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Homework completion and self-regulatory ability have both been extensively studied to examine their impact on learning achievement. Moreover, the reciprocal nature of how these two qualities affect one another is also an area of research. While evidence shows that voluntary completion of assigned homework predicts self-regulation in students, a natural question is whether this can be facilitated with mandatory homework assignments. Research to this extent has been tentative: results are often positive, but issues with experimental design preclude strong conclusions or repeatability of the experiment. This paper aims to quantify the effect of mandatory homework assignments on learning achievement at the tertiary level while improving on the experimental design of existing research. [ABSTRACT FROM AUTHOR]

Teaching Mathematics to tertiary students can be a challenge to educators, mainly because they must deal with learners' varying levels of readiness. Some of the factors attributing to the variability are learners' perceptions of mathematics, their previous learning experiences, and fear of failure. We implemented a teaching approach to facilitate student ownership through active peer involvement and flexibility with assessments. In this paper, we analyze students' perceptions of learning mathematics when using the new approach for three consecutive semesters. We discuss the results of our study and the factors that helped students overcome their inhibitions and appreciate mathematical concepts. [ABSTRACT FROM AUTHOR]

This paper discusses the ways in which teacher educators can effectively engage prospective teachers (PTs) in lesson study during mathematics methods courses. Evidence from this work suggests that engagement in lesson study provides PTs with opportunities to strengthen their knowledge about mathematics, students, and pedagogy. More specifically, the results demonstrated that lesson study helped PTs to engage in deep and thoughtful discussions about mathematics, reflect on their teaching, and make effective changes to their lessons that showed noticeable improvements in student learning. Recommendations from this work provide specific methods-course suggestions on the implementation of lesson study as a model for PTs' professional and practitioner development, including strategies and guiding questions that teacher educators can utilize to help deepen PTs' knowledge about mathematics, teaching, and student learning. [ABSTRACT FROM AUTHOR]

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one that they themselves can justify. This experiment was conducted in the Discrete Mathematical Structures course; as it contains several subtopics, each of which uses a discrete set of elements with specific conditions. The textbook does not mention how those conditions are effectively put to use, and often uses the natural numbers as the default domain. Students are required to identify in their journals the exact properties that the elements need to have, justify how they are being put to use, and in ambitious cases attempt to sharpen them if possible. This activity can be adapted to different contexts and is not specific to the topic of Discrete Mathematical Structures. [ABSTRACT FROM PUBLISHER]

Inquiry-based pedagogies have a strong presence in proof-based undergraduate mathematics courses, but can be difficult to implement in courses that are large, procedural, or highly computational. An introductory course in statistics would thus seem an unlikely candidate for an inquiry-based approach, as these courses typically steer well clear of proof, have a list of required topics, and depend critically on computational software. On the other hand, the American Statistical Association (ASA) has long advocated the sort of active and exploratory class design that in many respects parallels traditional inquiry-based learning (IBL). This paper reports on the author’s recent attempt to implement an inquiry-based course in introductory statistics that fuses established IBL techniques with the specific pedagogical recommendations of the ASA. A signature feature of this course is that many of the inquiry-based activities are explicitly tied to computer work in the open source language R. [ABSTRACT FROM PUBLISHER]

The current work is the first article in a two-paper series exploring the role of explicit learning objectives in undergraduate mathematics instruction. A definition of student-learning objective (SLO) is introduced. We give examples of SLOs for topics from introductory college and university mathematics courses. We list potential advantages of a general program of grounding mathematics instruction in a set of such explicit SLOs. In the second paper in this series, an explicit, step-by-step algorithm for creating sets of student learning objectives will be described and its use illustrated. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to highlight the possibilities and benefits of incorporating games into college mathematics classrooms. This is illustrated through the personal success of using the board gameThe Resistanceto teach validity and soundness of arguments in a discrete mathematics course. Along the way, we will give some recent history of board games and rationale for incorporating them into classes. [ABSTRACT FROM PUBLISHER]

This paper describes the results of a two-semester-long study of the effects of student-centered instruction on Precalculus courses. We also describe our teaching approaches centering around students, which include a mixture of lectures, student presentations, group work, discussion, and guided investigations. Students were taught with either the traditional, and still dominant, lecture-based, instructor-centered teaching methods, or with the collaborative student-centered methods. We found that the average over all students was higher on quizzes when they were taught with student-centered methods. Moreover, the students in the lower quantiles scored significantly higher than their counterparts in the traditional lecture-based classrooms. This suggests that not only are student-centered approaches more effective than instructor-centered approaches, but that they are particularly helpful to those students who are struggling with Precalculus. [ABSTRACT FROM PUBLISHER]

