# Secondary

Some useful resources for secondary school students

Constructing theories: A case study in geometry, with an extension to biology

# K. P. Mohanan, Tara Mohanan

This book is an attempt to introduce the reader to the art and craft of theory construction. While we use geometry as the terrain for practice, our focus is on the methodological strategies and techniques of value in all domains of theory construction, not on the ‘facts’ of geometry that students learn in textbooks. We expect the series to be useful for researchers and research students across disciplines, but have also tried to make the content and the style accessible to high school students.

Conceptual Inquiry: Democracy

# K. P. Mohanan

This recording of a classroom session delves into the concept of democracy. Students are attempting to clarify the concept.

Appearance vs. Reality 1

(Constructing & Evaluating Knowledge series -1)

# K. P. Mohanan, Tara Mohanan

This is the third dialogue in a series on Constructing and Evaluation Knowledge. In this dialogue, Rafa and his mother Samira discuss the relationship between what we observe and what actually exists.

Counterexample

(Expositions on concepts involved in inquiry series -3)

# Madhav Kaushish

A counterexample is an example that refutes a claim. This article works through examples of counterexamples and includes some exercises for you to work on.

Region of Inexactness

(Expositions on concepts involved in inquiry series -1)

# K. P. Mohanan, Tara Mohanan

In this article, we explore the concept of the region of inexactness, the amount of fuzziness involved in reporting observations about the world.

Axioms of Rational Inquiry

# K. P. Mohanan, Tara Mohanan

In this article, we explore the concept of the region of inexactness, the amount of fuzziness involved in reporting observations about the world.

Theory of Motion

# K. P. Mohanan, Tara Mohanan

This book is an introduction to how we construct theories in science to explain natural phenomena, in this case, the phenomena clustering around the motion of inanimate objects. It aims to help the young reader gain an experiential understanding of the way scientists think, and of the kinds of questions they ask, and develop the capacity to think like a scientist. The abilities needed for this are important because they can be extended to thinking, inquiring, and formulating questions not only in other domains of academic knowledge, but also in life beyond academics. This we see as the main benefit of the book. The reader would also gain a better understanding of some of the foundational concepts in physics. We expect the book to be useful for researchers and research students across disciplines. The background knowledge of science and mathematics needed for access to the content is what one would have most likely have learnt in Class 8 in school.

Appearance vs. Reality 2

(Constructing & Evaluating Knowledge series -2)

# K. P. Mohanan, Tara Mohanan

This is a fourth in a series of dialogues on Constructing and Evaluating Knowledge. This continues from the previous dialogue and discusses the relationship between observation and reality.

Validity and Soundness in Arguments

# K. P. Mohanan, Tara Mohanan

An argument may make a logical conclusion given a set of premises, but the premises themselves may not be considered acceptable. Similarly, an argument may happen to reach a logical conclusion, but the reasoning used to get there may be invalid. This article explores the notions of validity and soundness, concepts crucial to reasoning and arguing effectively.

Logical Contradiction

(Expositions on concepts involved in inquiry series -2)

# K. P. Mohanan, Tara Mohanan

What are logical contradictions? This article explores this question through examples. It also leaves you with some exercises to work on.

Representing Positive Integers

# Madhav Kaushish

There is a important distinction to make between numbers and representations of numbers. In this article, we explore various different number representations and their characteristics.