Judy Anderson – University of Sydney
While currently employed as a senior lecturer in mathematics education at the University of Sydney, I previously worked at the NSW Board of Studies as a senior mathematics curriculum officer with responsibility for developing the current Kindergarten to Year 10 mathematics curriculum. I am particularly interested in the way curriculum presents and encompasses the process strands and teachers’ implementation of processes including problem solving. Problem solving is a key component of the school mathematics curriculum throughout the world. However, problem solving is difficult to teach since students need to develop a range of knowledge, skills and attributes. As Australia continues to develop a national curriculum, it is important to learn from other countries about the best approach to including problem solving in the curriculum and supporting teachers to implement recommendations. International approaches to supporting teachers are varied with some countries developing realistic tasks (e.g. Holland), and others reducing the content and providing ongoing professional development (e.g. Singapore). While providing valuable resources and more time are important steps, it is possible that problem solving in the mathematics curriculum will only become valued when it is included in high-stakes assessment. Examining the efforts of other countries and considering the constraints and affordances to teaching problem solving will inform the efforts required for successful national curriculum implementation in Australia.
Peter Boon – Freudenthal Institute, Netherlands
Over the last decade I have designed numerous java applets – English versions of some of these can be found on the WisWeb website. The background to this work is discussed in my article “Designing Didactical Tools And Microworlds For Mathematics Education“. A recent article on software design within educational design processes can be found in the May 2009 issue of Educational Designer.
In the last few years I have been working on the integration of these digital activities (applets) in longer learning trajectories that are embedded in a digital learning environment. In close cooperation with schools and teachers we have built the DME (Digital Math Environment). This is an internet based learning environment that is now used by more than 100 Dutch schools. Embedding the applets in the DME offers several new possibilities that improve the usability of applets in educational practices. For example, students’ work is stored and can be made accessible for teachers. Also the acivities can be arranged and cusomized by teachers. A recent development within the DME-project is the design of a (mathematical) authoring tool for making new digital activities for students without the need for programming. Applets can now be used (in a flexible way) as interactive components within learning trajectories. I think that the development and use of this kind of authoring facility is necessary in the design of rich and versatile digital curriculum materials.
Hugh Burkhardt – Shell Centre for Mathematical Education, University of Nottingham, UK
Hugh Burkhardt takes an ‘engineering’ view of educational research and development – that it is about systematic design and development to make a complex system work better, with theory as a guide and empirical evidence the ultimate arbiter. His core interest is in the dynamics of curriculum change. He sees assessment as one important ‘tool for change’ among the many that are needed to help achieve some resemblance between goals of policy and outcomes in practice. This has been reflected in a series of projects and products that integrate high-stakes assessment, teaching materials, and curriculum development support. www.toolkit forchange.org complements such specific tools by directly addressing the barriers that change agents face in making improvement programmes work in their school systems. This work is ongoing in both the UK and the US. His other interests include making mathematics more functional for everyone through teaching real problem solving and mathematical modeling, computer-aided math education, software interface design and human-computer interaction.
Georgia Cobbs –
It is the intent of the legislature . . . that every Montanan, whether Indian or non-Indian, be encouraged to learn about the distinct and unique heritage of American Indians in a culturally responsive manner . . . all school personnel should have an understanding and awareness of Indian tribes to help them relate effectively with Indian students and parents . . . Every educational agency and all educational personnel will work cooperatively with Montana tribes . . . when providing instruction and implementing an educational goal (MCA 20-1-501). Challenges with this legislation is how to model curricula and pedagogical frameworks for our students that appropriately incorporates tribal knowledge, diversity, and ways of knowing. Students complete a capstone experience of an integrated block of methods courses: math, social studies, science and reading. Faculty that teach these courses collaborate to ensure that the fundamental values of IEFA are addressed in a systematic, authentic, and intellectually rigorous manner.
