Amazon, Walmart, and other large-scale retailers owe their success partly to efficient inventory management. For such firms, holding too little inventory risks losing sales, whereas holding idle inventory wastes money. Therefore profits hinge on the inventory level chosen. In this activity, students investigate a simplified inventory-control…

This study is a descriptive examination of uptake that occurred during classroom discourse in 33 Algebra I classrooms in nine U.S. states. Uptake refers to the act of taking up mathematical comments, questions, and constructions as objects of discourse. Uptake is important because it can be used for scaffolding authentic opportunities to learn and…

Admittedly, the Fundamental Theorem of Calculus-TFA holds an important role in the Complex Analysis-CA, as well as in other mathematical branches. In this article, we bring a discussion about the TFA, the Rouché's theorem and the winding number with the intention to analyze the roots of a polynomial equation. We propose also a description for a…

Classroom discourse is a valuable teaching and learning tool. Discussions allow students to improve their communication and reasoning skills in mathematics and help teachers assess students' understanding of mathematical ideas. To get the greatest benefit from discussion, teachers must elicit student thinking, listen carefully to their ideas,…

To engage students, many teachers wish to connect the mathematics they are teaching to other branches of mathematics or to real-world applications. The lesson presented in this article, which uses the algebraic skill of finding the equation of a line between two points and the geometric axiom that any two points define a line, does both. A…

A low-cost and portable colorimeter kit has been designed and developed as an educational tool at Penn State University by Dr. Daniel Sykes for K-12 schools' integrated STEM learning. This scientific instrument allows students to learn how scientists utilize light as a means to study the chemical and physical properties of materials with an…

This quantitative study was designed to determine the impact of course gap--the time period between semesters in which students take a particular course--on student achievement in mathematics. The testing instrument used was the Pennsylvania System of School Assessment (PSSA), given annually to all students in Grades 3 through 11. The study…

Historically, algebra has served as a gatekeeper that divides students into academic programs with varying opportunities to learn and controls access to higher education and career opportunities. Successful completion of Algebra 1 demonstrates mathematical proficiency and allows access to a sequential and progressive path of advanced study that…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

This study is a descriptive examination of uptake that occurred during classroom discourse in 33 Algebra I classrooms in nine U.S. states. Uptake refers to the act of taking up mathematical comments, questions, and constructions as objects of discourse. Uptake is important because it can be used for scaffolding authentic opportunities to learn and…

This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

The major purpose of this study was to examine the similarities and differences in the contents of algebra topic in selected elementary school mathematics textbooks of Finland and Taiwan. The mathematics curriculum market leaders of Finland and Taiwan, Laskutaito and Kang Hsuan, were examined using content analysis method. Results show that while…

This large-scale effectiveness trial found a significant positive effect for high schools using Cognitive Tutor Algebra I (CTAI) in their second year of implementation, relative to similar schools that continued to use existing textbook-based algebra curricula. This positive result is important for educators and policymakers seeking ways to…

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students' learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented…

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…