Mathematical Explorations in the Classroom
January 23-25, 2022
Exploring Mathematical Explorations: We set the context for the workshop by discussing mathematical explorations conducted by secondary school students: the purpose of explorations, their characteristics, teachers’ role in guiding them and task design to enable them. We offer some illustrations.
Math Circles: The Maths Circle involves a group of carefully selected students, who meet online once in two weeks on weekends for a few hours to discuss carefully chosen mathematical explorations. For details, see here.
Enhancing students’ engagement in mathematics through technology-enabled explorations: In this session, we shall highlight the role of mathematical explorations in providing opportunities to students to formulate problems, discover patterns, make and test conjectures and approach solutions via multiple paths of inquiry. Examples of students’ investigations in topics such as Fractals, Genetics and probability will be discussed to illustrate that the appropriate use of technology can enhance students’ mathematical thinking. Evidence of progression in students’ thinking, as they engage with explorations and their positive feedback leads to a convincing argument for integrating such explorations in the school curriculum. During the session, participants will be given the opportunity to explore some of the problems with MS Excel.
Geometry in Islamic Art: Geometric patterns are an important part of Islamic Art adorning the sacred places of Islam, ornate palaces and other decorative artefacts such as ceramics, metalwork and tapestries. These patterns are made of precisely proportioned shapes drawn on a grid of circles and straight lines and can be constructed using a pencil, straightedge and compass. In this session, we will look at the symmetries and tiling units of some patterns and create some of these using a straightedge and compass and/or Geogebra. This provides a motivation for the constructions of school geometry and could lead to conversations on symmetry, transformation and tessellations. Below are some examples of Islamic art that abound in India.
Try, Tile, Triangle: If you thought a triangle was interesting, then tiling triangles will be even more so. Do all triangles tile? What quadrilaterals do they form when they tile? Can we generalise our observations? During this session, we move from doodling to observing to conjecturing and then generalising, running the gamut from seeing mathematics to experiencing mathematics. Exploration plus – possibly with Mathigon polypad!
Explorations in data citizenship: Data literacy is an important educational goal in a data-driven world. Data citizenship takes this a step further by recognizing that data collection, processing and analysis critically impact citizens’ lives. It aims at citizens participating in and shaping a culture that respects the need for reliable data and regulates its creation and use. In this session, we will look at ways in which we can explore publicly available data including those in commonly used apps such as Google Maps to understand how mathematics can illuminate social reality.
Mathematical Modelling through Explorations in Crafts: One of the fundamental guiding principles in the National Education Policy 2020 is: “No hard separation between the arts and sciences, between curricular and extracurricular activities, …” This provides scope for teachers to do explorations and mathematical modelling that are relevant to students and teachers alike. In this session, we will do a few explorations in crafts (crochet and knitting) that help us build simple mathematical models. We will use Excel to do this. We will also discuss some examples of “mathematical modelling” that are actually not mathematical modelling and these could in fact harm students. This will be followed by a discussion in zoom breakout sessions where participant teachers will discuss specific examples.
Lady Sriram College, Delhi
Inst. of Math. Sciences, Chennai (Retd)
Azim Premji Univ, Bengaluru (visiting)