Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

About half of students attending community colleges leave school before finishing their intended goals. To increase students' retention and to prevent the multiple-repeater problem, Queensborough Community College (QCC) offered a short-term workshop for remedial-mathematics students. This was another chance to exit remediation instead of repeating…

The work described in this report is the second phase of a project to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low vision. This report describes the development and results of the second feedback study performed for our…

Between 2003 and 2013, the proportion of California eighth graders enrolled in algebra or a more advanced course nearly doubled to 65%. In this article, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…

One area of algebraic thinking essential for students' success is a relational understanding of the equal sign. Research has indicated a positive correlation between students' relational understanding of the equal sign and their equation-solving performance, suggesting that students' early conception of the equal sign may affect their learning and…

Human beings are having a profound impact on the environment. The opportunity to investigate this timely issue during one or two class periods gives algebra and precalculus students insight into a sustainability topic of great international concern--carbon footprints. Students use mathematical thinking in matters that are pertinent to their…

This dissertation consisted of three different, but conceptually related manuscripts. The series of manuscripts examined psychosocial factors of learning including attitude towards mathematics, motivation to learn mathematics, and satisfaction from the mathematics instruction in both redesigned and traditionally- taught college algebra courses at…

Efforts to enhance the aesthetic impact of mathematics lessons must account for the role of teachers in shaping the unfolding mathematical content of their enacted lessons. In this paper, we draw from Dietiker (2015) to describe differences in the mathematical stories of the enacted lessons of two veteran teachers teaching the same lesson. We…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with reform textbooks either containing the original practice problems or in which a portion of those problems were converted into…

This report addresses a renewed interest in individualized instruction, driven in part by advances in technology and assessment as well as a persistent desire to increase the access, efficiency, and cost effectiveness of training and education. Using computer-based instruction we delivered extremely efficient instruction targeted to low knowledge…

We analyzed a pool of items from an admissions test for differential item functioning (DIF) for groups based on age, socioeconomic status, citizenship, or English language status using Mantel-Haenszel and item response theory. DIF items were systematically examined to identify its possible sources by item type, content, and wording. DIF was…

Forty 4th and 9th grade students participated individually in tutorial interviews centered on a problem-solving activity designed for learning basic algebra mechanics through diagrammatic modeling of an engaging narrative about a buccaneering giant burying and unearthing her treasure on a desert island. Participants were randomly assigned to…

This report presents a question-driven exploration of growth and achievement data using SAS EVAAS reports. The purpose of this exploration was to bring additional data, information, and ways of thinking about student growth to ongoing district conversations about the measurement of campus-level student growth.

Language is often depicted as the sine qua non of mathematical thinking, a view buttressed by findings of language-of-training effects among bilinguals. These findings, however, have been limited to studies of arithmetic. Nothing is known about the potential influence of language on the ability to learn rules about the relations among variables…