The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

This paper investigates the possible influence of attitude on seven Year 11 students' use of a Computer Algebra System (CAS) during a class activity where students could choose to use CAS or pen-and-paper in solving a range of problems. Investigation of anxiety, confidence, liking and usefulness through a survey and interview revealed that these…

Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

The primary goal of the study presented in this dissertation is to describe 11th-graders' understandings, through different representations, of: (1) the definition of function, (2) the production of a function, and (3) the interpretation of a function. In addition, this dissertation seeks to describe the relationship between 11th-graders' scores…

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…