The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

The purpose of this study was to compare students' performances in a freshmen level quantitative reasoning course (QR) under three different instructional models. A cohort of 155 freshmen students was placed in one of the three models: needing a prerequisite course, corequisite (students enroll simultaneously in QR course and a course that…

Intelligent tutors based on expert systems often struggle to provide formative feedback on complex, ill-defined problems where answers are unknown. Hybrid crowdsourcing systems that combine the intelligence of multiple novices in face-to-face settings might provide an alternate approach for providing intelligent formative feedback. The purpose of…

The purpose of the study focused on the instructional strategies that support creation of creative and innovative education. The sample for this study consisted of 11 experts in the field of instructional strategies that support innovation of education. Among them, five were specialists in design and development of teaching and learning, three…

This article provides benchmark data on within-group effect sizes from published randomized clinical trials that supported the efficacy of problem-solving therapy (PST) for depression among adults. Benchmarks are broken down by type of depression (major or minor), type of outcome measure (interview or self-report scale), whether PST was provided…

Most large-scale summative assessments present results in terms of cumulative scores. Although such descriptions can provide insights into general trends over time, they do not provide detail of how students solved the tasks. Less restrictive access to raw data from these summative assessments has occurred in recent years, resulting in…

Purpose: The purpose of this paper is to explore educator collaborative inquiry in the shared workspace in professional learning communities (PLCs). Specifically, this investigation was part of an ongoing investigation of well-established PLC collaborative interactions and self-directed learning of educators as part of the shared workspace as a…

As times change we need to continually review what our education systems offer and where priorities might lie. The Technology and Knowledge Ages of the twenty-first century have brought about new understandings, new ways of doing things, and an array of new career and workplace opportunities. Employees today are expected to bring more than an…

This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is…

Bias is part of the human condition and becoming aware of how to avoid bias will help to ensure greater accuracy in the work of assessment. In this paper the authors discuss three different theoretical frameworks that can be applied when assessing student work for cognitive skills such as critical thinking and problem solving. Each of the…

This study discusses the need, development, and validation of the Innovation Test Instrument (ITI). This article outlines how the researchers identified the content domain of the assessment and created test items. Then, it describes initial validation testing of the instrument. The findings suggest that the ITI is a good first step in creating an…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Background: There is a considerable body of evidence to suggest that behavioural activation for depression is an equally effective but less complex treatment than cognitive behavioural therapy. It may therefore be more suitable for those who are cognitively impaired (i.e. early-stage dementia or mild cognitive impairment) or have a learning…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

Mathematics needs to take on a real-world quality, and students need to be able to identify and connect the value of what they are learning within the classroom to life outside the classroom. Creating a connection between the mathematics learned within a classroom and its value to life in the outside world is critical to effectively engage…