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…

Low levels of student success in introductory college math courses are rampant. There are several reasons for low pass rates in these courses, with the most serious issue being lack of concept mastery. To aid students in concept mastery, adaptive learning systems were created. These systems adapt instruction for each student and create an…

We detail a learning progressions approach to early algebra research and how existing work around learning progressions and trajectories in mathematics and science education has informed our development of a four-component theoretical framework consisting of: a curricular progression of learning goals across big algebraic ideas; an instructional…

In this dissertation, the following "network computing problem" is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function f of the messages. The objective is to maximize the average number of times f can be computed per network usage, i.e., the "computing…

The method of "Double False Position" is an arithmetic approach to solving linear equations that pre-dates current algebraic methods by more than 3,000 years. The method applies to problems that, in algebraic notation, would be expressed as y = L(x), where L(x) is a linear function of x. Double False Position works by evaluating the described…

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

We investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID. Students who worked with the ID that offered limited representations and tools ("illustrating ID") looked for ways to bypass the designed constraints: they changed the…

When learning the order of operations, students are instructed to adhere to a directive when determining the numerical value of an arithmetic expression. A more typical approach is the use of a popular mnemonic called PEDMAS (parentheses, exponents, division, multiplication, addition, subtraction). The literature is scant on conceptual approaches…

This two-part investigation (a) assessed the impact of the Jaime Escalante Math Program (JEMP), a structured summer mathematics intervention program, on the math achievement of urban middle school students, (b) identified the characteristics of the program that the administrators and teachers perceived to contribute to student achievement, and (c)…