Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained…

This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

The rapid growth of digital technology, including the worldwide adoption of mobile and embedded computers, places new demands on K-grade 12 educators and their students. Young people should have an opportunity to learn the technical knowledge of computer science (e.g., computer programming, mathematical logic, and discrete mathematics) in order to…

The material in this booklet is concerned with a discussion and examination of geometric puzzles and the ideas which result from their study. The general idea of graphs is introduced as a tool which can be used to solve geometric puzzles. The fact that working with puzzles can lead to unexpected mathematical discoveries is stressed. Such topics as…

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)