Metacognition as a dimension of learning ranks highest in the revised Bloom’s Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly to evaluate their own progress and review their development in light of their personal goals. We observed positive affective changes (including engagement levels) in the students through the course of the semester. We argue that the weekly metacognitive and self-reflective activities helped students keep their focus on learning deeply and allowed them to remain engaged and motivated through the semester. A brief theoretical discussion is included, and other possible contexts suitable for the described activities are suggested. [ABSTRACT FROM PUBLISHER]

Mathematics for liberal arts courses are a staple of most mathematics departments and are often populated with students who have disengaged from mathematics. Inquiry-based learning is a student-centered pedagogical tool for re-engaging students in mathematics. In this paper, we introduce a Special Issue ofPRIMUSon “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.” [ABSTRACT FROM PUBLISHER]

This article focuses on the philosophy of creativity and its enhancement through an undergraduate research experience. In this paper we offer suggestions for infusing the undergraduate mathematics and science curriculum with research experiences as a way of fostering creativity in our students. We refer to the termresearchbroadly, offering suggestions to accommodate students from various backgrounds and with different goals. We posit that creativity is a necessary component of scientific thinking, producing students that are motivated, passionate, skilled, adaptable, and responsible. Research experiences at the undergraduate level instill a deep sense of personalized education and learning that can make the entire university experience extremely pleasurable and of lasting value. [ABSTRACT FROM PUBLISHER]

Elementary education makes use of manipulatives in the teaching of fundamental mathematical concepts. As the age of the students progress, mathematics becomes much more abstract and concepts such as the integral become harder for some students to visualize. One approach we have implemented is the use of construction paper as a manipulative. This simple hands-on object can be used to demonstrate the basic properties of integrals to students who struggle greatly with the underlying ideas, especially when they are first encountered. Through the treatment of the integral as something that can be held in the hand and modified with the use of scissors, many of the basic properties of integrals can be demonstrated, as well as the intuition behind the Fundamental Theorem of Calculus. [ABSTRACT FROM PUBLISHER]

Two types of students at our university college were combined with the aim of bringing different knowledge together and in this way improving the learning environment. Based on observations and interviews, the project only partly turned out as expected. In this paper we try to ascertain what went right and what went wrong, explain why, and suggest changes that could be made to improve the scheme. [ABSTRACT FROM AUTHOR]

This article describes key elements for mathematics teachers, through the faculty development process, to increase student engagement and motivation in learning mathematics. It addresses common barriers facing student motivation and achievement in the field of mathematics and provides potential remedies from a faculty development viewpoint to alleviate these barriers. The paper offers practical examples from the authors' own faculty development programs and experiences in teaching mathematics to both foster and grow the intellectual curiosity of students and offers suggestions for successful faculty development programs. [ABSTRACT FROM AUTHOR]

Two years ago I implemented a basic outline of each class for my students to take notes on for Calculus II at the United States Military Academy. The outline provided students with a shell of the class material for each day of class. Their job was to fill in the shell as we went through the material. The outlines provided students an easy method to organize their own notes exactly how I organized the class. Space was provided to fill in pertinent definitions, label figures, or drawings that I provided, and to work step-by-step examples that I planned to go over in the class. The reason behind this approach was to help the student follow the flow of the class without having to think about what they should write down and what they should not write down. The things I wanted them to write down were on the outlines. Essentially the outlines represented the minimum material each student needed to take away from each class. Further, I chose difficult problems to include in the outline that were not in the text for students to work on their own. After executing this style of teaching for three semesters the following paper discusses my experience implementing this technique. [ABSTRACT FROM AUTHOR]

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and investigations which can be used with their future middle school classes. Their study of calculus gives them a broader understanding of the formulae developed in the investigations. [ABSTRACT FROM AUTHOR]

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to this challenge may well determine the degree of relevance and importance that traditional mathematical theory eventually commands in newly emerging scientific and technological disciplines. In this paper, we will: (a) identify the forces that are acting on contemporary mathematics instruction; (b) examine some of the historical, social, and psychological underpinnings that have given rise to these forces; (c) enumerate the conditions which mathematics instruction must address if it is to remain a viable discipline; and (d) evaluate the relative success of a case study, addressing the role of mathematics instruction for technical career students, that has been designed to address these conditions. [ABSTRACT FROM AUTHOR]

The reform movement, with its bold and innovative approaches that focus on student-centered learning, has been able to uncover the richness in undergraduate mathematics. The most outstanding pedagogical practices take into account the environment in which learning occurs as well as the background of the student body. Mathematics educators should be aware that what count as the finest practices are institution dependent. This paper reports on three such pedagogical practices, with cooperative learning at their core, that have worked with remarkable success and could be adopted at different institutions. Formatted Interactive Lecture Leaves highlight the need for active learning by creating an interactive learning environment. Student Projects showcase the relevancy of mathematics by making connections to the diverse majors prevalent in our classrooms. The Program for Excellence in Mathematics, based on collaborative learning, challenges motivated students to strive for excellence. Details of these pedagogical practices as well as appropriate evidence of success are presented. [ABSTRACT FROM AUTHOR]