Historically, algebra has served as a gatekeeper that divides students into academic programs with varying opportunities to learn and controls access to higher education and career opportunities. Successful completion of Algebra 1 demonstrates mathematical proficiency and allows access to a sequential and progressive path of advanced study that…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

This study is a descriptive examination of uptake that occurred during classroom discourse in 33 Algebra I classrooms in nine U.S. states. Uptake refers to the act of taking up mathematical comments, questions, and constructions as objects of discourse. Uptake is important because it can be used for scaffolding authentic opportunities to learn and…

This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

The major purpose of this study was to examine the similarities and differences in the contents of algebra topic in selected elementary school mathematics textbooks of Finland and Taiwan. The mathematics curriculum market leaders of Finland and Taiwan, Laskutaito and Kang Hsuan, were examined using content analysis method. Results show that while…

This large-scale effectiveness trial found a significant positive effect for high schools using Cognitive Tutor Algebra I (CTAI) in their second year of implementation, relative to similar schools that continued to use existing textbook-based algebra curricula. This positive result is important for educators and policymakers seeking ways to…

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students' learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented…

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…

Intelligent tutoring systems (ITSs), which provide step-by-step guidance to students in problem-solving activities, have been shown to enhance student learning in a range of domains. However, they tend to be pre-established and cannot supply the tutoring function immediately from the diverse mathematical questions. The MITSAS (multiagent…

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

This study investigated the effects of graphic organiser and gender on students' academic achievement in algebraic word problem. Three research questions and three null hypotheses were used in guiding this study. Quasi experimental research was employed and Non-equivalent pre and post test design was used. The study involved the Senior Secondary…

As current mathematics standards, such as the Common Core, are being implemented throughout the United States, it has become evident that teachers need support to enact the tenets of those standards. To help in this endeavor, this article was published as a guideline to emphasize to mathematics education stakeholders that "effective teaching…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

Self-regulated learning (SRL) theorists propose that learners' motivations and cognitive and metacognitive processes interact dynamically during learning, yet researchers typically measure motivational constructs as stable factors. In this study, self-efficacy was assessed frequently to observe its variability during learning and how learners'…

This paper examines data from a larger study that focused upon students' experiences and motivations in a college algebra course. The study revealed that students failed this course because of various factors and continued to view this course as a "gatekeeper" class. Through a stepwise multiple regression, the analysis of the ARCS…