Linear algebra is best done with block matrices. As evidence in support of this thesis, we present numerous examples suitable for classroom presentation.

This paper compares the effectiveness of contextualized developmental intermediate algebra to the more traditional developmental intermediate algebra approach, for students at two community college campuses located in two counties in the Pacific Northwest. We assessed four student outcome measures of effectiveness: likelihood of passing algebra,…

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…

The authors question how hermetic texts in mathematics, history, and philosophy of mathematics, specifically those referring to abstract algebra, can be open to the understanding of researchers, teachers and students who are intentionally willing to understand them. This discussion suggests that the openness may happen through hermeneutic…

Due to low success of traditional, postsecondary remediation mathematics, The Maryland Mathematics Reform Initiative First in the World Grant (MMRI-FITW) sought to develop and implement a statistics pathway as an alternative to traditional algebra-based math, to accelerate developmental mathematics students' progress into credit-bearing…

Mathematical proof is a logically formed argument based on students' thinking process. A mathematical proof is a formal process which needs the ability of analytical thinking to solve. However, researchers still find students who complete the mathematical proof process through intuitive thinking. Students who have studied mathematical proof in the…

This paper analyses student views on an e-learning intervention that incorporated a content development tool and computer algebra systems, aimed at improving performance and applicability of mathematics knowledge. The study deliberately relied on open source tools, with high usability both online and offline, that can be customized to address the…

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra…

While the lion's share of mathematics education research in linear algebra has been concerned with the conceptual aspects of students' learning, this study focuses on procedural knowledge that undergraduates can develop in a typical first-year course. The study analyzes the methods that a large cohort of second-semester students applied in a final…

Mathematics faculty created a model for intermediate algebra integrating principles from the science of learning. The redesigned curriculum revolved around two big ideas (solving and graphing) and provided students with information about the formation of long-term memories, the benefits of distributed practice, the impact of physiological aspects…

We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

College Algebra has been the main credit bearing mathematics course for many college students, but only one in five students at the community college level were passing this course. Students that did not have a mathematics dependent major seen College Algebra as a gatekeeper for completing college. With several students struggling to complete…

Requiring that students enrolled in college algebra to spend hours in a computer lab has been a practice in colleges and universities to improve success and retention. In part, because students come with different backgrounds, skills, and the computer lab environment allows for personalized supplemental instruction and tutoring. However, the way…

This study describes how nine university professors managed their teaching when a shift from lecturing to inquiry-based learning was mandated in a large enrollment course, linear algebra for math majors. We describe the tensions that emerged and how they were resolved, in part via the production of worksheets that were used in teaching. We…