"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

Learners' choices as to whether and how to use visual representations during learning are an important yet understudied aspect of self-regulated learning. To gain insight, we developed a "choice-based" intelligent tutor in which students can choose whether and when to use diagrams to aid their problem solving in algebra. In an…

The purpose of this research is to examine the relationship between at-risk indicators including socioeconomic status, English language learners (ELL), and gender to student performance in the Algebra I End of Course assessment. The research questions presented in the non-experimental quantitative research design were: (1) What is the impact of…

The purpose of this quantitative research study is to determine through the foundational lens of the temporal motivational theory, if active procrastinators outnumber passive procrastinators, and outperform them on an online mathematics final exam. Conducted at an associate's degree granting institution in the southeastern region of the United…

The purpose of this study was to examine teachers' perceptions of the Illustrative Mathematics (IM) using data from teacher interviews from year 1 and year 3 of their implementation of IM. In year 1, 22 Algebra 1 teachers were interviewed; in year 3, 13 teachers participated. Interviews were conducted using a semi-structured protocol that included…

This exploratory study examined whether instruction aligned with the Institute of Education Sciences recommendations (i.e., use of worked examples, representations, deep questions) predicts student learning of early algebra, particularly inverse relations, in elementary classrooms. Instructional quality was determined through an…

We studied ALEKS PPL placement scores, SAT scores, and entry-course grades for a population of 1659 students who placed into College Algebra or below over a span of 5 years. In addition to representing an understudied range of placement level, the study was conducted at an HBCU with majority Black/African American students, a demographic that is…

Retaining mathematics majors is a pressing concern in many departments. We examined the pass rates of students across our mathematics major and then analyzed student persistence between math courses along with the underlying data collection required to make these analyses. We found that mathematics majors leaving the major after successfully…

In this investigation, the extent to which differences were present in the mathematics achievement by the ethnicity/race of Grade 3 students in Texas were analyzed. Data obtained from the Texas Education Agency Public Education Information Management System for all Texas Grade 3 students who took the State of Texas Assessment of Academic Readiness…

In this study, we evaluate an innovative method to improve the teaching of linear algebra. The use of peer instruction in conjunction with a seminar strategy and supported by didactic engineering is proposed as a means to facilitate the mastery of abstract concepts, the undertaking of innovative research in problem solving, and the practical…

Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions…

This study examined how community college students' reflective sentiments about learning with the Intelligent Tutoring System (ITS) ALEKS evolved in three developmental pre-Algebra Mathematics courses and how students' sentiments related to their metacognitive awareness and learning performance. Thirty-nine students participated in this study.…

This study concerns preservice teachers' knowledge of student thinking at the secondary level. In particular, it examines in what ways a three-week unit integrating content and student thinking was beneficial in developing preservice teachers' knowledge of student thinking associated with big ideas in algebra--such as variation, Cartesian…

In this article, we examine eighth graders' incorrect responses to a specific task on a national standardized assessment of mathematics. The task asked students to write the formula for the perimeter of a given figure as a function of a variable. We focus on incorrect responses to better understand students' difficulties with the algebraic…

This quantitative study examined the impact of a multi-subject double-dose STEM intervention on the academic achievement of underprepared 9th-grade males. The intervention consisted of heterogeneously grouped core classes of Algebra 1 and biology accompanied by a second multi-subject (Algebra 1 and biology) support class. This nine-week study did…