Untangling the “Knot” Your Typical Math problem

As students create and analyze mathematical knots, they develop their ability to reason spatially and engage in concepts not typically part of a geometry curriculum. Originally published in the May 2018 issue of TCM, this problem allows students to expand their understanding of mathematics by exploring knot theory.

An Analysis of the National Intended Geometry Curriculum

Geometrical concepts play a crucial role in developing spatial thinking and reasoning. Further, curricular materials play a key role in shaping student-learning experiences in the classroom. The organisation of the content of textbooks plays a decisive role in how and when students are introduced to concepts, especially given the ‘textbook-centric’ teaching practices observed in the Indian classroom. I thus analysed the geometry curriculum from grades one through eight through the lens of the five-level hierarchical van Hiele model of geometrical thinking.1 I organized the analysis to highlight conceptual details at two levels—across a chapter in a particular grade level and across chapters in all the eight grade levels. The analysis has illuminated the affordances of curricular materials to constantly connect students to multiple levels of geometric reasoning, but at the same time it points to the need for reorganizing the curriculum to enable students to systematically progress from visual-based to deduction-based reasoning. The analysis also calls for redesigning certain conceptual representations to promote relational geometrical understanding among students.

Tapering Timbers: Finding the Volume of Conical Frustums

Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?

Teaching Geometry through Problem-Based Learning

One secondary school's mathematics department decides to change its geometry curriculum.