In this paper we combine a logistic regression student model with an exercise selection procedure. As opposed to the body of prior work on strategies for selecting practice opportunities, we are working on an assumption of a finite amount of opportunities to teach the student. Our goal is to prescribe activities that would maximize the amount…

The current paper investigated the following research questions regarding measures of fidelity: (1) Is there a significant relationship between two different measures of fidelity of implementation: a survey of instructional practices and coded videos of classroom lessons? Does the strength of this relationship differ between treatment and control…

This study is an efficacy trial funded by a grant from the Institute of Education Sciences (IES) National Center for Education Research (NCER). Fifteen CPS high schools are receiving funding to implement two Algebra I credit recovery courses during the summer sessions of 2011 and 2012--one online and one face-to-face (f2f). These courses allow…

This quantitative study investigated relationships between higher level mathematics learning and multiplication fact fluency, multiplication fact speed-recall, and reading grade equivalency of eighth grade students in Algebra I and Pre-Algebra. Higher level mathematics learning was indicated by an average score of 80% or higher on first and second…

This study was designed to explore secondary mathematics teachers' beliefs about graphing calculators, their practices with the graphing calculators when teaching linear and quadratic functions, and the relationship between the teachers' beliefs and their practices. The study was conducted in two phases. In the first phase, 81 teachers…

Algebra is often described as the gateway to higher mathematics (Carpenter, Franke, & Levi, 2003; Kaput, 2008; Kaput & Blanton, 2001; Mason, 2008). Unfortunately, many students do not navigate this gateway successfully. Kaput (2008) and Mason (2008) suggested that this is due in part to the abrupt switch from arithmetic to algebra that…

Recent reform efforts in mathematics education call for the development of early algebraic reasoning, and for the provision of rich mathematical experiences for all students. In spite of such emphasis, many elementary school students, especially those with mathematical learning disabilities (MLD), often experience great difficulty in early algebra…

Public education has options with regard to educational settings and structures. States and school districts may select varying lengths for the school year, lengths for the school day, and lengths for individual class periods. In Utah, one measure of students' achievement is scores on the State's end-of-level criterion-referenced test (CRT) for…

In this report, I examine what students noticed as they participated in an instructional unit on quadratic functions and how a shift in what they noticed was conceptually connected to productive changes in their prior knowledge about linear functions. My results show that, over the course of the instructional unit, students' attention shifted…

How do mathematics teachers think of themselves? The construct of identity--how teachers see themselves--is an important and understudied construct in understanding mathematics teaching. This study investigates the use of Photo-Elicitation/Photovoice Interviews with six high school Algebra I teachers. Each teacher captured or chose photographs of…

In this paper we analyze and discuss students' performance in a CAS environment related to the simplification of rational expressions. Results indicate that if students have more initial paper-and-pencil techniques, the CAS environment spurs them to deeper theoretical reflections than for students who have fewer techniques. [For the complete…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

This multiple case study explores factors that shaped the curricular reasoning of mathematics faculty engaged in college algebra reform in community colleges. Overall, the study found that although proposed reform of college algebra is broad in scope and influenced by the student audience, competing influences emerge that can enable or constrain…

Technology permeates our daily lives; education has not been untouched. Liaw (2002) points out that "teachers, trainers, and instructional designers of computer-based or Web-based instruction would benefit by being more attentive to learners' perceptions toward Web-based environments." Reviewing the earlier research into student perceptions toward…

Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective…