Game Theory – An Alternative Mathematical Experience

Abstract: Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behavior in competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only basic understanding of mathematics. The course Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. We use four different topics (college admissions, social justice and majority voting, coalitions and cooperative games, and a bankruptcy problem from the Talmud) to investigate four areas in game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.

Roles of mathematics education in the development of 21st century competencies among secondary school students

Abstract: Many education systems around the world aim to promote 21st century competencies (21CC) among their students to prepare them to meet future challenges in careers and personal well-being in a globalised world. In Singapore, 21CC means that students are educated to become a confident person, self-directed learner, active contributor, and concerned citizen. There are strong links between these desirable outcomes and the aims and practice of mathematics education as spelt out in the curriculum framework. Confidence can be cultivated through exercises in critical thinking; self-directed learning through taking responsibility of one’s learning and engaging in metacognitive reflection; active contribution through working in teams to achieve common learning goals; and finally, concerns as Singapore citizens through working on mathematics applications and modelling with Singapore contexts. In this workshop, participants will explore these links by working through selected topics in the secondary school curriculum. The conceptualisation and examples developed in this workshop can be applied to inculcate 21CC through other mathematics topics or under different education systems.

Mathematics in twenty-first century life

Abstract: The 21st century is likely to be characterized in part by the amount of information available to citizens, in many different forms. School graduates will need to engage with quantitative information from many different perspectives: as voters, as consumers, as parents, as workers and as global citizens. As well as traditional media, such as radio, television and newspapers, information is provided in many other ways, including various forms of social media and the Internet. Some of this information is important to help students understand their world and to appreciate cultural and social differences among Singaporeans and between Singaporean and other nationalities. Other information is important for students to make good personal decisions about their health, their lives and their futures. Mathematics has the potential to contribute to the development of competencies to deal with these various kinds of information. In addition, mathematics has the potential to enrich students’ lives through engagement with the wider discipline of mathematics and seeing its place in wider society. In this workshop, we will consider examples of the sorts of information encountered by 21st century students and examine ways of supporting them to develop suitable information skills for confident and effective use. We will also consider the opportunities available to students in the popular domain to appreciate the nature and significance of mathematics more broadly, through encountering appropriate reading both in text and online.

Experience “MAGICAL” mathematics (I):

Abstract: In this workshop, the participants will be introduced to the use of cartoons and comics in teaching mathematics: the theoretical framework and the approach. A concrete package on teaching Mathematics to Secondary One Normal Technical students will be illustrated. Different modes of lesson delivery to engage different types of learners will be discussed.

Your students don’t have to be academically bright to reason and justify

Abstract: Justification tasks asking students to comment on, explain, prove or verify a mathematical result are becoming more widespread in the GCE O and N Level examinations. Commonly, such tasks are deemed as higher-order thinking questions meant for the more able students. As a result, many students tend to shun these tasks in tests and examinations. However, these tasks are not necessarily difficult and even less able students should be able to deal with them if properly taught. In this workshop, participants will learn about the various types of justification tasks, the demand for each type of justification task, the purposes of written justifications, and most importantly, teaching strategies for handling justification tasks. With increased clarity of the task demand and justification purposes, the participants may be better able to articulate them in the teaching process and to scaffold their learners to produce reasonably written justifications.

Helping Students to Improve their Reasoning in Algebra

Participants in this workshop will have the opportunity to discuss some issues related to secondary students’ reasoning in algebra. The workshop is open to all secondary mathematics teachers and will focus on some key ideas for teaching algebra that will enhance their students’ reasoning in the subject. Participants are strongly encouraged to bring samples of their students’ work and share any example of good practice in the teaching of algebra that enhances their own students’ reasoning.

Making statistics real in the classroom

To help students develop statistical competencies needed in the 21st century, a good approach is to show them how statistical distributions and methods learned in the classroom can be applied to real-world contexts and analyze real data. In addition, to help students gain better insight into properties of distributions like normal approximation to binomial and interpretation of methods like confidence intervals, we can provide them with opportunities to explore these properties and methods empirically through simulation. To these ends, the workshop will engage the participants with a variety of statistics questions based on real-world contexts and/or data, and show how statistical simulation can be performed using Excel.

Note: The workshop will be conducted in a computer lab using Excel.

Thinking slowly, critically and inventively about algebra

Abstract: As a framework for planning mathematics teaching I suggest that we need to think about how mathematics connects to the world, to other mathematical ideas, and to history and culture. In this workshop I will present some practical suggestions for making connections through algebra, and hence for developing critical and inventive thinking. The workshop will use technology, including spreadsheets and Geogebra.

What it takes to flip the class?

Abstract: The buzzword “flipped classroom” has been tossed around in the educational fraternity at the turn of the 21st century. Lage, Platt and Treglia published the paper “Inverting the Classroom: A Gateway to Creating an Inclusive Learning Environment” in 2000, but earlier works can be traced to Eric Mazur’s use of computer-aided instructions to take the place of lectures. The promises of this novel instructional approach are enticing: swapping the chronological order of direct teaching (in the form of lectures) and homework (in the form of exercises) seemed to have done wonders in the western classrooms. In the East, the flipped instruction seemed to take a little longer to break through the traditional practice of chalk-and-talk. Flipped classroom, as a type of blended learning, is understood in different ways by different people. The central topic of discussion in this workshop is to highlight the pedagogical theories underlying this relatively new instructional approach, and to explore some of the ways of flipping the Singapore classroom.

Remarks: This talk is generic enough to fit into the context of most subjects, but cites more exemplars from mathematics teaching.