Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

Several studies on analogical transfer to algebra word problems have demonstrated that adapting solutions learned from worked examples to nonisomorphic problems of the same type is challenging and that most instructional aids do not alleviate this difficulty. At the same time, various authors have suggested that transfer difficulties sometimes…

The celebrated Basel Problem, that of finding the infinite sum 1 + 1/ 4 + 1/9 + 1/16 + ..., was open for 91 years. In 1735 Euler showed that the sum is pi[superscript 2]/6. Dozens of other solutions have been found. We give one that is short and elementary.

We use a novel approach to evaluate the indefinite integral of 1/(1 + x4) and use this to evaluate the improper integral of this integrand from 0 to [infinity]. Our method has advantages over other methods in ease of implementation and accessibility.

Multidisciplinary teams are responsible for identifying reasonable accommodations that mediate the impact of a disability and level the playing field between those with and without disabilities on high-stakes mathematics assessments. However, minimal guidance is provided to teams selecting accommodations. This article provides a decision framework…

Teachers earn credentials at the beginning of their careers, but they learn new skills every day. While teachers are recognized for the time they spend in formal professional development settings, they often do not have the opportunity to demonstrate the full breadth of what they have learned, including in informal contexts. To address this,…

Given the current emphasis on science, technology, engineering, and math (STEM) education and its key attributes, middle school is an optimal time to implement STEM-based curricula. However, the interdisciplinary and open-ended nature of STEM projects often makes implementation difficult. In this article, we describe a professional development…

The subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

Although it is not a new idea, discourse continues to be a topic of discussion among teachers, teacher educators, and researchers in mathematics education. The National Council of Teachers (NCTM) and the Common Core State Standards for Mathematics (CCSSM 2010) describe mathematics classrooms as discourse communities in which whole-class…

In this paper, we report on the implementation of a novel compute-to-learn pedagogy, which is based upon the theories of situated cognition and meaningful learning. The "compute-to-learn" pedagogy is designed to simulate an authentic research experience as part of the undergraduate curriculum, including project development, teamwork,…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

Maori-medium pangarau classrooms occupy a unique space within the mathematics education landscape. The language of instruction is an endangered minority language and many teachers and learners in Maori-medium pangarau classrooms are second language (L2) learners of te reo Maori. Mobile technology could be used in Maori-medium pangarau classrooms…

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

A cohort program to increase retention of under-represented groups in chemistry was developed at the College of Saint Benedict/Saint John's University. In particular, this program chose to emphasize early career mentoring and early access to research. This goal was chosen because research has been repeatedly shown to increase scientific identity…