Success in math is important to all students; it provides them with college and career options in the fields of science, technology, engineering, and mathematics. In the middle grades, students build upon the critical skills taught in elementary school and prepare for entry into algebra, which is considered a gateway to later achievement in school…

An elementary proof using matrix theory is given for the following criterion: if "F"/"K" and "L"/"K" are field extensions, with "F" and "L" both contained in a common extension field, then "F" and "L" are linearly disjoint over "K" if (and only if) some…

Current reforms in mathematics education have called for a stronger emphasis on the teaching and learning of algebra for all students at all grade levels. Succeeding in algebra can prepare students to learn and understand more advanced mathematics in the future. One topic in algebra--the equal sign--has received considerable attention in middle…

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

Objective: This article examines the effectiveness of remediation for community college students who are identified as having the lowest skills in math. Method: We use transcript data from a state community college system and take advantage of a regression discontinuity design that compares statistically identical students who are assigned to the…

The effect of high school study of mathematics on numeracy performance of sports and exercise science (SES) students is not clear. To investigate this further, we tested the numeracy skills of 401 students enrolled in a Bachelor of Health Sciences degree in SES using a multiple-choice survey consisting of four background questions and 39 numeracy…

Concurrent enrollment refers to partnerships between postsecondary institutions and schools through which secondary school students can complete a university class taught by a qualifying secondary school teacher at their secondary school. We propose that concurrent enrollment programs are an under-recognized tool for extending the impact of…

Historical student data can help elucidate the factors that promote student success in mathematics courses. Herein we use both multiple regression and principal component analyses to explore ten years of historical data from over 20,000 students in an introductory college-level Algebra course in an urban American research university with a diverse…

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

Classroom culture is established through both conversations and practices. Traditionally in mathematics class, the focus is primarily on the latter; that is, students are shown what "doing mathematics" looks like, and then asked that they try it themselves. This article discusses three mathematical conversations that help bring…

Students' understanding and proficiency with rational number concepts and operations is considered a key foundational skill for future success in algebra. As middle school students work with these concepts, teachers need timely data to determine whether students are making adequate progress. The purpose of this article is to document the content…

This paper reports the changes that occurred in the didactic approaches of three professors who participated in a project intended to develop new ways of teaching mathematics to second year university students. An enactivist perspective is used to address the process of change that emerged as a result from interactions during project meetings. We…