Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems.…

Previous research has shown that students form fragmented understandings about variability even after instruction and that these primitive notions function as obstacles to a robust understanding of variability. To investigate the effect of disruptions to students' primitive notions of variability, we examined undergraduate students' reasoning…

Achieving meaningful educational outcomes requires scalable strategies for mastering mathematical concepts and skills, with student engagement at the core. This paper examines the use of comprehensive, technology-enhanced activities designed to promote active learning and deeper conceptual understanding. Specifically, it focuses on the integration…

Background: The present study delves into the debate surrounding the effectiveness of homework, focusing specifically on the use of online homework in teaching decimal numbers to 5th and 6th grade primary school students. It highlights the challenges students face in representing and identifying decimal numbers, a concept that is often difficult…

Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game "Settlers of Catan" develop a stronger grasp of basic probability concepts…

Productive struggle--expending effort to make sense of something beyond one's current level of understanding--aids in learning mathematics concepts and procedures. In this study, we surveyed 197 parents with children in the 1st to the 5th grade on their beliefs about productive struggle. Beliefs were assessed via questionnaire and rating of a…

In this paper I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time…

This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…

This paper presents the results of a study on Calculus students' use of web-based homework. We collected data from students' web-based homework usage, such as their grades, time spent, number of attempts used to solve problems, and problem solutions. We also collected grades on in-class quizzes, which were given the day after homework had been…

We discuss an implementation of the research-based Pathways precalculus curriculum in a large-lecture format supported by recitations, clickers, and online homework. We describe our approach to adapting the implementation of Pathways precalculus from a small class to a large lecture instructional format. We report data on student learning and…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

Two studies (Trautwein 2007 and Dettmers et al. 2010) show a positive correlation between high-quality homework and mathematics achievement. Students who completed their homework assignments scored better on assessments. However, these studies also showed no relationship between time spent on homework and resulting student achievement. This helped…

Enhancing students' conceptual understanding and increasing student motivation to effectively participate in classroom discussions are important for instructors of mathematics. Web-based homework management systems provide alternatives to the traditional pen-and-paper based approaches. In addition, these tools facilitate the creation of a…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp. a program designed for very gifted students who have already demonstrated high interest in studying mathematics. Prerequisites for the course were mastery of Algebra I and at least one preliminary year…