Mark Coleman – Melbourne Grammar School, Australia
For the past 9 years I have taught Science exclusively with Y7 & 8 boys. Under the umbrella of the Ithaka Project, this time has allowed me to develop a clear view of what junior science is in terms of its content, responsibilities and how it relates to other disciplines. In particular I have endeavoured to find and develop authentic classroom activities and assessments that reflect my values and which have a clear purpose to my students. This search has forced me to overhaul the area of the school for which I am responsible. Having to bring other staff along required system change and, most importantly, clear justifications for that change and obvious benefits for the other staff involved. This has involved clarification of the meaning of language we commonly used, establishment of a reputation within our organisation as agents of change, consistent encouragement of cross-campus communication and a clear willingness to bridge the perceived gap between theory and practice.
Rita Crust – Shell Centre for Mathematical Education, University of Nottingham, UK
I am the lead designer in the Mathematics Assessment Resource Service, MARS, Shell Centre team with particular responsibility for assessment design. I am an experienced teacher, teacher educator, chief examiner and designer of curriculum and assessment. I lead the design of MARS US tests and classroom assessment tasks and co-ordinate the design work of MARS for several projects. For many years I have been a Principal Examiner in Mathematics for various UK examination boards. Since 1982 the MARS team has designed and developed assessment tasks and support materials specifically to stimulate systemic improvement, funded by Government agencies, large-scale assessment providers, foundation and school systems in the UK and the US (including NSF, CTB, Noyce Foundation, and various school systems) The MARS materials are developed and refined through an iterative process of testing in classrooms, using feedback to guide revision until they work well with the target groups of users. The initial trials are qualitative: for assessment tasks the later stages provide psychometric data and robust scoring schemes reinforced by specimen responses.
I am the founder and director of the Engineering is Elementary: Engineering and Technology Lessons for Children (EiE) project. EiE is creating a research-based, standards-driven, and classroom-tested curriculum that integrates engineering and technology concepts and skills with elementary science topics. The EiE team is creating 20 units; each unit reinforces an elementary school science topic while focusing on a specific field of engineering. EiE lessons also connect with mathematics, language arts, and social studies. In additional to curriculum and resource development, the project also engages in professional development, and research and assessment. One of my areas of interest focuses on how to design materials that work for all children. I am especially interested in design that will invite and engage students who have traditionally been underrepresented in science and engineering, and underserved by the educational system. Such “at risk” populations include girls, minorities, people with disabilities, children on Individualized Education, Plans, English Language Learners, and children from low socioeconomic backgrounds. Understanding how to foster and scaffold all students‚Äô conceptual understanding, inquiry, and problem solving skills has been a central theme of our work. Another area of interest is the interplay between research and curriculum development, particularly when you are exploring a relatively new domain like elementary engineering about which little is known. How can we best structure research projects so they both inform and are informed by development and testing? What constraints and opportunities do such opportunities present?
Phil Daro – University of California, Berkeley, USA
Phil Daro currently directs the development of a middle school mathematics program inspired by the Japanese curriculum, works on advancing the design and use of leadership tools for change at every level of the educational system, and consults with states and school districts on their accountability systems and mathematics programs. He has served as Executive Director of The Public Forum on School Accountability, directed the New Standards Project (leader in standards and standards based test development) and Research and Development for the National Center for Education and the Economy (NCEE), responsibilities included test development, development of mathematics curriculum, and staff development programs, consulted to the New York City School District, the El Paso Collaborative, Los Angeles School District, Chicago Public Schools, Denver Public Schools, states of Vermont, Georgia, Kentuckey, Rhode Island, and California and others. He directed large scale teacher professional development programs for the University of California including the California Mathematics Project and the Americam Mathematics Project. His sixteen years at the University included six years directing projects to help states develop standards, accountability and testing systems. He has held leadership positions with the California Department of Education. Mr. Daro has served on a number of California and national Boards and committees including: NAEP Validity Committee; RAND Mathematics Education Research Panel; College Board Mathematics Framework Committee; ACHIEVE Technical (Assessment) Advisory Group, Mathematics Work Group; Technical Advisory Committee to National Goals Panel for World Class Standards, National Governors Association; Title I Commission organized by Council of Chief State School Officers; Mathematical Sciences Education Board of the National Research Council; California Public Broadcasting Commission; and The Accrediting Commission for Senior Colleges and Universities (WASC). He has taught mathematics and is the father of three daughters.
