Computational thinking is one of the skills critical for successfully solving problems posed in a technology driven and complex society. The limited opportunities in school settings to help students develop computational thinking skills underscores the need for helping teachers integrate it in their practices. Besides developing the knowledge of…

The traditional theories behaviorism, cognitivism, constructivism and connectivism are regarded as essential theories of learning. However, transformational learning theory works with critical thinking in adult learning. This process is based on their experience and it is followed by the steps of thinking and transformation process in perspective…

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

Background: Problem exploration includes identifying, framing, and defining design problems and bounding problem spaces. Intentional and unintentional changes in problem understanding naturally occur as designers explore design problems to create solutions. Through problem exploration, new perspectives on the problem can emerge along with new and…

Universal design for learning is intended to provide opportunities for all students to be successful. An exploration of Mr. Morales's middle school social studies classroom reveals the universal design for learning principles of multiple means of engagement, representation, and action and expression infused throughout every lesson. These…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

Prompted by the evidence of international tests of achievement that Swedish students have poor equation solving skills, this paper presents an interview study of upper secondary students' understanding of the topic. Students, from both vocational and academic tracks in two typical suburban upper secondary schools were invited to explain how a…

In this paper, we derive an equation for the distance covered by a free-falling body as a function of time valid for any arbitrary distance. The equation, interestingly, yields exactly the time according to the Kepler's third law in the limiting case of very large distance compared to the radius of the Earth. The equation, of course, reduces to…

The aim of this study is to determine the extent to which prospective teachers' metacognitive skills, problem solving skills and academic self-efficacy explain their critical thinking tendencies. This study, designed as correlational survey method, was conducted with 229 prospective teachers studying at Van Yüzüncü Yil University, Faculty of…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

Should the topic of judgment have a place in the preparation and development of school leaders? This question serves as the focus for an examination of the nature of judgment and obstacles to good judgment. Judgment is defined as the ability to arrive at and make a choice when faced with incomplete information, uncertain conditions, and/or…

The need for methods, techniques and approaches that we can develop high-level thinking skills in important activities increases day by day in order to achieve effective use of technology and change in information and communication technologies. In particular, the diversity, complexity of technical skills and to gain technical skills required to…

Cognitive model [CM] is the description of individual's problem-solving method on selected tasks at a precise level to make meaningful inference on his/her strengths and weaknesses. CM serves as a foundation in developing a cognitive diagnostic assessment [CDA] that links the interpretation of test score to the attributes. This study employed the…

The mathematics education field recognizes the importance of noticing children's mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers' knowledge of children's mathematical thinking and…