This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

Only knowledge is not sufficient to make students succeed in the world. Students need to attain 21st century skills like problem-solving, creativity, innovation, metacognition, communication etc. to endure in the modern world. Problem-solving skill is one of the fundamental human cognitive processes. Whenever students face a situation where they…

The primary purpose of this paper is to introduce essential elements of cognitive information processing (CIP) theory, research, and practice as they existed at the time of this writing. The introduction that follows describes the nature of career choices and career interventions, and the integration of theory, research, and practice. After the…

What our century requires is an individual who can recognize and solve a problem, think in a critical manner, are productive, responsible, and open to innovation, and are capable of cooperating with others. The requirements of our era are also reflected on education. Education systems change and improve accordingly; thereby new education systems…

Patterns are a ubiquitous phenomenon. They exist in nature's plant species emerging as a complete order from truncated matter. Patterns are also present in the fine arts where the aesthetic properties of form exist and conjugate through paintings and sculptures. Mathematical patterns, the focus of this position paper, dominate financial scenarios,…

Project-Based Learning (PBL) is a widely adopted pedagogy that ignites students' interest of a subject through the investigation of an authentic problem and cultivates their abilities of innovation and self-learning. Traditional PBL often involves a project of complexity and significant scale, which, under the time constraint of a course, is often…

Creative and critical thinking skills are the abilities, which can sometimes be used interchangeably in definition. In fact, they have different constructs because they differentiate in outcome of human behaviours. Also one of today's requirements is that individuals should approach everyday problems by using both competences. So, one of the…

Austin Independent School District (AISD) teacher appraisal results from 2014-2015 were used to identify areas of need for professional development in 2015-2016. Results from the Professional Development and Appraisal System and Professional Pathways for Teachers (PPfT) were included. This executive summary provides highlights from the full report…

This report summarizes the results of the 2013-2014 AISD teacher appraisal and related survey items with emphasis on areas of need for additional professional development.

Student teachers make errors in their practicum. Then, they learn and fix those errors. This is the standard arc within a successful practicum. Some students make errors that they do not fix and then make more errors that again remain unfixed. This downward spiral increases in pace until the classroom becomes chaos. These students at the…

This article describes steps of teaching problem solving to college students and provides examples in the context of a university course. The steps involve (1) identifying the types of problems and types of problem solving methods to be covered, (2) instructing the students in problem-recognition and problem solving methods, along with ways of…

Because of the large number of students involved, statewide assessments used throughout the United States are designed to be highly efficient with respect to administration and scoring. This constrains the formats that can be used and consequently limits testing to a subset of competencies typically associated with the education standards being…

This paper proposes a theoretical review of the term "metacognition". It was introduced by John Flavell in the early 1970s based on the term "metamemory" previously conceived by the same scholar (Flavell 1971). Flavell (1979) viewed metacognition as learners' knowledge of their own cognition, defining it as "knowledge and cognition about cognitive…

This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…

Creativity is a talent that undergirds invention and innovation, making it an important skill in today's society. Although students are often told to "be creative," they many times do not know how and have little practice in this skill. This document presents an analysis of 33 creative products made by adult participants at a state conference for…