He is Vice-Chair of ISDDE.
Frank Davis – TERC, Cambridge, Mass. USA
I lead a non-profit research and development group that has as a mission improved mathematics and science learning for diverse communities of learners. This work assumes that system reform and change in both formal and informal learning and teaching environments.
Lewis Lum and Tom Dick have been working extensively with the TI-Nspire software platform in designing what have come to be called ‘Action-Consequence’ interactive documents. These are essentially learning environments where students interact at the level of the device screen. The design principle guiding the authoring of these documents is the requirement that students be able to immediately take some mathematically meaningful action on an object with an immediately visual (and mathematically meaningful) consequence. We have several examples of such environments produced for use with elementary algebra and geometry topics and are currently pursuing a collection for use in calculus instruction.
Brian Doig – Deakin University, Australia
Current work involves the design of mathematical tasks to elicit young children‚Äôs developing mathematical understandings. The target group of children are those in their prior-to-school years: that is, no formal education in mathematics as yet. The tasks are in a highly structured format but the look and feel of the tasks, from the children’s perspective, is that of games. It is the intention that children‚Äôs responses to these games will be placed on a continuum of mathematical development to allow early childhood educators to gauge and address children’s mathematical needs. The games cover a range of aspects of mathematics, including number, chance, measurement, and mathematical structure. All games use simple equipment. An over-arching feature that we wish these games to have is that they should begin with play with concrete materials, and then move on to playing mentally. To date several children have been interviewed and issues with the games revealed. Discussion within the working group is seen as assisting in the development of better tasks (games).
Alex Friedlander – Weizmann Institute of Science, Israel
Working for 35 years in design of activities, comprehensive curriculum projects and research on learning materials at the middle grades and elementary levels.
I am a designer of curriculum materials for mathematics education in primary schools. One of my projects is www.rekenweb.nl , a website with mathematical games. Another project is on the ‘mathematics of change’ and the use of the computer to help children understand graphs.
Louis Gomez – University of Pittsburgh, USA
One definition of scale is successfully catalyzing collective action. Our work on the analysis, design, and implementation of networked improvement communities in education aims to specify principles and workable social arrangements that support diverse groups of people working on shared problems within a common framework. This framework specifies common outcomes and how improvement transpires as a function of collective action. We hypothesize that designing tools that operationalize the common framework in a usable form is important for catalyzing and coordinating system change.
Sutarto Hadi – Lambung Mangkurat University, Indonesia
The demand for PMRI (Indonesian adaptation of realistic mathematics education) implementation in primary schools is high. The capacity of TEC (Teacher Education College) to support the implementation is limited. How to cope with the limited number of faculties staff is an important issue in the PMRI movement. This is the small history of how the role of key teachers was born. A key teacher is a highly motivated teacher who is a role model in the school if it comes to PMRI. A key teacher helps his/her colleagues in designing PMRI lessons, a key teacher is supportive, is teaching together with his/her colleagus, can observe lessons and give feedback.
Teachers have a forum where they can meet regularly, that is called KKG: Kelompok Kerja Guru (literaly translated: teacher working group). This paper describes how teachers developed into the role of key teachers, what their role in the movement means, how key teachers work together with their KKG forum as a vehicle to disseminate PMRI in their own school.
