In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses…

Evidence is presented for the immediate apprehension of exact small quantities. Participants performed a quantification task (are the number of items greater or smaller than?), and carry-over effects were examined between numbers requiring the same response. Carry-over effects between small numbers were strongly affected by repeats of pattern and…

Learning Management Systems (LMS) collect large amounts of data. Data mining techniques can be applied to analyse their web data log files. The instructors may use this data for assessing and measuring their courses. In this respect, we have proposed a methodology for analysing LMS courses and students' activity. This methodology uses a Markov…

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

An approach to teaching sequences is described. The method is based on finding generating functions. (SD)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

This paper discusses ways of discussing limits in the secondary classroom. Particular attention is paid to showing that hypothesized answers are not limits to given sequences. (SD)

The card game SET has attracted the attention of math and game enthusiasts alike. In this article, I present a first semester Abstract Algebra project that guides the students through an algebraic formulation of the game. There are many interesting mathematical questions that one can ask about the game, and I illustrate how the project can be used…

Teaching ideas are shared in three separate articles titled, "Something Different for Middle School Mathematics,""A Discovery Approach for the Y-Intercept," and "How to Get Off the Track in One Easy Lesson". (JT)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

Stresses that powers are all based on geometric progressions which start at unity. Various patterns are discussed. (MNS)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

Through the use of sequences, geometric progressions and permutations, the author investigates some interesting and unusual questions concerning the number of moves required by each disc in solving the Tower of Hanoi puzzle. (JT)

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)