The present study investigates problem-solving skill alongside more widely recognized settlement and sociodemographic factors in first-generation (1G) and second-generation (2G) immigrant students' science and mathematics achievement. A total of 113,767 students (ages 15-16 years) from 17 countries were drawn from the 2003 Programme for…

In modern CAD and CAM manufacturing companies, engineers design parts for machines and consumable goods. Many of these parts are cut on CNC machines. Whether using a CNC lathe, milling machine, or router, the ideas and designs of engineers must be translated into a machine-readable form called G & M Code that can be used to cut parts to precise…

In this article, the CLICK ("C"omputer Games and "L"iteracy "I"ntegrated with "C"ontent "K"nowledge) design model for high school education is proposed and developed as an instructional response to concerns about content coverage versus deeper content knowledge, learners' inability to grasp the meanings embedded in complex text, and disregard for…

External performance assessments for teachers of mathematics have traditionally been accomplished through reviews of student comments as well as through formal evaluations by superiors. Additionally, evaluating lecture-based teaching (as opposed to more active learning environments) focuses primarily on classroom performance, curriculum planning,…

When offering online classes, it is necessary to ensure that all course material and objectives will be covered and learners will be successful in the course. This becomes especially important when the same class material and objectives are offered in a three-, five-, and fourteen-week format. This paper outlines the difficulty of delivering…

Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching "word problem (WP) story grammar" on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or…

This article looks at the question of whether and how a geometrical cube may be determined as the solution set of a single equation. Beyond this being an interesting and surprising result for upper high school and first year college students, we argue that, as an investigative activity, it has value in refining students' images of what solutions…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

This paper examines some of the ways gifted students are said to be different from non-gifted students by comparing the responses of 475, 9-year-old "gifted" students with those of 230 average-attaining 13-year-old students on the same mathematical problem-solving questions. The questions were specifically written for mathematically…

We solve two problems that arise when constructing picture frames using only a table saw. First, to cut a cove running the length of a board (given the width of the cove and the angle the cove makes with the face of the board) we calculate the height of the blade and the angle the board should be turned as it is passed over the blade. Second, to…

In this article, we consider some generalizations of Fibonacci numbers. We consider k-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + F[subscript k,n]), the (k, l)-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + lF[subscript k,n]), and the Fibonacci…

This study examined achievement patterns of middle school students enrolled in Standards-based curricula, in particular those curricula that were funded from a solicitation of proposals through the National Science Foundation (NSF) in the early 1990s (NSF RFP 91-100). Approximately 1400 middle-grades students who had used either the Connected…

The purpose of this study was to examine the proportional reasoning skills of Turkish middle school students. It was also aimed at revealing the differences in students' performances in terms of their gender, grade level, and problem types--missing value and numerical comparison. The study was conducted with two sixth and seventh grade classes…

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

The effectiveness of a pentop computer when teaching multiplication facts to three middle school students with mild intellectual disabilities was examined. A multiple probe design was used to assess the students learning of one and two digit multiplication facts over a 2-3 week intervention period. During the intervention phase, students used a…