Laurence Holt – Wireless Generation, USA
Wireless Generation creates innovative tools, systems, and services that help educators teach smarter. With its mobile assessment software, the company invented a better way to give classroom assessments and make data-based instructional decisions. Now Wireless Generation has broken new ground with technology that analyzes student data and customizes curriculum to individual learning needs. Wireless Generation also builds large-scale data systems, such as New York City’s ARIS, that centralize student data and give educators and parents unprecedented visibility into learning. A Web 2.0 collaboration and knowledge network for educators propagates proven approaches across schools. Wireless Generation currently serves more than 200,000 educators and 3 million students. More information is available at www.WirelessGeneration.com.
Kees Hoogland – APS – Dutch National Centre for School Improvement
I am an international consultant and researcher in mathematics education and mathematical literacy. During the 1980s and 1990s I was co-author and editor of a successful mathematics textbook series for secondary education in the Netherlands: Moderne Wiskunde. From 2001 I have been involved as a project leader in the support project for the Indonesian PMRI movement. One of the focal points of that project is the creation of a bottom up Indonesian text book series on realistic mathematics for primary education. From 2000 I have been a key person in the development of Mathematical Literacy in the Netherlands which resulted in a project to develop web based multimedia learning materials for vocational and adult mathematics literacy education, which I am leading. Their designing is an attempt to create exemplary materials for a sophisticated numeracy concept. My research supports this design and focuses on how people learn and use numeracy skills in everyday life and working situations.
Glenda Lappan – Michigan State University, USA
The curriculum materials used to engage students in learning mathematics are one of the central tools available to teachers at a grade level. The CMP design team considers the following kinds of questions to drive the mathematics to be developed: What is the central mathematics theme for a particular grade level? How is it chosen? What is important for students at the grade level to know and be able to do? How does this theme interact with other supporting themes for the grade level? How is the mathematics of a grade level knitted together with the mathematics to be developed in the next grade level? How does the mathematics build on the grade level before the target grade level? How well do the problems selected for development in the materials promote mathematics proficiencies for students including conceptual understanding, procedural fluency, strategic competence (the ability to formulate, represent, and solve mathematical problems), and adaptive reasoning (the capacity to think logically and to informally and formally justify one’s reasoning)? (NRC, 2001, p. 131) Interactions around such design ‘principles’ and goals can push the discussion group to consider alternatives that may lead to more powerful, useful, and engaging mathematics experiences for students.
Editor’s note: In 2008 Elizabeth Phillips and Glenda Lappan were awarded one of the first ‘Eddies’ – the ISDDE Prize in Educational Design – for Connected Mathematics.
Would connecting the study of appropriate elementary/middle science concepts to the logical sequence of concepts outlined in most elementary/middle mathematics curricula strengthen students’ understanding and performance? Would leveraging the science curriculum to provide the context and the mathematics curriculum to provide the skills and critical thinking increase student comprehension and achievement? We believe a restructured sequence coordinating existing elementary/middle math and science curricula incorporating cross-field connections to leverage a transfer of knowledge would strengthen students’ understanding. Continuum models developed to characterize the nature of integrated curricula can be modified to provide a theoretical basis for coordinating existing but separate, mathematics and science curriculum, building upon the natural connections between the disciplines. Within a unit of study some concepts are discipline-specific and should be studied as such but some concepts might be enhanced with supporting concepts from the other discipline. Taking advantage of these natural “targeted connections” requires well-coordinated curricula that are closely aligned and taught simultaneously. Research-based mathematics and science curricula with documented evidence of positive impacts on student performance would be examined to create detailed concept maps outlining the concepts and processes found in each unit. A coordinated scope and sequence chart detailing when each concept or skill is taught would facilitate the creation of an instructional timeline coordinating the units across the disciplines. As the curricula examined already have documented evidence related to student success, additional gains would be attributed to the sequence in which the units are presented and the impact of the “targeted connections” lessons incorporated.
Lewis Lum – University of Portland, Oregon, USA.
I am a ‘tech resource’ for TINspire.
Cheryl Malm – Northwest Missouri State University, USA
See Patricia Lucido for paper synopsys.
