Hologram recording and holographic interferometry are intrinsically sensitive to phase changes, and therefore both are easily perturbed by minuscule optical path perturbations. It is therefore very convenient to bank on holographic setups with a reduced number of optical components. Here we present a compact off-axis holographic setup that…

Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred to as abstract algebra. Current pedagogy conceals from the student many of the great ideas generated by significant problems in the history of the discipline. In…

The purpose of this study is to investigate the mathematical literacy of the 15-year-old students in terms of PISA mathematical literacy questions. The research model of this study is the survey model in the quantitative models. The sample of this study was composed of 1.227 students who received formal education in five different types of schools…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

This paper shows how GeoGebra--a dynamic mathematics software--can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra…

It is a well-documented finding that high school students in schools across the nation, including California, fail to achieve at the proficient level in mathematics, based on standardized test scores. The purpose of this research study was to compare the findings of students taught using traditional instructional methodologies versus cooperative…

The purpose of this study was to investigate if a relationship existed between an at risk high school student's perceived relationship with the Algebra I teacher and the student's academic performance and attendance in Algebra I. A correlational study design was used to investigate this study. One hundred thirty eight students who were…

This current paper uses data collected as part of an efficacy trial funded by a grant from the Institute of Education Sciences (IES) National Center for Education Research (NCER) (See Symposium Justification and Paper #1 for a more complete description of the focus of the broader study). Since participation in the study was voluntary, students…

Comparison is a powerful tool that has been shown to improve learning in a variety of domains. In both laboratory studies and small-scale classroom studies, having learners compare and contrast worked examples has been shown to reliably lead to gains in students' knowledge. Comparison is also integral to "best practices" in mathematics…

The study was designed to probe students' thinking about which numerical values can be assigned to algebraic letters. The data from students in Year 7 (n = 533), Year 8 (n = 377) and Year 9 (n = 172) was analysed using response patterns. The data confirmed that each year contained students with two misconceptions; "Different Letter means…

Previous studies have reported on primary children's algebraic thinking and generalising in a range of problem settings but there is little evidence of primary teachers' knowledge of algebraic thinking. In this paper the development in algebraic thinking of one primary teacher who taught a research lesson in a Japanese Lesson Study project…

In the fall of 2009, the National Center on Education and the Economy initiated a series of research programs designed to support the high school reform program, "Excellence for All," based on more than 20 years of research on the school reform programs of the countries with the most successful education programs worldwide. Several…

Distance learning has become increasingly popular among higher learning institutions, and more academic disciplines, such as mathematics, are now being offered at a distance. This experimental study investigated whether an objectivist-based teaching strategy or a constructivist-based teaching strategy yields greater achievement scores for adult…

Performance standards are a powerful way to communicate K-12 student achievement (e.g., proficiency) and are the cornerstone of standards-based reform. As education reform shifts the focus to college and career readiness, approaches for setting performance standards need to be revised. We argue that the focus on assessing student readiness can…