The purpose of the present research is defining the direction and level of the relationship between 8th grade students' translating among multiple representations skills and their algebraic reasoning and revealing the predictive power on algebraic reasoning. The research was conducted in accordance with relational survey model, which is a…

Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…

Using multiple external representations is advocated for learning in STEM education. This learning approach assumes that multiple external representations promote richer mental representations and a deeper understanding of the concept. In mathematics, the concept of function is a prototypical content area in which multiple representations are…

Researchers have identified students' difficulties reasoning about inverse functions. Through our review of this literature, three meanings stand out: a formal, 'undoing', and quantitative meaning. Using these meanings as a guide, we analyzed student work collected from a lesson on the topic of inverse functions taught by an experienced high…

This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

The purpose of this case study was to examine prospective mathematics teachers' lessons in the context of choice and use of representations while teaching limit. The participants were four senior prospective mathematics teachers. The data were obtained from the participants' lessons plans, the video recordings of their lessons, and the…

This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

To understand multiple representations in algebra, students must be able to describe relationships through a variety of formats, such as graphs, tables, pictures, and equations. NCTM indicates that varied representations are "essential elements in supporting students' understanding of mathematical concepts and relationships" (NCTM…

Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics…

A total of 100 3- and 5-year-old children were trained and assessed individually on the concept of equilateral triangle at three levels of attainment: concrete, identity, and classificatory. Five training conditions existed: (1) visual inspection; (2) visual inspection and verbal orienting instruction; (3) visual inspection, free haptic activity,…

Describes a study which measured how ninth-grade students integrated information about mathematical concepts when working with Triple Representation Model software. Tables, graphs, and algebraic functions were linked, allowing students to manipulate several representations of the same concept. Examples of mathematical problems and student case…

Presented is a series of 88 lessons designed by classroom teachers to help junior high school students reinforce social studies skills. Lessons are categorized into four main skill areas: (1) using reference aids; (2) understanding tables, graphs, and cartoons; (3) developing graphic skills; and (4) evaluating information. For each skill area,…

This study examined the effects of an inductive multimedia program, including graphs, on subjects' ability to create linear functions and conceptualize variables from word problems. Subjects were 98 undergraduate students in two sections of a computer literacy course. Students' achievements were assessed via pre- and posttests, which were parallel…