Mathematical problems and puzzles that require commitment and perseverance to solve can help foster deep mathematics understanding in students. In this brief, the author describes factors that influence productive struggle, shares four examples of how teachers often respond to their students' productive struggles, and offers four strategies to…

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as…

Problem-solving skills in creative, open-ended domains are both important and little understood. These domains are generally ill-structured, have extremely large exploration spaces, and require high levels of specialized skill in order to produce quality solutions. We investigate problem-solving behavior in one such domain, the…

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 Inclusive Assessment of Computational Thinking (CT) designed for accessibility and learner variability was studied in over 50 classes in US schools (grades 3-8). The validation studies of IACT sampled thousands of students to establish IACT's construct and concurrent validity as well as test-retest reliability. IACT items for each CT practice…

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…

This work presents the assessment of the development and evolution of an active methodology (Project-Based Learning--PBL) implemented on the course "Unit Operations in Environmental Engineering", within the bachelor's degree in Environmental Engineering, with the purpose of decreasing the dropout rate in this course. After the initial…

Math is increasingly recognized as a critical part of what young children are exposed to and learn in early childhood programs. Geometry is one of three focal areas emphasized for early childhood, and opportunities for geometry learning are present in many manipulatives present in early childhood classrooms. Yet geometry remains an understudied…

We present in this work a demonstration of the maze-solving problem with electricity. Electric current flowing in a maze as a printed circuit produces Joule heating and the right way is instantaneously revealed with infrared thermal imaging. The basic properties of electric current can be discussed in this context, with this challenging question:…

The use of current and emerging tools in education is becoming a blistering topic among educators and educational institutions. Gaming in education may be viewed as an interference to learning but its role in education is to increase students' motivation and engagement, to enhance visual skills, to improve students' interaction and collaboration…

Some years back, the author found the following problem in a spatial puzzle book: how many ways can you put four blocks together, face to face (with no vertical rotation symmetry)? He gave each student just four blocks and they collectively tried combinations to eventually agree on the answer of 15. He used to think it was a halfway decent task,…

Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5-6 years) in a block puzzle…

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.…

Mastery behaviours -- seeking out challenging tasks and continuing to work on them despite difficulties -- are integral to achievement but difficult to measure with precision. The current study reports on the development and validation of the computer-based persistence, effort, resilience, and challenge-seeking (PERC) task in two demographically…