The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in…

Trigonometry is one of the fundamental topics taught in high school and university curricula, but it is considered as one of the most challenging subjects for teaching and learning. In the current study Mason's theory of attention has been used to examine undergraduate student's perception of the transformation of sinusoidal functions. Two types…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

Immersive 3D Multi User Learning Environments (MULE) have shown sufficient success to warrant their consideration as a mainstream educational paradigm. These are based on 3D Multi User Virtual Environment platforms (MUVE), and although they have been used for various innovative educational projects their complex permission systems and large…

Graphs in physics are central to the analysis of phenomena and to learning about a system's behavior. The ways students handle graphs are frequently researched. Students' misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

Charter schools exist under the umbrella of public education, but are not subject to the same level of public oversight or accountability measures as traditional public schools in North Carolina and many other states (BiFulco and Ladd, 2006, Bettinger, 2004). There is a lack of easily accessible efficiency data on charter schools. The primary aim…

Interdisciplinary research collaboration is needed to perform transformative science and accelerate innovation. The Science of Team Science strives to investigate, evaluate, and foster team science, including institutional policies that may promote or hinder collaborative interdisciplinary research and the resources and infrastructure needed to…

Students of mathematics teacher candidates are required to have good math and communication skills. Therefore, students of mathematics teacher candidates need to have good imagery modalities like the rational-irrational function graph. To get the imaginary student of mathematics teacher candidate in describing the rational-irrational function…

It is common practice for assessment programs to organize qualifying sessions during which the raters (often known as "markers" or "judges") demonstrate their consistency before operational rating commences. Because of the high-stakes nature of many rating activities, the research community tends to continuously explore new…

Intelligent tutoring systems can support students in solving multi-step tasks by providing hints regarding what to do next. However, engineering such next-step hints manually or via an expert model becomes infeasible if the space of possible states is too large. Therefore, several approaches have emerged to infer next-step hints automatically,…

Course selection can be a daunting task, especially for first year students. Sub-optimal selection can lead to bad performance of students and increase the dropout rate. Given the availability of historic data about student performances, it is possible to aid students in the selection of appropriate courses. Here, we propose a method to compose a…

Issues arising in the music industry in response to the availability of digital music files provide an opportunity for exposing undergraduate students to economic analyses rarely covered in the undergraduate economics curriculum. Three of these analyses are covered here: the optimal copyright term, the effect of piracy or illegal file sharing, and…

Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance.…