Susan McKenney – University of Twente, Netherlands
I have a background in early childhood education, although I have also taught and conducted research in primary as well as junior secondary schools. In recent years, I have grown especially interested in exploring and supporting the interplay between curriculum development and teacher professional development. During the last 10 years, I have been engaged in a variety of design-based research endeavors that strive to maximize the natural synergy between these two processes. Much of my work on “learning by design” relates to designing teacher guides, learner material or other supportive curriculum documents.
Will Morony – Australian Association of Mathematics Teachers
As Executive Officer of Australia’s national association for teachers of mathematics my work has an emphasis on informing and supporting ‘change’. The scale for these changes ranges from the individual teacher – through, for example, materials and initiatives to assist teacher professional development – through to the national – in relation to curriculum, policies and programs. The extent to which ‘design’ principles can guide my work varies with the locus of control for the program funding, but my goal is to increasingly work and argue from a design-based perspective.
Daniel Pead – Shell Centre for Mathematical Eductation, University of Nottingham, UK
I have been working on the design and development of educational software since 1984 – including small applets for mathematics education (some of the software which used to accompany Malcolm Swan’s red book), multimedia products (I made major contributions to the design of the Bowland Maths professional development materials) and computer-based assessment (design of problem solving tasks for the World Class Tests project). A recurring interest is how to produce computer-based materials which support and encourage good teaching and assessment practice, ensuring that the technology is a means to an end, not an end in itself. Technology can greatly enrich teaching and assessment, but over-enthusiastic use may also promote a reductive, over-structured approach which is anathema to many current pedagogical aspirations (such as true formative assessment and promotion of thinking skills and less structured activities). I feel that a key solution to this is to promote a better mix of educational and technological skills amongst software designers, to ensure that the products match the pedagogical objectives.
Shelley Peers – Primary Connections Project, Australian Academy of Science
I am Project Director for ‘Primary Connections: linking science with literacy’ which combines professional learning with curriculum resources for use in Australian primary schools to improve the teaching and learning of science. Expanding uptake of the inquiry-based approach is our current challenge, hence I would be interested in hearing about work in this area. In particular, the strategies for building relationships with education departments, principals and teachers; processes for systemic engagement; adoption of scalable models of professional learning for sustainability. We have published a professional learning training manual and DVD, and 19 curriculum units in hard copy, with accompanying web resources such as a unit planner and assessment rubrics. We have trained approx 400 facilitators, 900 curriculum leaders, and 125 university lecturers and tutors in the approach.
Elizabeth Phillips – Michigan State University
My work (with Glenda Lappan, James Fey, and Susan Friel) involves designing, developing, field-testing, and evaluating a problem-centered mathematics curriculum for middle school teachers and students. This work involves identifying the important mathematical ideas relevant to the middle grades, unpacking the understanding of these ideas and then embedding these understandings in a sequence of problems (sometimes called hypothetical learning trajectories) that help students develop the understanding. Furthermore these mathematical sequences must build on each other to form a unit and in turn units must build on and connect to previous units within a grade and across grades to form a complete and coherent curricula – both for students and teachers. The work has been challenging, but promising. We are doing an in depth analysis of the curriculum to find opportunities to strengthen students’ mathematical understanding and reasoning and to find ways to talk about curriculum development that might be helpful to future generations of curriculum developers.
Editor’s note: In 2008 Elizabeth Phillips and Glenda Lappan were awarded one of the first ‘Eddies’ – the ISDDE Prize in Educational Design – for Connected Mathematics.
Robyn Pierce – University of Melbourne
I am interested in researching principles for the design of lessons that help teachers access the various potential affordances of technology for teaching mathematics. In the past two years we have studied the design of lessons through a process akin to ‚Äòlesson study‚Äô. This process is usually used to promote teachers‚Äô professional development but in our case the focus was on the lesson rather than the teaching per se. Each of three lessons has been developed by the research team in collaboration with teachers. The lesson, as planned, was taught with other teachers and some researchers observing. Feedback was provided by way of a survey of all participants (including students) and a focus group discussion with teachers and researchers, The lesson was revised in the light of this feedback and then introduced to a second school where the process was repeated.
