We examined how parent math attitudes and practices relate to emergent math skills in 72 preschoolers from low-income households. Specifically, we investigated parents' views about the importance of math learning, their confidence in teaching math, their perceptions of child interest in math, and their time spent engaging their child in math…

A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…

This paper links educational psychology research about curiosity to teacher moves that are effective in an inquiry-based mathematics classroom. Three vignettes will show explicit teacher moves (staging disagreement, intriguing anecdotes, and creating a safe space) for different audiences (math majors, mathematics for liberal arts students, and…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

One of the reported methods of cheating in online environments in the literature is CAMEO (Copying Answers using Multiple Existences Online), where harvesting accounts are used to obtain correct answers that are later submitted in the master account which gives the student credit to obtain a certificate. In previous research, we developed an…

Many students begin higher education unprepared for college-level work in mathematics and must take non-credit developmental courses. Furthermore, many are "math-phobic" and avoid courses, majors and careers that involve quantitative work. Yet science, technology, engineering and mathematics (STEM) fields are among the few job-growth…

Comparison is a powerful tool that has been shown to improve learning in a variety of domains. In both laboratory studies and small-scale classroom studies, having learners compare and contrast worked examples has been shown to reliably lead to gains in students' knowledge. Comparison is also integral to "best practices" in mathematics…

In this brief article, Christina Kuriacose provides four sample performance assessments. Spanning grade levels, these assessments are strong examples of teacher-developed performance assessments from schools within the Center for Collaborative Education's Quality Performance Assessment network. These performance tasks demonstrate the pedagogical…

Nearly two dozen states now administer online exams. These tests have real consequences: their results feed into accountability systems, which have been used for more than a decade to hold schools and districts accountable for their students' learning. We examine the rollout of computer-based testing in Massachusetts over 2 years to investigate…

Third- through fifth-grade students participating in a classroom teaching experiment investigating the impact of an Early Algebra Learning Progression completed pre- and post-assessment items addressing their abilities to engage in functional thinking. We found that after a sustained early algebra intervention, students grew in their abilities to…

Whether teaching in a classroom or a Massive Online Open Course it is crucial to present the material in a way that benefits the audience as a whole. We identify two important tasks to solve towards this objective; (1) group students so that they can maximally benefit from peer interaction and (2) find an optimal schedule of the educational…

The goal of this research study was to gain an understanding of high school teachers' perceptions of the role of history of mathematics in the classroom as well as their underlying view of mathematics as a discipline. High school teachers from 379 Public High Schools in Massachusetts were contacted and encouraged to take an on-line Likert scale…

In this article, we highlight the need for a precisely defined construct in score-based validation and discuss the contribution of cognitive theories to accurately and comprehensively defining the construct. We propose a framework for integrating cognitively based theoretical and empirical evidence to specify and evaluate the construct. We apply…