Workshops

Workshops for Primary School Teachers

P1 - Collaborative problem solving as modelling in the middle years of schooling
By Dr Judy Anderson, President of AAMT, The University of Sydney, Australia

Abstract: The problem-solving process involves questioning, applying strategies, communicating, reasoning and reflecting. Using these processes in a collaborative situation mirrors mathematical modelling. Rich mathematical tasks can be used as a catalyst for middle years students to develop deeper understanding of mathematical ideas, problem-solving skills and techniques, and collaborative responsibility. This workshop will present several tasks and describe how to use them with students in upper primary and lower secondary classrooms.

P2 - Mathematical modelling for primary mathematics
By Ms Dawn Ng Kit Ee, National Institute of Education, Singapore

Abstract: Mathematical modelling is a new focus in the Singapore mathematics syllabus. This is an introductory workshop for mathematical modelling specifically for primary 4 to 6 teachers. The following will be discussed during the workshop:

• What is mathematical modelling?
• Key features of mathematical modelling tasks
• Some mathematical modelling tasks at primary level
• Facilitating mathematical modelling tasks
• Evaluating of students’ work during mathematical modelling tasks

P3 - Infusing mathematical applications in the primary mathematics lessons
By Dr Yeo Kai Kow Joseph, National Institute of Education, Singapore

Abstract: This workshop will assist primary mathematics teachers to examine the techniques and processes of infusing mathematical applications for their primary school pupils. The workshop will also provide the mathematics teachers with the opportunity to engage in realistic activities so that mathematical concepts and ideas can be taught and expressed in contexts closer to their pupils’ own experiences. It will also discuss the rationale for infusing mathematical applications in the classroom and illustrate some examples of mathematical applications.

P4 - Experiencing mathematical modelling in a PBL setting: Task features and design
By Mr Eric Chan Chun Ming, National Institute of Education, Singapore

Abstract: The recent emphasis in mathematical problem solving is on helping children to develop process components like reasoning, communicating, and making connections. The use of realistic tasks with modelling elements can help to facilitate those processes when situated in a problem-based learning (PBL) instructional setting. In this workshop, teachers will be engaged in solving mathematical modelling tasks in a short-cycle PBL instructional setting. Through the experience, teachers will analyze for features that characterize modelling tasks and the design that go into developing such tasks. Teachers will also improve on a given modelling task and craft questions related to the improved task.

P5 - Supporting students’ mathematical communication within modelling activities
By Professor Glenda Anthony, Massey University, New Zealand

Abstract: Mathematical modelling activities typically afford students opportunities to engage in mathematical conversations—conversations that involve the mathematical practices of conjectures, explanations, and justifications. We know from research that student mathematical learning benefits from explicit assistance to develop skills in learning to communicate about and through mathematics. Drawing on research studies involving New Zealand primary teachers, this workshop will explore a range of strategies that teachers can use to support young students’ development of mathematical communication practices. Specifically, we will look at ways to establish norms of participation for diverse students alongside strategies that both teachers and students can use to model and develop increasingly effective mathematical argumentation skills.

P6 - Mathematical modelling for primary school
By Dr Yeap Ban Har, National Institute of Education, Singapore

Abstract: In this workshop participants will be engaged in a mathematical modelling task that is suitable for primary-level students. Some assessment tools connected with the tasks will also be described. The task used in the workshop serves as a prototype for teachers to develop other mathematical modelling tasks.

Workshops for Secondary School and Junior College Teachers

SJ1 - Mathematical modelling in lower secondary level
By Professor Gabriele Kaiser, University of Hamburg, Germany

Abstract: The workshop will offer the participants possibilities to work in groups on smaller modelling problems suitable for teaching in lower secondary level (students from age 10-16). The participants will develop possible solutions for a few selected examples such as number of people in a traffic jam, amount of water in big water reservoirs, surface of a body. Afterwards results will be presented and the pedagogical potential of the problems will be discussed. Afterwards experiences with modelling examples in school and recommendations, how to tackle modelling examples in mathematics lessons will be described.

SJ2 - Designing and using modelling tasks at the secondary school level
By Dr Gloria Stillman, University of Melbourne, Australia

Abstract: Deciding on the desired elements of modelling tasks is a necessary precursor to their inclusion in teaching and assessment programs. Several tasks at different schooling levels will be analysed during this workshop to identify qualities of tasks that have worked in the classroom. This information will be used to illustrate a set of design principles that can be used in the selection and design of new modelling tasks for the classroom. It will also be illustrated how implementations of the same task may or may not follow a modelling approach depending on the teacher’s actions. This understanding can then contribute to the planning of teaching using particular tasks, such as the identification of necessary prerequisite knowledge and skills (including modelling competencies), possible interventions for introduction at key points if required, and the scaffolding of significant learning episodes.

SJ3 - Mathematical Modelling in the Singapore Mathematics Curriculum (Secondary)
by Gayatri Balakrishnan (Ministry of Education, Singapore)

Abstract: Mathematical modelling is one of the processes introduced in the 2007 revised mathematics framework. How can we introduce elements of mathematical modelling into our secondary mathematics curriculum? How can we make the learning of mathematics more interesting and relevant for our students? This workshop will introduce participants to the different stages and elements in the mathematical modelling process and how these stages and elements can be used to enhance the learning of mathematics and its applications. During the session, ideas will be shared on how mathematical modelling can be infused into the secondary mathematics curriculum through the adaptation of existing resources.

