In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

As educators, it is important for us to recognize that our assessment methods affect student attitudes. If we want students to learn from their mistakes and counteract a fixed-mindset of learning, perhaps we should look at what we incentivize in the classroom. Some professors are attempting to counteract math and test anxiety, poor STEM retention,…

While you may be ready to make the change to implementing Mastery Grading, you may still wonder exactly how to do this. This paper seeks to compile recommendations on implementing mastery grading from various sources as well as examples from our own experiences. The reader should expect a detailed overview of the components involved in mastery…

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…

Standards-based grading (SBG), sometimes called learning objectives-based assessment (LOBA), is an assessment model that relies on students demonstrating mastery of learning objectives (sometimes referred to as standards). The goal of this grading system is to focus students on mastering learning objectives rather than on accumulating points. I…

This case study highlights a high school math teacher's successful journey of taking the steps needed to move away from traditional teaching methods to innovative pedagogies supporting mastery-based teaching and learning. Mastery-based learning (also called competency-based learning) is a shift away from traditional, one-size-fits-all teaching.…

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their…

In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…

Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently…

Outlines an instructional plan working within the existing structure of most colleges that produces higher levels of student achievement through the manipulation of time. Described are the objective-based unit design, group instruction, initial test, corrective procedures, and retest. Lists 10 references. (YP)