Christian Schunn – Learning Research and Development Center University of Pittsburgh, USA
Designing for systems change requires taking a systems perspective to the design task, which involves three elements. First, it involves developing a model of the overall system to be changed (i.e., what subsystems are a critical element of the overall functioning system that needs to be changed). This step helps to ensure that the design includes all the critical elements. Second, it involves determining requirements associated with key decision makers (e.g., consistency with existing policies, dimensions of change that are valued by decision makers). Third, it identifying resources available for use (e.g., existing materials, partners, teacher training opportunities). Because the systems change is typically much too large to be accomplished all it once, design for systems change will typically also require a growth model, which often is a capacity-building theory of action. I will present an example in which this approach was taken to reform science teaching at the middle school level in a large US school district. A variety of data was collected and we found that very substantial change took place over the course of two years, as well as creating capacity for later reform work. But lessons were also learned about how this systems change work could have been even more effective.
Matt Skoss – NT DET/Possum Educational Services, Australia
Involved in the provision of professional learning experiences (Mathematics with integration of ICT) to classroom teachers (EC to 12), as well as supporting leading teachers in their role of providing strategic support to teachers at a school/regional level. Classroom teachers supported included those in remote Indigenous settings. Interested in exploring the application of Web 2.0 tools (eg. wikis, nings, twitter, etc) as well as hardware enabling collboration (eg. iPod Touch).
I am currently conducting, with my colleagues, a research and development project on the design of formative assessment. The main research question is how to make formative assessment ‘educationally tractible’. We are writing ‘specific mathematics assessments that reveal thinking’, which we call smart-tests. These provide teachers with almost immediate computer-based diagnostic assessment on students’ conceptual understanding on a wide range of topics.
Elizabeth Stage – Michigan State University, Australia
I’ve worked on standards, assessments, professional development, curriculum materials, and policy. I’m still trying to figure out how to improve math and science teaching and learning. Why is it so hard to overcome the status quo, at least in the U.S., at least in California?
Max Stephens – University of Melbourne, Australia
My current research uses number sentences involving two unknown numbers to identify some key junctures between relational thinking on number sentences and an ability to deal with sentences involving literal symbols. I have developed a questionnaire which focusses on how students are able to make generalisations on sentences involving two unknown numbers, and how these influenced their performance on sentences involving literal symbols. The questionnaire has now been translated and used with success in China, Brazil and Indonesia as well as in Australia. It aims to identify some key linkages as students make a transition from arithmetic to algebra.
Malcolm Swan – Shell Centre for Mathematical Eductation, University of Nottingham, UK
Malcolm Swan is Professor of Mathematics Education at the University of Nottingham. He leads the Shell Centre design team, playing the principal role in the design and development of many of its products, including the ‘boxes’ that pioneered the integration of assessment, curriculum and professional development. His research is mainly into the theory, development and evaluation of teaching situations in mathematics education. This includes: the design of situations which foster reflection, discussion and metacognitive activity; the design of situations in which children construct mathematical concepts and develop problem solving strategies; and the design of formative and evaluative assessment. Malcolm has recently led the design of curriculum and professional development resources that have been sent to all mathematics teachers in Further and Secondary Education in England.
Editor’s note: In 2008. Malcolm was awarded one of the first ‘Eddies’ the ISDDE Prize in Educational Design, for The Language of Functions and Graphs, also known as ‘The Red Box’.
- Accommodation & Tours
- Invitations, Registration & Presentations
- Plenary Lecture 1: Glenda Lappan & Betty Phillips – Designing and Developing a School Mathematics Curriculum
- Plenary Lecture 2 – Shelley Peers – Can we make a difference in primary science?
- Plenary Lecture 3 – Malcolm Swan – Values, Principles and Design in Mathematics Education
- Working Groups & Themes