[Note that there has been a change of this workshop and does not correspond to the one advertised in the poster]

SJ4 - Developing students’ understanding and interpretation of tables of data using a five step framework
By Dr Marian Kemp, Murdoch University, Western Australia

Abstract: Everyday there are reports on television, in the newspapers and on the Internet that involve interpretation of data collected from a variety of sources and contexts. These can include statistics from crime, health, environmental, traffic, poverty and other areas. Reading and interpreting this statistical information is not easy for most people because such tasks can be really quite complex. To fully understand the information conveyed in text, tables and graphs and to comprehend the implications of such information requires transformations between the real world and the mathematical world and an understanding of what the numbers can tell us. This hands-on workshop will model the use a Five Step Framework based on the SOLO model designed to help mathematics students develop the skills required to read and interpret tables of data, an important aspect of applying mathematical thinking to everyday information.

SJ5 - Mathematical modelling using hand-held technology
By Mr Paul Poh Tze Thiam, Yishun Junior College and Dr Soon Yee Ping, Mathlodge

Abstract: This workshop aims to share with the participants the use of handheld technology like graphics calculators and handheld CAS for mathematical modelling. This handheld technology enables students to undertake mathematical modelling and problem solving in and beyond classroom environment due to its portability. It also allows for self-paced, independent work either individually or in small groups. Examples of practical applications of mathematics related to the Secondary and Junior College curriculum will be shown. Participants will have an opportunity to use some of the handheld technologies for mathematical modelling examples.

SJ6 Applications of mathematical content and processes in real life
By Mr Joseph Yeo Boon Wooi, National Institute of Education, Singapore

Note: This workshop is for secondary school teachers.

Abstract: Many students like to know why they study various topics in mathematics. Very often, teachers cannot think of a real-life application for most of the topics, or the examples that they have are beyond the level of the students. In the first part of this workshop, we will look at applications of mathematical content in the workplace that students can understand, e.g., using similar triangles in radiation oncology, encoding of computer data using large primes, and optimisation problems involving calculus. But the students may not be interested in these professions, so we will discuss the rationale of a broad-based curriculum. Then we will examine how mathematical content can be useful in daily lives, e.g., knowing how big is a 9.0 earthquake as compared to a 8.5 one, and realising that the probability of the same number appearing as the first and second prize in the 4D draw on 27 Jun 2007 is not 1 in 100 000 000 as reported in the newspapers. In the second part of this workshop, we will look at how mathematical processes, such as problem solving, investigation, and analytical and critical thinking, are important in both daily and working lives, e.g., analysing statistical data in newspapers critically so as not to be deceived by biased reporting, and solving authentic and unfamiliar problems in the workplace.

SJ7 - The Computer lab in the classroom: Using Texas Instrument (TI) Nspire as a hand-held manipulative for teaching and learning secondary school mathematics
By Dr Rosalind Phang and Dr Tang Wee Kee

Abstract: The graphing calculator (GC) has moved beyond being just a computation tool, and is now a convenient hand-held calculator that encompasses a wide range of tools which can be used to deepen our students’ knowledge of complex mathematics. The workshop will discuss how this tool replaces the various computer software commonly used for exploring mathematics in our secondary school classrooms. This workshop will explore ways to use the TI Nspire GC as a visual tool to explore and discover mathematics. Using examples in algebra, geometry and statistics, participants will experience how the TI Nspire GC can be used to engage students in numerous ways without having to leave the classroom.

SJ8 - Connecting secondary school mathematics with the real world
By Ms Pushparani d/o K. Nadarajah, Master Teacher (West 3), Ministry of Education, Singapore

Abstract: : Mathematics provides a way of viewing and making a sense of the word. It has many connections with other subjects and links with many careers ranging from Science, Engineering, Finance and IT. With rapid technological advancement in the global landscape, mathematics would assume greater importance. Approaches in mathematics education have attempted to present mathematics in context and to encourage its use and application. Through these connections, we could make learning of mathematics meaningful, relevant, challenging and real. Students need encouragement and opportunities to move out of their comfort zone and to establish these connections. Real world context problems would invite students and sometimes force them to use their real-world knowledge and personal experiences to analyze and solve the problems. The aim of this workshop is to share many ideas and strategies to establish links with the real world so that it becomes part of the mathematics culture in their classrooms.

SJ9 - Mathematical modelling: Using mathematics to make decisions
By Dr Toh Tin-Lam, National Institute of Education, Singapore

Abstract: Mathematics is a very powerful problem-solving tool. The process of using the power of mathematics to solve real world problems is known as mathematical modeling. In this workshop, the participants will be introduced to some aspects of mathematical modeling in helping one make decisions in real world situation. The content can be easily understood and can be applicable to secondary school mathematics students.

SJ10 - Enhancing mathematics teaching through hand-held graphing technology
By Dr Ng Wee Leng, National Institute of Education, Singapore

Abstract: Handheld graphing technology, if used appropriately in the mathematics classroom, has the potential to enhance teaching and learning of mathematics by empowering students to learn across different visual representations of a mathematical problem. With the aid of such technology, teachers have the means to help students develop a deeper understanding of mathematical concepts, broaden their critical thinking skills and discover meaningful real-world connections. In this workshop, participants will explore ways to enhance teaching of mathematics through the TI-Nspire Technology.

SJ11 - GenSing: Generative activities using technology: Hands on activities used in Singapore classrooms
by Dr Sarah Davis, National Institute of Education, Singapore

Abstract: This session will allow participants to experience a series of Secondary 1, 2 and 3 activities as students. All activities use the TI Navigator classroom network, graphing calculators and were created based on the principles of Generative Design.