This randomized controlled study investigated the efficacy of a Tier 1 intervention, schema-based instruction (SBI), designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment (SBI) or control (business-as-usual) condition.…

Taking into account the Science, Technology, Engineering, Mathematics (STEM) integration, it is important to investigate teachers' understandings, perceptions about STEM and how STEM practices should be incorporated into the classroom in order to explore the perceptions of science teachers on this subject and provide important information to…

This note describes a course designed to prepare community college instructors and K-12 teachers for teaching foundational aspects of quantitative reasoning. A body of literature on quantitative reasoning and quantitative literacy informed the course design. The note describes the course content, which includes engaging in case studies, reading…

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…

Tutoring technologies for supporting learning from errors via negative feedback are highly developed and have proven their worth in empirical evaluations. However, observations of empirical tutoring dialogs highlight the importance of positive feedback in the practice of expert tutoring. We hypothesize that positive feedback works by reducing…

A core component of applied educational and child psychology practice is the skilfulness with which practitioners are able to rigorously structure and conceptualise complex real world human problems. This is done in such a way that when they (with others) jointly work on them, there is an increased likelihood of positive outcomes being achieved…