During the 2021-22 school year, the Mathematics Standards Review Committee reviewed the 2007 Minnesota K-12 Academic Standards in Mathematics, other states' recently revised standards, current academic research, K-12 instructional best practices and public feedback. This review process followed the guidelines in Minnesota Statutes 2023, section…

W scores are used in a number of commercially available tests. Due to their complex nature, it can be hard for applied researchers and practitioners to understand them or even acquire information about them beyond what is provided in technical manuals. In this article, we provide information regarding the background and derivation of W scores that…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

Distinguishing between good and bad science is not easy. Evaluating whether or not a claim really is supported by good research is like buying a car. There is an optimal solution to the problem, which is to read and digest all of the relevant research, but most people do not have time to execute the optimal solution. What they need is a good…

Because of response disturbances such as guessing, cheating, or carelessness, item response models often can only approximate the "true" individual response probabilities. As a consequence, maximum-likelihood estimates of ability will be biased. Typically, the nature and extent to which response disturbances are present is unknown, and, therefore,…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

The one-parameter logistic model with ability-based guessing (1PL-AG) has been recently developed to account for effect of ability on guessing behavior in multiple-choice items. In this study, the authors developed algorithms for computerized classification testing under the 1PL-AG and conducted a series of simulations to evaluate their…

Basic issues in understanding Item Response Theory (IRT), or Latent Trait Theory, measurement models are discussed. These theories have gained popularity because of their promise to provide greater precision and control in measurement involving both achievement and attitude instruments. IRT models implement probabilistic techniques that yield…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

We present a multiple spells-competing risks model of stopout, dropout, reenrollment, and graduation behavior. We find that students who experience an initial stopout are more likely to experience subsequent stopouts (occurrence dependence) and are less likely to graduate. We also find evidence of the impact of the length of an initial spell on…

There is a strong and consistent relationship between PSAT/NMSQT scores and AP Examination grades for nearly all courses--higher scores on the PSAT/NMSQT indicate a higher probability of success on AP Examinations. PSAT/NMSQT verbal or mathematics scores are often more highly related to AP Examination grades than overall high school GPA, number of…