emphasis in the draft Australian Curriculum seems to focus on using technology to teach the same curriculum to which we have become accustomed … a form of retrofitting … rather than reconsider the scope and sequence of the curriculum in the light of available technologies

This is of course an

opinion

, not an empirical findingSlide60

Technology, research and practice in mathematics educationSlide61

Research and practice

How does research influence practice?In general, not only for the particular case of technologyWhat are the problems?How might we strengthen the links?Slide62

A litmus test?

Julie is teaching her Maths 2D class next semester, starting a unit on calculus with a group of students not in the strongest stream. She has been teaching for six years now and is a competent user of technologies.Should students use the CAS calculator? Why? How? For what?

Will some computer software be useful? Which? How should she use it?

Could the Internet be useful here? How? For what?

Could her Interactive White Board be used? How? Why?

What will research tell her about such things?

Where should she look?Slide63

Clicker 4: Consulting research

Think of some maths you have taught to students recently with technology. Which of

the following best describes you?

1. I consulted a research source for advice

before I started.

2. I had previously consulted research, so

didn’t need to do so again.

3. I did not consult any research.

4. I haven’t taught

maths

to students

recently with technology.Slide64

Possibility 1: Practitioners accessing researchers

Attend the MERGA conference (in their home city)Attend the joint AAMT-MERGA conference(s)In Alice Springs

next July

Interrogate the MERGA website for conference or journal publications

Obtain published research advice

Research journals are usually not written for the audience of teachers

Very expensive and inaccessible in most schools

Interpretations of ‘impact’ within ERA focus on research colleagues not colleagues in schools

“Voices from the field” in

MERJ is

a welcome initiativeSlide65

Possibility 2: Researchers advising practitioners

Researchers can advise practitioners directly“What research says” monographs?Earlier research syntheses published by NCTM67

th

NCTM Yearbook: technology-supported mathematics learning environments

(2005) is a good example

Association of Mathematics Educators (Singapore) Handbooks

Write advice papers based on research in journals for teachers

It is hard to write these; partly because research findings often do not readily translate to practice

Not many people try to do this, as the rewards are few

Conduct targeted conferences (

eg

ACER conference 2010

) for the purpose

Impact unavoidably limited to those who can attendSlide66

Clicker 5: Advising practitioners

In the last two years, have you submitted a paper based on your research to a publication meant for maths teachers?

1. Yes, and it was accepted

2. Yes, but it was rejected

3. No Slide67

Possibility 3: Materials development

Classroom materials and curricula can be developed following classroom-based researchCAS-CAT projectTinkerPlots, Geometer’s

SketchPad

materials

Hillary

Shuard

project

Calculator Aware Numeracy materials

(Some) calculator manufacturer materials are based on work in schools

MATHS300 software

Materials themselves can be researched

Even trialing seems rare for Australian school textbooks?

UCSMP experienceSlide68

Possibility 4: Professional development

Pre-service teacher educationInformed by research (eg Goos,

Stillman

& Vale’s

Teaching Secondary School Mathematics: Research and Practice for the 21

st

Century

)

Limited short-term impact on the field, as most teachers are already teaching!

Teacher conferences

Seems rare for

research

to be the basis of presentations?

Rare for researchers to see these as important?

Even rarer for their institutions to do so in the world of ERA?

Teacher courses (

Eg

2008 Summer School)

Happen rarely and impact on only a few?Slide69

Clicker 6: Teacher meetings

In the past year, have you attended a conference or meeting of teachers inorder to discuss your research?1. Yes2. No

3. I’ve not been involved in research in the past year.Slide70

Possibility 5: Researchers and practitioners working together

Action research projectsEg, AGQTP, ASSISTMClassroom-based research generallyTeaching experiments, case studies, field trials

Funding?

Time-span?

Queensland team (

Goos

, Geiger,

Renshaw

, Galbraith, …) is a very good example

We need more good examplesSlide71

Clicker 7: Working together

In the past year, have you worked in a school with a team of colleagues on a research project?1. Yes; I am a school teacher member of the

research team

2. Yes; I am a member of the research team,

but not a school teacher

3. No; although my students were involved

in a research project

4. NoSlide72

Possibility 6: Web-based support

ACARA intentions are to provide significant online advice and support to teachersHow can advice informed by research on technology be best included in that?Who will do it?Especially in light of the limited inclusion of technology into the curriculum itself to date

MERGA website is outstanding, although the materials are not written with practice in mind

NCETM

example in the UK seems to have much to commend it.

Here

is an

example about Interactive White Boards.

Is there scope for an Australian version?

Very significant funding is needed

Not only about technology, of courseSlide73

Concluding remarksSlide74

If …

The technology is designed to capture important mathematical ideas faithfully; andIt is improved with the aid of suitable research with students; andThe curriculum is written and assessed on the assumption that technology is available; andCurriculum materials and tasks have been developed accordingly; and

The teacher is adequately supported to use the technology confidently and well in the classroom; then

It will ‘work’Slide75

Bringing it all together: some final observations

There is a rich resource of research on technology already available … with many gapsIt is already clear that technology has much to offer

While the world of technology itself keeps changing rapidly

Much of the research is not written directly for teachers

Focus of some research is on teacher practices,

recognising

that what happens in classrooms is of great importance, not only the technology itself

Professional development is a direct object of study

Building partnerships between research and practice is a critical part of making joint progress

… so, finally, what is the relationship between research and practice…?Slide76

Research and practice

Practice

ResearchSlide77

Clicker 8: Did you like that picture?

1. Yes2. No3. I didn’t understand it, so I can’t tell.Slide78

Thank you

B.Kissane@Murdoch.edu.auhttp://

wwwstaff.murdoch.edu.au/~kissane