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…

To promote the implementation of manipulatives into mathematics instruction, this research project examined how the instructional practices of four Grade 9 applied mathematics teachers related to their beliefs about the use of manipulatives in teaching mathematics, its effects on students' learning, and enabling and disabling factors. Teacher…

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state-mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our…

What if every middle school student learned to create a robot in math class? What if every middle school had a robotics team? Would students view mathematics differently? Would they have a different relationship with technology? Might they see science and engineering as fields driven by innovation rather than memorization? As students find…

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,…

A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

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…

When examining transformations of the plane in geometry, teachers typically have students experiment with transformations of polygons. Students are usually quick to notice patterns with ordered pairs. The Common Core State Standard, Geometry, Congruence 2 (G-CO.2), requires students to describe transformations as functions that take points in the…

When confronted with a challenging problem, many solvers may at first think that not enough information has been provided. If, however, they suspect that the problem is solvable, this feeling typically influences them to persevere as well as monitor and reflect on their efforts. In this article the authors present four nonroutine tasks that they…

Capstone courses have been recommended as a way for pre-service secondary mathematics teachers (PSMT) to connect the mathematics they learn in university to the mathematics they will teach in high schools. However, not much is known about the nature of these courses in the U.S. Through a survey of departments of mathematics and education, the…

What types of performance do we encourage in our mathematics students? How do these performances reflect students' identity constructions? This paper uses a performance metaphor for identity to analyse interviews with teachers and students in their first year of secondary school. "Perseverance" is valued by teachers, yet many mathematics…

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…

This study examines the use of a digital video annotation tool used by beginning in-service secondary science and mathematics teachers in the Teacher Induction Network (TIN). TIN is an online induction program in its ninth year of existence and has served over 180 teachers. The need to provide spaces for beginning teachers to reflect on their…

Students should learn mathematics with understanding. This is one of the ideas in the literature on mathematics education that everyone supports, from educational politicians to curriculum developers, from researchers to teachers, and from parents to students. In order to decide whether or not students understand mathematics we should first…