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…

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…

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…

This is an exploratory study about engaging students in mathematics learning both inside and outside of the classroom of an introductory proof course. The author utilized the framework of scholarship of teaching and learning as a guide to ensure the research process was carried out systematically. This study was conducted through one cycle of…

Assessments of instructional quality based on classroom observations and artifacts have the potential to measure and improve mathematics instruction and learning. This article describes the Instructional Quality Assessment (IQA) Mathematics Toolkit and examines its ability to identify the nature and quality of classroom instruction. The IQA…

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

This paper describes writing assignments from a modern algebra course which were used to foster the development of proof-writing skills. Each assignment consists of proofs and mathematical work supposedly written by fictional characters, where the proofs are designed to illustrate common misconceptions, difficult points, and typical writing flaws.…