This study explored the influence of proof understanding strategies and negative self-concept on undergraduate Afghan students' achievement in modern algebra 1. To examine the relationships among proof understanding strategies, negative self-concept and achievement in modern algebra 1, we used structural equation modeling on data collected from…

Linear algebra is best done with block matrices. As evidence in support of this thesis, we present numerous examples suitable for classroom presentation.

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for…

This paper compares the effectiveness of contextualized developmental intermediate algebra to the more traditional developmental intermediate algebra approach, for students at two community college campuses located in two counties in the Pacific Northwest. We assessed four student outcome measures of effectiveness: likelihood of passing algebra,…

Building off of other studies that examined the effectiveness of double-dose algebra programs such as Nomi and Allensworth (2009), this dissertation compared the performance outcomes of students enrolled in one of two alternatives to traditional high school algebra, a double-dose and a single-dose algebra program. This work utilized multiple…

The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and interviewed the participants about the effectiveness of the program for the mathematics learning of the students with LD at the…

Numerical magnitude knowledge is related to current math abilities and predictive of future math learning. However, this relationship has previously been shown only for knowledge of positive magnitudes; the present study is the first, to our knowledge, to examine the connection between magnitude knowledge and math ability with negative integers.…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format…

The present study is a systematic meta-analytic study of 38 primary sources investigating the effectiveness of algebra interventions for students who are struggling. We systematically searched and screened over 1,300 records for studies to include. We computed summary effect sizes for each of the 12 interventions included. We conducted 4 separate…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

An algebraic model uses a set of algebra equations to precisely describe a situation. Constructing such models is a fundamental skill required by US standards for both math and science. It is usually taught with algebra word problems. However, many students still lack the skill, even after taking several algebra courses in high school and college.…

When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…