This article presents an original puzzle that supports students' development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought. The "Triangle Puzzle" is one of many tools teachers can use to guide students' learning of geometry. The Van Hiele's theory provides a way to assess and support this…

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

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 Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

As part of promoting and improving pattern discovery skills among school children, a Sudoku puzzle can be used as example of a problem solving task. A simplified version of the puzzle will be used first to explain the aim and reinforce the rules of solving the puzzle. Three strategies--"Strategy of Obvious Missing Number, Strategy of…

In this article we show how the Sudoku puzzle and the three simple rules determining its solution can be used as an introduction to proof-based mathematics. In the completion of the puzzle, students can construct multi-step solutions that involve sequencing of steps, use methods such as backtracking and proof by cases, and proof by contradiction…

Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…

To help fifth- through eighth-grade students develop their deductive reasoning skills, the author used a ten-week supplementary curriculum so that students could answer logic questions. The curriculum, a series of lessons built around language-independent logic puzzles, has been used in classrooms of fifth through eighth grades. In most cases,…

In this article, a systematic approach is given for solving a magic star puzzle that usually is accomplished by trial and error or "brute force." A connection is made to the symmetries of a cube, thus the name Magic Hexahedron.

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…