Workshops - Secondary

Theme: Big Ideas in Mathematics

S1: The Four Dimensions of Disciplinary Thinking: An Approach to Seeing and “Implementing” Big Ideas from Curriculum Documents

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Prof Choy Ban Heng, Singapore

Abstract: Big ideas and Learning Experiences are included in our latest mathematics curriculum to enhance students’ understanding and appreciation of mathematics. While Learning Experiences are conceptualized in terms of mathematical tasks, big ideas are intended to be infused rather than explicitly taught. In some ways, big ideas become the invisible hand that guide the teaching and learning of mathematics. This poses a new problem for teachers: how do teachers support students to see and appreciate big ideas in the curriculum? One approach to do this is to think of mathematics as a discipline. I suggest that teachers can think about big ideas using the four dimensions of disciplinary thinking (Mansilla & Gardner, 1999), and implement these big ideas through mathematics tasks. In this presentation-workshop, I will introduce the four dimensions of disciplinary thinking, guide participants to notice the big ideas (Sherin, Jacobs, & Philipp, 2011) in the curriculum documents, and design tasks that bring out these big ideas to students. For this interactive workshop, teacher-participants are encouraged to bring along the latest syllabus documents for reference.

S2: Using Typical Problems to Enhance Students’ Reasoning in Mathematics

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Prof Dindyal Jaguthsing, Singapore

Abstract: In school mathematics, several students are lured by the procedural aspects and focus on learning only the “how” at the expense of the “how and why”. While this instrumental view may serve the purpose of a few, it denies the majority of students including low performing students, an opportunity to see mathematics from a higher vantage point. The “why” is important in developing students’ reasoning to see the connections between the different concepts they learn in mathematics. In this workshop meant for secondary school teachers, I will focus on how to use “typical problems” that are easily accessible to teachers, to enhance students’ reasoning in mathematics so as to meet the dual purpose of developing students’ procedural skills as well as conceptual fluency that is suitable for students across all performance levels.

S3:Big Idea: From Within-topic to Across-topics

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Prof Leong Yew Hoong, Singapore

Abstract: When I think of “Big idea”, I visualise myself sitting at the teacher’s desk at the cusp of launching into a new topic with the class and asking, “What is this one central mathematical point that controls the organisation of my contents for this topic – and that I should keep taking reference from throughout the teaching of the topic?” It is so important that if students miss this point, they miss … the point (in the learning of mathematics). We may start by taking a topic, say, addition of fractions, and inquire into the big idea in this topic. We then broaden our inquiry to look at other topics in the secondary mathematics syllabus where this big idea is repeated and hence are occasions for me as a teacher to reinforce it.

S4: Teaching towards big ideas in mathematics

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Mdm Low Leng, Singapore

Abstract: When students learn by rote or memorisation, they will view mathematics as a collection of isolated and meaningless knowledge. To empower students to transfer their learning to new context and regard mathematics as meaningful, they need rich learning experiences to construct core mathematical concepts and principles. This requires teachers to make a pedagogical shift to present mathematics as a coherent and connected body of knowledge. In this workshop, big ideas for effective teaching and learning of mathematics will be highlighted in the context of the various content strands. Working in groups, participants will explore how big ideas can be used to link different activities for students to have a more connected schema of mathematics. Teaching towards big ideas facilitates students to better organise their knowledge and develop a greater appreciation of mathematics.

S5: Inquiry in a Japanese Math Classroom: Using Students’ Mathematics to Develop a Curriculum (for Lower Sec)

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Ms Pauline Anne Therese M. Mangulabnan, Japan

Abstract: In some cases in Japan, a junior high school class is composed of both students who go to after-school private tutors and those who do not. Such extremes may pose a problem on students’ engagement and motivation in the mathematics classroom. In this workshop, we look at how some Japanese junior high school mathematics teachers utilize individual and collaborative inquiry to design mathematical units that both address issues raised by and strategically make use of students’ varying mathematical backgrounds and experiences. We take a closer look into the mathematical tasks prepared by the teacher, as well as the students’ responses which reshaped the implementation of the unit and encouraged deeper mathematical inquiry. The redesign of the lesson is a by-product of the teacher’s own refection on students’ struggles, alternate conceptions and feedback while in action. Hence, the effects of how a teacher reflects upon her mathematics class and her students’ voices to improve one’s practice will also be discussed.

S6: Mathematical Modeling and Modeling Mathematics in Problem Solving

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Prof Padmanabhan Seshaiyer, USA

Abstract: In this workshop, we will engage teacher participants in considering mathematical modeling as a big idea using real world tasks with the various attributes including Open-endedness; Problem-posing; Creativity and choices and; Iteration and revisions. The workshop will also include inquiry-based activities to help teachers understand the ways in which models are essential in teaching and learning mathematics; to clarify differences in mathematical modeling and modeling mathematics in problem solving and; to share best mathematical practices that are critical to mathematical modeling and modeling mathematics in problem solving.

S7: Mathematics Task Design for Responsible Citizenship

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Prof David Wagner, Canada

Abstract: Participants in this workshop will discuss principles for designing mathematics tasks that address the United Nations’ Sustainable Development Goals. We will then work in groups to begin collaborative work on exercises and assessments that follow the principles.

S8: Linking Big Ideas in Mathematics, Pedagogy, and Assessment in Statistics Topics

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Dr Wong Khoon Yoong, Singapore

Abstract: “Big ideas” or “essential understandings” in mathematics are core concepts and principles that can be found in different topics, such as “equivalence” in numbers and algebra and “patterns” in numerous topics. Highlighting big ideas will help teachers and students appreciate coherence among the topics included in the curriculum. Similarly, there are big ideas in pedagogy and assessment. At this workshop, participants will explore links among these three kinds of big ideas for the Statistics topics included in the secondary mathematics curriculum. The intended outcome is to enrich the mathematics pedagogical content knowledge of the participants, so that they can provide more coherent and meaningful learning experiences about Statistics to their students.

S9: Empirical Modelling

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Prof Yap Von Bing, Singapore

Abstract: This workshop will focus on teaching secondary school students mathematical modelling of empirical problems, where the data (hence the variables) are given, and prediction is the question of interest. The scope may seem restricted, but it will be argued that it is a good place to start, and it affords a sound connection to probabilistic modelling introduced at the H2 level, and to more advanced training in statistics or data science. Some learning points include (i) the discrepancy between the real problem and the mathematical model, manifested in the contrast between data and predictions, (ii) consideration in the complete specification of the model, and (iii) testing predictions by new observations.

S10: Practical Ways of Infusing Big Ideas in the Classroom

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Dr Yeo Boon Wooi Joseph, Singapore

Abstract: What are some big ideas in secondary school mathematics? How can teachers convey these big ideas at the level of their students? In this workshop, the facilitator will suggest some practical ways of infusing big ideas in the classroom, including how to design mathematical tasks that are rich enough to bring out the essence of these big ideas. Then the participants will work in groups to refine the suggestions and to brainstorm for other practical ways to imbue other big ideas. The big ideas that will be discussed in the workshop include, but are not limited to, equivalence, invariance, functions and models.

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