By using the Cauchy-Schwarz inequality a new proof of several standard inequalities is given. A new proof of Young's inequality is given by using Holder's inequality. A new application of the above inequalities is included.

This article shows that when applying resampling methods to the problem of comparing two proportions, students can discover that whether you resample with or without replacement can make a big difference.

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

In this article, the authors describe how mathematics teachers and art teachers were able to enthusiastically engage seventh- and eighth-grade students in an interdisciplinary activity focused on scaling, proportional reasoning, and measurement by recreating artwork on a famous private collection. Using the artwork from The Barnes Foundation in…

This study investigated the development of length measurement ideas in students from prekindergarten through 2nd grade. The main purpose was to evaluate and elaborate the developmental progression, or levels of thinking, of a hypothesized learning trajectory for length measurement to ensure that the sequence of levels of thinking is consistent…

This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers' (PSTs') mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists chiefly…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

Instructors ("N"?=?204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain-specific topics,…

In this paper, the authors describe how two institutions are helping their undergraduate biology students build quantitative competencies. Incorporation of quantitative skills and reasoning in biology are framed through a discussion of two cases that both concern introductory biology courses, but differ in the complexity of the mathematics and the…

In a search for ways to capture foundation phase children's competence in mathematics, a small research team was put together at a South African university four years ago. At first, working only in a single school where the objective was to model 80 learners' growth in competence over four years, the team transformed into a very different entity.…

Students with specific learning disabilities (SLD) in mathematics can typically experience long-lasting problems when developing fluency with basic math facts despite the use of evidence-based practices. One recently developed intervention to promote memorization and fact-fluency is Mastering Math Facts (MMF). MMF is a commercially-available…

In this study, repeated measures design was employed to compare low performing students' achievements in factoring cubic polynomials using three strategies. Twenty-five low-performing Grade 12 students from a secondary school in Limpopo province took part in the study. Data was collected using achievement test and was analysed using repeated…

The technology principle in the "Principles and Standards for School Mathematics" (NCTM, 2000) states that technology plays an important role in how teachers teach mathematics and in how students learn mathematics. The purpose of this sequential explanatory mixed methods study was to examine the impact of interactive applets on students'…

In a new era of Common Core State Standards (CCSS), teachers are expected to provide more rigorous, coherent, and focused curriculum at every grade level. To respond to the call for higher expectations across the curriculum and certainly within reading, writing, and mathematics, educators should work closely together to create mathematically…