Keynote Lectures

Theme: Big Ideas in Mathematics

Keynote 1 (Plenary) :
(1+1) = 3: Revisiting Mathematics Education from a Communication Perspective in the Era of the 4th Industrial Revolution

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Prof Jung Younbo, Singapore

Abstract: In recent years, as our society enters the era of the 4th industrial revolution where we experience the fusion between the physical and digital worlds, new ideas of disruptive innovation have been proposed, and their applications introduced to education in forms of technological innovations (e.g., massive open online courses [MOOC] with virtual reality, and digital tutors with artificial intelligence [AI]). What consequences and implications will such technologies have for the future of teaching and learning? Will technology-enhanced learning fundamentally change the way students learn in the classroom everyday? What will happen to human teachers? Indeed, there are so many thrilling questions waiting for answers. In my presentation, I propose to revisit the whole education process from a communication perspective, using a basic communication model consisting of the sender, the receiver, the message, and the channel. Such a holistic approach, instead of focusing on a part of the process, may allow us to think about the very fundamental question of what mathematics education is and to have a better understanding of how to lead the education revolution.

Keynote 2 (Primary):
‘Big Ideas’ in Primary Mathematics: Reconceptualising Curriculum

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Prof Chris Hurst, Australia

Abstract: Mathematics curricula around the world tend to be structured in a linear fashion with content assigned to year levels. Unfortunately, such an approach does not emphasize the many links and connections that exist within and between the ‘big ideas’ of mathematics. It is suggested here that a focus on ‘big ideas’ would enable a richer and more conceptual teaching approach to be adopted, rather than a procedural one.

But what are the ‘big ideas’? Charles (2005) described them as ideas that are central to the learning of mathematics and which link numerous mathematical ideas into a coherent whole. As well, Charles and others have noted that it would be difficult to obtain uniform agreement as to exactly what, and how many, ‘big ideas’ there actually are. This is a strength of ‘big idea’ thinking in that considering what ‘big ideas’ are requires people to deconstruct their mathematical knowledge and reconstruct it. It is an important teaching skill to be able to work back from a mature level of understanding of a concept and identify the core underpinning elements that lead to such a level of understanding.

There are other advantages to teachers considering the mathematics curriculum along the lines of ‘big ideas’. First, the more connections within and between ‘big ideas’ that a teacher knows about, the deeper his/her understanding is likely to be, and the greater the likelihood of him/her being able to make these connections explicit to students. Second, the connected nature of ‘big ideas’ enhances transfer and reduces the amount to be remembered. Third, effective teachers know how ‘big ideas’ connect topics across grade levels, know how concepts are developed at each level, and how these connect to previous and subsequent grades.

If learning is to be sustainable, teaching must be based on broad, deep, and connected conceptual understanding of key ideas. It is not helpful to teach children procedures for doing mathematics unless they really understand how and why those procedures work. Thinking in terms of the ‘big ideas’ of mathematics makes such connections explicit.

In addition to the above, this presentation will address the following:
  • Teaching the ‘big content ideas’ through the ‘big process ideas’
  • Considering what the ‘big ideas’ of primary mathematics might be
  • Working backwards and identifying the ‘micro-content’ that underpins some ‘big ideas’
  • Considering what a curriculum based on ‘big ideas’ might look like.

Keynote 3 (Primary):
Making Connections

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Dr Chan Chun Ming Eric, Singapore

Abstract: Pupils learn about multiplication ideas in Primary 1 and 2 and then progress towards the learning of the multiplication algorithm in Primary 3. The column method of multiplication has been the standard format taught in the curriculum. This talk extends on the idea of multiplication with respect to making connections of various multiplication methods and the sense making of the workings behind these methods. Getting pupils to learn about the different strategies and why they work provides affordances for a more interesting classroom discourse which in turn supports the meaningful learning of mathematics.

Keynote 4 (Secondary):
Mathematics for Responsible Citizenship

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Prof David Wagner, Canada

Abstract: I respond to the Sustainable Development Goals outlined by the United Nations. Implications for mathematics teaching include changing classroom communication practices, reconsidering contexts for mathematical examples, and rethinking what mathematics is most necessary. I acknowledge the challenging scope of these possibilities for change, and reflect on possible first steps and next steps for mathematics teachers who want to take the needs of society and the environment seriously.

Keynote5 (Secondary):
Deconstructing Big Ideas: Perspectives and Way Forward

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Prof Chua Boon Liang, Singapore

Abstract: Big ideas in mathematics are essential building blocks not only for learners to develop a deep understanding of mathematics content but also for teachers to create connections between concepts and skills when they teach so that mathematics becomes a coherent set of ideas. Mathematics students must be conscious of these big ideas so that they do not view mathematics simply as a set of disconnected concepts. Mathematics teachers, too, need to understand the big ideas so that they can translate them into their teaching practices. In this lecture, I will unpack the notion of Big Ideas in mathematics to illustrate how secondary school mathematics teachers can exemplify them in the classroom.

Keynote 6 (Junior College):
Some Great Breakthrough Ideas in Mathematics

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Prof Koh Khee Meng, Singapore

Abstract: There are numerous breakthrough ideas in the rich history of mathematics. In this talk, I shall present some of them pertaining to our A-level mathematics content. These include number systems, trigonometric functions, logarithm, Cartesian coordinates, limit, and Fundamental Theorem of Calculus. It is hoped that at the end of the talk, we all can appreciate how significant and influential these ideas were in the development of mathematics, and in turn be fired in our passion for teaching mathematics.

Keynote 7 (Junior College):
Teaching Mathematics – A Modest Call to Consider Big Ideas

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Prof Tay Eng Guan, Singapore

Abstract: Big Ideas are defined here as overarching concepts that occur in various mathematical topics in a syllabus. Knowing these will guide teachers to help students develop a better understanding of mathematics, by making visible the central ideas, the coherence and connection across topics and the continuity across levels. In this talk, I shall give a few examples of Big Ideas across the junior college syllabus. For example, “solving equations” may be a Big Idea in mathematics teaching and learning. In the syllabus, students encounter solving linear, quadratic, simultaneous, trigonometric and differential equations. Students should learn that these often involve isolating the variable and expressing it as a range of numbers or as an expression in terms of another variable. A ‘target expression’ approach would then involve suitable algebraic manipulations, e.g. completing the square, partial fraction decomposition. A deeper consideration of what mathematics is will guide our discussion.

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