An apparatus for teaching statistics concepts includes a simulation module that generates a simulation of subject elements moving from a first portion of a simulated space to a second portion of the simulated space, where the simulated space has a treatment path and a non-treatment path. A propensity module utilizes one or more propensity inputs to the simulation module to affect a propensity of the subject elements to move on the treatment path to have treatment functions applied. A treatment module applies the treatment functions to the subject elements moving on the treatment path, where the treatment functions are configured to affect at least one output measure of the subject elements. A display module displays the simulation of the subject elements having the propensity inputs applied, application of the treatment functions, and the at least one output measure.

A CPR training device is disclosed comprising a first member including a mouthpiece portion and a first engaging portion, a second member including an output portion and a second engaging portion, and an air passageway. The first engaging portion and the second engaging portion cooperates to form a filter seating arrangement at a filter seat position when assembled together to secure a filter within the CPR training device. The air passageway is open to air outside of the CPR training device only through the mouthpiece portion and the output portion. The filter is disposed in the air passageway at the filter seat position.

Various techniques are disclosed for facilitating a computer-supported collaborative session that includes at least two participants using different computing devices to view a canvas that is configured to contain objects added by one or more of the participants. The computer-supported collaborative session is configured to permit participants to mark and/or edit selected objects presented on the canvas. Participants may use a mobile device camera to capture images or video clips, and post the captured images or video clips to the canvas by emailing or text messaging the captured image to a designated email address or phone number.

Various techniques are disclosed for facilitating a computer-supported collaborative session that includes at least two participants using different computing devices to view a canvas that is configured to contain objects added by one or more of the participants. The computer-supported collaborative session is configured to permit participants to mark and/or edit selected objects presented on the canvas. Participants may use a mobile device camera to capture images or video clips, and post the captured images or video clips to the canvas by emailing or text messaging the captured image to a designated email address or phone number.

Various techniques are disclosed for facilitating a computer-supported collaborative session that includes at least two participants using different computing devices to view a canvas that is configured to contain objects added by one or more of the participants. The computer-supported collaborative session is configured to permit participants to mark and/or edit selected objects presented on the canvas. Participants may use a mobile device camera to capture images or video clips, and post the captured images or video clips to the canvas by emailing or text messaging the captured image to a designated email address or phone number.

Systems and methods to define a scenario of conditions comprising the steps of defining at least one condition for at least one educational objective, the at least one condition being represented by a constraint and scheduling the conditions into a scenario of conditions. In some embodiments, the scheduling is performed by analyzing the constraints using constraint programming. In some embodiments, the constraints comprise mathematical or computational constraints representing a range of variables. Also disclosed are systems and methods to monitor a scenario of conditions.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface finishes, such as color, shading, cross-hatching or real or apparent texture.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface finishes, such as color, shading, cross-hatching or real or apparent texture.

Apparatus and methods based on applied cognitive science, where children play the lead role in storylines staged upon a rule-enforcing apparatus and by so doing, become self-enlightened about denumerability, rank-wise denumerability, addition, subtraction, multiplication, division, and other change-of-state processes encountered in mathematics and the quantifiable sciences.

Embodiments of the invention comprise approaches for streamlining and accelerating the communication of applied knowledge to end-users, particularly in science, technology, engineering, and mathematic (STEM) disciplines. Through a framework that leverages consistency and immersive teaching tools, complexity is substantially removed from the knowledge transfer process.