Evidence shows that to improve student persistence in mathematics, we must change our course design to encourage students to have a growth mindset. By using standards-based grading, students earn grades based on their actual learning, so they are motivated to persist with difficult topics until they achieve understanding. Mastery-based testing has…

Administrative problems such as computer malfunction and power outage occasionally lead to missing item scores and hence to incomplete data on mastery tests such as the AP and U.S. Medical Licensing examinations. Investigators are often interested in estimating the probabilities of passing of the examinees with incomplete data on mastery tests.…

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course content. Mastery-based testing can help to address this by allowing the instructor to align course grades with mastery of the learning objectives for the…

Mastery-based testing is an assessment scheme that challenges students to provide complete solutions to problems derived from clear course concepts. Students are allowed multiple attempts to demonstrate mastery, which helps create a classroom environment where students value persistence toward thorough understanding. In this paper, we describe in…

This article is the second of a series of articles appearing in "Communiqué" about how school psychologists can adopt and promote the evidence-based practices in math assessment and instruction. The focus of this article is on measuring math skills for screening, diagnostic decisions, and progress monitoring. [For the first article in…

This paper gives a blueprint for reacting to the various issues that an instructor will face in their day-to-day life as the manager of a Mastery-Based Testing (MBT) classroom. For example, I created a rubric to compare traditional testing with MBT, adapted my office hours to accommodate more retake opportunities, and required effort between…

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,…

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…

Grading according to standards, competencies, or concepts is nothing new.With the current grading system gaining more scrutiny, parts of the basic framework of how we grade students are being questioned. Stephens (2010) and Marzano and Heflebower (2011) reinforced the notion that homework, behavior, attendance, notebooks, and group work should not…

After a brief review of recent advances in sequential analysis involving sequential generalized likelihood ratio tests, we discuss their use in psychometric testing and extend the asymptotic optimality theory of these sequential tests to the case of sequentially generated experiments, of particular interest in computerized adaptive testing. We…

On Monday, the teacher assigns her class a list of 20 spelling words to learn. On Friday, she tests the students on how well they learned to spell these words. This "mastery measurement" is the traditional way of determining student progress. The next spelling mastery test will indicate mastery of the next week's 20 new words, a new skill.…

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster, or to continue sampling and administering another random test item. The framework of minimax sequential decision theory (minimum information approach) is used; that is,…

Formulates optimal sequential rules for mastery testing using an approach derived from Bayesian sequential decision theory to consider both threshold and linear loss structures. Adopts the binomial probability distribution as the psychometric model. Provides an empirical example for concept-learning in medicine. (SLD)

When students are taught to mastery, they become smarter, acquire information faster, and develop efficient strategies for learning. Teachers must have an understanding of what mastery is and how to achieve it in their students. However, teachers cannot teach to mastery without referencing the performance of their students. In addition, teachers…

In this paper, we apply sequential one-sided confidence interval estimation procedures with beta-protection to adaptive mastery testing. The procedures of fixed-width and fixed proportional accuracy confidence interval estimation can be viewed as extensions of one-sided confidence interval procedures. It can be shown that the adaptive mastery…