Although the term "risk-taking" often has negative connotations, the reality is that the willingness to engage in some risky activities provides opportunities to learn new skills, try new behaviours and ultimately reach our potential. Challenge and risk, in particular during outdoor play, allows children to test the limits of their…

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with A's chosen x- or y-axis. It becomes necessary in such cases to develop…

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naive students were administered kinematics problems and…

Hungarian pediatrician Emmi Pikler theorized that freedom of movement facilitates infants' development and learning. The self-education promoted by freedom to move gives an infant a lasting view of herself as a competent learner. Pikler's approach also emphasizes the importance of helping each child feel respected and secure. The author examines…

Clay's Reading Recovery has been one of the most effective one-to-one tutorial sessions. To make the daily lesson more interesting and fully engage the at-risk readers, the author modified Clay's Reading Recovery Program by conceptualizing phonics and semiotics into early intervention. In this case study, three at-risk first graders formed an…

This study demonstrates an existence proof for "productive failure": engaging students in solving complex, ill-structured problems without the provision of support structures can be a productive exercise in failure. In a computer-supported collaborative learning setting, eleventh-grade science students were randomly assigned to one of…

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle…

The focus of the article is on the complex cognitive process involved in learning the concept of "straightness" in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight…

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…

We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed,…

The 11th International Conference on Educational Data Mining (EDM 2018) is held under the auspices of the International Educational Data Mining Society at the Templeton Landing in Buffalo, New York. This year's EDM conference was highly competitive, with 145 long and short paper submissions. Of these, 23 were accepted as full papers and 37…

Students use the relationship between the speed of a ball and the time that a player has to react to it to understand uniform motion problems. Includes activity sheets. (Author/NB)

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.