Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

Mastery grading is an approach to grading in which students are assigned term grades based on whether they meet certain enumerated objectives, rather than accumulating points. In this note, I describe my experiences using a mastery system, which I call techniques grading, which applies the insights behind the standards-based and specifications…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

We report on a research study conducted within a transition-to-proof course for mathematics majors at a large public university. Within the course, students explored famously unproven conjectures and reflected on how their perspectives of mathematics changed through this exploration (if at all). In this report we share students' takeaways from the…

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

Workshops can be a powerful tool to support students as they develop proof-writing skills. In a workshop, each student writes a proof, provides feedback on other students' work, and reflects on critiques from peers. Workshops can be used in any class that emphasizes writing proofs or other forms of mathematical writing. They are highly efficient…

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…

In this note, I argue for and discuss my experiences with explicitly incorporating principles of critical and creative thinking in a transitions course which serves mathematics, mathematics education, and statistics majors. I describe several specific assignments and classroom tasks designed to enhance critical and creative thinking. I also…

Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

Deep Reinforcement Learning (DRL) has been shown to be a very powerful technique in recent years on a wide range of applications. Much of the prior DRL work took the "online" learning approach. However, given the challenges of building accurate simulations for modeling student learning, we investigated applying DRL to induce a…

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

This research was purposed to develop module and learning model and instrument of proofing ability in algebra structure through cooperative learning with helping map concept media for students of mathematic major and mathematics education in State University and Private University in North Sumatra province. The subject of this research was the…