Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

In this study, we investigated how empirical indicators of test-taking engagement can be defined, empirically validated, and used to describe group differences in the context of the Programme of International Assessment of Adult Competences (PIAAC). The approach was to distinguish between disengaged and engaged response behavior by means of…

The aim of this study is to reveal the relationship between the secondary school students' attitudes towards the educational computer games, and their reflective thinking skills. As the model of the research, it's utilized from the correlational research model. The target population of the study consists of secondary school students that receive…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

This study aims to synthesize the research findings on the effects of K-12 invention education regarding creativity, attitudes toward invention, attitudes toward science, and tendency for technological problem solving in South Korea. Meta-analyses were conducted by calculating the effect size of 37 studies, including theses and journal papers…

We describe an important elaboration of our multiscale/multiresolution model for solving the Traveling Salesman Problem (TSP). Our previous model emulated the non-uniform distribution of receptors on the human retina and the shifts of visual attention. This model produced near-optimal solutions of TSP in linear time by performing hierarchical…

"Media Clips" appears in every issue of "Mathematics Teacher," offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. The theme of this issue's "Media Clip" revolves around four items relating to lumber. These items include: A Q&A published in the…

The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further…

Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions to one specific problem in cyber space. Therefore, the authors feel it is necessary to map problems to solutions using graph partition and weighted bipartite matching. This article proposes an efficient algorithm to partition…

Current philosophy and practice urge, even require for funding, that programs be empirically based and grounded in empirically proven emerging, promising, or best practices. In most of the human services, including youth programs, services, and practices, this requirement is a goal as well as an ideal. Empirical research and evaluation can be used…

Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the…

Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

We show that inside every triangle the locus of points satisfying a natural proportionality relationship is a parabola and go on to describe how this triangle-parabola relationship was used by Archimedes to find the area between a line and a parabola.

We investigated the effects of distraction on attention and task performance during toddlerhood. Thirty toddlers (24- to 26-month-olds) completed different tasks (2 of each: categorization, problem solving, memory, free play) in one of two conditions: No Distraction or Distraction. The results revealed that the distractor had varying effects on…

The experiment described in this test was aimed at identifying DNA repair proteins in human and yeast cells. Terms to be familiar with before you start to solve the test: DNA repair, germline mutation, somatic mutation, inherited disease, cancer, restriction endonuclease, radioactive labeling, [alpha-[superscript 32]P]ATP, [gamma-[superscript…