Abstracts of Presentations

Jumping Tasks: Not too High, not too Low, but Just Nice

Ast/P Choy Ban Heng

Tasks are important for developing competencies in mathematics and language classrooms. Particularly, in lesson study, a well-designed jumping task provides students opportunities to solve problems, discuss ideas, and reason together. Consequently, teachers have to spend time to think about how tasks can be used to facilitate and encourage student thinking during lesson study discussions. However, designing such tasks is challenging and teachers often find it difficult to connect the task with the concept they are teaching. In this presentation, we will present some of the tasks designed by the teachers in our study, and examine the design of these tasks in terms of three principles: the content principle, the activity principle, and the documentation principle (Choy, 2018). In addition, we will highlight the challenges our teachers face, and suggest how teachers can be supported as they design jumping tasks as part of the lesson study discussions using these three principles. Last but not least, we will discuss our insights into the teachers’ pedagogical reasoning as they design tasks to facilitate collaborative learning and listening in Math classrooms, as well as the implications for lesson study practitioners.

Reference:
Choy, B. H. (2018). From Task to Activity: Noticing Affordances, Design, and Orchestration. In P. C. Toh & B. L. Chua (Eds.), Mathematics Instruction: Goals, Tasks and Activities (pp. 11-31). Singapore: World Scientific.

 

Proof and Proving in the Singapore School Mathematics Curriculum

Navinesh

Research on proof and proving in schools has been mainly researched in the US. There is a general belief that proof and proving is inaccessible to students in primary and secondary schools and hence not prioritised as much in the syllabus. Teachers do also face problems in the teaching of proofs. How then can we facilitate the teaching of proofs in the curriculum? Proofs are the foundations of mathematics and involve multiple modes of reasoning which are advocated in the Singapore Mathematics Curriculum Framework. In this presentation, we will look at three types of reasoning commonly cited in literature related to proofs in particular, and, how we can attempt to structure such reasoning into a model. The presentation concludes with a short group activity on proof and proving at the secondary level.

Differentiated Instruction in a Secondary Mathematics Classroom

Vinnie Goh and Toh Tin Lam

This presentation provides a literature review of the theories underlying differentiated instruction. Based on the literature review, we will suggest strategies to design differentiated instruction in Secondary Mathematics classrooms. Our literature review shows that various theories, including Dunn and Dunn’s Learning Styles Model, Gardner’s Multiple Intelligence Theory and Constructivism theories by Piaget and Vygotsky, are the basis for developing differentiated instruction in classrooms. Suggestions to enact differentiated instruction in the mathematics classroom include differentiation based on content, process and product in order to accommodate students’ readiness, interest level and learning profiles.

Seeding Māori and Pasifika Success in Tertiary Mathematics

Chin Sze Looi

In New Zealand, Māori and Pacific Island (MPI) students are underrepresented in tertiary mathematics courses and achieve significantly lower results. The project focuses on enhancing MPI achievement through creating culturally-meaningful resources which will better prepare MPI students for tertiary mathematics and plant seeds of success. In this presentation, I will share some of the tasks which were co-created with MPI students.

Talk in a Mathematics Lesson

Wong Lai Fong

A wide variety of talk occur within a mathematics lesson. However, the mere presence of talk does not ensure that understanding follows – only meaningful math talk can enhance learning. We can examine math talk from the perspectives of the teacher (teaching talk) and the students (learning talk) according to Alexander’s (2017) dialogic teaching framework. In this presentation, teaching episodes enacted in the interactions between a competent and experienced teacher and his students will be shared to illustrate the kinds of math talk (univocal and dialogic) and how the teacher uses the students’ talk to generate meaning and creates the learning moment where students construct their own knowledge.

Use of Regularization Methods in the Detection of Adulteration in Olive Oil

Soh Chin Gi

Olive oil is known to have health benefits, but is costly to produce. Fourier-transform infrared (FTIR) spectroscopy is a viable means to detect adulteration in olive oil. However, spectroscopy data is high-dimensional, and has high correlation between wavenumbers leading to challenges in statistical analysis. One possible way to overcome the challenges associated with the high dimension of the data is through the addition of a penalty term, in a process known as regularization. Some regularization methods that aid in the construction of a parsimonious and interpretable model for the detection of adulteration in olive oil samples will be presented.

Dimension Reduction Methods and its Applications

Ast/P Zhu Ying

Dimension reduction plays an important role in feature extraction for high dimensional data. When data is linearly separable, classic approach like principal component analysis works well as a linear projection technique. However, in the case of linearly inseparable data, a nonlinear technique is required to reduce the dimensionality of a dataset. In this talk the ideas of linear and non-linear dimension reduction methods are introduced to identify patterns that well represent the data. Real-life examples will be presented in areas of image processing and reconstruction.

On Cross-intersecting Sperner families

Willie Wong

Two subsets X and Y of N_n are said to be independent if X⊈Y and Y⊈X. A Sperner family (or antichain) A of N_n is a collection of pairwise independent subsets of N_n, i.e. ∀ X,Y∈A, X⊈Y. Two sets A and B are said to be cross-intersecting if X∩Y≠∅ for all X∈A and Y∈B. Given two cross-intersecting Sperner families A and B of N_n, we prove that |A|+|B|≤2(n¦⌈n\/2⌉ ) if n is odd, and |A|+|B|≤(n¦(n\/2))+(n¦((n\/2)+1)) if n is even. Furthermore, all extremal and almost-extremal families for A and B are determined.

Maximal Point Spaces of DCPO of Intervals

Yuen Wen Jun

To consider cases in which a space is homeomorphic to the maximal point space of a related to the maximal point space of a related partially ordered set. Two cases included are R with the poset of closed intervals of R with inverse inclusion order, and a complete lattice L with a few additional properties with the corresponding poset of closed intervals of L with reverse inclusion order.

Statistics on Ascent Sequences

Dr. Huifang Yan

Ascent sequences were introduced by Bousquet-Melou et al. to unify three other combinatorial structures: (2+2)-free posets, a family of permutations avoiding a certain pattern and a class of involutions introduced by Stoimenow. All these combinatorial objects are enumerated by the Fishburn number Fn for memory of Fishburn's pioneering work on the interval orders. In this talk, we will present some results concerning the equidistribution of several statistics on ascent sequences and related objects.