Venue: National Institute of Education, Singapore

Dr Hang Kim Hoo and Ms Chong Woon Hui

Jurong Junior College

‘One of the greatest paradoxes of mathematics education is that, although we mathematics
teachers are immersed in mathematical work every day of our professional lives,
most of us nevertheless have little experience with the kind of work that research
mathematicians do. Our ideas of what doing & using mathematics looks like are based
mainly on our own experiences as students.’

Weiss & Moore-Russo (2012)

We teach who we are. We teach what and how we do. What and how we learn and use mathematics shape our ideas on mathematics instruction, which often form the foundation on which we eventually build our own teaching.

The above premises provided the impetus for a group of junior college mathematics teachers to embark on a long term professional development journey to revisit, retrace or re-learn mathematics to explicate the mathematical practices of mathematicians when they do or use mathematics. The practices and habits of minds of research mathematicians involve generating new or refining existing mathematical ideas and methods. In particular, the moves that the mathematicians use to generate new questions include problem posing and task variation techniques. This workshop will highlight and illustrate how the use of some of these techniques can help create tasks that can concurrently develop mathematical thinking and problem solving skills, insights and dispositions among both the teachers and their students.

Mdm Nai yuan Ting

Yishun Junior College

Abstract: Students offering “A” Level H2 Mathematics often find the following concepts difficult, such as the convergence of a series, the behaviour of graphs near asymptotes, drawing the graphs of y = f '($x$) (f ' is the first derivative of f with respect to $x$) and \(y = \frac{1}{{{\rm{f}}\left( x \right)}}\) from the graph of f when the equation of f is not given, and the use of parametric equations in differentiation and integration. Students sometimes may think that they understand a mathematical concept, but when tasked to solve other variations of a mathematical problem using the same concept, they often find themselves challenged conceptually. For example, students are able to draw, without the use of graphic calculator, the graph of $y$ = f '($x$) from the graph of f for the case of f being a quadratic, cubic or even a quartic polynomial. However, when tasked to draw the graph of $y$ = f '($x$) from the graph of f with a horizontal asymptote and a vertical asymptote, students will often encounter some difficulties.

In this workshop, we will analyse the difficulties that students may have in some of the concepts at “A” Level Mathematics, and discuss how teachers could come up with meaningful mathematical tasks to deepen the students’ conceptual understanding in their classroom instruction. The principles to consider when designing and developing mathematical tasks as well as assessment of the learning outcomes of the mathematical tasks will also be discussed.

Dr Teo Kok Ming

National Institute of Education Singapore

Abstract: The aim of this workshop is to discuss the use of tasks and activities in the teaching of H2 Further Mathematics. In particular, the presenter will share with the participants some examples of tasks and activities that could be used to develop an understanding of some mathematical concepts and processes in linear algebra topic in H2 Further Mathematics.

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