In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

Many elementary education programs have only one mathematics methods course designed for preservice teachers (PTs). Such courses typically cover a range of content and present a challenge for mathematics teacher educators (MTEs) who strive to prepare their PTs to teach mathematics in equitable and humane ways. Due to the "stand-alone"…

"The Enactment Project" seeks to find out in more detail what is happening in Singapore mathematics classrooms. In particular, the video data of 30 teachers suggests that there is a distinctive Singapore secondary mathematics pedagogy, almost like its DNA, which is characterized by cycles of Development, Seatwork and Review (DSR). This…

Personalized education systems recommend learning contents to students based on their capacity to accelerate their learning. This paper proposes a personalized exercise recommendation system for online self-directed learning. We first improve the performance of knowledge tracing models. Existing deep knowledge tracing models, such as Dynamic…

One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

In the context of rapid technological changes and modernization of society, the issue of ensuring adequacy of content in secondary education based on the use of advanced information technologies (ICT) is being updated. The necessity of an appropriate level of primary intellectual activity development in a person in terms of the current trends in…

In order to improve problem-solving dispositions, a section of an inquiry-based math sequence for first-year business students was linked with a section of our general education English sequence. We describe how the linked classes worked and compare some preliminary results from linked and unlinked sections of the math sequence.

In the Spring of 2011, two of the authors of this paper taught number theory courses at their respective institutions. Twice during the semester, students in each class submitted proofs of two to three theorems to be peer reviewed by students in the other class. Each student wrote anonymous and formal referee reports of the submitted theorems,…

The recent introduction of a new course in mathematical modeling at Manhattan College has provided students with a valuable opportunity to gain practical experience utilizing tools in applying their mathematical abilities to a real-world problem. This paper describes the steps taken to create this class, from obtaining a real-world partner…

Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

Real Analysis is a required class for most undergraduate mathematics majors, but it is also one of the most difficult classes they will take. In this article, the author compares two approaches to teaching in the two analysis classes she has taught. The first one was taught in a traditional lecture-homework-exam format, while the second was taught…

Approaches to standards, curriculum development, and pedagogy are remarkably diverse; however, recent years have seen a growing movement to base each of these on learning trajectories. In this paper, I discuss and compare the various terms and conceptions of this construct, present our definition, differentiate between our conception and that of…

Academic skill development requires engagement in effortful academic behaviors. Although students may be more likely to choose to engage in behaviors that require less effort, they also may be motivated to complete assignments that they have already begun. Seventh-grade students (N = 88) began a mathematics computation worksheet, but were stopped…

Solution-focused brief counseling (SFBC) is an efficient and direct approach to therapy that emphasizes problem identification and solutions. A multiple-baseline-across-participants design was used to evaluate the effects of a SFBC intervention on mathematics assignment completion and accuracy across six fifth-grade students who were failing math.…